// Giac integration test file: "0 Independent test suites\Apostol Problems.txt"
// "nock" means we do not check the antiderivative
I:=i;
lst:=[

// Martin Welz - posts on Sci.Math.Symbolic

// 4 June 2010

//  {x*(x^2 + 3)/(2*a^2 + b^2*(x^2 + 1))^(5/2)*Log[(Sqrt[2]*x*Sqrt[2*a^2 + b^2*(x^2 + 1)] - 2*x*a + b*(x^2 + 1))/x], x, 0, Sqrt[2]*(43*a^6 + 63*b^2*a^4 + 33*b^4*a^2 + 5*b^6)*(ArcTan[b*(x/Sqrt[2*a^2 + b^2])]/(6*b^4*Sqrt[2*a^2 + b^2]*(3*a^2 + b^2)^3)) + Sqrt[2]*(Sqrt[4*a^2 + b^2] + a)^3*(3*a*Sqrt[4*a^2 + b^2] - 7*a^2 - 2*b^2)*(Log[Sqrt[2]*(Sqrt[4*a^2 + b^2] - a)*Sqrt[2*a^2 + b^2*(x^2 + 1)] + b*x*Sqrt[4*a^2 + b^2] + 2*a^2 - 2*b*x*a + b^2]/(6*b^4*(3*a^2 + b^2)^3)) + Sqrt[2]*(Sqrt[4*a^2 + b^2] - a)^3*(3*a*Sqrt[4*a^2 + b^2] + 7*a^2 + 2*b^2)*(Log[Sqrt[2]*(Sqrt[4*a^2 + b^2] + a)*Sqrt[2*a^2 + b^2*(x^2 + 1)] + b*x*Sqrt[4*a^2 + b^2] - 2*a^2 + 2*b*x*a - b^2]/(6*b^4*(3*a^2 + b^2)^3)) - (4*a^2 + b^2*(3*x^2 + 5))*(Log[(Sqrt[2]*x*Sqrt[2*a^2 + b^2*(x^2 + 1)] - 2*x*a + b*(x^2 + 1))/x]/(3*b^4*(2*a^2 + b^2*(x^2 + 1))^(3/2))) - (4*a^2 + 5*b^2)*(Log[(Sqrt[2*a^2 + b^2*(x^2 + 1)] - Sqrt[2*a^2 + b^2])/x]/(3*b^4*(2*a^2 + b^2)^(3/2))) + Sqrt[2]*(2*a^2 + b^2)*(Log[Sqrt[2*a^2 + b^2*(x^2 + 1)] - Sqrt[2]*a]/(6*b^4*a^3)) - Sqrt[2]*(5*a^2 + b^2)*(8*a^6 + 9*b^2*a^4 + 6*b^4*a^2 + b^6)*(Log[2*a^2 + b^2*(x^2 + 1)]/(12*b^4*a^3*(3*a^2 + b^2)^3)) + Sqrt[2]*(b^2 - a^2)*((Sqrt[2]*Sqrt[2*a^2 + b^2*(x^2 + 1)]*(10*a^6 + 2*b*x*a^5 + 16*b^2*a^4 + 7*b^4*a^2 + b^6) + 12*a^7 + 6*b*x*a^6 + 16*b^2*a^5 + 5*b^3*x*a^4 + 7*b^4*a^3 + b^5*x*a^2 + b^6*a)/(6*b^4*a^2*(2*a^2 + b^2)*(2*a^2 + b^2*(x^2 + 1))*(3*a^2 + b^2)^2))} 

//  The following two integrands are equivalent! 
[1/sqrt(1-a*x),x,1,-2*sqrt(1-a*x)/a],
[1/2*(log(-1+a*x)-2*log(-sqrt(-1+a*x)))/(Pi*sqrt(-1+a*x)),x,5,-2*sqrt(1-a*x)/a,log(-1+a*x)*sqrt(-1+a*x)/(a*Pi)-2*log(-sqrt(-1+a*x))*sqrt(-1+a*x)/(a*Pi)],

// 6 June 2010
//  {Sqrt[b^2*x^2 + 2*a^2 + b^2]/(b^3*x^4 + 4*a*b^2*x^3 + 2*a^2*b*x^2 + 4*a*x*(2*a^2 + b^2) - b*(2*a^2 + b^2)), x, 0, 0}
// {Sqrt[b^2*x^2 + 2*a^2 + b^2]/(b^3*x^6 + 4*a*b^2*x^5 + b*x^4*(2*a^2 + b^2) + 8*a*x^3*(a^2 + b^2) - b^3*x^2 + 4*a*x*(2*a^2 + b^2) - b*(2*a^2 + b^2)), x, 0, 0}

// {x/((b^2*x^2 + 2*a^2 + b^2)*((b*x^2 - 2*a*x + b)*Sqrt[b^2*x^2 + 2*a^2 + b^2] + Sqrt[2]*b^2*x^3 + Sqrt[2]*x*(2*a^2 + b^2))), x, 0, 0} 

// 20 June 2010

// Problem //1
[1/(2*x+sqrt(1+x^2))^2,x,9,4/3*x/(1-3*x^2)-1/3*arctanh(x*sqrt(3))/sqrt(3)+1/3*arctanh(1/2*sqrt(3)*sqrt(1+x^2))/sqrt(3)-2/3*sqrt(1+x^2)/(1-3*x^2)],

// Problem //2
[1/((-4+3*x^2)^2*sqrt(-1+x^2)),x,3,5/16*arctanh(1/2*x/sqrt(-1+x^2))+3/8*x*sqrt(-1+x^2)/(4-3*x^2)],

// Problem //3
[1/(2*sqrt(x)+sqrt(1+x))^2,x,8,8/9/(1-3*x)-8/9*arcsinh(sqrt(x))+10/9*arctanh(2*sqrt(x)/sqrt(1+x))+5/9*log(1-3*x)-4/3*sqrt(x)*sqrt(1+x)/(1-3*x)],

// Problem //4
[sqrt(-1+x^2)/(-I+x)^2,x,6,arctanh(x/sqrt(-1+x^2))-I*arctan((1-I*x)/(sqrt(2)*sqrt(-1+x^2)))/sqrt(2)+sqrt(-1+x^2)/(I-x)],

// Problem //5
[1/((1+x^2)^2*sqrt(-1+x^2)),x,3,3/4*arctanh(x*sqrt(2)/sqrt(-1+x^2))/sqrt(2)-1/4*x*sqrt(-1+x^2)/(1+x^2)],

// Problem //6
[1/(sqrt(-1+x)*(sqrt(-1+x)+sqrt(x))^2),x,4,4/3*(-1+x)^(3/2)-4/3*x^(3/2)+2*sqrt(-1+x)],

// Problem //7
[1/(sqrt(-1+x^2)*(sqrt(x)+sqrt(-1+x^2))^2),x,-18,1/5*(2-4*x)/(sqrt(x)+sqrt(-1+x^2))-1/50*arctan(sqrt(-1+x^2)*sqrt(-2+2*sqrt(5))/(2-x*(1-sqrt(5))))*sqrt(-110+50*sqrt(5))+1/25*arctan(1/2*sqrt(x)*sqrt(2+2*sqrt(5)))*sqrt(-110+50*sqrt(5))-1/25*arctanh(1/2*sqrt(x)*sqrt(-2+2*sqrt(5)))*sqrt(110+50*sqrt(5))-1/50*arctanh(sqrt(-1+x^2)*sqrt(2+2*sqrt(5))/(2-x-x*sqrt(5)))*sqrt(110+50*sqrt(5))],
[(sqrt(x)-sqrt(-1+x^2))^2/((1+x-x^2)^2*sqrt(-1+x^2)),x,-25,1/5*(2-4*x)/(sqrt(x)+sqrt(-1+x^2))-1/50*arctan(sqrt(-1+x^2)*sqrt(-2+2*sqrt(5))/(2-x*(1-sqrt(5))))*sqrt(-110+50*sqrt(5))+1/25*arctan(1/2*sqrt(x)*sqrt(2+2*sqrt(5)))*sqrt(-110+50*sqrt(5))-1/25*arctanh(1/2*sqrt(x)*sqrt(-2+2*sqrt(5)))*sqrt(110+50*sqrt(5))-1/50*arctanh(sqrt(-1+x^2)*sqrt(2+2*sqrt(5))/(2-x-x*sqrt(5)))*sqrt(110+50*sqrt(5))],
[1/((1+x)^2*sqrt(2)*sqrt(-I+x^2))+1/((1+x)^2*sqrt(2)*sqrt(I+x^2)),x,7,arctanh((I+x)/(sqrt(1-I)*sqrt(-I+x^2)))/((1-I)^(3/2)*sqrt(2))-arctanh((I-x)/(sqrt(1+I)*sqrt(I+x^2)))/((1+I)^(3/2)*sqrt(2))+(-1/2-1/2*I)*sqrt(-I+x^2)/((1+x)*sqrt(2))+(-1/2+1/2*I)*sqrt(I+x^2)/((1+x)*sqrt(2))],

// Problem //8
[sqrt(x^2+sqrt(1+x^4))/((1+x)^2*sqrt(1+x^4)),x,7,-1/4*(1-I)^(3/2)*arctanh((1+I*x)/(sqrt(1-I)*sqrt(1-I*x^2)))-1/4*(1+I)^(3/2)*arctanh((1-I*x)/(sqrt(1+I)*sqrt(1+I*x^2)))-1/2*sqrt(1-I*x^2)/(1+x)-1/2*sqrt(1+I*x^2)/(1+x)],
[sqrt(x^2+sqrt(1+x^4))/((1+x)*sqrt(1+x^4)),x,5,-1/2*arctanh((1+I*x)/(sqrt(1-I)*sqrt(1-I*x^2)))*sqrt(1-I)-1/2*arctanh((1-I*x)/(sqrt(1+I)*sqrt(1+I*x^2)))*sqrt(1+I)],
[sqrt(x^2+sqrt(1+x^4))/sqrt(1+x^4),x,2,arctanh(x*sqrt(2)/sqrt(x^2+sqrt(1+x^4)))/sqrt(2)],
[sqrt(-x^2+sqrt(1+x^4))/sqrt(1+x^4),x,2,arctan(x*sqrt(2)/sqrt(-x^2+sqrt(1+x^4)))/sqrt(2)],

// Problem //9
[((-1+x)^(3/2)+(1+x)^(3/2))/((-1+x)^(3/2)*(1+x)^(3/2)),x,2,(-2)/sqrt(-1+x)+(-2)/sqrt(1+x)],

// 15 August 2010
[(x+sqrt(a+x^2))^b,x,3,-1/2*a*(x+sqrt(a+x^2))^(-1+b)/(1-b)+1/2*(x+sqrt(a+x^2))^(1+b)/(1+b)],
[(x-sqrt(a+x^2))^b,x,3,-1/2*a*(x-sqrt(a+x^2))^(-1+b)/(1-b)+1/2*(x-sqrt(a+x^2))^(1+b)/(1+b)],
[(x+sqrt(a+x^2))^b/sqrt(a+x^2),x,2,(x+sqrt(a+x^2))^b/b],
[(x-sqrt(a+x^2))^b/sqrt(a+x^2),x,2,-(x-sqrt(a+x^2))^b/b],
[1/(a+b*exp(p*x))^2,x,3,1/(a*(a+b*exp(p*x))*p)+x/a^2-log(a+b*exp(p*x))/(a^2*p)],
[1/(b/exp(p*x)+a*exp(p*x))^2,x,2,(-1/2)/(a*(b+a*exp(2*p*x))*p)],
[x/(b/exp(p*x)+a*exp(p*x))^2,x,6,1/2*x/(a*b*p)-1/2*x/(a*(b+a*exp(2*p*x))*p)-1/4*log(b+a*exp(2*p*x))/(a*b*p^2)],

// 2 September 2012

// Example from Welz's paper "Two-term Recurrence Formulae for Indefinite Algebraic Integrals" available at https://arxiv.org/abs/1209.3758v2
[(1-x+3*x^2)/((1+x+x^2)^2*sqrt(1-x+x^2)),x,6,arctan((1+x)*sqrt(2)/sqrt(1-x+x^2))*sqrt(2)-arctanh((1-x)*sqrt(2/3)/sqrt(1-x+x^2))/sqrt(6)+(1+x)*sqrt(1-x+x^2)/(1+x+x^2)],

// 21 January 2013

//  From James Davenport's algint package documentation for Reduce 
[sqrt(x+sqrt(a^2+x^2))/sqrt(a^2+x^2),x,2,2*sqrt(x+sqrt(a^2+x^2))],
[sqrt(b*x+sqrt(a+b^2*x^2))/sqrt(a+b^2*x^2),x,2,2*sqrt(b*x+sqrt(a+b^2*x^2))/b],
[1/(x*sqrt(a^2+x^2)*sqrt(x+sqrt(a^2+x^2))),x,5,-2*arctan(sqrt(x+sqrt(a^2+x^2))/sqrt(a))/a^(3/2)-2*arctanh(sqrt(x+sqrt(a^2+x^2))/sqrt(a))/a^(3/2)],
[sqrt(x+sqrt(a^2+x^2))/x,x,6,-2*arctan(sqrt(x+sqrt(a^2+x^2))/sqrt(a))*sqrt(a)-2*arctanh(sqrt(x+sqrt(a^2+x^2))/sqrt(a))*sqrt(a)+2*sqrt(x+sqrt(a^2+x^2))],

// 17 September 2014
[x^3*log(2+x)^3*log(3+x),x,359,-302177/1152*x+8029/2304*x^2-763/3456*x^3+3/256*x^4+377/64*(2+x)^2-71/216*(2+x)^3+3/256*(2+x)^4+2069/144*log(2+x)-187/64*x^2*log(2+x)+83/288*x^3*log(2+x)-3/128*x^4*log(2+x)+6733/32*(2+x)*log(2+x)-377/32*(2+x)^2*log(2+x)+71/72*(2+x)^3*log(2+x)-3/64*(2+x)^4*log(2+x)-43/12*log(2+x)^2-17/48*x^3*log(2+x)^2+3/64*x^4*log(2+x)^2-1251/16*(2+x)*log(2+x)^2+273/32*(2+x)^2*log(2+x)^2-3/4*(2+x)^3*log(2+x)^2+3/64*(2+x)^4*log(2+x)^2+65/4*(2+x)*log(2+x)^3-33/8*(2+x)^2*log(2+x)^3+3/4*(2+x)^3*log(2+x)^3-1/16*(2+x)^4*log(2+x)^3+3891/128*log(3+x)-115/48*x^2*log(3+x)+37/144*x^3*log(3+x)-3/128*x^4*log(3+x)+415/12*(3+x)*log(3+x)-4083/32*log(2+x)*log(3+x)-25*x*log(2+x)*log(3+x)+13/4*x^2*log(2+x)*log(3+x)-7/12*x^3*log(2+x)*log(3+x)+3/32*x^4*log(2+x)*log(3+x)+963/16*log(2+x)^2*log(3+x)+6*x*log(2+x)^2*log(3+x)-3/2*x^2*log(2+x)^2*log(3+x)+1/2*x^3*log(2+x)^2*log(3+x)-3/16*x^4*log(2+x)^2*log(3+x)-81/4*log(2+x)^3*log(3+x)+1/4*x^4*log(2+x)^3*log(3+x)-5609/96*polylog(2,-2-x)+563/8*log(2+x)*polylog(2,-2-x)-195/4*log(2+x)^2*polylog(2,-2-x)-563/8*polylog(3,-2-x)+195/2*log(2+x)*polylog(3,-2-x)-195/2*polylog(4,-2-x)],

//  12 January 2016
[(x+sqrt(b+x^2))^a/sqrt(b+x^2),x,2,(x+sqrt(b+x^2))^a/a],
[(x+sqrt(b+x^2))^a,x,3,-1/2*b*(x+sqrt(b+x^2))^(-1+a)/(1-a)+1/2*(x+sqrt(b+x^2))^(1+a)/(1+a)],
[(6+3*x^a+2*x^(2*a))^(1/a)*(x^a+x^(2*a)+x^(3*a)),x,2,1/6*x^(1+a)*(6+3*x^a+2*x^(2*a))^(1+1/a)/(1+a)],
[1/(x*(1-x^2)^(1/3)),x,5,-1/2*log(x)+3/4*log(1-(1-x^2)^(1/3))+1/2*arctan((1+2*(1-x^2)^(1/3))/sqrt(3))*sqrt(3)],
[1/(x*(1-x^2)^(2/3)),x,5,-1/2*log(x)+3/4*log(1-(1-x^2)^(1/3))-1/2*arctan((1+2*(1-x^2)^(1/3))/sqrt(3))*sqrt(3)],
[1/(1-x^3)^(1/3),x,1,1/2*log(x+(1-x^3)^(1/3))-arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)],
[1/(x*(1-x^3)^(1/3)),x,5,-1/2*log(x)+1/2*log(1-(1-x^3)^(1/3))+arctan((1+2*(1-x^3)^(1/3))/sqrt(3))/sqrt(3)],
[1/((1+x)*(1-x^3)^(1/3)),x,1,-1/4*log((1-x)*(1+x)^2)/2^(1/3)+3/4*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)-1/2*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))*sqrt(3)/2^(1/3)],
[x/((1+x)*(1-x^3)^(1/3)),x,3,1/4*log((1-x)*(1+x)^2)/2^(1/3)+1/2*log(x+(1-x^3)^(1/3))-3/4*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)-arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+1/2*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))*sqrt(3)/2^(1/3)],
[1/(x*(2-3*x+x^2)^(1/3)),x,-2,-1/4*log(2-x)/2^(1/3)-1/2*log(x)/2^(1/3)+3/4*log(2-x-2^(2/3)*(2-3*x+x^2)^(1/3))/2^(1/3)-1/2*arctan(1/sqrt(3)+2^(1/3)*(2-x)/((2-3*x+x^2)^(1/3)*sqrt(3)))*sqrt(3)/2^(1/3)],
[1/(-5+7*x-3*x^2+x^3)^(1/3),x,-5,1/4*log(1-x)-3/4*log(1-x+(-5+7*x-3*x^2+x^3)^(1/3))+1/2*arctan(1/sqrt(3)+2*(-1+x)/((-5+7*x-3*x^2+x^3)^(1/3)*sqrt(3)))*sqrt(3)],
[1/(x*(-q+x^2))^(1/3),x,-5,1/4*log(x)-3/4*log(-x+(x*(-q+x^2))^(1/3))+1/2*arctan(1/sqrt(3)+2*x/((x*(-q+x^2))^(1/3)*sqrt(3)))*sqrt(3)],
[1/((-1+x)*(q-2*x+x^2))^(1/3),x,-5,1/4*log(1-x)-3/4*log(1-x+((-1+x)*(q-2*x+x^2))^(1/3))+1/2*arctan(1/sqrt(3)+2*(-1+x)/(((-1+x)*(q-2*x+x^2))^(1/3)*sqrt(3)))*sqrt(3)],
[1/(x*((-1+x)*(q-2*q*x+x^2))^(1/3)),x,-2,1/4*log(1-x)/q^(1/3)+1/2*log(x)/q^(1/3)-3/4*log(-q^(1/3)*(-1+x)+((-1+x)*(q-2*q*x+x^2))^(1/3))/q^(1/3)+1/2*arctan(1/sqrt(3)+2*q^(1/3)*(-1+x)/(((-1+x)*(q-2*q*x+x^2))^(1/3)*sqrt(3)))*sqrt(3)/q^(1/3)],
[(2-(1+k)*x)/(((1-x)*x*(1-k*x))^(1/3)*(1-(1+k)*x)),x,-3,1/2*log(x)/k^(1/3)+1/2*log(1-(1+k)*x)/k^(1/3)-3/2*log(-k^(1/3)*x+((1-x)*x*(1-k*x))^(1/3))/k^(1/3)+arctan((1+2*k^(1/3)*x/((1-x)*x*(1-k*x))^(1/3))/sqrt(3))*sqrt(3)/k^(1/3)],
[(1-k*x)/((1+(-2+k)*x)*((1-x)*x*(1-k*x))^(2/3)),x,-1,log(1-(2-k)*x)/(2^(2/3)*(1-k)^(1/3))+1/2*log(1-k*x)/(2^(2/3)*(1-k)^(1/3))-3/2*log(-1+k*x+2^(2/3)*(1-k)^(1/3)*((1-x)*x*(1-k*x))^(1/3))/(2^(2/3)*(1-k)^(1/3))-arctan((1+2^(1/3)*(1-k*x)/((1-k)^(1/3)*((1-x)*x*(1-k*x))^(1/3)))/sqrt(3))*sqrt(3)/(2^(2/3)*(1-k)^(1/3))],
[(a+b*x+c*x^2)/((1-x+x^2)*(1-x^3)^(1/3)),x,19,1/12*(a+b)*log((1-x)*(1+x)^2)/2^(1/3)-1/6*(a-c)*log(1+x^3)/2^(1/3)-1/6*(b+c)*log(1+x^3)/2^(1/3)+1/6*(a+b)*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/3*(a+b)*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+1/2*(b+c)*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+1/2*(a-c)*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)+1/2*c*log(x+(1-x^3)^(1/3))-1/4*(a+b)*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)+(a+b)*arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))+1/2*(a+b)*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))-c*arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-(a-c)*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))+(b+c)*arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)),1/12*(a+b)*log((1-x)*(1+x)^2)/2^(1/3)-1/6*a*log(1+x^3)/2^(1/3)+1/6*c*log(1+x^3)/2^(1/3)-1/6*(b+c)*log(1+x^3)/2^(1/3)+1/6*(a+b)*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/3*(a+b)*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+1/2*(b+c)*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+1/2*a*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)-1/2*c*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)+1/2*c*log(x+(1-x^3)^(1/3))-1/4*(a+b)*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)+(a+b)*arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))+1/2*(a+b)*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))-c*arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-a*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))+c*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))+(b+c)*arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],

//  27 March 2016
[1/((3-2*x)^(11/2)*(1+x+2*x^2)^5),x,0,(-19255/395136)/(3-2*x)^(9/2)+(-462025/30118144)/(3-2*x)^(7/2)+(-38491/8605184)/(3-2*x)^(5/2)+(-141045/120472576)/(3-2*x)^(3/2)+1/28*x/((3-2*x)^(9/2)*(1+x+2*x^2)^4)+1/1176*(23+73*x)/((3-2*x)^(9/2)*(1+x+2*x^2)^3)+1/32928*(1387+3049*x)/((3-2*x)^(9/2)*(1+x+2*x^2)^2)+5/153664*(3049+4377*x)/((3-2*x)^(9/2)*(1+x+2*x^2))+(-38225/240945152)/sqrt(3-2*x)+5/6746464256*log(3-2*x+sqrt(14)-sqrt(3-2*x)*sqrt(7+2*sqrt(14)))*sqrt(1/2*(-149046503977+40815066112*sqrt(14)))-5/6746464256*log(3-2*x+sqrt(14)+sqrt(3-2*x)*sqrt(7+2*sqrt(14)))*sqrt(1/2*(-149046503977+40815066112*sqrt(14)))+5/3373232128*arctan((-2*sqrt(3-2*x)+sqrt(7+2*sqrt(14)))/sqrt(-7+2*sqrt(14)))*sqrt(1/2*(149046503977+40815066112*sqrt(14)))-5/3373232128*arctan((2*sqrt(3-2*x)+sqrt(7+2*sqrt(14)))/sqrt(-7+2*sqrt(14)))*sqrt(1/2*(149046503977+40815066112*sqrt(14)))],
[1/((3-2*x)^(21/2)*(1+x+2*x^2)^10),x,0,4718120139975/351733660450816/(3-2*x)^(19/2)+(-815900548375/629418129227776)/(3-2*x)^(17/2)+(-3029508823715/1555033025150976)/(3-2*x)^(15/2)+(-13515743021825/13476952884641792)/(3-2*x)^(13/2)+(-5846828446875/14513641568075776)/(3-2*x)^(11/2)+(-37283626871975/261245548225363968)/(3-2*x)^(9/2)+(-132355162272575/2844673747342852096)/(3-2*x)^(7/2)+(-11557581705725/812763927812243456)/(3-2*x)^(5/2)+(-46601678385075/11378694989371408384)/(3-2*x)^(3/2)+1/63*x/((3-2*x)^(19/2)*(1+x+2*x^2)^9)+1/7056*(53+173*x)/((3-2*x)^(19/2)*(1+x+2*x^2)^8)+1/691488*(8477+21409*x)/((3-2*x)^(19/2)*(1+x+2*x^2)^7)+5/6453888*(21409+47471*x)/((3-2*x)^(19/2)*(1+x+2*x^2)^6)+41/90354432*(47471+92875*x)/((3-2*x)^(19/2)*(1+x+2*x^2)^5)+41/5059848192*(3436375+5677637*x)/((3-2*x)^(19/2)*(1+x+2*x^2)^4)+451/10119696384*(811091+998691*x)/((3-2*x)^(19/2)*(1+x+2*x^2)^3)+451/283351498752*(28962039+14627273*x)/((3-2*x)^(19/2)*(1+x+2*x^2)^2)+11275/3966920982528*(14627273-35058731*x)/((3-2*x)^(19/2)*(1+x+2*x^2))+(-24229218097975/22757389978742816768)/sqrt(3-2*x)+11275/637206919404798869504*log(3-2*x+sqrt(14)-sqrt(3-2*x)*sqrt(7+2*sqrt(14)))*(9756589235-2148932869*sqrt(14))*sqrt(1/2*(-7+2*sqrt(14)))-11275/637206919404798869504*log(3-2*x+sqrt(14)+sqrt(3-2*x)*sqrt(7+2*sqrt(14)))*(9756589235-2148932869*sqrt(14))*sqrt(1/2*(-7+2*sqrt(14)))+11275/318603459702399434752*arctan((-2*sqrt(3-2*x)+sqrt(7+2*sqrt(14)))/sqrt(-7+2*sqrt(14)))*(9756589235+2148932869*sqrt(14))*sqrt(1/2*(7+2*sqrt(14)))-11275/318603459702399434752*arctan((2*sqrt(3-2*x)+sqrt(7+2*sqrt(14)))/sqrt(-7+2*sqrt(14)))*(9756589235+2148932869*sqrt(14))*sqrt(1/2*(7+2*sqrt(14)))],
[1/((3-2*x)^(41/2)*(1+x+2*x^2)^20),x,49,(-13056959628363355534285785425/106924014357253562723941220352)/(3-2*x)^(39/2)+(-3948194343291401740321996415/202881463139404195937734623232)/(3-2*x)^(37/2)+(-304688229262620222736480811/537361713180043545997243056128)/(3-2*x)^(35/2)+2124315846756567455653862925/1688851098565851144562763890688/(3-2*x)^(33/2)+47657515074514118796095929535/66632852434325399703658138959872/(3-2*x)^(31/2)+34911619993974714062172751985/124667917457770102671360389021696/(3-2*x)^(29/2)+149066309808794760843017404825/1624981820656451683095663001731072/(3-2*x)^(27/2)+15848613964169066543734380171/601845118761648771516912222863360/(3-2*x)^(25/2)+11155168222970774232376891145/1685166332532616560247354224017408/(3-2*x)^(23/2)+14011818498091020272474956375/10110997995195699361484125344104448/(3-2*x)^(21/2)+173441368149804378661935869705/896508488907352010051592447177261056/(3-2*x)^(19/2)+(-22724090823469905152713519545/1604278348571050965355481221264572416)/(3-2*x)^(17/2)+(-101190274412779618678573275245/3963511214116714149701777134888943616)/(3-2*x)^(15/2)+(-460503190416958283087439337135/34350430522344855964082068502370844672)/(3-2*x)^(13/2)+(-2211619588790911794826342607495/406920484649315986036049119181931544576)/(3-2*x)^(11/2)+(-143401467550777247627940437025/73985542663511997461099839851260280832)/(3-2*x)^(9/2)+(-4611053278117143010907562317585/7250583181024175751187784305423507521536)/(3-2*x)^(7/2)+(-405965372440630510720926890227/2071595194578335928910795515835287863296)/(3-2*x)^(5/2)+(-4986681479187781853417316522775/87006998172290109014253411665082090258432)/(3-2*x)^(3/2)+1/133*x/((3-2*x)^(39/2)*(1+x+2*x^2)^19)+1/33516*(113+373*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^18)+1/7976808*(40657+107329*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^17)+5/595601664*(751303+1831285*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^16)+1/25015269888*(184959785+429411497*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^15)+1/4902992898048*(41652915209+92630823167*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^14)+1/297448235814912*(2871555518177+6100156355517*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^13)+1/7138757659557888*(77559130805859+156274047129113*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^12)+5/1099368679571914752*(2656658801194921+5020880176134289*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^11)+1/3420258114223734784*(45187921585208601+78752911037377255*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^10)+1/430952522392190582784*(6063974149878048635+9477172618423641847*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^9)+1/48266682507925345271808*(691833601144925854831+919498192874055581221*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^8)+23/1576711628592227945545728*(919498192874055581221+908287136092467468517*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^7)+115/10187982830903626725064704*(908287136092467468517+298281884944522225747*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^6)+23/20375965661807253450129408*(2599313568802265110081-10426142448623187379187*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^5)-23/20018492580021161284337664*(10426142448623187379187+27513723463194262383705*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^4)-115/76434244396444433994743808*(26513224428169016478843+30673415406553789342019*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^3)-115/125891696652967303050166272*(88411609113007981044643-5712269536245152162963*x)/((3-2*x)^(39/2)*(1+x+2*x^2)^2)+115/195831528126838026966925312*(28561347681225760814815+965934812839019490346107*x)/((3-2*x)^(39/2)*(1+x+2*x^2))+(-927027754781476746208047620505/58004665448193406009502274443388060172288)/sqrt(3-2*x)+115/1624130632549415368266063684414865684824064*log(3-2*x+sqrt(14)-sqrt(3-2*x)*sqrt(7+2*sqrt(14)))*(30297118912219360725028693061-8061110911143276053983022787*sqrt(14))*sqrt(1/2*(-7+2*sqrt(14)))-115/1624130632549415368266063684414865684824064*log(3-2*x+sqrt(14)+sqrt(3-2*x)*sqrt(7+2*sqrt(14)))*(30297118912219360725028693061-8061110911143276053983022787*sqrt(14))*sqrt(1/2*(-7+2*sqrt(14)))+115/812065316274707684133031842207432842412032*arctan((-2*sqrt(3-2*x)+sqrt(7+2*sqrt(14)))/sqrt(-7+2*sqrt(14)))*(30297118912219360725028693061+8061110911143276053983022787*sqrt(14))*sqrt(1/2*(7+2*sqrt(14)))-115/812065316274707684133031842207432842412032*arctan((2*sqrt(3-2*x)+sqrt(7+2*sqrt(14)))/sqrt(-7+2*sqrt(14)))*(30297118912219360725028693061+8061110911143276053983022787*sqrt(14))*sqrt(1/2*(7+2*sqrt(14)))],
[ff(x),x,x],//[1/((3-2*x+x^2)^(11/2)*(1+x+2*x^2)^5),x,14,1/123480000*(-3450497+2004270*x)/(3-2*x+x^2)^(9/2)+1/411600000*(-4878869+2578034*x)/(3-2*x+x^2)^(7/2)+1/6860000000*(-30316369+15043110*x)/(3-2*x+x^2)^(5/2)+1/41160000000*(-63043297+29625922*x)/(3-2*x+x^2)^(3/2)+1/280*(-1+10*x)/((3-2*x+x^2)^(9/2)*(1+x+2*x^2)^4)+1/1050*(28+67*x)/((3-2*x+x^2)^(9/2)*(1+x+2*x^2)^3)+1/117600*(5485+8878*x)/((3-2*x+x^2)^(9/2)*(1+x+2*x^2)^2)+3/343000*(8822+8233*x)/((3-2*x+x^2)^(9/2)*(1+x+2*x^2))-31/411600000000*(7434109-3088870*x)/sqrt(3-2*x+x^2)-1/137200000000*arctanh((308108167+x*(932587773-620347970*sqrt(2))-312239803*sqrt(2))*sqrt(5/7/(-151363871237318045+110320475741093888*sqrt(2)))/sqrt(3-2*x+x^2))*sqrt(1/70*(-151363871237318045+110320475741093888*sqrt(2)))+1/137200000000*arctan((308108167+312239803*sqrt(2)+x*(932587773+620347970*sqrt(2)))*sqrt(5/7/(151363871237318045+110320475741093888*sqrt(2)))/sqrt(3-2*x+x^2))*sqrt(1/70*(151363871237318045+110320475741093888*sqrt(2)))],
[ff(x),x,x],//[1/((3-2*x+x^2)^(21/2)*(1+x+2*x^2)^10),x,24,1/1840124479200000000*(37358055634422583-14024622879097678*x)/(3-2*x+x^2)^(19/2)+1/104273720488000000000*(476849951294984711-125181871472148210*x)/(3-2*x+x^2)^(17/2)+1/15641058073200000000000*(7851758375483333511+1942164996204584234*x)/(3-2*x+x^2)^(15/2)-11/406667509903200000000000*(7502325106308201089-7813986379726516886*x)/(3-2*x+x^2)^(13/2)-3/1147010925368000000000000*(69053268515296359011-44840736195018286006*x)/(3-2*x+x^2)^(11/2)+1/9384634843920000000000000*(-838519439380295335657+466189390555853643870*x)/(3-2*x+x^2)^(9/2)+1/31282116146400000000000000*(-1117646664729238460189+568839749685437871554*x)/(3-2*x+x^2)^(7/2)+1/521368602440000000000000000*(-6551405511565449301689+3127298559983309301910*x)/(3-2*x+x^2)^(5/2)+1/1042737204880000000000000000*(-4179039782398459850819+1886993445589652402694*x)/(3-2*x+x^2)^(3/2)+1/630*(-1+10*x)/((3-2*x+x^2)^(19/2)*(1+x+2*x^2)^9)+1/88200*(887+2218*x)/((3-2*x+x^2)^(19/2)*(1+x+2*x^2)^8)+1/1080450*(14453+29371*x)/((3-2*x+x^2)^(19/2)*(1+x+2*x^2)^7)+1/605052000*(8837931+17459234*x)/((3-2*x+x^2)^(19/2)*(1+x+2*x^2)^6)+1/26471025000*(447940041+813432205*x)/((3-2*x+x^2)^(19/2)*(1+x+2*x^2)^5)+1/29647548000000*(592729157441+911061463974*x)/((3-2*x+x^2)^(19/2)*(1+x+2*x^2)^4)+1/12353145000000*(277010166219+310705340015*x)/((3-2*x+x^2)^(19/2)*(1+x+2*x^2)^3)+1/276710448000000*(5488221294349+1384103301166*x)/((3-2*x+x^2)^(19/2)*(1+x+2*x^2)^2)+1/2421216420000000*(-37857197792117-146548895467025*x)/((3-2*x+x^2)^(19/2)*(1+x+2*x^2))+1/10427372048800000000000000000*(-12105495874518671061833+5117656435043679338190*x)/sqrt(3-2*x+x^2)-1/32282885600000000000000000*arctanh((272944589523248381749+x*(656826642296538601431-464885615909893491590*sqrt(2))-191941026386645109841*sqrt(2))*sqrt(5/7/(-81042225921274689605478944797800854846405+57305922523001707126026363878666500308992*sqrt(2)))/sqrt(3-2*x+x^2))*sqrt(1/70*(-81042225921274689605478944797800854846405+57305922523001707126026363878666500308992*sqrt(2)))+1/32282885600000000000000000*arctan((272944589523248381749+191941026386645109841*sqrt(2)+x*(656826642296538601431+464885615909893491590*sqrt(2)))*sqrt(5/7/(81042225921274689605478944797800854846405+57305922523001707126026363878666500308992*sqrt(2)))/sqrt(3-2*x+x^2))*sqrt(1/70*(81042225921274689605478944797800854846405+57305922523001707126026363878666500308992*sqrt(2)))],

//  {1/((1 + x + 2*x^2)^20*(3 - 2*x + x^2)^(41/2)), x, 44, -((3383098994350701191445410431293305057 - 4267253240538659853185782736614548266*x)/(525136027977674906956800000000000000000*(3 - 2*x + x^2)^(39/2))) - (78177705015622070276322636989526467357 - 46302218258158218301107776830095849518*x)/(10226333176407353451264000000000000000000*(3 - 2*x + x^2)^(37/2)) - (590941515369388885204630563227557418493 - 284553012686483535620642865600923199674*x)/(170438886273455890854400000000000000000000*(3 - 2*x + x^2)^(35/2)) - (762583115349707009263396051658444299451 - 316786081987045018642707627274029983850*x)/(661703911414593458611200000000000000000000*(3 - 2*x + x^2)^(33/2)) - (20504482297963009703756354886476682604921 - 7087722971997170533955928118157817528778*x)/(68376070846174657389824000000000000000000000*(3 - 2*x + x^2)^(31/2)) - (1094782756101056712471590885456644828438471 - 231319367589693551565762758087902994595834*x)/(19829060545390650643048960000000000000000000000*(3 - 2*x + x^2)^(29/2)) - (11012693190699376908809163895637681160105723 + 17696165071101966113331245255080607119456186*x)/(5353846347255475673623219200000000000000000000000*(3 - 2*x + x^2)^(27/2)) + (23*(18006082293219149330614702781906676996906581 - 12878862225352936849259678853843700644232934*x))/(102958583601066839877369600000000000000000000000000*(3 - 2*x + x^2)^(25/2)) + (3754355493750207391617343068085143489914966741 - 1976623777595197423359895741289079398167213586*x)/(1578698281883024878119667200000000000000000000000000*(3 - 2*x + x^2)^(23/2)) + (34322768124014799813009030113095008046843253 - 15319362686882129647628001638529620053980446*x)/(37439484945842487228134400000000000000000000000000*(3 - 2*x + x^2)^(21/2)) + (1953413335087203199033100669694117118003927337 - 733793240328640817816796967921215709697806706*x)/(7113502139710072573345536000000000000000000000000000*(3 - 2*x + x^2)^(19/2)) + (8322318541720916240549421691461341741448155507 - 2188425336528033679699131827282128928574446618*x)/(134366151527856926385415680000000000000000000000000000*(3 - 2*x + x^2)^(17/2)) + (137736099847510239083414355324468252291068692723 + 33478342054315312692979309199522921351750372786*x)/(20154922729178538957812352000000000000000000000000000000*(3 - 2*x + x^2)^(15/2)) - (1430395239362680496541085612662519163791606856135 - 1495983440171367688360072315937267940781419612058*x)/(524027990958642012903121152000000000000000000000000000000*(3 - 2*x + x^2)^(13/2)) - (46873324150704277658299560286668706773614009227097 - 30488099877102642762965997747126514882873436125826*x)/(19214359668483540473114442240000000000000000000000000000000*(3 - 2*x + x^2)^(11/2)) - (2090128362125698805507947714009988943496892649558547 - 1163930059835896170450961511486397522547379198063338*x)/(1729292370163518642580299801600000000000000000000000000000000*(3 - 2*x + x^2)^(9/2)) - (8369636990081146161067558056610779041437928173813933 - 4269376136031342769573244116290179332114846542231394*x)/(17292923701635186425802998016000000000000000000000000000000000*(3 - 2*x + x^2)^(7/2)) - (49166828083706788194824969884579797183621714007506697 - 23559210708081011868758976108072328010974084474928758*x)/(288215395027253107096716633600000000000000000000000000000000000*(3 - 2*x + x^2)^(5/2)) - (94521492350271713145340025542493858321141702707908121 - 43021608081072494822903916879274373698601078834559154*x)/(1729292370163518642580299801600000000000000000000000000000000000*(3 - 2*x + x^2)^(3/2)) - (279132222218499281305380296125539838445333294423861707 - 121216775195529638294422516813426829250767045105497738*x)/(17292923701635186425802998016000000000000000000000000000000000000*Sqrt[3 - 2*x + x^2]) - (1 - 10*x)/(1330*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^19) + (1877 + 4778*x)/(418950*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^18) + (39403 + 85822*x)/(7122150*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^17) + (13*(233559 + 522986*x))/(531787200*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^16) + (87552089 + 193315879*x)/(13959414000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^15) + (383091931241 + 813307430102*x)/(54720902880000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^14) + (15997439501471 + 32531972209601*x)/(2074834234200000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^13) + (11661968128341449 + 22618400149542870*x)/(1394288605382400000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^12) + (3*(44358079769457553 + 81352009087314543*x))/(14911142029784000000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^11) + (55501961232421996697 + 95060342178362451574*x)/(5964456811913600000000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^10) + (4402445415670842624937 + 6915121726888913987767*x)/(469700973938196000000000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^9) + (9405293191839054568597199 + 13154801664162951037742138*x)/(1052130181621559040000000000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^8) + (33329414380999440825700335 + 39194075260407572910301649*x)/(4296198241621366080000000000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^7) + (3079446144576372279132551987 + 2588106060473365045793782354*x)/(555201003532607308800000000000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^6) + (51676596892030833963565793623 - 3738166859166819756452589047*x)/(24290043904551569760000000000000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^5) - (18477591983841452420673740004241 + 27597746968514352562858392071302*x)/(9068283057699252710400000000000000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^4) - (133360959223342832431783756808269 - 49432151929857088186548766720461*x)/(34006061466372197664000000000000000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^3) + (1057289143422928552044099202272635 + 2439572907056622740540415493441154*x)/(115414511643445034496000000000000000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)^2) + (27710574638863668700887240018723697 - 1800525975551829959478731340624273*x)/(336625658960048017280000000000000000*(3 - 2*x + x^2)^(39/2)*(1 + x + 2*x^2)) + (53*Sqrt[(1/70)*(879210910919588630492825297744872020413651017635360866499074296032260778656372643901 + 621696002391807670114685903911372073177064710967794175872353924738917423916160909312*Sqrt[2])]*ArcTan[(1/Sqrt[3 - 2*x + x^2])*(Sqrt[5/(7*(879210910919588630492825297744872020413651017635360866499074296032260778656372643901 + 621696002391807670114685903911372073177064710967794175872353924738917423916160909312*Sqrt[2]))]*(896457640030471180988134177305100813179145 + 634009778425632881804463219060525222303381*Sqrt[2] + (2164477196881736944597060615426151257785907 + 1530467418456104062792597396365626035482526*Sqrt[2])*x))])/416873881065074944000000000000000000000000000000000000 - (53*Sqrt[(1/70)*(-879210910919588630492825297744872020413651017635360866499074296032260778656372643901 + 621696002391807670114685903911372073177064710967794175872353924738917423916160909312*Sqrt[2])]*ArcTanh[(1/Sqrt[3 - 2*x + x^2])*(Sqrt[5/(7*(-879210910919588630492825297744872020413651017635360866499074296032260778656372643901 + 621696002391807670114685903911372073177064710967794175872353924738917423916160909312*Sqrt[2]))]*(896457640030471180988134177305100813179145 - 634009778425632881804463219060525222303381*Sqrt[2] + (2164477196881736944597060615426151257785907 - 1530467418456104062792597396365626035482526*Sqrt[2])*x))])/416873881065074944000000000000000000000000000000000000} 

//  19 June 2016
[(-a+x-sqrt(1+a^2))/((-a+x+sqrt(1+a^2))*sqrt((-a+x)*(1+x^2))),x,-9,-arctan((-a+x)*sqrt(2)*sqrt(-a+sqrt(1+a^2))/sqrt((-a+x)*(1+x^2)))*sqrt(2)*sqrt(a+sqrt(1+a^2))],

//  17 August 2016
[(a+b*x)/((1-x^2)^(1/3)*(3+x^2)),x,7,-1/6*a*arctanh(x)/2^(2/3)+1/2*a*arctanh(x/(1+2^(1/3)*(1-x^2)^(1/3)))/2^(2/3)-1/4*b*log(3+x^2)/2^(2/3)+3/4*b*log(2^(2/3)-(1-x^2)^(1/3))/2^(2/3)+1/2*a*arctan(sqrt(3)/x)/(2^(2/3)*sqrt(3))+1/2*a*arctan((1-2^(1/3)*(1-x^2)^(1/3))*sqrt(3)/x)/(2^(2/3)*sqrt(3))+1/2*b*arctan((1+(2-2*x^2)^(1/3))/sqrt(3))*sqrt(3)/2^(2/3)],
[(a+b*x)/((3-x^2)*(1+x^2)^(1/3)),x,7,-1/6*a*arctan(x)/2^(2/3)+1/2*a*arctan(x/(1+2^(1/3)*(1+x^2)^(1/3)))/2^(2/3)+1/4*b*log(3-x^2)/2^(2/3)-3/4*b*log(2^(2/3)-(1+x^2)^(1/3))/2^(2/3)-1/2*a*arctanh(sqrt(3)/x)/(2^(2/3)*sqrt(3))-1/2*a*arctanh((1-2^(1/3)*(1+x^2)^(1/3))*sqrt(3)/x)/(2^(2/3)*sqrt(3))-1/2*b*arctan((1+2^(1/3)*(1+x^2)^(1/3))/sqrt(3))*sqrt(3)/2^(2/3)],
[1/(x*(4-6*x+3*x^2)^(1/3)),x,1,-1/2*log(x)/2^(2/3)+1/2*log(6-3*x-3*2^(1/3)*(4-6*x+3*x^2)^(1/3))/2^(2/3)-arctan(1/sqrt(3)+2^(2/3)*(2-x)/((4-6*x+3*x^2)^(1/3)*sqrt(3)))/(2^(2/3)*sqrt(3))],
[x*(1-x^3)^(1/3),x,2,1/3*x^2*(1-x^3)^(1/3)-1/6*log(-x-(1-x^3)^(1/3))-1/3*arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)],
[(1-x^3)^(1/3)/x,x,6,(1-x^3)^(1/3)-1/2*log(x)+1/2*log(1-(1-x^3)^(1/3))-arctan((1+2*(1-x^3)^(1/3))/sqrt(3))/sqrt(3)],
[(1-x^3)^(1/3)/(1+x),x,25,(1-x^3)^(1/3)-1/3*2^(1/3)*log(1+x^3)+1/3*log(2^(2/3)+(-1+x)/(1-x^3)^(1/3))/2^(2/3)-1/3*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)+1/3*2^(1/3)*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))-1/6*log(2*2^(1/3)+(1-x)^2/(1-x^3)^(2/3)+2^(2/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)+log(2^(1/3)-(1-x^3)^(1/3))/2^(2/3)-1/2*log(-x-(1-x^3)^(1/3))+log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(2/3)+2^(1/3)*arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))-arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+2^(1/3)*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-2^(1/3)*arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/sqrt(3)],
[(1-x^3)^(1/3)/(1-x+x^2),x,19,-1/2*log(-3*(-1+x)*(1-x+x^2))/2^(2/3)+1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(2/3)+3/2*log(-2^(1/3)*(-1+x)+(1-x^3)^(1/3))/2^(2/3)+1/2*log(x+(1-x^3)^(1/3))-1/2*log(2^(1/3)*x+(1-x^3)^(1/3))/2^(2/3)+arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))-arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))+arctan((1+2*2^(1/3)*(-1+x)/(1-x^3)^(1/3))/sqrt(3))*sqrt(3)/2^(2/3),1/3*log(1+x^3)/2^(2/3)+1/3*log(2^(2/3)+(-1+x)/(1-x^3)^(1/3))/2^(2/3)-1/3*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)+1/3*2^(1/3)*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))-1/6*log(2*2^(1/3)+(1-x)^2/(1-x^3)^(2/3)+2^(2/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)+1/2*log(-x-(1-x^3)^(1/3))-log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(2/3)+2^(1/3)*arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))+arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-2^(1/3)*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)],

//  22 September 2016
//  {1/(x^3 - 3*x^2 + 7*x - 4)^(1/3), x, 0, 0}

// {1/(x*(3*x^2 - 6*x + 5)^(1/3)), x, 0, 0} 
[(1-x^3)^(1/3)/(2+x),x,12,(1-x^3)^(1/3)+1/2*x*AppellF1(1/3,-1/3,1,4/3,x^3,-1/8*x^3)-3^(1/6)*arctan(2/3*(1-x^3)^(1/3)/3^(1/6)+1/sqrt(3))+3^(1/6)*arctan((1-3^(2/3)*x/(1-x^3)^(1/3))/sqrt(3))-log(8+x^3)/3^(1/3)+1/2*3^(2/3)*log(3^(2/3)-(1-x^3)^(1/3))-log(-x-(1-x^3)^(1/3))+1/2*3^(2/3)*log(-1/2*3^(2/3)*x-(1-x^3)^(1/3))-2*arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)],
[(2+x)/((1+x+x^2)*(2+x^3)^(1/3)),x,9,-1/2*x^2*AppellF1(2/3,1,1/3,5/3,x^3,-1/2*x^3)/2^(1/3)+arctan((3^(1/3)+2*(2+x^3)^(1/3))/3^(5/6))/3^(5/6)+2*arctan((1+2*3^(1/3)*x/(2+x^3)^(1/3))/sqrt(3))/3^(5/6)+1/6*log(1-x^3)/3^(1/3)+1/2*log(3^(1/3)-(2+x^3)^(1/3))/3^(1/3)-log(3^(1/3)*x-(2+x^3)^(1/3))/3^(1/3)],

//  14 January 2017
[(3-3*x+30*x^2+160*x^3)/(9+24*x-12*x^2+80*x^3+320*x^4),x,1,1/8*log(9+24*x-12*x^2+80*x^3+320*x^4)],
[(3+12*x+20*x^2)/(9+24*x-12*x^2+80*x^3+320*x^4),x,1,-1/2*arctan(1/5*(7-40*x)/sqrt(11))/sqrt(11)+1/2*arctan(1/6*(57+30*x-40*x^2+800*x^3)/sqrt(11))/sqrt(11)],
[(-84-576*x-400*x^2+2560*x^3)/(9+24*x-12*x^2+80*x^3+320*x^4),x,2,2*log(9+24*x-12*x^2+80*x^3+320*x^4)+2*arctan(1/5*(7-40*x)/sqrt(11))*sqrt(11)-2*arctan(1/6*(57+30*x-40*x^2+800*x^3)/sqrt(11))*sqrt(11)],

//  31 January 2017
[sqrt(1-x^4)/(1+x^4),x,1,1/2*arctan(x*(1+x^2)/sqrt(1-x^4))+1/2*arctanh(x*(1-x^2)/sqrt(1-x^4))],
[sqrt(1+x^4)/(1-x^4),x,4,1/2*arctan(x*sqrt(2)/sqrt(1+x^4))/sqrt(2)+1/2*arctanh(x*sqrt(2)/sqrt(1+x^4))/sqrt(2)],

//  7 February 2017
[sqrt(1+p*x^2+x^4)/(1-x^4),x,4,1/4*arctan(x*sqrt(2-p)/sqrt(1+p*x^2+x^4))*sqrt(2-p)+1/4*arctanh(x*sqrt(2+p)/sqrt(1+p*x^2+x^4))*sqrt(2+p)],
[sqrt(1+p*x^2-x^4)/(1+x^4),x,1,1/2*arctanh(1/2*x*(p-2*x^2+sqrt(4+p^2))*sqrt(-p+sqrt(4+p^2))/(sqrt(2)*sqrt(1+p*x^2-x^4)))*sqrt(-p+sqrt(4+p^2))/sqrt(2)-1/2*arctan(1/2*x*(p-2*x^2-sqrt(4+p^2))*sqrt(p+sqrt(4+p^2))/(sqrt(2)*sqrt(1+p*x^2-x^4)))*sqrt(p+sqrt(4+p^2))/sqrt(2)],

//  28 August 2017
//  {(3 + x^2)/((1 + x^2)*(1 + 6*x^2 + x^4)^(1/4)), x, 0, 0}

// {(3 - x^2)/((1 - x^2)*(1 - 6*x^2 + x^4)^(1/4)), x, 0, 0} 
[(a+b*x)/((2-x^2)*(-1+x^2)^(1/4)),x,7,-b*arctan((-1+x^2)^(1/4))+b*arctanh((-1+x^2)^(1/4))+1/2*a*arctan(x/((-1+x^2)^(1/4)*sqrt(2)))/sqrt(2)+1/2*a*arctanh(x/((-1+x^2)^(1/4)*sqrt(2)))/sqrt(2)],
[(a+b*x)/((-1-x^2)^(1/4)*(2+x^2)),x,7,b*arctan((-1-x^2)^(1/4))-b*arctanh((-1-x^2)^(1/4))+1/2*a*arctan(x/((-1-x^2)^(1/4)*sqrt(2)))/sqrt(2)+1/2*a*arctanh(x/((-1-x^2)^(1/4)*sqrt(2)))/sqrt(2)],
[(a+b*x)/((1-x^2)^(1/4)*(2-x^2)),x,3,1/2*a*arctan((1-sqrt(1-x^2))/(x*(1-x^2)^(1/4)))+1/2*a*arctanh((1+sqrt(1-x^2))/(x*(1-x^2)^(1/4)))+b*arctan((1-sqrt(1-x^2))/((1-x^2)^(1/4)*sqrt(2)))/sqrt(2)+b*arctanh((1+sqrt(1-x^2))/((1-x^2)^(1/4)*sqrt(2)))/sqrt(2)],
[(a+b*x)/((1+x^2)^(1/4)*(2+x^2)),x,3,-1/2*a*arctan((1+sqrt(1+x^2))/(x*(1+x^2)^(1/4)))-1/2*a*arctanh((1-sqrt(1+x^2))/(x*(1+x^2)^(1/4)))-b*arctan((1-sqrt(1+x^2))/((1+x^2)^(1/4)*sqrt(2)))/sqrt(2)-b*arctanh((1+sqrt(1+x^2))/((1+x^2)^(1/4)*sqrt(2)))/sqrt(2)],

//  20 January 2018
[x/((4-x^3)*sqrt(1-x^3)),x,1,-1/3*arctanh((1+2^(1/3)*x)/sqrt(1-x^3))/2^(2/3)+1/9*arctanh(sqrt(1-x^3))/2^(2/3)-1/3*arctan((1-2^(1/3)*x)*sqrt(3)/sqrt(1-x^3))/(2^(2/3)*sqrt(3))+1/3*arctan(sqrt(1-x^3)/sqrt(3))/(2^(2/3)*sqrt(3))],
[x/((4-d*x^3)*sqrt(-1+d*x^3)),x,1,-1/3*arctan((1+2^(1/3)*d^(1/3)*x)/sqrt(-1+d*x^3))/(2^(2/3)*d^(2/3))-1/9*arctan(sqrt(-1+d*x^3))/(2^(2/3)*d^(2/3))-1/3*arctanh((1-2^(1/3)*d^(1/3)*x)*sqrt(3)/sqrt(-1+d*x^3))/(2^(2/3)*d^(2/3)*sqrt(3))-1/3*arctanh(sqrt(-1+d*x^3)/sqrt(3))/(2^(2/3)*d^(2/3)*sqrt(3))],
[x/((8+x^3)*sqrt(-1+x^3)),x,8,1/18*arctan(1/3*(1-x)^2/sqrt(-1+x^3))+1/18*arctan(1/3*sqrt(-1+x^3))-1/6*arctanh((1-x)*sqrt(3)/sqrt(-1+x^3))/sqrt(3)],
[x/((8-d*x^3)*sqrt(1+d*x^3)),x,8,1/18*arctanh(1/3*(1+d^(1/3)*x)^2/sqrt(1+d*x^3))/d^(2/3)-1/18*arctanh(1/3*sqrt(1+d*x^3))/d^(2/3)-1/6*arctan((1+d^(1/3)*x)*sqrt(3)/sqrt(1+d*x^3))/(d^(2/3)*sqrt(3))],

//  25 January 2018
[1/((1-3*x^2)^(1/3)*(3-x^2)),x,1,1/4*arctan((1-(1-3*x^2)^(1/3))/x)+1/4*arctanh(x/sqrt(3))/sqrt(3)-1/4*arctanh(1/3*(1-(1-3*x^2)^(1/3))^2/(x*sqrt(3)))/sqrt(3)],
[1/((3+x^2)*(1+3*x^2)^(1/3)),x,1,-1/4*arctanh((1-(1+3*x^2)^(1/3))/x)+1/4*arctan(x/sqrt(3))/sqrt(3)+1/4*arctan(1/3*(1-(1+3*x^2)^(1/3))^2/(x*sqrt(3)))/sqrt(3)],
[1/((1-x^2)^(1/3)*(3+x^2)),x,1,-1/6*arctanh(x)/2^(2/3)+1/2*arctanh(x/(1+2^(1/3)*(1-x^2)^(1/3)))/2^(2/3)+1/2*arctan(sqrt(3)/x)/(2^(2/3)*sqrt(3))+1/2*arctan((1-2^(1/3)*(1-x^2)^(1/3))*sqrt(3)/x)/(2^(2/3)*sqrt(3))],
[1/((3-x^2)*(1+x^2)^(1/3)),x,1,-1/6*arctan(x)/2^(2/3)+1/2*arctan(x/(1+2^(1/3)*(1+x^2)^(1/3)))/2^(2/3)-1/2*arctanh(sqrt(3)/x)/(2^(2/3)*sqrt(3))-1/2*arctanh((1-2^(1/3)*(1+x^2)^(1/3))*sqrt(3)/x)/(2^(2/3)*sqrt(3))],

//  27 January 2018
[(a+x)/((-a+x)*sqrt(a^2*x-(1+a^2)*x^2+x^3)),x,4,-2*arctan((1-a)*sqrt(x)/sqrt(a^2-(1+a^2)*x+x^2))*sqrt(x)*sqrt(a^2-(1+a^2)*x+x^2)/((1-a)*sqrt(a^2*x-(1+a^2)*x^2+x^3))],
[(-2+a+x)/((-a+x)*sqrt((2-a)*a*x+(-1-2*a+a^2)*x^2+x^3)),x,-5,0],
[(-a+(-1+2*a)*x)/((-a+x)*sqrt(a^2*x-(-1+2*a+a^2)*x^2+(-1+2*a)*x^3)),x,-7,log((-a^2+2*a*x+x^2-2*(x+sqrt((1-x)*x*(a^2+x-2*a*x))))/(a-x)^2)],

//  7 February 2018
[(1-2^(1/3)*x)/((2^(2/3)+x)*sqrt(1+x^3)),x,2,2*arctan((1+2^(1/3)*x)*sqrt(3)/sqrt(1+x^3))/sqrt(3)],

//  14 February 2018
[(1+x)/((-2+x)*sqrt(1+x^3)),x,2,-2/3*arctanh(1/3*(1+x)^2/sqrt(1+x^3))],

//  21 February 2018
[x/((10+x^3+6*sqrt(3))*sqrt(1+x^3)),x,1,-1/2*arctan(3^(1/4)*(1+x)*(1+sqrt(3))/(sqrt(2)*sqrt(1+x^3)))*(2-sqrt(3))/(3^(3/4)*sqrt(2))-1/3*arctan((1-sqrt(3))*sqrt(1+x^3)/(3^(3/4)*sqrt(2)))*(2-sqrt(3))/(3^(3/4)*sqrt(2))-1/6*arctanh(3^(1/4)*(1+x)*(1-sqrt(3))/(sqrt(2)*sqrt(1+x^3)))*(2-sqrt(3))/(3^(1/4)*sqrt(2))-1/3*arctanh(3^(1/4)*(1-2*x+sqrt(3))/(sqrt(2)*sqrt(1+x^3)))*(2-sqrt(3))/(3^(1/4)*sqrt(2))],
[x/((10+x^3-6*sqrt(3))*sqrt(1+x^3)),x,1,-1/3*arctan(3^(1/4)*(1-2*x-sqrt(3))/(sqrt(2)*sqrt(1+x^3)))*(2+sqrt(3))/(3^(1/4)*sqrt(2))-1/6*arctan(3^(1/4)*(1+x)*(1+sqrt(3))/(sqrt(2)*sqrt(1+x^3)))*(2+sqrt(3))/(3^(1/4)*sqrt(2))+1/2*arctanh(3^(1/4)*(1+x)*(1-sqrt(3))/(sqrt(2)*sqrt(1+x^3)))*(2+sqrt(3))/(3^(3/4)*sqrt(2))+1/3*arctanh((1+sqrt(3))*sqrt(1+x^3)/(3^(3/4)*sqrt(2)))*(2+sqrt(3))/(3^(3/4)*sqrt(2))],
[x/((-10+x^3-6*sqrt(3))*sqrt(-1+x^3)),x,1,1/6*arctan(3^(1/4)*(1-x)*(1-sqrt(3))/(sqrt(2)*sqrt(-1+x^3)))*(2-sqrt(3))/(3^(1/4)*sqrt(2))+1/3*arctan(3^(1/4)*(1+2*x+sqrt(3))/(sqrt(2)*sqrt(-1+x^3)))*(2-sqrt(3))/(3^(1/4)*sqrt(2))+1/2*arctanh(3^(1/4)*(1-x)*(1+sqrt(3))/(sqrt(2)*sqrt(-1+x^3)))*(2-sqrt(3))/(3^(3/4)*sqrt(2))-1/3*arctanh((1-sqrt(3))*sqrt(-1+x^3)/(3^(3/4)*sqrt(2)))*(2-sqrt(3))/(3^(3/4)*sqrt(2))],
[x/((-10+x^3+6*sqrt(3))*sqrt(-1+x^3)),x,1,-1/2*arctan(3^(1/4)*(1-x)*(1-sqrt(3))/(sqrt(2)*sqrt(-1+x^3)))*(2+sqrt(3))/(3^(3/4)*sqrt(2))+1/3*arctan((1+sqrt(3))*sqrt(-1+x^3)/(3^(3/4)*sqrt(2)))*(2+sqrt(3))/(3^(3/4)*sqrt(2))+1/3*arctanh(3^(1/4)*(1+2*x-sqrt(3))/(sqrt(2)*sqrt(-1+x^3)))*(2+sqrt(3))/(3^(1/4)*sqrt(2))+1/6*arctanh(3^(1/4)*(1-x)*(1+sqrt(3))/(sqrt(2)*sqrt(-1+x^3)))*(2+sqrt(3))/(3^(1/4)*sqrt(2))],

//  24 February 2018 via email
[(1+x-sqrt(3))/((1+x+sqrt(3))*sqrt(-4+x^4+4*x^2*sqrt(3))),x,2,1/3*arctanh((1+x-sqrt(3))^2/(sqrt(3*(-3+2*sqrt(3)))*sqrt(-4+x^4+4*x^2*sqrt(3))))*sqrt(-3+2*sqrt(3))],
[(1+x+sqrt(3))/((1+x-sqrt(3))*sqrt(-4+x^4-4*x^2*sqrt(3))),x,2,-1/3*arctan((1+x+sqrt(3))^2/(sqrt(3*(3+2*sqrt(3)))*sqrt(-4+x^4-4*x^2*sqrt(3))))*sqrt(3+2*sqrt(3))],

//  1 March 2018
[(-1+x)/((1+x)*(2+x^3)^(1/3)),x,1,log(1+x)-3/2*log(2+x-(2+x^3)^(1/3))+arctan((1+2*(2+x)/(2+x^3)^(1/3))/sqrt(3))*sqrt(3)],
[1/((1+x)*(2+x^3)^(1/3)),x,3,-1/2*log(1+x)+3/4*log(2+x-(2+x^3)^(1/3))-1/4*log(-x+(2+x^3)^(1/3))+1/2*arctan((1+2*x/(2+x^3)^(1/3))/sqrt(3))/sqrt(3)-1/2*arctan((1+2*(2+x)/(2+x^3)^(1/3))/sqrt(3))*sqrt(3)],

//  1 April 2018

//  {(x^2 + 2*x - 3)/((x^4 - 8*x^3 + 94*x^2 + 552*x + 657)*Sqrt[x^3 - 15*x - 22]), x, 0, 0} 

// 26 September 2018
[1/((1-x^3)*(a+b*x^3)^(1/3)),x,1,1/6*log(1-x^3)/(a+b)^(1/3)-1/2*log((a+b)^(1/3)*x-(a+b*x^3)^(1/3))/(a+b)^(1/3)+arctan((1+2*(a+b)^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/((a+b)^(1/3)*sqrt(3))],
[(1+x)/((1+x+x^2)*(a+b*x^3)^(1/3)),x,8,1/2*log((a+b)^(1/3)-(a+b*x^3)^(1/3))/(a+b)^(1/3)-1/2*log((a+b)^(1/3)*x-(a+b*x^3)^(1/3))/(a+b)^(1/3)+arctan((1+2*(a+b)^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/((a+b)^(1/3)*sqrt(3))+arctan((1+2*(a+b*x^3)^(1/3)/(a+b)^(1/3))/sqrt(3))/((a+b)^(1/3)*sqrt(3))],
[x^2/((1-x^3)*(a+b*x^3)^(1/3)),x,5,1/6*log(1-x^3)/(a+b)^(1/3)-1/2*log((a+b)^(1/3)-(a+b*x^3)^(1/3))/(a+b)^(1/3)-arctan((1+2*(a+b*x^3)^(1/3)/(a+b)^(1/3))/sqrt(3))/((a+b)^(1/3)*sqrt(3))],

// 12 October 2018
[1/((1-x^3)^(1/3)*(1+x^3)),x,1,-1/6*log(1+x^3)/2^(1/3)+1/2*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)-arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x/((1-x^3)^(1/3)*(1+x^3)),x,8,1/12*log((1-x)*(1+x)^2)/2^(1/3)+1/6*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/3*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/4*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)+arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))+1/2*arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],
[x^2/((1-x^3)^(1/3)*(1+x^3)),x,5,-1/6*log(1+x^3)/2^(1/3)+1/2*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],

//  Integrands are equal. 
[(1+x)/((1-x+x^2)*(1-x^3)^(1/3)),x,-16,1/2*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))*sqrt(3)/2^(1/3)],
[(1+x)^2/((1-x^3)^(1/3)*(1+x^3)),x,-17,1/2*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))*sqrt(3)/2^(1/3)],
[(1-x)/((1+x+x^2)*(1+x^3)^(1/3)),x,-16,-1/2*log(1+2^(2/3)*(1+x)^2/(1+x^3)^(2/3)-2^(1/3)*(1+x)/(1+x^3)^(1/3))/2^(1/3)+log(1+2^(1/3)*(1+x)/(1+x^3)^(1/3))/2^(1/3)-arctan((1-2*2^(1/3)*(1+x)/(1+x^3)^(1/3))/sqrt(3))*sqrt(3)/2^(1/3)],

//  Integrands are equal. 
[(1-x^3)^(2/3)/(1+x+x^2)^2,x,5,1/(1-x^3)^(1/3)+x/(1-x^3)^(1/3)-x^2*hypergeom([2/3,4/3],[5/3],x^3)],
[(1-x)/((1+x+x^2)*(1-x^3)^(1/3)),x,5,1/(1-x^3)^(1/3)+x/(1-x^3)^(1/3)-x^2*hypergeom([2/3,4/3],[5/3],x^3)],
[(1-x)^2/(1-x^3)^(4/3),x,3,(1+(1-2*x)*x)/(1-x^3)^(1/3)+x^2*hypergeom([1/3,2/3],[5/3],x^3)],

// 16 October 2018
[(1-x^3)^(2/3),x,2,1/3*x*(1-x^3)^(2/3)+1/3*log(x+(1-x^3)^(1/3))-2/3*arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)],
[(1-x^3)^(2/3)/x,x,6,1/2*(1-x^3)^(2/3)-1/2*log(x)+1/2*log(1-(1-x^3)^(1/3))+arctan((1+2*(1-x^3)^(1/3))/sqrt(3))/sqrt(3)],
[(1-x^3)^(2/3)/(a+b*x),x,13,1/2*(1-x^3)^(2/3)/b-1/2*(a^3+b^3)*x^2*AppellF1(2/3,1/3,1,5/3,x^3,-b^3*x^3/a^3)/(a^2*b^2)+1/2*a*x^2*hypergeom([1/3,2/3],[5/3],x^3)/b^2-1/3*(a^3+b^3)^(2/3)*log(a^3+b^3*x^3)/b^3+1/2*(a^3+b^3)^(2/3)*log(-(a^3+b^3)^(1/3)*x/a-(1-x^3)^(1/3))/b^3-1/2*a^2*log(x+(1-x^3)^(1/3))/b^3+1/2*(a^3+b^3)^(2/3)*log((a^3+b^3)^(1/3)-b*(1-x^3)^(1/3))/b^3+a^2*arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/(b^3*sqrt(3))-(a^3+b^3)^(2/3)*arctan((1-2*(a^3+b^3)^(1/3)*x/(a*(1-x^3)^(1/3)))/sqrt(3))/(b^3*sqrt(3))+(a^3+b^3)^(2/3)*arctan((1+2*b*(1-x^3)^(1/3)/(a^3+b^3)^(1/3))/sqrt(3))/(b^3*sqrt(3))],

// 17 October 2018
[(1-x^3)^(2/3)/(1-x+x^2)^2,x,13,-1/3*(1-x^3)^(2/3)/(1+x^3)+1/3*x*(1-x^3)^(2/3)/(1+x^3)+2/3*x^2*(1-x^3)^(2/3)/(1+x^3)+1/3*x^2*hypergeom([1/3,2/3],[5/3],x^3)-1/3*log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+1/3*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)-1/3*2^(2/3)*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-1/3*2^(2/3)*arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/sqrt(3)],
[(1-2*x)*(1-x^3)^(2/3)/(1-x+x^2)^2,x,14,(1-x^3)^(2/3)/(1-x+x^2)+log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)-log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)+log(x+(1-x^3)^(1/3))-2*arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+2^(2/3)*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+2^(2/3)*arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/sqrt(3),(1-x^3)^(2/3)/(1+x^3)+x*(1-x^3)^(2/3)/(1+x^3)+log(2^(1/3)-(1-x^3)^(1/3))/2^(1/3)+1/3*log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)-2/3*2^(2/3)*log(-2^(1/3)*x-(1-x^3)^(1/3))+log(x+(1-x^3)^(1/3))-2*arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+2^(2/3)*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+2^(2/3)*arctan((1+2^(2/3)*(1-x^3)^(1/3))/sqrt(3))/sqrt(3)],

// 22 October 2018
[(1-x^3)^(2/3)/(1+x),x,5,1/2*(1-x^3)^(2/3)+1/2*x^2*hypergeom([1/3,2/3],[5/3],x^3)-1/2*log((1-x)*(1+x)^2)/2^(1/3)-1/2*log(x+(1-x^3)^(1/3))+3/2*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)+arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))*sqrt(3)/2^(1/3)],
[(1-x+x^2)*(1-x^3)^(2/3)/(1+x^3),x,6,1/2*(1-x^3)^(2/3)+1/2*x^2*hypergeom([1/3,2/3],[5/3],x^3)-1/2*log((1-x)*(1+x)^2)/2^(1/3)-1/2*log(x+(1-x^3)^(1/3))+3/2*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)+arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))*sqrt(3)/2^(1/3)],

// 24 October 2018
[(1-x^3)^(2/3)/(1+x^3),x,3,-1/3*log(1+x^3)/2^(1/3)+log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)-1/2*log(x+(1-x^3)^(1/3))+arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-2^(2/3)*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)],
[x*(1-x^3)^(2/3)/(1+x^3),x,10,-1/2*x^2*hypergeom([1/3,2/3],[5/3],x^3)+1/6*log((1-x)*(1+x)^2)/2^(1/3)+1/3*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)-1/3*2^(2/3)*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))-1/2*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)+2^(2/3)*arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))],

// 4 November 2018
[(1-x)*(1-x^3)^(2/3)/(1+x^3),x,-17,1/2*x^2*hypergeom([1/3,2/3],[5/3],x^3)-1/6*log((1-x)*(1+x)^2)/2^(1/3)-1/3*log(1+x^3)/2^(1/3)-1/3*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(1/3)+1/3*2^(2/3)*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))+log(-2^(1/3)*x-(1-x^3)^(1/3))/2^(1/3)-1/2*log(x+(1-x^3)^(1/3))+1/2*log(-1+x+2^(2/3)*(1-x^3)^(1/3))/2^(1/3)-2^(2/3)*arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))+arctan((1-2*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)-2^(2/3)*arctan((1-2*2^(1/3)*x/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)],

//  {(1 + x^3)*(1 - x^3)^(2/3)/(1 + x^3 + x^6), x, 0, 0} 
[(1-x^3)^(1/3)/(1+x^3),x,14,1/3*log(2^(2/3)+(-1+x)/(1-x^3)^(1/3))/2^(2/3)-1/3*log(1+2^(2/3)*(1-x)^2/(1-x^3)^(2/3)-2^(1/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)+1/3*2^(1/3)*log(1+2^(1/3)*(1-x)/(1-x^3)^(1/3))-1/6*log(2*2^(1/3)+(1-x)^2/(1-x^3)^(2/3)+2^(2/3)*(1-x)/(1-x^3)^(1/3))/2^(2/3)+2^(1/3)*arctan((1-2*2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/sqrt(3)+arctan((1+2^(1/3)*(1-x)/(1-x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))]
]:;

auto_assume(1);
res:=[]:;
S:=182; S:=size(lst);
failint:=[]; failsimp:=[]; nock:=[]; ass:=[];
print("Integration independent test suites, Welz "+S);
file:=fopen("intindw.tst");
T0:=time();
for j from 0 to S-1 do
  l:=eval(lst,1)[j]; 
  f:=l[0]; v:=l[1]; hyp:=l[2]; print(f);
  purge(unquote(v));
  if (type(hyp)==string) expr(hyp); // eval assumption
  print(j+1,f,v,hyp,about(unquote(v)));
  try { g:=integrate(f,unquote(v)); } catch(err){ g:="integrate(err)"; }
  s:=""+eval(g,1);
  h:=false;
  fail:=size(s.find("integrate("))>0 || hyp==x;
  if (fail) failint.append(j+1);
  if (hyp=="nock") nock.append(j+1);
  if (hyp.type==string && size(hyp.find("assume("))>0) ass.append(j+1);
  if (hyp!="nock" && !fail)  h:=simplify(diff(g,unquote(v))-f); else print("nock");
  purge(unquote(assumptions));
  fgh:=""+eval([j+1,f,g,h],1);
  if (eval(h,1)!=0) failsimp.append(j+1);
  print(fgh);
  //res.append([f,g,h]); print(res[size(res)-1]);
  fprint(file,"",fgh);
od:;
fprint(file,"","Time:",time()-T0,", tests: ",S,", integration failures: ",size(failint),failint,", simplification failures: ",size(failsimp),failsimp,", not cheked: ",size(nock),nock,", assumptions: ",size(ass),ass);
fclose(file);
print("Integration independent test suites, Welz ","tests: ",S,", integration failures: ",size(failint),failint,", simplification failures: ",size(failsimp),failsimp,", not cheked: ",size(nock),nock,", assumptions: ",size(ass),ass);
//res;
