# Maple integration test file: "2 Exponentials\2.3 Exponential functions.txt"

lst:=[

# Integration Problems Involving Exponentials

# Integrands of the form (G^(h (f+g x)))^m (a+b (F^(e (c+d x)))^n)^p

# Integrands of the form F^(e+f x) (a+b F^(e+f x))^p
[exp(x)/(4+6*exp(x)),x,2,1/6*log(2+3*exp(x))],
[exp(x)/(a+b*exp(x)),x,2,log(a+b*exp(x))/b],
[exp(d*x)/(a+b*exp(c+d*x)),x,3,log(a+b*exp(c+d*x))/(b*d*exp(c))],
[exp(c+d*x)/(a+b*exp(c+d*x)),x,2,log(a+b*exp(c+d*x))/(b*d)],
[exp(x)*(a+b*exp(x))^n,x,2,(a+b*exp(x))^(1+n)/(b*(1+n))],
[exp(d*x)*(a+b*exp(c+d*x))^n,x,3,(a+b*exp(c+d*x))^(1+n)/(b*d*exp(c)*(1+n))],
[exp(c+d*x)*(a+b*exp(c+d*x))^n,x,2,(a+b*exp(c+d*x))^(1+n)/(b*d*(1+n))],
[F^x/(a+b*F^x),x,2,log(a+b*F^x)/(b*log(F))],
[F^(d*x)/(a+b*F^(c+d*x)),x,3,log(a+b*F^(c+d*x))/(b*d*F^c*log(F))],
[F^(c+d*x)/(a+b*F^(c+d*x)),x,2,log(a+b*F^(c+d*x))/(b*d*log(F))],
[F^x*(a+b*F^x)^n,x,2,(a+b*F^x)^(1+n)/(b*(1+n)*log(F))],
[F^(d*x)*(a+b*F^(c+d*x))^n,x,3,(a+b*F^(c+d*x))^(1+n)/(b*d*F^c*(1+n)*log(F))],
[F^(c+d*x)*(a+b*F^(c+d*x))^n,x,2,(a+b*F^(c+d*x))^(1+n)/(b*d*(1+n)*log(F))],

# Integrands of the form (G^(h (f+g x)))^m (a+b (F^(e (c+d x)))^n)^p when d e n Log[f]=g h m Log[g]
[(exp(x))^n*(a+b*(exp(x))^n)^p,x,2,(a+b*(exp(x))^n)^(1+p)/(b*n*(1+p))],
[exp(n*x)*(a+b*(exp(x))^n)^p,x,3,exp(n*x)*(a+b*(exp(x))^n)^(1+p)/(b*(exp(x))^n*n*(1+p))],
[(F^(e*(c+d*x)))^n*(a+b*(F^(e*(c+d*x)))^n)^p,x,2,(a+b*(F^(e*(c+d*x)))^n)^(1+p)/(b*d*e*n*(1+p)*log(F))],
[(a+b*(F^(e*(c+d*x)))^n)^p*(G^(h*(f+g*x)))^(d*e*n*log(F)/(g*h*log(G))),x,3,(a+b*(F^(e*(c+d*x)))^n)^(1+p)*(G^(h*(f+g*x)))^(d*e*n*log(F)/(g*h*log(G)))/(b*d*e*(F^(e*(c+d*x)))^n*n*(1+p)*log(F))],

# Integrands of the form G^(h (f+g x)) (a+b F^(e (c+d x)))^p
[exp(2*x)/(a+b*exp(x)),x,3,exp(x)/b-a*log(a+b*exp(x))/b^2],
[exp(2*x)/(a+b*exp(x))^2,x,3,a/(b^2*(a+b*exp(x)))+log(a+b*exp(x))/b^2],
[exp(2*x)/(a+b*exp(x))^3,x,2,1/2*exp(2*x)/(a*(a+b*exp(x))^2)],
[exp(2*x)/(a+b*exp(x))^4,x,3,1/3*a/(b^2*(a+b*exp(x))^3)+(-1/2)/(b^2*(a+b*exp(x))^2)],
[exp(4*x)/(a+b*exp(2*x)),x,3,1/2*exp(2*x)/b-1/2*a*log(a+b*exp(2*x))/b^2],
[exp(4*x)/(a+b*exp(2*x))^2,x,3,1/2*a/(b^2*(a+b*exp(2*x)))+1/2*log(a+b*exp(2*x))/b^2],
[exp(4*x)/(a+b*exp(2*x))^3,x,2,1/4*exp(4*x)/(a*(a+b*exp(2*x))^2)],
[exp(4*x)/(a+b*exp(2*x))^4,x,3,1/6*a/(b^2*(a+b*exp(2*x))^3)+(-1/4)/(b^2*(a+b*exp(2*x))^2)],
[exp(4*x)/(a+b*exp(2*x))^(2/3),x,3,-3/2*a*(a+b*exp(2*x))^(1/3)/b^2+3/8*(a+b*exp(2*x))^(4/3)/b^2],
[(a+b*exp(n*x))/exp(n*x),x,3,-a/(exp(n*x)*n)+b*x],
[(a+b*exp(n*x))^2/exp(n*x),x,3,-a^2/(exp(n*x)*n)+b^2*exp(n*x)/n+2*a*b*x],
[(a+b*exp(n*x))^3/exp(n*x),x,3,-a^3/(exp(n*x)*n)+3*a*b^2*exp(n*x)/n+1/2*b^3*exp(2*n*x)/n+3*a^2*b*x],
[1/(exp(n*x)*(a+b*exp(n*x))),x,3,(-1)/(a*exp(n*x)*n)-b*x/a^2+b*log(a+b*exp(n*x))/(a^2*n)],
[1/(exp(n*x)*(a+b*exp(n*x))^2),x,3,(-1)/(a^2*exp(n*x)*n)-b/(a^2*(a+b*exp(n*x))*n)-2*b*x/a^3+2*b*log(a+b*exp(n*x))/(a^3*n)],
[1/(exp(n*x)*(a+b*exp(n*x))^3),x,3,(-1)/(a^3*exp(n*x)*n)-1/2*b/(a^2*(a+b*exp(n*x))^2*n)-2*b/(a^3*(a+b*exp(n*x))*n)-3*b*x/a^4+3*b*log(a+b*exp(n*x))/(a^4*n)],
[f^(a+b*x)/(c+d*f^(e+2*b*x)),x,2,f^(a-1/2*e)*arctan(f^(1/2*e+b*x)*sqrt(d)/sqrt(c))/(b*log(f)*sqrt(c)*sqrt(d))],
[f^(a+2*b*x)/(c+d*f^(e+2*b*x)),x,3,1/2*f^(a-e)*log(c+d*f^(e+2*b*x))/(b*d*log(f))],
[f^(a+3*b*x)/(c+d*f^(e+2*b*x)),x,3,f^(1/2*(2*a-3*e)+1/2*(e+2*b*x))/(b*d*log(f))-f^(a-3/2*e)*arctan(f^(1/2*(e+2*b*x))*sqrt(d)/sqrt(c))*sqrt(c)/(b*d^(3/2)*log(f))],
[f^(a+4*b*x)/(c+d*f^(e+2*b*x)),x,3,1/2*f^(a-e+2*b*x)/(b*d*log(f))-1/2*c*f^(a-2*e)*log(c+d*f^(e+2*b*x))/(b*d^2*log(f))],
[f^(a+5*b*x)/(c+d*f^(e+2*b*x)),x,4,-c*f^(1/2*(2*a-5*e)+1/2*(e+2*b*x))/(b*d^2*log(f))+1/3*f^(1/2*(2*a-5*e)+3/2*(e+2*b*x))/(b*d*log(f))+c^(3/2)*f^(a-5/2*e)*arctan(f^(1/2*(e+2*b*x))*sqrt(d)/sqrt(c))/(b*d^(5/2)*log(f))],
[exp(x)/(1+exp(2*x)),x,2,arctan(exp(x))],
[exp(x)/(1-exp(2*x)),x,2,arctanh(exp(x))],
[exp(x)*x/(1-exp(2*x)),x,3,x*arctanh(exp(x))+1/2*polylog(2,-exp(x))-1/2*polylog(2,exp(x))],
[exp(x)*x^2/(1-exp(2*x)),x,8,x^2*arctanh(exp(x))+x*polylog(2,-exp(x))-x*polylog(2,exp(x))-polylog(3,-exp(x))+polylog(3,exp(x))],
[exp(x)*x^3/(1-exp(2*x)),x,10,x^3*arctanh(exp(x))+3/2*x^2*polylog(2,-exp(x))-3/2*x^2*polylog(2,exp(x))-3*x*polylog(3,-exp(x))+3*x*polylog(3,exp(x))+3*polylog(4,-exp(x))-3*polylog(4,exp(x))],
[f^x/(a+b*f^(2*x)),x,2,arctan(f^x*sqrt(b)/sqrt(a))/(log(f)*sqrt(a)*sqrt(b))],
[f^x*x/(a+b*f^(2*x)),x,6,x*arctan(f^x*sqrt(b)/sqrt(a))/(log(f)*sqrt(a)*sqrt(b))-1/2*I*polylog(2,-I*f^x*sqrt(b)/sqrt(a))/(log(f)^2*sqrt(a)*sqrt(b))+1/2*I*polylog(2,I*f^x*sqrt(b)/sqrt(a))/(log(f)^2*sqrt(a)*sqrt(b))],
[f^x*x^2/(a+b*f^(2*x)),x,9,x^2*arctan(f^x*sqrt(b)/sqrt(a))/(log(f)*sqrt(a)*sqrt(b))-I*x*polylog(2,-I*f^x*sqrt(b)/sqrt(a))/(log(f)^2*sqrt(a)*sqrt(b))+I*x*polylog(2,I*f^x*sqrt(b)/sqrt(a))/(log(f)^2*sqrt(a)*sqrt(b))+I*polylog(3,-I*f^x*sqrt(b)/sqrt(a))/(log(f)^3*sqrt(a)*sqrt(b))-I*polylog(3,I*f^x*sqrt(b)/sqrt(a))/(log(f)^3*sqrt(a)*sqrt(b))],
[f^x*x^3/(a+b*f^(2*x)),x,11,x^3*arctan(f^x*sqrt(b)/sqrt(a))/(log(f)*sqrt(a)*sqrt(b))-3/2*I*x^2*polylog(2,-I*f^x*sqrt(b)/sqrt(a))/(log(f)^2*sqrt(a)*sqrt(b))+3/2*I*x^2*polylog(2,I*f^x*sqrt(b)/sqrt(a))/(log(f)^2*sqrt(a)*sqrt(b))+3*I*x*polylog(3,-I*f^x*sqrt(b)/sqrt(a))/(log(f)^3*sqrt(a)*sqrt(b))-3*I*x*polylog(3,I*f^x*sqrt(b)/sqrt(a))/(log(f)^3*sqrt(a)*sqrt(b))-3*I*polylog(4,-I*f^x*sqrt(b)/sqrt(a))/(log(f)^4*sqrt(a)*sqrt(b))+3*I*polylog(4,I*f^x*sqrt(b)/sqrt(a))/(log(f)^4*sqrt(a)*sqrt(b))],
[f^x/(a+b*f^(2*x))^2,x,3,1/2*f^x/(a*(a+b*f^(2*x))*log(f))+1/2*arctan(f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)*sqrt(b))],
[f^x*x/(a+b*f^(2*x))^2,x,8,1/2*f^x*x/(a*(a+b*f^(2*x))*log(f))-1/2*arctan(f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^2*sqrt(b))+1/2*x*arctan(f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)*sqrt(b))-1/4*I*polylog(2,-I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^2*sqrt(b))+1/4*I*polylog(2,I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^2*sqrt(b))],
[f^x*x^2/(a+b*f^(2*x))^2,x,16,1/2*f^x*x^2/(a*(a+b*f^(2*x))*log(f))-x*arctan(f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^2*sqrt(b))+1/2*x^2*arctan(f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)*sqrt(b))+1/2*I*polylog(2,-I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^3*sqrt(b))-1/2*I*x*polylog(2,-I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^2*sqrt(b))-1/2*I*polylog(2,I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^3*sqrt(b))+1/2*I*x*polylog(2,I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^2*sqrt(b))+1/2*I*polylog(3,-I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^3*sqrt(b))-1/2*I*polylog(3,I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^3*sqrt(b))],
[f^x*x^3/(a+b*f^(2*x))^2,x,21,1/2*f^x*x^3/(a*(a+b*f^(2*x))*log(f))-3/2*x^2*arctan(f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^2*sqrt(b))+1/2*x^3*arctan(f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)*sqrt(b))+3/2*I*x*polylog(2,-I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^3*sqrt(b))-3/4*I*x^2*polylog(2,-I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^2*sqrt(b))-3/2*I*x*polylog(2,I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^3*sqrt(b))+3/4*I*x^2*polylog(2,I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^2*sqrt(b))-3/2*I*polylog(3,-I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^4*sqrt(b))+3/2*I*x*polylog(3,-I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^3*sqrt(b))+3/2*I*polylog(3,I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^4*sqrt(b))-3/2*I*x*polylog(3,I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^3*sqrt(b))-3/2*I*polylog(4,-I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^4*sqrt(b))+3/2*I*polylog(4,I*f^x*sqrt(b)/sqrt(a))/(a^(3/2)*log(f)^4*sqrt(b))],
[f^x/(a+b*f^(2*x))^3,x,4,1/4*f^x/(a*(a+b*f^(2*x))^2*log(f))+3/8*f^x/(a^2*(a+b*f^(2*x))*log(f))+3/8*arctan(f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)*sqrt(b))],
[f^x*x/(a+b*f^(2*x))^3,x,11,-1/8*f^x/(a^2*(a+b*f^(2*x))*log(f)^2)+1/4*f^x*x/(a*(a+b*f^(2*x))^2*log(f))+3/8*f^x*x/(a^2*(a+b*f^(2*x))*log(f))-1/2*arctan(f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)^2*sqrt(b))+3/8*x*arctan(f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)*sqrt(b))-3/16*I*polylog(2,-I*f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)^2*sqrt(b))+3/16*I*polylog(2,I*f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)^2*sqrt(b))],
[f^x*x^2/(a+b*f^(2*x))^3,x,24,-1/4*f^x*x/(a^2*(a+b*f^(2*x))*log(f)^2)+1/4*f^x*x^2/(a*(a+b*f^(2*x))^2*log(f))+3/8*f^x*x^2/(a^2*(a+b*f^(2*x))*log(f))+1/4*arctan(f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)^3*sqrt(b))-x*arctan(f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)^2*sqrt(b))+3/8*x^2*arctan(f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)*sqrt(b))+1/2*I*polylog(2,-I*f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)^3*sqrt(b))-3/8*I*x*polylog(2,-I*f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)^2*sqrt(b))-1/2*I*polylog(2,I*f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)^3*sqrt(b))+3/8*I*x*polylog(2,I*f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)^2*sqrt(b))+3/8*I*polylog(3,-I*f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)^3*sqrt(b))-3/8*I*polylog(3,I*f^x*sqrt(b)/sqrt(a))/(a^(5/2)*log(f)^3*sqrt(b))],

#  {x^3*f^x/(a + b*f^(2*x))^3, x, 30, (3*x*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(4*a^(5/2)*Sqrt[b]*Log[f]^3) - (3*f^x*x^2)/(8*a^2*(a + b*f^(2*x))*Log[f]^2) - (3*x^2*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(2*a^(5/2)*Sqrt[b]*Log[f]^2) + (x^3*((2*a^(3/2)*f^x)/(a + b*f^(2*x))^2 + (3*Sqrt[a]*f^x)/(a + b*f^(2*x)) + (3*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b]))/(8*a^(5/2)*Log[f]) - (3*I*(2 - 8*x*Log[f] + 3*x^2*Log[f]^2)*PolyLog[2, -((I*Sqrt[b]*f^x)/Sqrt[a])])/(16*a^(5/2)*Sqrt[b]*Log[f]^4) + (3*I*(2 - 8*x*Log[f] + 3*x^2*Log[f]^2)*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(16*a^(5/2)*Sqrt[b]*Log[f]^4) - (3*I*(4 - 3*x*Log[f])*PolyLog[3, -((I*Sqrt[b]*f^x)/Sqrt[a])])/(8*a^(5/2)*Sqrt[b]*Log[f]^4) + (3*I*(4 - 3*x*Log[f])*PolyLog[3, (I*Sqrt[b]*f^x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[b]*Log[f]^4) - (9*I*PolyLog[4, -((I*Sqrt[b]*f^x)/Sqrt[a])])/(8*a^(5/2)*Sqrt[b]*Log[f]^4) + (9*I*PolyLog[4, (I*Sqrt[b]*f^x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[b]*Log[f]^4)} 
[1/(b/f^x+a*f^x),x,2,arctan(f^x*sqrt(a)/sqrt(b))/(log(f)*sqrt(a)*sqrt(b))],
[x/(b/f^x+a*f^x),x,6,x*arctan(f^x*sqrt(a)/sqrt(b))/(log(f)*sqrt(a)*sqrt(b))-1/2*I*polylog(2,-I*f^x*sqrt(a)/sqrt(b))/(log(f)^2*sqrt(a)*sqrt(b))+1/2*I*polylog(2,I*f^x*sqrt(a)/sqrt(b))/(log(f)^2*sqrt(a)*sqrt(b))],
[x^2/(b/f^x+a*f^x),x,9,x^2*arctan(f^x*sqrt(a)/sqrt(b))/(log(f)*sqrt(a)*sqrt(b))-I*x*polylog(2,-I*f^x*sqrt(a)/sqrt(b))/(log(f)^2*sqrt(a)*sqrt(b))+I*x*polylog(2,I*f^x*sqrt(a)/sqrt(b))/(log(f)^2*sqrt(a)*sqrt(b))+I*polylog(3,-I*f^x*sqrt(a)/sqrt(b))/(log(f)^3*sqrt(a)*sqrt(b))-I*polylog(3,I*f^x*sqrt(a)/sqrt(b))/(log(f)^3*sqrt(a)*sqrt(b))],
[x^3/(b/f^x+a*f^x),x,11,x^3*arctan(f^x*sqrt(a)/sqrt(b))/(log(f)*sqrt(a)*sqrt(b))-3/2*I*x^2*polylog(2,-I*f^x*sqrt(a)/sqrt(b))/(log(f)^2*sqrt(a)*sqrt(b))+3/2*I*x^2*polylog(2,I*f^x*sqrt(a)/sqrt(b))/(log(f)^2*sqrt(a)*sqrt(b))+3*I*x*polylog(3,-I*f^x*sqrt(a)/sqrt(b))/(log(f)^3*sqrt(a)*sqrt(b))-3*I*x*polylog(3,I*f^x*sqrt(a)/sqrt(b))/(log(f)^3*sqrt(a)*sqrt(b))-3*I*polylog(4,-I*f^x*sqrt(a)/sqrt(b))/(log(f)^4*sqrt(a)*sqrt(b))+3*I*polylog(4,I*f^x*sqrt(a)/sqrt(b))/(log(f)^4*sqrt(a)*sqrt(b))],
[1/(b/f^x+a*f^x)^2,x,2,(-1/2)/(a*(b+a*f^(2*x))*log(f))],
[x/(b/f^x+a*f^x)^2,x,6,1/2*x/(a*b*log(f))-1/2*x/(a*(b+a*f^(2*x))*log(f))-1/4*log(b+a*f^(2*x))/(a*b*log(f)^2)],
[x^2/(b/f^x+a*f^x)^2,x,6,1/2*x^2/(a*b*log(f))-1/2*x^2/(a*(b+a*f^(2*x))*log(f))-1/2*x*log(1+a*f^(2*x)/b)/(a*b*log(f)^2)-1/4*polylog(2,-a*f^(2*x)/b)/(a*b*log(f)^3)],
[x^3/(b/f^x+a*f^x)^2,x,7,1/2*x^3/(a*b*log(f))-1/2*x^3/(a*(b+a*f^(2*x))*log(f))-3/4*x^2*log(1+a*f^(2*x)/b)/(a*b*log(f)^2)-3/4*x*polylog(2,-a*f^(2*x)/b)/(a*b*log(f)^3)+3/8*polylog(3,-a*f^(2*x)/b)/(a*b*log(f)^4)],
[1/(b/f^x+a*f^x)^3,x,4,-1/4*f^x/(a*(b+a*f^(2*x))^2*log(f))+1/8*f^x/(a*b*(b+a*f^(2*x))*log(f))+1/8*arctan(f^x*sqrt(a)/sqrt(b))/(a^(3/2)*b^(3/2)*log(f))],
[x/(b/f^x+a*f^x)^3,x,22,1/8*f^x/(a*b*(b+a*f^(2*x))*log(f)^2)-1/4*f^x*x/(a*(b+a*f^(2*x))^2*log(f))+1/8*f^x*x/(a*b*(b+a*f^(2*x))*log(f))+1/8*x*arctan(f^x*sqrt(a)/sqrt(b))/(a^(3/2)*b^(3/2)*log(f))-1/16*I*polylog(2,-I*f^x*sqrt(a)/sqrt(b))/(a^(3/2)*b^(3/2)*log(f)^2)+1/16*I*polylog(2,I*f^x*sqrt(a)/sqrt(b))/(a^(3/2)*b^(3/2)*log(f)^2)],
[x^2/(b/f^x+a*f^x)^3,x,43,-1/4*arctan(f^x*sqrt(a)/sqrt(b))/(a^(3/2)*b^(3/2)*log(f)^3)+1/4*f^x*x/(a*b*(b+a*f^(2*x))*log(f)^2)-1/4*f^x*x^2/(a*(b+a*f^(2*x))^2*log(f))+1/8*f^x*x^2/(a*b*(b+a*f^(2*x))*log(f))+1/8*x^2*arctan(f^x*sqrt(a)/sqrt(b))/(a^(3/2)*b^(3/2)*log(f))-1/8*I*x*polylog(2,-I*f^x*sqrt(a)/sqrt(b))/(a^(3/2)*b^(3/2)*log(f)^2)+1/8*I*x*polylog(2,I*f^x*sqrt(a)/sqrt(b))/(a^(3/2)*b^(3/2)*log(f)^2)+1/8*I*polylog(3,-I*f^x*sqrt(a)/sqrt(b))/(a^(3/2)*b^(3/2)*log(f)^3)-1/8*I*polylog(3,I*f^x*sqrt(a)/sqrt(b))/(a^(3/2)*b^(3/2)*log(f)^3)],

#  {x^3/(a*f^x + b*f^(-x))^3, x, 49, -((3*x*ArcTan[(Sqrt[a]*f^x)/Sqrt[b]])/(4*a^(3/2)*b^(3/2)*Log[f]^3)) + (3*f^x*x^2)/(8*a*b*(b + a*f^(2*x))*Log[f]^2) - (f^x*(5 + (3*a*f^(2*x))/b)*x^3)/(8*a*(b + a*f^(2*x))^2*Log[f]) + (x^3*((4*Sqrt[a]*Sqrt[b]*f^x)/(b + a*f^(2*x)) + ArcTan[(Sqrt[a]*f^x)/Sqrt[b]]))/(8*a^(3/2)*b^(3/2)*Log[f]) + (3*I*(2 - x^2*Log[f]^2)*PolyLog[2, -((I*Sqrt[a]*f^x)/Sqrt[b])])/(16*a^(3/2)*b^(3/2)*Log[f]^4) - (3*I*(2 - x^2*Log[f]^2)*PolyLog[2, (I*Sqrt[a]*f^x)/Sqrt[b]])/(16*a^(3/2)*b^(3/2)*Log[f]^4) + (3*I*x*PolyLog[3, -((I*Sqrt[a]*f^x)/Sqrt[b])])/(8*a^(3/2)*b^(3/2)*Log[f]^3) - (3*I*x*PolyLog[3, (I*Sqrt[a]*f^x)/Sqrt[b]])/(8*a^(3/2)*b^(3/2)*Log[f]^3) - (3*I*PolyLog[4, -((I*Sqrt[a]*f^x)/Sqrt[b])])/(8*a^(3/2)*b^(3/2)*Log[f]^4) + (3*I*PolyLog[4, (I*Sqrt[a]*f^x)/Sqrt[b]])/(8*a^(3/2)*b^(3/2)*Log[f]^4)} 
[f^(a+b*x+c*x^2)*g^(d+e*x+f*x^2),x,3,1/2*f^a*g^d*erfi(1/2*(b*log(f)+e*log(g)+2*x*(c*log(f)+f*log(g)))/sqrt(c*log(f)+f*log(g)))*sqrt(Pi)/(exp(1/4*(b*log(f)+e*log(g))^2/(c*log(f)+f*log(g)))*sqrt(c*log(f)+f*log(g)))],
[F^(e*(c+d*x))*(a+b*G^(h*(f+g*x)))^n,x,2,F^(e*(c+d*x))*(a+b*G^(h*(f+g*x)))^n*hypergeom([-n,d*e*log(F)/(g*h*log(G))],[1+d*e*log(F)/(g*h*log(G))],-b*G^(h*(f+g*x))/a)/(d*e*(1+b*G^(h*(f+g*x))/a)^n*log(F))],
[F^(e*(c+d*x))*H^(t*(r+s*x))/(a+b*F^(e*(c+d*x))),x,2,H^(t*(r+s*x))*hypergeom([1,-s*t*log(H)/(d*e*log(F))],[1-s*t*log(H)/(d*e*log(F))],-a/(b*F^(e*(c+d*x))))/(b*s*t*log(H))],
[F^(e*(f+d*x))*H^(t*(r+s*x))/(a+b*F^(e*(c+d*x))),x,2,H^(t*(r+s*x))*hypergeom([1,-s*t*log(H)/(d*e*log(F))],[1-s*t*log(H)/(d*e*log(F))],-a/(b*F^(e*(c+d*x))))/(b*F^(e*(c-f))*s*t*log(H))],

# Integrands of the form x^m F^(a+b x^n)

# n>0
[f^(a+b*x^2)*x^m,x,1,-1/2*f^a*x^(1+m)*GAMMA(1/2*(1+m),-b*x^2*log(f))*(-b*x^2*log(f))^(1/2*(-1-m))],
[f^(a+b*x^2)*x^11,x,1,-1/2*f^(a+b*x^2)*(120-120*b*x^2*log(f)+60*b^2*x^4*log(f)^2-20*b^3*x^6*log(f)^3+5*b^4*x^8*log(f)^4-b^5*x^10*log(f)^5)/(b^6*log(f)^6)],
[f^(a+b*x^2)*x^9,x,1,1/2*f^(a+b*x^2)*(24-24*b*x^2*log(f)+12*b^2*x^4*log(f)^2-4*b^3*x^6*log(f)^3+b^4*x^8*log(f)^4)/(b^5*log(f)^5)],
[f^(a+b*x^2)*x^7,x,4,-3*f^(a+b*x^2)/(b^4*log(f)^4)+3*f^(a+b*x^2)*x^2/(b^3*log(f)^3)-3/2*f^(a+b*x^2)*x^4/(b^2*log(f)^2)+1/2*f^(a+b*x^2)*x^6/(b*log(f))],
[f^(a+b*x^2)*x^5,x,3,f^(a+b*x^2)/(b^3*log(f)^3)-f^(a+b*x^2)*x^2/(b^2*log(f)^2)+1/2*f^(a+b*x^2)*x^4/(b*log(f))],
[f^(a+b*x^2)*x^3,x,2,-1/2*f^(a+b*x^2)/(b^2*log(f)^2)+1/2*f^(a+b*x^2)*x^2/(b*log(f))],
[f^(a+b*x^2)*x,x,1,1/2*f^(a+b*x^2)/(b*log(f))],
[f^(a+b*x^2)/x,x,1,1/2*f^a*Ei(b*x^2*log(f))],
[f^(a+b*x^2)/x^3,x,2,-1/2*f^(a+b*x^2)/x^2+1/2*b*f^a*Ei(b*x^2*log(f))*log(f)],
[f^(a+b*x^2)/x^5,x,3,-1/4*f^(a+b*x^2)/x^4-1/4*b*f^(a+b*x^2)*log(f)/x^2+1/4*b^2*f^a*Ei(b*x^2*log(f))*log(f)^2],
[f^(a+b*x^2)/x^7,x,4,-1/6*f^(a+b*x^2)/x^6-1/12*b*f^(a+b*x^2)*log(f)/x^4-1/12*b^2*f^(a+b*x^2)*log(f)^2/x^2+1/12*b^3*f^a*Ei(b*x^2*log(f))*log(f)^3],
[f^(a+b*x^2)/x^9,x,1,-1/2*b^4*f^a*GAMMA(-4,-b*x^2*log(f))*log(f)^4],
[f^(a+b*x^2)/x^11,x,1,1/2*b^5*f^a*GAMMA(-5,-b*x^2*log(f))*log(f)^5],
[f^(a+b*x^2)*x^12,x,1,-1/2*f^a*x^13*GAMMA(13/2,-b*x^2*log(f))/(-b*x^2*log(f))^(13/2)],
[f^(a+b*x^2)*x^10,x,1,-1/2*f^a*x^11*GAMMA(11/2,-b*x^2*log(f))/(-b*x^2*log(f))^(11/2)],
[f^(a+b*x^2)*x^8,x,5,-105/16*f^(a+b*x^2)*x/(b^4*log(f)^4)+35/8*f^(a+b*x^2)*x^3/(b^3*log(f)^3)-7/4*f^(a+b*x^2)*x^5/(b^2*log(f)^2)+1/2*f^(a+b*x^2)*x^7/(b*log(f))+105/32*f^a*erfi(x*sqrt(b)*sqrt(log(f)))*sqrt(Pi)/(b^(9/2)*log(f)^(9/2))],
[f^(a+b*x^2)*x^6,x,4,15/8*f^(a+b*x^2)*x/(b^3*log(f)^3)-5/4*f^(a+b*x^2)*x^3/(b^2*log(f)^2)+1/2*f^(a+b*x^2)*x^5/(b*log(f))-15/16*f^a*erfi(x*sqrt(b)*sqrt(log(f)))*sqrt(Pi)/(b^(7/2)*log(f)^(7/2))],
[f^(a+b*x^2)*x^4,x,3,-3/4*f^(a+b*x^2)*x/(b^2*log(f)^2)+1/2*f^(a+b*x^2)*x^3/(b*log(f))+3/8*f^a*erfi(x*sqrt(b)*sqrt(log(f)))*sqrt(Pi)/(b^(5/2)*log(f)^(5/2))],
[f^(a+b*x^2)*x^2,x,2,1/2*f^(a+b*x^2)*x/(b*log(f))-1/4*f^a*erfi(x*sqrt(b)*sqrt(log(f)))*sqrt(Pi)/(b^(3/2)*log(f)^(3/2))],
[f^(a+b*x^2),x,1,1/2*f^a*erfi(x*sqrt(b)*sqrt(log(f)))*sqrt(Pi)/(sqrt(b)*sqrt(log(f)))],
[f^(a+b*x^2)/x^2,x,2,-f^(a+b*x^2)/x+f^a*erfi(x*sqrt(b)*sqrt(log(f)))*sqrt(b)*sqrt(Pi)*sqrt(log(f))],
[f^(a+b*x^2)/x^4,x,3,-1/3*f^(a+b*x^2)/x^3-2/3*b*f^(a+b*x^2)*log(f)/x+2/3*b^(3/2)*f^a*erfi(x*sqrt(b)*sqrt(log(f)))*log(f)^(3/2)*sqrt(Pi)],
[f^(a+b*x^2)/x^6,x,4,-1/5*f^(a+b*x^2)/x^5-2/15*b*f^(a+b*x^2)*log(f)/x^3-4/15*b^2*f^(a+b*x^2)*log(f)^2/x+4/15*b^(5/2)*f^a*erfi(x*sqrt(b)*sqrt(log(f)))*log(f)^(5/2)*sqrt(Pi)],
[f^(a+b*x^2)/x^8,x,5,-1/7*f^(a+b*x^2)/x^7-2/35*b*f^(a+b*x^2)*log(f)/x^5-4/105*b^2*f^(a+b*x^2)*log(f)^2/x^3-8/105*b^3*f^(a+b*x^2)*log(f)^3/x+8/105*b^(7/2)*f^a*erfi(x*sqrt(b)*sqrt(log(f)))*log(f)^(7/2)*sqrt(Pi)],
[f^(a+b*x^2)/x^10,x,1,-1/2*f^a*GAMMA(-9/2,-b*x^2*log(f))*(-b*x^2*log(f))^(9/2)/x^9],
[f^(a+b*x^2)/x^12,x,1,-1/2*f^a*GAMMA(-11/2,-b*x^2*log(f))*(-b*x^2*log(f))^(11/2)/x^11],
[f^(a+b*x^3)*x^m,x,1,-1/3*f^a*x^(1+m)*GAMMA(1/3*(1+m),-b*x^3*log(f))*(-b*x^3*log(f))^(1/3*(-1-m))],
[f^(a+b*x^3)*x^17,x,1,-1/3*f^(a+b*x^3)*(120-120*b*x^3*log(f)+60*b^2*x^6*log(f)^2-20*b^3*x^9*log(f)^3+5*b^4*x^12*log(f)^4-b^5*x^15*log(f)^5)/(b^6*log(f)^6)],
[f^(a+b*x^3)*x^14,x,1,1/3*f^(a+b*x^3)*(24-24*b*x^3*log(f)+12*b^2*x^6*log(f)^2-4*b^3*x^9*log(f)^3+b^4*x^12*log(f)^4)/(b^5*log(f)^5)],
[f^(a+b*x^3)*x^11,x,4,-2*f^(a+b*x^3)/(b^4*log(f)^4)+2*f^(a+b*x^3)*x^3/(b^3*log(f)^3)-f^(a+b*x^3)*x^6/(b^2*log(f)^2)+1/3*f^(a+b*x^3)*x^9/(b*log(f))],
[f^(a+b*x^3)*x^8,x,3,2/3*f^(a+b*x^3)/(b^3*log(f)^3)-2/3*f^(a+b*x^3)*x^3/(b^2*log(f)^2)+1/3*f^(a+b*x^3)*x^6/(b*log(f))],
[f^(a+b*x^3)*x^5,x,2,-1/3*f^(a+b*x^3)/(b^2*log(f)^2)+1/3*f^(a+b*x^3)*x^3/(b*log(f))],
[f^(a+b*x^3)*x^2,x,1,1/3*f^(a+b*x^3)/(b*log(f))],
[f^(a+b*x^3)/x,x,1,1/3*f^a*Ei(b*x^3*log(f))],
[f^(a+b*x^3)/x^4,x,2,-1/3*f^(a+b*x^3)/x^3+1/3*b*f^a*Ei(b*x^3*log(f))*log(f)],
[f^(a+b*x^3)/x^7,x,3,-1/6*f^(a+b*x^3)/x^6-1/6*b*f^(a+b*x^3)*log(f)/x^3+1/6*b^2*f^a*Ei(b*x^3*log(f))*log(f)^2],
[f^(a+b*x^3)/x^10,x,4,-1/9*f^(a+b*x^3)/x^9-1/18*b*f^(a+b*x^3)*log(f)/x^6-1/18*b^2*f^(a+b*x^3)*log(f)^2/x^3+1/18*b^3*f^a*Ei(b*x^3*log(f))*log(f)^3],
[f^(a+b*x^3)/x^13,x,1,-1/3*b^4*f^a*GAMMA(-4,-b*x^3*log(f))*log(f)^4],
[f^(a+b*x^3)/x^16,x,1,1/3*b^5*f^a*GAMMA(-5,-b*x^3*log(f))*log(f)^5],
[f^(a+b*x^3)*x^4,x,1,-1/3*f^a*x^5*GAMMA(5/3,-b*x^3*log(f))/(-b*x^3*log(f))^(5/3)],
[f^(a+b*x^3)*x^3,x,1,-1/3*f^a*x^4*GAMMA(4/3,-b*x^3*log(f))/(-b*x^3*log(f))^(4/3)],
[f^(a+b*x^3)*x,x,1,-1/3*f^a*x^2*GAMMA(2/3,-b*x^3*log(f))/(-b*x^3*log(f))^(2/3)],
[f^(a+b*x^3),x,1,-1/3*f^a*x*GAMMA(1/3,-b*x^3*log(f))/(-b*x^3*log(f))^(1/3)],
[f^(a+b*x^3)/x^2,x,1,-1/3*f^a*GAMMA(-1/3,-b*x^3*log(f))*(-b*x^3*log(f))^(1/3)/x],
[f^(a+b*x^3)/x^3,x,1,-1/3*f^a*GAMMA(-2/3,-b*x^3*log(f))*(-b*x^3*log(f))^(2/3)/x^2],
[exp(4*x^3)*x^2,x,1,1/12*exp(4*x^3)],

# n<0
[f^(a+b/x)*x^m,x,1,f^a*x^(1+m)*GAMMA(-1-m,-b*log(f)/x)*(-b*log(f)/x)^(1+m)],
[f^(a+b/x)*x^4,x,1,-b^5*f^a*GAMMA(-5,-b*log(f)/x)*log(f)^5],
[f^(a+b/x)*x^3,x,1,b^4*f^a*GAMMA(-4,-b*log(f)/x)*log(f)^4],
[f^(a+b/x)*x^2,x,4,1/3*f^(a+b/x)*x^3+1/6*b*f^(a+b/x)*x^2*log(f)+1/6*b^2*f^(a+b/x)*x*log(f)^2-1/6*b^3*f^a*Ei(b*log(f)/x)*log(f)^3],
[f^(a+b/x)*x,x,3,1/2*f^(a+b/x)*x^2+1/2*b*f^(a+b/x)*x*log(f)-1/2*b^2*f^a*Ei(b*log(f)/x)*log(f)^2],
[f^(a+b/x),x,2,f^(a+b/x)*x-b*f^a*Ei(b*log(f)/x)*log(f)],
[f^(a+b/x)/x,x,1,-f^a*Ei(b*log(f)/x)],
[f^(a+b/x)/x^2,x,1,-f^(a+b/x)/(b*log(f))],
[f^(a+b/x)/x^3,x,2,f^(a+b/x)/(b^2*log(f)^2)-f^(a+b/x)/(b*x*log(f))],
[f^(a+b/x)/x^4,x,3,-2*f^(a+b/x)/(b^3*log(f)^3)+2*f^(a+b/x)/(b^2*x*log(f)^2)-f^(a+b/x)/(b*x^2*log(f))],
[f^(a+b/x)/x^5,x,4,6*f^(a+b/x)/(b^4*log(f)^4)-6*f^(a+b/x)/(b^3*x*log(f)^3)+3*f^(a+b/x)/(b^2*x^2*log(f)^2)-f^(a+b/x)/(b*x^3*log(f))],
[f^(a+b/x)/x^6,x,1,-f^(a+b/x)*(24*x^4-24*b*x^3*log(f)+12*b^2*x^2*log(f)^2-4*b^3*x*log(f)^3+b^4*log(f)^4)/(b^5*x^4*log(f)^5)],
[f^(a+b/x)/x^7,x,1,f^(a+b/x)*(120*x^5-120*b*x^4*log(f)+60*b^2*x^3*log(f)^2-20*b^3*x^2*log(f)^3+5*b^4*x*log(f)^4-b^5*log(f)^5)/(b^6*x^5*log(f)^6)],
[f^(a+b/x^2)*x^m,x,1,1/2*f^a*x^(1+m)*GAMMA(1/2*(-1-m),-b*log(f)/x^2)*(-b*log(f)/x^2)^(1/2*(1+m))],
[f^(a+b/x^2)*x^9,x,1,-1/2*b^5*f^a*GAMMA(-5,-b*log(f)/x^2)*log(f)^5],
[f^(a+b/x^2)*x^7,x,1,1/2*b^4*f^a*GAMMA(-4,-b*log(f)/x^2)*log(f)^4],
[f^(a+b/x^2)*x^5,x,4,1/6*f^(a+b/x^2)*x^6+1/12*b*f^(a+b/x^2)*x^4*log(f)+1/12*b^2*f^(a+b/x^2)*x^2*log(f)^2-1/12*b^3*f^a*Ei(b*log(f)/x^2)*log(f)^3],
[f^(a+b/x^2)*x^3,x,3,1/4*f^(a+b/x^2)*x^4+1/4*b*f^(a+b/x^2)*x^2*log(f)-1/4*b^2*f^a*Ei(b*log(f)/x^2)*log(f)^2],
[f^(a+b/x^2)*x,x,2,1/2*f^(a+b/x^2)*x^2-1/2*b*f^a*Ei(b*log(f)/x^2)*log(f)],
[f^(a+b/x^2)/x,x,1,-1/2*f^a*Ei(b*log(f)/x^2)],
[f^(a+b/x^2)/x^3,x,1,-1/2*f^(a+b/x^2)/(b*log(f))],
[f^(a+b/x^2)/x^5,x,2,1/2*f^(a+b/x^2)/(b^2*log(f)^2)-1/2*f^(a+b/x^2)/(b*x^2*log(f))],
[f^(a+b/x^2)/x^7,x,3,-f^(a+b/x^2)/(b^3*log(f)^3)+f^(a+b/x^2)/(b^2*x^2*log(f)^2)-1/2*f^(a+b/x^2)/(b*x^4*log(f))],
[f^(a+b/x^2)/x^9,x,4,3*f^(a+b/x^2)/(b^4*log(f)^4)-3*f^(a+b/x^2)/(b^3*x^2*log(f)^3)+3/2*f^(a+b/x^2)/(b^2*x^4*log(f)^2)-1/2*f^(a+b/x^2)/(b*x^6*log(f))],
[f^(a+b/x^2)/x^11,x,1,-1/2*f^(a+b/x^2)*(24*x^8-24*b*x^6*log(f)+12*b^2*x^4*log(f)^2-4*b^3*x^2*log(f)^3+b^4*log(f)^4)/(b^5*x^8*log(f)^5)],
[f^(a+b/x^2)/x^13,x,1,1/2*f^(a+b/x^2)*(120*x^10-120*b*x^8*log(f)+60*b^2*x^6*log(f)^2-20*b^3*x^4*log(f)^3+5*b^4*x^2*log(f)^4-b^5*log(f)^5)/(b^6*x^10*log(f)^6)],
[f^(a+b/x^2)*x^10,x,1,1/2*f^a*x^11*GAMMA(-11/2,-b*log(f)/x^2)*(-b*log(f)/x^2)^(11/2)],
[f^(a+b/x^2)*x^8,x,1,1/2*f^a*x^9*GAMMA(-9/2,-b*log(f)/x^2)*(-b*log(f)/x^2)^(9/2)],
[f^(a+b/x^2)*x^6,x,6,1/7*f^(a+b/x^2)*x^7+2/35*b*f^(a+b/x^2)*x^5*log(f)+4/105*b^2*f^(a+b/x^2)*x^3*log(f)^2+8/105*b^3*f^(a+b/x^2)*x*log(f)^3-8/105*b^(7/2)*f^a*erfi(sqrt(b)*sqrt(log(f))/x)*log(f)^(7/2)*sqrt(Pi)],
[f^(a+b/x^2)*x^4,x,5,1/5*f^(a+b/x^2)*x^5+2/15*b*f^(a+b/x^2)*x^3*log(f)+4/15*b^2*f^(a+b/x^2)*x*log(f)^2-4/15*b^(5/2)*f^a*erfi(sqrt(b)*sqrt(log(f))/x)*log(f)^(5/2)*sqrt(Pi)],
[f^(a+b/x^2)*x^2,x,4,1/3*f^(a+b/x^2)*x^3+2/3*b*f^(a+b/x^2)*x*log(f)-2/3*b^(3/2)*f^a*erfi(sqrt(b)*sqrt(log(f))/x)*log(f)^(3/2)*sqrt(Pi)],
[f^(a+b/x^2),x,3,f^(a+b/x^2)*x-f^a*erfi(sqrt(b)*sqrt(log(f))/x)*sqrt(b)*sqrt(Pi)*sqrt(log(f))],
[f^(a+b/x^2)/x^2,x,2,-1/2*f^a*erfi(sqrt(b)*sqrt(log(f))/x)*sqrt(Pi)/(sqrt(b)*sqrt(log(f)))],
[f^(a+b/x^2)/x^4,x,3,-1/2*f^(a+b/x^2)/(b*x*log(f))+1/4*f^a*erfi(sqrt(b)*sqrt(log(f))/x)*sqrt(Pi)/(b^(3/2)*log(f)^(3/2))],
[f^(a+b/x^2)/x^6,x,4,3/4*f^(a+b/x^2)/(b^2*x*log(f)^2)-1/2*f^(a+b/x^2)/(b*x^3*log(f))-3/8*f^a*erfi(sqrt(b)*sqrt(log(f))/x)*sqrt(Pi)/(b^(5/2)*log(f)^(5/2))],
[f^(a+b/x^2)/x^8,x,5,-15/8*f^(a+b/x^2)/(b^3*x*log(f)^3)+5/4*f^(a+b/x^2)/(b^2*x^3*log(f)^2)-1/2*f^(a+b/x^2)/(b*x^5*log(f))+15/16*f^a*erfi(sqrt(b)*sqrt(log(f))/x)*sqrt(Pi)/(b^(7/2)*log(f)^(7/2))],
[f^(a+b/x^2)/x^10,x,6,105/16*f^(a+b/x^2)/(b^4*x*log(f)^4)-35/8*f^(a+b/x^2)/(b^3*x^3*log(f)^3)+7/4*f^(a+b/x^2)/(b^2*x^5*log(f)^2)-1/2*f^(a+b/x^2)/(b*x^7*log(f))-105/32*f^a*erfi(sqrt(b)*sqrt(log(f))/x)*sqrt(Pi)/(b^(9/2)*log(f)^(9/2))],
[f^(a+b/x^2)/x^12,x,1,1/2*f^a*GAMMA(11/2,-b*log(f)/x^2)/(x^11*(-b*log(f)/x^2)^(11/2))],
[f^(a+b/x^2)/x^14,x,1,1/2*f^a*GAMMA(13/2,-b*log(f)/x^2)/(x^13*(-b*log(f)/x^2)^(13/2))],
[f^(a+b/x^3)*x^m,x,1,1/3*f^a*x^(1+m)*GAMMA(1/3*(-1-m),-b*log(f)/x^3)*(-b*log(f)/x^3)^(1/3*(1+m))],
[f^(a+b/x^3)*x^14,x,1,-1/3*b^5*f^a*GAMMA(-5,-b*log(f)/x^3)*log(f)^5],
[f^(a+b/x^3)*x^11,x,1,1/3*b^4*f^a*GAMMA(-4,-b*log(f)/x^3)*log(f)^4],
[f^(a+b/x^3)*x^8,x,4,1/9*f^(a+b/x^3)*x^9+1/18*b*f^(a+b/x^3)*x^6*log(f)+1/18*b^2*f^(a+b/x^3)*x^3*log(f)^2-1/18*b^3*f^a*Ei(b*log(f)/x^3)*log(f)^3],
[f^(a+b/x^3)*x^5,x,3,1/6*f^(a+b/x^3)*x^6+1/6*b*f^(a+b/x^3)*x^3*log(f)-1/6*b^2*f^a*Ei(b*log(f)/x^3)*log(f)^2],
[f^(a+b/x^3)*x^2,x,2,1/3*f^(a+b/x^3)*x^3-1/3*b*f^a*Ei(b*log(f)/x^3)*log(f)],
[f^(a+b/x^3)/x,x,1,-1/3*f^a*Ei(b*log(f)/x^3)],
[f^(a+b/x^3)/x^4,x,1,-1/3*f^(a+b/x^3)/(b*log(f))],
[f^(a+b/x^3)/x^7,x,2,1/3*f^(a+b/x^3)/(b^2*log(f)^2)-1/3*f^(a+b/x^3)/(b*x^3*log(f))],
[f^(a+b/x^3)/x^10,x,3,-2/3*f^(a+b/x^3)/(b^3*log(f)^3)+2/3*f^(a+b/x^3)/(b^2*x^3*log(f)^2)-1/3*f^(a+b/x^3)/(b*x^6*log(f))],
[f^(a+b/x^3)/x^13,x,4,2*f^(a+b/x^3)/(b^4*log(f)^4)-2*f^(a+b/x^3)/(b^3*x^3*log(f)^3)+f^(a+b/x^3)/(b^2*x^6*log(f)^2)-1/3*f^(a+b/x^3)/(b*x^9*log(f))],
[f^(a+b/x^3)/x^16,x,1,-1/3*f^(a+b/x^3)*(24*x^12-24*b*x^9*log(f)+12*b^2*x^6*log(f)^2-4*b^3*x^3*log(f)^3+b^4*log(f)^4)/(b^5*x^12*log(f)^5)],
[f^(a+b/x^3)/x^19,x,1,1/3*f^(a+b/x^3)*(120*x^15-120*b*x^12*log(f)+60*b^2*x^9*log(f)^2-20*b^3*x^6*log(f)^3+5*b^4*x^3*log(f)^4-b^5*log(f)^5)/(b^6*x^15*log(f)^6)],
[f^(a+b/x^3)*x^4,x,1,1/3*f^a*x^5*GAMMA(-5/3,-b*log(f)/x^3)*(-b*log(f)/x^3)^(5/3)],
[f^(a+b/x^3)*x^3,x,1,1/3*f^a*x^4*GAMMA(-4/3,-b*log(f)/x^3)*(-b*log(f)/x^3)^(4/3)],
[f^(a+b/x^3)*x,x,1,1/3*f^a*x^2*GAMMA(-2/3,-b*log(f)/x^3)*(-b*log(f)/x^3)^(2/3)],
[f^(a+b/x^3),x,1,1/3*f^a*x*GAMMA(-1/3,-b*log(f)/x^3)*(-b*log(f)/x^3)^(1/3)],
[f^(a+b/x^3)/x^2,x,1,1/3*f^a*GAMMA(1/3,-b*log(f)/x^3)/(x*(-b*log(f)/x^3)^(1/3))],
[f^(a+b/x^3)/x^3,x,1,1/3*f^a*GAMMA(2/3,-b*log(f)/x^3)/(x^2*(-b*log(f)/x^3)^(2/3))],
[f^(a+b/x^3)/x^5,x,1,1/3*f^a*GAMMA(4/3,-b*log(f)/x^3)/(x^4*(-b*log(f)/x^3)^(4/3))],

# n symbolic
[f^(a+b*x^n)*x^m,x,1,-f^a*x^(1+m)*GAMMA((1+m)/n,-b*x^n*log(f))/(n*(-b*x^n*log(f))^((1+m)/n))],
[f^(a+b*x^n)*x^3,x,1,-f^a*x^4*GAMMA(4/n,-b*x^n*log(f))/(n*(-b*x^n*log(f))^(4/n))],
[f^(a+b*x^n)*x^2,x,1,-f^a*x^3*GAMMA(3/n,-b*x^n*log(f))/(n*(-b*x^n*log(f))^(3/n))],
[f^(a+b*x^n)*x,x,1,-f^a*x^2*GAMMA(2/n,-b*x^n*log(f))/(n*(-b*x^n*log(f))^(2/n))],
[f^(a+b*x^n),x,1,-f^a*x*GAMMA(1/n,-b*x^n*log(f))/(n*(-b*x^n*log(f))^(1/n))],
[f^(a+b*x^n)/x,x,1,f^a*Ei(b*x^n*log(f))/n],
[f^(a+b*x^n)/x^2,x,1,-f^a*GAMMA((-1)/n,-b*x^n*log(f))*(-b*x^n*log(f))^(1/n)/(n*x)],
[f^(a+b*x^n)/x^3,x,1,-f^a*GAMMA((-2)/n,-b*x^n*log(f))*(-b*x^n*log(f))^(2/n)/(n*x^2)],
[f^(a+b*x^n)/x^4,x,1,-f^a*GAMMA((-3)/n,-b*x^n*log(f))*(-b*x^n*log(f))^(3/n)/(n*x^3)],
[f^(a+b*x^n)*x^(-1+3*n),x,3,2*f^(a+b*x^n)/(b^3*n*log(f)^3)-2*f^(a+b*x^n)*x^n/(b^2*n*log(f)^2)+f^(a+b*x^n)*x^(2*n)/(b*n*log(f))],
[f^(a+b*x^n)*x^(-1+2*n),x,2,-f^(a+b*x^n)/(b^2*n*log(f)^2)+f^(a+b*x^n)*x^n/(b*n*log(f))],
[f^(a+b*x^n)*x^(-1+n),x,1,f^(a+b*x^n)/(b*n*log(f))],
[f^(a+b*x^n)/x,x,1,f^a*Ei(b*x^n*log(f))/n],
[f^(a+b*x^n)*x^(-1-n),x,2,-f^(a+b*x^n)/(n*x^n)+b*f^a*Ei(b*x^n*log(f))*log(f)/n],
[f^(a+b*x^n)*x^(-1-2*n),x,3,-1/2*f^(a+b*x^n)/(n*x^(2*n))-1/2*b*f^(a+b*x^n)*log(f)/(n*x^n)+1/2*b^2*f^a*Ei(b*x^n*log(f))*log(f)^2/n],
[f^(a+b*x^n)*x^(-1+5/2*n),x,4,-3/2*f^(a+b*x^n)*x^(1/2*n)/(b^2*n*log(f)^2)+f^(a+b*x^n)*x^(3/2*n)/(b*n*log(f))+3/4*f^a*erfi(x^(1/2*n)*sqrt(b)*sqrt(log(f)))*sqrt(Pi)/(b^(5/2)*n*log(f)^(5/2))],
[f^(a+b*x^n)*x^(-1+3/2*n),x,3,f^(a+b*x^n)*x^(1/2*n)/(b*n*log(f))-1/2*f^a*erfi(x^(1/2*n)*sqrt(b)*sqrt(log(f)))*sqrt(Pi)/(b^(3/2)*n*log(f)^(3/2))],
[f^(a+b*x^n)*x^(-1+1/2*n),x,2,f^a*erfi(x^(1/2*n)*sqrt(b)*sqrt(log(f)))*sqrt(Pi)/(n*sqrt(b)*sqrt(log(f)))],
[f^(a+b*x^n)*x^(-1-1/2*n),x,3,-2*f^(a+b*x^n)/(n*x^(1/2*n))+2*f^a*erfi(x^(1/2*n)*sqrt(b)*sqrt(log(f)))*sqrt(b)*sqrt(Pi)*sqrt(log(f))/n],
[f^(a+b*x^n)*x^(-1-3/2*n),x,4,-2/3*f^(a+b*x^n)/(n*x^(3/2*n))-4/3*b*f^(a+b*x^n)*log(f)/(n*x^(1/2*n))+4/3*b^(3/2)*f^a*erfi(x^(1/2*n)*sqrt(b)*sqrt(log(f)))*log(f)^(3/2)*sqrt(Pi)/n],
[exp((-0.1)*x)*x,x,2,(-100.)*exp((-0.1)*x)+(-10.)*exp((-0.1)*x)*x],

# Integrands of the form x^m F^(c (a+b x)^n)

# Integrands of the form x^m F^(c (a+b x)^n)

# n>0
[f^(c*(a+b*x)^2)*x^3,x,8,-1/2*f^(c*(a+b*x)^2)/(b^4*c^2*log(f)^2)+3/2*a^2*f^(c*(a+b*x)^2)/(b^4*c*log(f))-3/2*a*f^(c*(a+b*x)^2)*(a+b*x)/(b^4*c*log(f))+1/2*f^(c*(a+b*x)^2)*(a+b*x)^2/(b^4*c*log(f))+3/4*a*erfi((a+b*x)*sqrt(c)*sqrt(log(f)))*sqrt(Pi)/(b^4*c^(3/2)*log(f)^(3/2))-1/2*a^3*erfi((a+b*x)*sqrt(c)*sqrt(log(f)))*sqrt(Pi)/(b^4*sqrt(c)*sqrt(log(f)))],
[f^(c*(a+b*x)^2)*x^2,x,6,-a*f^(c*(a+b*x)^2)/(b^3*c*log(f))+1/2*f^(c*(a+b*x)^2)*(a+b*x)/(b^3*c*log(f))-1/4*erfi((a+b*x)*sqrt(c)*sqrt(log(f)))*sqrt(Pi)/(b^3*c^(3/2)*log(f)^(3/2))+1/2*a^2*erfi((a+b*x)*sqrt(c)*sqrt(log(f)))*sqrt(Pi)/(b^3*sqrt(c)*sqrt(log(f)))],
[f^(c*(a+b*x)^2)*x,x,4,1/2*f^(c*(a+b*x)^2)/(b^2*c*log(f))-1/2*a*erfi((a+b*x)*sqrt(c)*sqrt(log(f)))*sqrt(Pi)/(b^2*sqrt(c)*sqrt(log(f)))],
[f^(c*(a+b*x)^2),x,1,1/2*erfi((a+b*x)*sqrt(c)*sqrt(log(f)))*sqrt(Pi)/(b*sqrt(c)*sqrt(log(f)))],
[f^(c*(a+b*x)^2)/x,x,0,Unintegrable(f^(c*(a+b*x)^2)/x,x)],
[f^(c*(a+b*x)^2)/x^2,x,2,-f^(c*(a+b*x)^2)/x+b*erfi((a+b*x)*sqrt(c)*sqrt(log(f)))*sqrt(c)*sqrt(Pi)*sqrt(log(f))+2*a*b*c*log(f)*Unintegrable(f^(c*(a+b*x)^2)/x,x)],
[f^(c*(a+b*x)^2)/x^3,x,3,-1/2*f^(c*(a+b*x)^2)/x^2-a*b*c*f^(c*(a+b*x)^2)*log(f)/x+a*b^2*c^(3/2)*erfi((a+b*x)*sqrt(c)*sqrt(log(f)))*log(f)^(3/2)*sqrt(Pi)+b^2*c*log(f)*Unintegrable(f^(c*(a+b*x)^2)/x,x)+2*a^2*b^2*c^2*log(f)^2*Unintegrable(f^(c*(a+b*x)^2)/x,x)],
[f^(c*(a+b*x)^3)*x^2,x,5,1/3*f^(c*(a+b*x)^3)/(b^3*c*log(f))+2/3*a*(a+b*x)^2*GAMMA(2/3,-c*(a+b*x)^3*log(f))/(b^3*(-c*(a+b*x)^3*log(f))^(2/3))-1/3*a^2*(a+b*x)*GAMMA(1/3,-c*(a+b*x)^3*log(f))/(b^3*(-c*(a+b*x)^3*log(f))^(1/3))],
[f^(c*(a+b*x)^3)*x,x,4,-1/3*(a+b*x)^2*GAMMA(2/3,-c*(a+b*x)^3*log(f))/(b^2*(-c*(a+b*x)^3*log(f))^(2/3))+1/3*a*(a+b*x)*GAMMA(1/3,-c*(a+b*x)^3*log(f))/(b^2*(-c*(a+b*x)^3*log(f))^(1/3))],
[f^(c*(a+b*x)^3),x,1,-1/3*(a+b*x)*GAMMA(1/3,-c*(a+b*x)^3*log(f))/(b*(-c*(a+b*x)^3*log(f))^(1/3))],
[f^(c*(a+b*x)^3)/x,x,0,Unintegrable(f^(c*(a+b*x)^3)/x,x)],
[f^(c*(a+b*x)^3)/x^2,x,5,-f^(c*(a+b*x)^3)/x-b*c*(a+b*x)^2*GAMMA(2/3,-c*(a+b*x)^3*log(f))*log(f)/(-c*(a+b*x)^3*log(f))^(2/3)-a*b*c*(a+b*x)*GAMMA(1/3,-c*(a+b*x)^3*log(f))*log(f)/(-c*(a+b*x)^3*log(f))^(1/3)+3*a^2*b*c*log(f)*Unintegrable(f^(c*(a+b*x)^3)/x,x)],
[f^(c*(a+b*x)^3)/x^3,x,9,-1/2*f^(c*(a+b*x)^3)/x^2-3/2*a^2*b*c*f^(c*(a+b*x)^3)*log(f)/x-3/2*a^2*b^2*c^2*(a+b*x)^2*GAMMA(2/3,-c*(a+b*x)^3*log(f))*log(f)^2/(-c*(a+b*x)^3*log(f))^(2/3)-1/2*b^2*c*(a+b*x)*GAMMA(1/3,-c*(a+b*x)^3*log(f))*log(f)/(-c*(a+b*x)^3*log(f))^(1/3)-3/2*a^3*b^2*c^2*(a+b*x)*GAMMA(1/3,-c*(a+b*x)^3*log(f))*log(f)^2/(-c*(a+b*x)^3*log(f))^(1/3)+3*a*b^2*c*log(f)*Unintegrable(f^(c*(a+b*x)^3)/x,x)+9/2*a^4*b^2*c^2*log(f)^2*Unintegrable(f^(c*(a+b*x)^3)/x,x)],
[exp(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^4,x,8,2*a^2*exp((a+b*x)^3)/b^5-1/3*a^4*(a+b*x)*GAMMA(1/3,-(a+b*x)^3)/(b^5*(-(a+b*x)^3)^(1/3))+4/3*a^3*(a+b*x)^2*GAMMA(2/3,-(a+b*x)^3)/(b^5*(-(a+b*x)^3)^(2/3))+4/3*a*(a+b*x)^4*GAMMA(4/3,-(a+b*x)^3)/(b^5*(-(a+b*x)^3)^(4/3))-1/3*(a+b*x)^5*GAMMA(5/3,-(a+b*x)^3)/(b^5*(-(a+b*x)^3)^(5/3))],
[exp(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^3,x,7,-a*exp((a+b*x)^3)/b^4+1/3*a^3*(a+b*x)*GAMMA(1/3,-(a+b*x)^3)/(b^4*(-(a+b*x)^3)^(1/3))-a^2*(a+b*x)^2*GAMMA(2/3,-(a+b*x)^3)/(b^4*(-(a+b*x)^3)^(2/3))-1/3*(a+b*x)^4*GAMMA(4/3,-(a+b*x)^3)/(b^4*(-(a+b*x)^3)^(4/3))],
[exp(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^2,x,6,1/3*exp((a+b*x)^3)/b^3-1/3*a^2*(a+b*x)*GAMMA(1/3,-(a+b*x)^3)/(b^3*(-(a+b*x)^3)^(1/3))+2/3*a*(a+b*x)^2*GAMMA(2/3,-(a+b*x)^3)/(b^3*(-(a+b*x)^3)^(2/3))],
[exp(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x,x,5,1/3*a*(a+b*x)*GAMMA(1/3,-(a+b*x)^3)/(b^2*(-(a+b*x)^3)^(1/3))-1/3*(a+b*x)^2*GAMMA(2/3,-(a+b*x)^3)/(b^2*(-(a+b*x)^3)^(2/3))],
[exp(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3),x,2,-1/3*(a+b*x)*GAMMA(1/3,-(a+b*x)^3)/(b*(-(a+b*x)^3)^(1/3))],
[exp(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)/x,x,0,CannotIntegrate(exp(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)/x,x)],
[exp(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^m,x,0,CannotIntegrate(exp(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^m,x)],
[exp(sqrt(5+3*x)),x,3,-2/3*exp(sqrt(5+3*x))+2/3*exp(sqrt(5+3*x))*sqrt(5+3*x)],

# n<0
[f^(c/(a+b*x))*x^4,x,13,a^4*f^(c/(a+b*x))*(a+b*x)/b^5-2*a^3*f^(c/(a+b*x))*(a+b*x)^2/b^5+2*a^2*f^(c/(a+b*x))*(a+b*x)^3/b^5-2*a^3*c*f^(c/(a+b*x))*(a+b*x)*log(f)/b^5+a^2*c*f^(c/(a+b*x))*(a+b*x)^2*log(f)/b^5-a^4*c*Ei(c*log(f)/(a+b*x))*log(f)/b^5+a^2*c^2*f^(c/(a+b*x))*(a+b*x)*log(f)^2/b^5+2*a^3*c^2*Ei(c*log(f)/(a+b*x))*log(f)^2/b^5-a^2*c^3*Ei(c*log(f)/(a+b*x))*log(f)^3/b^5-4*a*c^4*GAMMA(-4,-c*log(f)/(a+b*x))*log(f)^4/b^5-c^5*GAMMA(-5,-c*log(f)/(a+b*x))*log(f)^5/b^5],
[f^(c/(a+b*x))*x^3,x,12,-a^3*f^(c/(a+b*x))*(a+b*x)/b^4+3/2*a^2*f^(c/(a+b*x))*(a+b*x)^2/b^4-a*f^(c/(a+b*x))*(a+b*x)^3/b^4+3/2*a^2*c*f^(c/(a+b*x))*(a+b*x)*log(f)/b^4-1/2*a*c*f^(c/(a+b*x))*(a+b*x)^2*log(f)/b^4+a^3*c*Ei(c*log(f)/(a+b*x))*log(f)/b^4-1/2*a*c^2*f^(c/(a+b*x))*(a+b*x)*log(f)^2/b^4-3/2*a^2*c^2*Ei(c*log(f)/(a+b*x))*log(f)^2/b^4+1/2*a*c^3*Ei(c*log(f)/(a+b*x))*log(f)^3/b^4+c^4*GAMMA(-4,-c*log(f)/(a+b*x))*log(f)^4/b^4],
[f^(c/(a+b*x))*x^2,x,11,a^2*f^(c/(a+b*x))*(a+b*x)/b^3-a*f^(c/(a+b*x))*(a+b*x)^2/b^3+1/3*f^(c/(a+b*x))*(a+b*x)^3/b^3-a*c*f^(c/(a+b*x))*(a+b*x)*log(f)/b^3+1/6*c*f^(c/(a+b*x))*(a+b*x)^2*log(f)/b^3-a^2*c*Ei(c*log(f)/(a+b*x))*log(f)/b^3+1/6*c^2*f^(c/(a+b*x))*(a+b*x)*log(f)^2/b^3+a*c^2*Ei(c*log(f)/(a+b*x))*log(f)^2/b^3-1/6*c^3*Ei(c*log(f)/(a+b*x))*log(f)^3/b^3],
[f^(c/(a+b*x))*x,x,7,-a*f^(c/(a+b*x))*(a+b*x)/b^2+1/2*f^(c/(a+b*x))*(a+b*x)^2/b^2+1/2*c*f^(c/(a+b*x))*(a+b*x)*log(f)/b^2+a*c*Ei(c*log(f)/(a+b*x))*log(f)/b^2-1/2*c^2*Ei(c*log(f)/(a+b*x))*log(f)^2/b^2],
[f^(c/(a+b*x)),x,2,f^(c/(a+b*x))*(a+b*x)/b-c*Ei(c*log(f)/(a+b*x))*log(f)/b],
[f^(c/(a+b*x))/x,x,4,-Ei(c*log(f)/(a+b*x))+f^(c/a)*Ei(-b*c*x*log(f)/(a*(a+b*x)))],
[f^(c/(a+b*x))/x^2,x,9,-b*f^(c/(a+b*x))/a-f^(c/(a+b*x))/x-b*c*f^(c/a)*Ei(-b*c*x*log(f)/(a*(a+b*x)))*log(f)/a^2],
[f^(c/(a+b*x))/x^3,x,18,1/2*b^2*f^(c/(a+b*x))/a^2-1/2*f^(c/(a+b*x))/x^2+1/2*b^2*c*f^(c/(a+b*x))*log(f)/a^3+1/2*b*c*f^(c/(a+b*x))*log(f)/(a^2*x)+b^2*c*f^(c/a)*Ei(-b*c*x*log(f)/(a*(a+b*x)))*log(f)/a^3+1/2*b^2*c^2*f^(c/a)*Ei(-b*c*x*log(f)/(a*(a+b*x)))*log(f)^2/a^4],
[f^(c/(a+b*x)^2)*x^4,x,19,a^4*f^(c/(a+b*x)^2)*(a+b*x)/b^5-2*a^3*f^(c/(a+b*x)^2)*(a+b*x)^2/b^5+2*a^2*f^(c/(a+b*x)^2)*(a+b*x)^3/b^5-a*f^(c/(a+b*x)^2)*(a+b*x)^4/b^5+1/5*f^(c/(a+b*x)^2)*(a+b*x)^5/b^5+4*a^2*c*f^(c/(a+b*x)^2)*(a+b*x)*log(f)/b^5-a*c*f^(c/(a+b*x)^2)*(a+b*x)^2*log(f)/b^5+2/15*c*f^(c/(a+b*x)^2)*(a+b*x)^3*log(f)/b^5+2*a^3*c*Ei(c*log(f)/(a+b*x)^2)*log(f)/b^5+4/15*c^2*f^(c/(a+b*x)^2)*(a+b*x)*log(f)^2/b^5+a*c^2*Ei(c*log(f)/(a+b*x)^2)*log(f)^2/b^5-4*a^2*c^(3/2)*erfi(sqrt(c)*sqrt(log(f))/(a+b*x))*log(f)^(3/2)*sqrt(Pi)/b^5-4/15*c^(5/2)*erfi(sqrt(c)*sqrt(log(f))/(a+b*x))*log(f)^(5/2)*sqrt(Pi)/b^5-a^4*erfi(sqrt(c)*sqrt(log(f))/(a+b*x))*sqrt(c)*sqrt(Pi)*sqrt(log(f))/b^5],
[f^(c/(a+b*x)^2)*x^3,x,14,-a^3*f^(c/(a+b*x)^2)*(a+b*x)/b^4+3/2*a^2*f^(c/(a+b*x)^2)*(a+b*x)^2/b^4-a*f^(c/(a+b*x)^2)*(a+b*x)^3/b^4+1/4*f^(c/(a+b*x)^2)*(a+b*x)^4/b^4-2*a*c*f^(c/(a+b*x)^2)*(a+b*x)*log(f)/b^4+1/4*c*f^(c/(a+b*x)^2)*(a+b*x)^2*log(f)/b^4-3/2*a^2*c*Ei(c*log(f)/(a+b*x)^2)*log(f)/b^4-1/4*c^2*Ei(c*log(f)/(a+b*x)^2)*log(f)^2/b^4+2*a*c^(3/2)*erfi(sqrt(c)*sqrt(log(f))/(a+b*x))*log(f)^(3/2)*sqrt(Pi)/b^4+a^3*erfi(sqrt(c)*sqrt(log(f))/(a+b*x))*sqrt(c)*sqrt(Pi)*sqrt(log(f))/b^4],
[f^(c/(a+b*x)^2)*x^2,x,11,a^2*f^(c/(a+b*x)^2)*(a+b*x)/b^3-a*f^(c/(a+b*x)^2)*(a+b*x)^2/b^3+1/3*f^(c/(a+b*x)^2)*(a+b*x)^3/b^3+2/3*c*f^(c/(a+b*x)^2)*(a+b*x)*log(f)/b^3+a*c*Ei(c*log(f)/(a+b*x)^2)*log(f)/b^3-2/3*c^(3/2)*erfi(sqrt(c)*sqrt(log(f))/(a+b*x))*log(f)^(3/2)*sqrt(Pi)/b^3-a^2*erfi(sqrt(c)*sqrt(log(f))/(a+b*x))*sqrt(c)*sqrt(Pi)*sqrt(log(f))/b^3],
[f^(c/(a+b*x)^2)*x,x,7,-a*f^(c/(a+b*x)^2)*(a+b*x)/b^2+1/2*f^(c/(a+b*x)^2)*(a+b*x)^2/b^2-1/2*c*Ei(c*log(f)/(a+b*x)^2)*log(f)/b^2+a*erfi(sqrt(c)*sqrt(log(f))/(a+b*x))*sqrt(c)*sqrt(Pi)*sqrt(log(f))/b^2],
[f^(c/(a+b*x)^2),x,3,f^(c/(a+b*x)^2)*(a+b*x)/b-erfi(sqrt(c)*sqrt(log(f))/(a+b*x))*sqrt(c)*sqrt(Pi)*sqrt(log(f))/b],
[f^(c/(a+b*x)^2)/x,x,0,Unintegrable(f^(c/(a+b*x)^2)/x,x)],
[f^(c/(a+b*x)^2)/x^2,x,0,CannotIntegrate(f^(c/(a+b*x)^2)/x^2,x)],
[f^(c/(a+b*x)^2)/x^3,x,0,CannotIntegrate(f^(c/(a+b*x)^2)/x^3,x)],
[f^(c/(a+b*x)^3)*x^4,x,8,2*a^2*f^(c/(a+b*x)^3)*(a+b*x)^3/b^5-2*a^2*c*Ei(c*log(f)/(a+b*x)^3)*log(f)/b^5+1/3*a^4*(a+b*x)*GAMMA(-1/3,-c*log(f)/(a+b*x)^3)*(-c*log(f)/(a+b*x)^3)^(1/3)/b^5-4/3*a^3*(a+b*x)^2*GAMMA(-2/3,-c*log(f)/(a+b*x)^3)*(-c*log(f)/(a+b*x)^3)^(2/3)/b^5-4/3*a*(a+b*x)^4*GAMMA(-4/3,-c*log(f)/(a+b*x)^3)*(-c*log(f)/(a+b*x)^3)^(4/3)/b^5+1/3*(a+b*x)^5*GAMMA(-5/3,-c*log(f)/(a+b*x)^3)*(-c*log(f)/(a+b*x)^3)^(5/3)/b^5],
[f^(c/(a+b*x)^3)*x^3,x,7,-a*f^(c/(a+b*x)^3)*(a+b*x)^3/b^4+a*c*Ei(c*log(f)/(a+b*x)^3)*log(f)/b^4-1/3*a^3*(a+b*x)*GAMMA(-1/3,-c*log(f)/(a+b*x)^3)*(-c*log(f)/(a+b*x)^3)^(1/3)/b^4+a^2*(a+b*x)^2*GAMMA(-2/3,-c*log(f)/(a+b*x)^3)*(-c*log(f)/(a+b*x)^3)^(2/3)/b^4+1/3*(a+b*x)^4*GAMMA(-4/3,-c*log(f)/(a+b*x)^3)*(-c*log(f)/(a+b*x)^3)^(4/3)/b^4],
[f^(c/(a+b*x)^3)*x^2,x,6,1/3*f^(c/(a+b*x)^3)*(a+b*x)^3/b^3-1/3*c*Ei(c*log(f)/(a+b*x)^3)*log(f)/b^3+1/3*a^2*(a+b*x)*GAMMA(-1/3,-c*log(f)/(a+b*x)^3)*(-c*log(f)/(a+b*x)^3)^(1/3)/b^3-2/3*a*(a+b*x)^2*GAMMA(-2/3,-c*log(f)/(a+b*x)^3)*(-c*log(f)/(a+b*x)^3)^(2/3)/b^3],
[f^(c/(a+b*x)^3)*x,x,4,-1/3*a*(a+b*x)*GAMMA(-1/3,-c*log(f)/(a+b*x)^3)*(-c*log(f)/(a+b*x)^3)^(1/3)/b^2+1/3*(a+b*x)^2*GAMMA(-2/3,-c*log(f)/(a+b*x)^3)*(-c*log(f)/(a+b*x)^3)^(2/3)/b^2],
[f^(c/(a+b*x)^3),x,1,1/3*(a+b*x)*GAMMA(-1/3,-c*log(f)/(a+b*x)^3)*(-c*log(f)/(a+b*x)^3)^(1/3)/b],
[f^(c/(a+b*x)^3)/x,x,0,Unintegrable(f^(c/(a+b*x)^3)/x,x)],
[f^(c/(a+b*x)^3)/x^2,x,0,CannotIntegrate(f^(c/(a+b*x)^3)/x^2,x)],
[f^(c/(a+b*x)^3)/x^3,x,0,CannotIntegrate(f^(c/(a+b*x)^3)/x^3,x)],

# Integrands of the form x^m F^(c (a+b x)^n) with m symbolic
[f^(c*(a+b*x)^3)*x^m,x,0,CannotIntegrate(f^(c*(a+b*x)^3)*x^m,x)],
[f^(c*(a+b*x)^2)*x^m,x,1,Unintegrable(f^(a^2*c+2*a*b*c*x+b^2*c*x^2)*x^m,x)],
[f^(c*(a+b*x))*x^m,x,1,f^(a*c)*x^m*GAMMA(1+m,-b*c*x*log(f))/(b*c*log(f)*(-b*c*x*log(f))^m)],
[f^(c/(a+b*x))*x^m,x,0,CannotIntegrate(f^(c/(a+b*x))*x^m,x)],
[f^(c/(a+b*x)^2)*x^m,x,0,CannotIntegrate(f^(c/(a+b*x)^2)*x^m,x)],
[f^(c/(a+b*x)^3)*x^m,x,0,CannotIntegrate(f^(c/(a+b*x)^3)*x^m,x)],

# Integrands of the form x^m F^(c (a+b x)^n) with n symbolic
[f^(c*(a+b*x)^n)*x^m,x,0,CannotIntegrate(f^(c*(a+b*x)^n)*x^m,x)],
[f^(c*(a+b*x)^n)*x^3,x,6,-(a+b*x)^4*GAMMA(4/n,-c*(a+b*x)^n*log(f))/(b^4*n*(-c*(a+b*x)^n*log(f))^(4/n))+3*a*(a+b*x)^3*GAMMA(3/n,-c*(a+b*x)^n*log(f))/(b^4*n*(-c*(a+b*x)^n*log(f))^(3/n))-3*a^2*(a+b*x)^2*GAMMA(2/n,-c*(a+b*x)^n*log(f))/(b^4*n*(-c*(a+b*x)^n*log(f))^(2/n))+a^3*(a+b*x)*GAMMA(1/n,-c*(a+b*x)^n*log(f))/(b^4*n*(-c*(a+b*x)^n*log(f))^(1/n))],
[f^(c*(a+b*x)^n)*x^2,x,5,-(a+b*x)^3*GAMMA(3/n,-c*(a+b*x)^n*log(f))/(b^3*n*(-c*(a+b*x)^n*log(f))^(3/n))+2*a*(a+b*x)^2*GAMMA(2/n,-c*(a+b*x)^n*log(f))/(b^3*n*(-c*(a+b*x)^n*log(f))^(2/n))-a^2*(a+b*x)*GAMMA(1/n,-c*(a+b*x)^n*log(f))/(b^3*n*(-c*(a+b*x)^n*log(f))^(1/n))],
[f^(c*(a+b*x)^n)*x,x,4,-(a+b*x)^2*GAMMA(2/n,-c*(a+b*x)^n*log(f))/(b^2*n*(-c*(a+b*x)^n*log(f))^(2/n))+a*(a+b*x)*GAMMA(1/n,-c*(a+b*x)^n*log(f))/(b^2*n*(-c*(a+b*x)^n*log(f))^(1/n))],
[f^(c*(a+b*x)^n),x,1,-(a+b*x)*GAMMA(1/n,-c*(a+b*x)^n*log(f))/(b*n*(-c*(a+b*x)^n*log(f))^(1/n))],
[f^(c*(a+b*x)^n)/x,x,0,Unintegrable(f^(c*(a+b*x)^n)/x,x)],
[f^(c*(a+b*x)^n)/x^2,x,0,CannotIntegrate(f^(c*(a+b*x)^n)/x^2,x)],
[f^(c*(a+b*x)^n)/x^3,x,0,CannotIntegrate(f^(c*(a+b*x)^n)/x^3,x)],

# Integrands of the form (c+d x)^m F^(a+b (c+d x)^n)

# n>0
[F^(a+b*(c+d*x)^2)*(c+d*x)^m,x,1,-1/2*F^a*(c+d*x)^(1+m)*GAMMA(1/2*(1+m),-b*(c+d*x)^2*log(F))*(-b*(c+d*x)^2*log(F))^(1/2*(-1-m))/d],
[F^(a+b*(c+d*x)^2)*(c+d*x)^11,x,1,-1/2*F^(a+b*(c+d*x)^2)*(120-120*b*(c+d*x)^2*log(F)+60*b^2*(c+d*x)^4*log(F)^2-20*b^3*(c+d*x)^6*log(F)^3+5*b^4*(c+d*x)^8*log(F)^4-b^5*(c+d*x)^10*log(F)^5)/(b^6*d*log(F)^6)],
[F^(a+b*(c+d*x)^2)*(c+d*x)^9,x,1,1/2*F^(a+b*(c+d*x)^2)*(24-24*b*(c+d*x)^2*log(F)+12*b^2*(c+d*x)^4*log(F)^2-4*b^3*(c+d*x)^6*log(F)^3+b^4*(c+d*x)^8*log(F)^4)/(b^5*d*log(F)^5)],
[F^(a+b*(c+d*x)^2)*(c+d*x)^7,x,4,-3*F^(a+b*(c+d*x)^2)/(b^4*d*log(F)^4)+3*F^(a+b*(c+d*x)^2)*(c+d*x)^2/(b^3*d*log(F)^3)-3/2*F^(a+b*(c+d*x)^2)*(c+d*x)^4/(b^2*d*log(F)^2)+1/2*F^(a+b*(c+d*x)^2)*(c+d*x)^6/(b*d*log(F))],
[F^(a+b*(c+d*x)^2)*(c+d*x)^5,x,3,F^(a+b*(c+d*x)^2)/(b^3*d*log(F)^3)-F^(a+b*(c+d*x)^2)*(c+d*x)^2/(b^2*d*log(F)^2)+1/2*F^(a+b*(c+d*x)^2)*(c+d*x)^4/(b*d*log(F))],
[F^(a+b*(c+d*x)^2)*(c+d*x)^3,x,2,-1/2*F^(a+b*(c+d*x)^2)/(b^2*d*log(F)^2)+1/2*F^(a+b*(c+d*x)^2)*(c+d*x)^2/(b*d*log(F))],
[F^(a+b*(c+d*x)^2)*(c+d*x),x,1,1/2*F^(a+b*(c+d*x)^2)/(b*d*log(F))],
[F^(a+b*(c+d*x)^2)/(c+d*x),x,1,1/2*F^a*Ei(b*(c+d*x)^2*log(F))/d],
[F^(a+b*(c+d*x)^2)/(c+d*x)^3,x,2,-1/2*F^(a+b*(c+d*x)^2)/(d*(c+d*x)^2)+1/2*b*F^a*Ei(b*(c+d*x)^2*log(F))*log(F)/d],
[F^(a+b*(c+d*x)^2)/(c+d*x)^5,x,3,-1/4*F^(a+b*(c+d*x)^2)/(d*(c+d*x)^4)-1/4*b*F^(a+b*(c+d*x)^2)*log(F)/(d*(c+d*x)^2)+1/4*b^2*F^a*Ei(b*(c+d*x)^2*log(F))*log(F)^2/d],
[F^(a+b*(c+d*x)^2)/(c+d*x)^7,x,4,-1/6*F^(a+b*(c+d*x)^2)/(d*(c+d*x)^6)-1/12*b*F^(a+b*(c+d*x)^2)*log(F)/(d*(c+d*x)^4)-1/12*b^2*F^(a+b*(c+d*x)^2)*log(F)^2/(d*(c+d*x)^2)+1/12*b^3*F^a*Ei(b*(c+d*x)^2*log(F))*log(F)^3/d],
[F^(a+b*(c+d*x)^2)/(c+d*x)^9,x,1,-1/2*b^4*F^a*GAMMA(-4,-b*(c+d*x)^2*log(F))*log(F)^4/d],
[F^(a+b*(c+d*x)^2)/(c+d*x)^11,x,1,1/2*b^5*F^a*GAMMA(-5,-b*(c+d*x)^2*log(F))*log(F)^5/d],
[F^(a+b*(c+d*x)^2)*(c+d*x)^12,x,1,-1/2*F^a*(c+d*x)^13*GAMMA(13/2,-b*(c+d*x)^2*log(F))/(d*(-b*(c+d*x)^2*log(F))^(13/2))],
[F^(a+b*(c+d*x)^2)*(c+d*x)^10,x,1,-1/2*F^a*(c+d*x)^11*GAMMA(11/2,-b*(c+d*x)^2*log(F))/(d*(-b*(c+d*x)^2*log(F))^(11/2))],
[F^(a+b*(c+d*x)^2)*(c+d*x)^8,x,5,-105/16*F^(a+b*(c+d*x)^2)*(c+d*x)/(b^4*d*log(F)^4)+35/8*F^(a+b*(c+d*x)^2)*(c+d*x)^3/(b^3*d*log(F)^3)-7/4*F^(a+b*(c+d*x)^2)*(c+d*x)^5/(b^2*d*log(F)^2)+1/2*F^(a+b*(c+d*x)^2)*(c+d*x)^7/(b*d*log(F))+105/32*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(b^(9/2)*d*log(F)^(9/2))],
[F^(a+b*(c+d*x)^2)*(c+d*x)^6,x,4,15/8*F^(a+b*(c+d*x)^2)*(c+d*x)/(b^3*d*log(F)^3)-5/4*F^(a+b*(c+d*x)^2)*(c+d*x)^3/(b^2*d*log(F)^2)+1/2*F^(a+b*(c+d*x)^2)*(c+d*x)^5/(b*d*log(F))-15/16*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(b^(7/2)*d*log(F)^(7/2))],
[F^(a+b*(c+d*x)^2)*(c+d*x)^4,x,3,-3/4*F^(a+b*(c+d*x)^2)*(c+d*x)/(b^2*d*log(F)^2)+1/2*F^(a+b*(c+d*x)^2)*(c+d*x)^3/(b*d*log(F))+3/8*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(b^(5/2)*d*log(F)^(5/2))],
[F^(a+b*(c+d*x)^2)*(c+d*x)^2,x,2,1/2*F^(a+b*(c+d*x)^2)*(c+d*x)/(b*d*log(F))-1/4*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(b^(3/2)*d*log(F)^(3/2))],
[F^(a+b*(c+d*x)^2),x,1,1/2*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(d*sqrt(b)*sqrt(log(F)))],
[F^(a+b*(c+d*x)^2)/(c+d*x)^2,x,2,-F^(a+b*(c+d*x)^2)/(d*(c+d*x))+F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(b)*sqrt(Pi)*sqrt(log(F))/d],
[F^(a+b*(c+d*x)^2)/(c+d*x)^4,x,3,-1/3*F^(a+b*(c+d*x)^2)/(d*(c+d*x)^3)-2/3*b*F^(a+b*(c+d*x)^2)*log(F)/(d*(c+d*x))+2/3*b^(3/2)*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*log(F)^(3/2)*sqrt(Pi)/d],
[F^(a+b*(c+d*x)^2)/(c+d*x)^6,x,4,-1/5*F^(a+b*(c+d*x)^2)/(d*(c+d*x)^5)-2/15*b*F^(a+b*(c+d*x)^2)*log(F)/(d*(c+d*x)^3)-4/15*b^2*F^(a+b*(c+d*x)^2)*log(F)^2/(d*(c+d*x))+4/15*b^(5/2)*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*log(F)^(5/2)*sqrt(Pi)/d],
[F^(a+b*(c+d*x)^2)/(c+d*x)^8,x,5,-1/7*F^(a+b*(c+d*x)^2)/(d*(c+d*x)^7)-2/35*b*F^(a+b*(c+d*x)^2)*log(F)/(d*(c+d*x)^5)-4/105*b^2*F^(a+b*(c+d*x)^2)*log(F)^2/(d*(c+d*x)^3)-8/105*b^3*F^(a+b*(c+d*x)^2)*log(F)^3/(d*(c+d*x))+8/105*b^(7/2)*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*log(F)^(7/2)*sqrt(Pi)/d],
[F^(a+b*(c+d*x)^2)/(c+d*x)^10,x,1,-1/2*F^a*GAMMA(-9/2,-b*(c+d*x)^2*log(F))*(-b*(c+d*x)^2*log(F))^(9/2)/(d*(c+d*x)^9)],
[F^(a+b*(c+d*x)^2)/(c+d*x)^12,x,1,-1/2*F^a*GAMMA(-11/2,-b*(c+d*x)^2*log(F))*(-b*(c+d*x)^2*log(F))^(11/2)/(d*(c+d*x)^11)],
[F^(a+b*(c+d*x)^3)*(c+d*x)^m,x,1,-1/3*F^a*(c+d*x)^(1+m)*GAMMA(1/3*(1+m),-b*(c+d*x)^3*log(F))*(-b*(c+d*x)^3*log(F))^(1/3*(-1-m))/d],
[F^(a+b*(c+d*x)^3)*(c+d*x)^17,x,1,-1/3*F^(a+b*(c+d*x)^3)*(120-120*b*(c+d*x)^3*log(F)+60*b^2*(c+d*x)^6*log(F)^2-20*b^3*(c+d*x)^9*log(F)^3+5*b^4*(c+d*x)^12*log(F)^4-b^5*(c+d*x)^15*log(F)^5)/(b^6*d*log(F)^6)],
[F^(a+b*(c+d*x)^3)*(c+d*x)^14,x,1,1/3*F^(a+b*(c+d*x)^3)*(24-24*b*(c+d*x)^3*log(F)+12*b^2*(c+d*x)^6*log(F)^2-4*b^3*(c+d*x)^9*log(F)^3+b^4*(c+d*x)^12*log(F)^4)/(b^5*d*log(F)^5)],
[F^(a+b*(c+d*x)^3)*(c+d*x)^11,x,4,-2*F^(a+b*(c+d*x)^3)/(b^4*d*log(F)^4)+2*F^(a+b*(c+d*x)^3)*(c+d*x)^3/(b^3*d*log(F)^3)-F^(a+b*(c+d*x)^3)*(c+d*x)^6/(b^2*d*log(F)^2)+1/3*F^(a+b*(c+d*x)^3)*(c+d*x)^9/(b*d*log(F))],
[F^(a+b*(c+d*x)^3)*(c+d*x)^8,x,3,2/3*F^(a+b*(c+d*x)^3)/(b^3*d*log(F)^3)-2/3*F^(a+b*(c+d*x)^3)*(c+d*x)^3/(b^2*d*log(F)^2)+1/3*F^(a+b*(c+d*x)^3)*(c+d*x)^6/(b*d*log(F))],
[F^(a+b*(c+d*x)^3)*(c+d*x)^5,x,2,-1/3*F^(a+b*(c+d*x)^3)/(b^2*d*log(F)^2)+1/3*F^(a+b*(c+d*x)^3)*(c+d*x)^3/(b*d*log(F))],
[F^(a+b*(c+d*x)^3)*(c+d*x)^2,x,1,1/3*F^(a+b*(c+d*x)^3)/(b*d*log(F))],
[F^(a+b*(c+d*x)^3)/(c+d*x),x,1,1/3*F^a*Ei(b*(c+d*x)^3*log(F))/d],
[F^(a+b*(c+d*x)^3)/(c+d*x)^4,x,2,-1/3*F^(a+b*(c+d*x)^3)/(d*(c+d*x)^3)+1/3*b*F^a*Ei(b*(c+d*x)^3*log(F))*log(F)/d],
[F^(a+b*(c+d*x)^3)/(c+d*x)^7,x,3,-1/6*F^(a+b*(c+d*x)^3)/(d*(c+d*x)^6)-1/6*b*F^(a+b*(c+d*x)^3)*log(F)/(d*(c+d*x)^3)+1/6*b^2*F^a*Ei(b*(c+d*x)^3*log(F))*log(F)^2/d],
[F^(a+b*(c+d*x)^3)/(c+d*x)^10,x,4,-1/9*F^(a+b*(c+d*x)^3)/(d*(c+d*x)^9)-1/18*b*F^(a+b*(c+d*x)^3)*log(F)/(d*(c+d*x)^6)-1/18*b^2*F^(a+b*(c+d*x)^3)*log(F)^2/(d*(c+d*x)^3)+1/18*b^3*F^a*Ei(b*(c+d*x)^3*log(F))*log(F)^3/d],
[F^(a+b*(c+d*x)^3)/(c+d*x)^13,x,1,-1/3*b^4*F^a*GAMMA(-4,-b*(c+d*x)^3*log(F))*log(F)^4/d],
[F^(a+b*(c+d*x)^3)/(c+d*x)^16,x,1,1/3*b^5*F^a*GAMMA(-5,-b*(c+d*x)^3*log(F))*log(F)^5/d],
[F^(a+b*(c+d*x)^3)*(c+d*x)^3,x,1,-1/3*F^a*(c+d*x)^4*GAMMA(4/3,-b*(c+d*x)^3*log(F))/(d*(-b*(c+d*x)^3*log(F))^(4/3))],
[F^(a+b*(c+d*x)^3)*(c+d*x),x,1,-1/3*F^a*(c+d*x)^2*GAMMA(2/3,-b*(c+d*x)^3*log(F))/(d*(-b*(c+d*x)^3*log(F))^(2/3))],
[F^(a+b*(c+d*x)^3),x,1,-1/3*F^a*(c+d*x)*GAMMA(1/3,-b*(c+d*x)^3*log(F))/(d*(-b*(c+d*x)^3*log(F))^(1/3))],
[F^(a+b*(c+d*x)^3)/(c+d*x)^2,x,1,-1/3*F^a*GAMMA(-1/3,-b*(c+d*x)^3*log(F))*(-b*(c+d*x)^3*log(F))^(1/3)/(d*(c+d*x))],
[F^(a+b*(c+d*x)^3)/(c+d*x)^3,x,1,-1/3*F^a*GAMMA(-2/3,-b*(c+d*x)^3*log(F))*(-b*(c+d*x)^3*log(F))^(2/3)/(d*(c+d*x)^2)],
[F^(a+b*(c+d*x)^3)/(c+d*x)^5,x,1,-1/3*F^a*GAMMA(-4/3,-b*(c+d*x)^3*log(F))*(-b*(c+d*x)^3*log(F))^(4/3)/(d*(c+d*x)^4)],
[f^(a+b*(c+d*x)^(1/2)),x,3,-2*f^(a+b*sqrt(c+d*x))/(b^2*d*log(f)^2)+2*f^(a+b*sqrt(c+d*x))*sqrt(c+d*x)/(b*d*log(f))],
[f^(a+b*(c+d*x)^(1/3)),x,4,6*f^(a+b*(c+d*x)^(1/3))/(b^3*d*log(f)^3)-6*f^(a+b*(c+d*x)^(1/3))*(c+d*x)^(1/3)/(b^2*d*log(f)^2)+3*f^(a+b*(c+d*x)^(1/3))*(c+d*x)^(2/3)/(b*d*log(f))],

# n<0
[F^(a+b/(c+d*x))*(c+d*x)^m,x,1,F^a*(c+d*x)^(1+m)*GAMMA(-1-m,-b*log(F)/(c+d*x))*(-b*log(F)/(c+d*x))^(1+m)/d],
[F^(a+b/(c+d*x))*(c+d*x)^4,x,1,-b^5*F^a*GAMMA(-5,-b*log(F)/(c+d*x))*log(F)^5/d],
[F^(a+b/(c+d*x))*(c+d*x)^3,x,1,b^4*F^a*GAMMA(-4,-b*log(F)/(c+d*x))*log(F)^4/d],
[F^(a+b/(c+d*x))*(c+d*x)^2,x,4,1/3*F^(a+b/(c+d*x))*(c+d*x)^3/d+1/6*b*F^(a+b/(c+d*x))*(c+d*x)^2*log(F)/d+1/6*b^2*F^(a+b/(c+d*x))*(c+d*x)*log(F)^2/d-1/6*b^3*F^a*Ei(b*log(F)/(c+d*x))*log(F)^3/d],
[F^(a+b/(c+d*x))*(c+d*x),x,3,1/2*F^(a+b/(c+d*x))*(c+d*x)^2/d+1/2*b*F^(a+b/(c+d*x))*(c+d*x)*log(F)/d-1/2*b^2*F^a*Ei(b*log(F)/(c+d*x))*log(F)^2/d],
[F^(a+b/(c+d*x)),x,2,F^(a+b/(c+d*x))*(c+d*x)/d-b*F^a*Ei(b*log(F)/(c+d*x))*log(F)/d],
[F^(a+b/(c+d*x))/(c+d*x),x,1,-F^a*Ei(b*log(F)/(c+d*x))/d],
[F^(a+b/(c+d*x))/(c+d*x)^2,x,1,-F^(a+b/(c+d*x))/(b*d*log(F))],
[F^(a+b/(c+d*x))/(c+d*x)^3,x,2,F^(a+b/(c+d*x))/(b^2*d*log(F)^2)-F^(a+b/(c+d*x))/(b*d*(c+d*x)*log(F))],
[F^(a+b/(c+d*x))/(c+d*x)^4,x,3,-2*F^(a+b/(c+d*x))/(b^3*d*log(F)^3)+2*F^(a+b/(c+d*x))/(b^2*d*(c+d*x)*log(F)^2)-F^(a+b/(c+d*x))/(b*d*(c+d*x)^2*log(F))],
[F^(a+b/(c+d*x))/(c+d*x)^5,x,4,6*F^(a+b/(c+d*x))/(b^4*d*log(F)^4)-6*F^(a+b/(c+d*x))/(b^3*d*(c+d*x)*log(F)^3)+3*F^(a+b/(c+d*x))/(b^2*d*(c+d*x)^2*log(F)^2)-F^(a+b/(c+d*x))/(b*d*(c+d*x)^3*log(F))],
[F^(a+b/(c+d*x))/(c+d*x)^6,x,1,-F^(a+b/(c+d*x))*(24*(c+d*x)^4-24*b*(c+d*x)^3*log(F)+12*b^2*(c+d*x)^2*log(F)^2-4*b^3*(c+d*x)*log(F)^3+b^4*log(F)^4)/(b^5*d*(c+d*x)^4*log(F)^5)],
[F^(a+b/(c+d*x))/(c+d*x)^7,x,1,F^(a+b/(c+d*x))*(120*(c+d*x)^5-120*b*(c+d*x)^4*log(F)+60*b^2*(c+d*x)^3*log(F)^2-20*b^3*(c+d*x)^2*log(F)^3+5*b^4*(c+d*x)*log(F)^4-b^5*log(F)^5)/(b^6*d*(c+d*x)^5*log(F)^6)],
[F^(a+b/(c+d*x)^2)*(c+d*x)^m,x,1,1/2*F^a*(c+d*x)^(1+m)*GAMMA(1/2*(-1-m),-b*log(F)/(c+d*x)^2)*(-b*log(F)/(c+d*x)^2)^(1/2*(1+m))/d],
[F^(a+b/(c+d*x)^2)*(c+d*x)^9,x,1,-1/2*b^5*F^a*GAMMA(-5,-b*log(F)/(c+d*x)^2)*log(F)^5/d],
[F^(a+b/(c+d*x)^2)*(c+d*x)^7,x,1,1/2*b^4*F^a*GAMMA(-4,-b*log(F)/(c+d*x)^2)*log(F)^4/d],
[F^(a+b/(c+d*x)^2)*(c+d*x)^5,x,4,1/6*F^(a+b/(c+d*x)^2)*(c+d*x)^6/d+1/12*b*F^(a+b/(c+d*x)^2)*(c+d*x)^4*log(F)/d+1/12*b^2*F^(a+b/(c+d*x)^2)*(c+d*x)^2*log(F)^2/d-1/12*b^3*F^a*Ei(b*log(F)/(c+d*x)^2)*log(F)^3/d],
[F^(a+b/(c+d*x)^2)*(c+d*x)^3,x,3,1/4*F^(a+b/(c+d*x)^2)*(c+d*x)^4/d+1/4*b*F^(a+b/(c+d*x)^2)*(c+d*x)^2*log(F)/d-1/4*b^2*F^a*Ei(b*log(F)/(c+d*x)^2)*log(F)^2/d],
[F^(a+b/(c+d*x)^2)*(c+d*x),x,2,1/2*F^(a+b/(c+d*x)^2)*(c+d*x)^2/d-1/2*b*F^a*Ei(b*log(F)/(c+d*x)^2)*log(F)/d],
[F^(a+b/(c+d*x)^2)/(c+d*x),x,1,-1/2*F^a*Ei(b*log(F)/(c+d*x)^2)/d],
[F^(a+b/(c+d*x)^2)/(c+d*x)^3,x,1,-1/2*F^(a+b/(c+d*x)^2)/(b*d*log(F))],
[F^(a+b/(c+d*x)^2)/(c+d*x)^5,x,2,1/2*F^(a+b/(c+d*x)^2)/(b^2*d*log(F)^2)-1/2*F^(a+b/(c+d*x)^2)/(b*d*(c+d*x)^2*log(F))],
[F^(a+b/(c+d*x)^2)/(c+d*x)^7,x,3,-F^(a+b/(c+d*x)^2)/(b^3*d*log(F)^3)+F^(a+b/(c+d*x)^2)/(b^2*d*(c+d*x)^2*log(F)^2)-1/2*F^(a+b/(c+d*x)^2)/(b*d*(c+d*x)^4*log(F))],
[F^(a+b/(c+d*x)^2)/(c+d*x)^9,x,4,3*F^(a+b/(c+d*x)^2)/(b^4*d*log(F)^4)-3*F^(a+b/(c+d*x)^2)/(b^3*d*(c+d*x)^2*log(F)^3)+3/2*F^(a+b/(c+d*x)^2)/(b^2*d*(c+d*x)^4*log(F)^2)-1/2*F^(a+b/(c+d*x)^2)/(b*d*(c+d*x)^6*log(F))],
[F^(a+b/(c+d*x)^2)/(c+d*x)^11,x,1,-1/2*F^(a+b/(c+d*x)^2)*(24*(c+d*x)^8-24*b*(c+d*x)^6*log(F)+12*b^2*(c+d*x)^4*log(F)^2-4*b^3*(c+d*x)^2*log(F)^3+b^4*log(F)^4)/(b^5*d*(c+d*x)^8*log(F)^5)],
[F^(a+b/(c+d*x)^2)/(c+d*x)^13,x,1,1/2*F^(a+b/(c+d*x)^2)*(120*(c+d*x)^10-120*b*(c+d*x)^8*log(F)+60*b^2*(c+d*x)^6*log(F)^2-20*b^3*(c+d*x)^4*log(F)^3+5*b^4*(c+d*x)^2*log(F)^4-b^5*log(F)^5)/(b^6*d*(c+d*x)^10*log(F)^6)],
[F^(a+b/(c+d*x)^2)*(c+d*x)^10,x,1,1/2*F^a*(c+d*x)^11*GAMMA(-11/2,-b*log(F)/(c+d*x)^2)*(-b*log(F)/(c+d*x)^2)^(11/2)/d],
[F^(a+b/(c+d*x)^2)*(c+d*x)^8,x,1,1/2*F^a*(c+d*x)^9*GAMMA(-9/2,-b*log(F)/(c+d*x)^2)*(-b*log(F)/(c+d*x)^2)^(9/2)/d],
[F^(a+b/(c+d*x)^2)*(c+d*x)^6,x,6,1/7*F^(a+b/(c+d*x)^2)*(c+d*x)^7/d+2/35*b*F^(a+b/(c+d*x)^2)*(c+d*x)^5*log(F)/d+4/105*b^2*F^(a+b/(c+d*x)^2)*(c+d*x)^3*log(F)^2/d+8/105*b^3*F^(a+b/(c+d*x)^2)*(c+d*x)*log(F)^3/d-8/105*b^(7/2)*F^a*erfi(sqrt(b)*sqrt(log(F))/(c+d*x))*log(F)^(7/2)*sqrt(Pi)/d],
[F^(a+b/(c+d*x)^2)*(c+d*x)^4,x,5,1/5*F^(a+b/(c+d*x)^2)*(c+d*x)^5/d+2/15*b*F^(a+b/(c+d*x)^2)*(c+d*x)^3*log(F)/d+4/15*b^2*F^(a+b/(c+d*x)^2)*(c+d*x)*log(F)^2/d-4/15*b^(5/2)*F^a*erfi(sqrt(b)*sqrt(log(F))/(c+d*x))*log(F)^(5/2)*sqrt(Pi)/d],
[F^(a+b/(c+d*x)^2)*(c+d*x)^2,x,4,1/3*F^(a+b/(c+d*x)^2)*(c+d*x)^3/d+2/3*b*F^(a+b/(c+d*x)^2)*(c+d*x)*log(F)/d-2/3*b^(3/2)*F^a*erfi(sqrt(b)*sqrt(log(F))/(c+d*x))*log(F)^(3/2)*sqrt(Pi)/d],
[F^(a+b/(c+d*x)^2),x,3,F^(a+b/(c+d*x)^2)*(c+d*x)/d-F^a*erfi(sqrt(b)*sqrt(log(F))/(c+d*x))*sqrt(b)*sqrt(Pi)*sqrt(log(F))/d],
[F^(a+b/(c+d*x)^2)/(c+d*x)^2,x,2,-1/2*F^a*erfi(sqrt(b)*sqrt(log(F))/(c+d*x))*sqrt(Pi)/(d*sqrt(b)*sqrt(log(F)))],
[F^(a+b/(c+d*x)^2)/(c+d*x)^4,x,3,-1/2*F^(a+b/(c+d*x)^2)/(b*d*(c+d*x)*log(F))+1/4*F^a*erfi(sqrt(b)*sqrt(log(F))/(c+d*x))*sqrt(Pi)/(b^(3/2)*d*log(F)^(3/2))],
[F^(a+b/(c+d*x)^2)/(c+d*x)^6,x,4,3/4*F^(a+b/(c+d*x)^2)/(b^2*d*(c+d*x)*log(F)^2)-1/2*F^(a+b/(c+d*x)^2)/(b*d*(c+d*x)^3*log(F))-3/8*F^a*erfi(sqrt(b)*sqrt(log(F))/(c+d*x))*sqrt(Pi)/(b^(5/2)*d*log(F)^(5/2))],
[F^(a+b/(c+d*x)^2)/(c+d*x)^8,x,5,-15/8*F^(a+b/(c+d*x)^2)/(b^3*d*(c+d*x)*log(F)^3)+5/4*F^(a+b/(c+d*x)^2)/(b^2*d*(c+d*x)^3*log(F)^2)-1/2*F^(a+b/(c+d*x)^2)/(b*d*(c+d*x)^5*log(F))+15/16*F^a*erfi(sqrt(b)*sqrt(log(F))/(c+d*x))*sqrt(Pi)/(b^(7/2)*d*log(F)^(7/2))],
[F^(a+b/(c+d*x)^2)/(c+d*x)^10,x,6,105/16*F^(a+b/(c+d*x)^2)/(b^4*d*(c+d*x)*log(F)^4)-35/8*F^(a+b/(c+d*x)^2)/(b^3*d*(c+d*x)^3*log(F)^3)+7/4*F^(a+b/(c+d*x)^2)/(b^2*d*(c+d*x)^5*log(F)^2)-1/2*F^(a+b/(c+d*x)^2)/(b*d*(c+d*x)^7*log(F))-105/32*F^a*erfi(sqrt(b)*sqrt(log(F))/(c+d*x))*sqrt(Pi)/(b^(9/2)*d*log(F)^(9/2))],
[F^(a+b/(c+d*x)^2)/(c+d*x)^12,x,1,1/2*F^a*GAMMA(11/2,-b*log(F)/(c+d*x)^2)/(d*(c+d*x)^11*(-b*log(F)/(c+d*x)^2)^(11/2))],
[F^(a+b/(c+d*x)^2)/(c+d*x)^14,x,1,1/2*F^a*GAMMA(13/2,-b*log(F)/(c+d*x)^2)/(d*(c+d*x)^13*(-b*log(F)/(c+d*x)^2)^(13/2))],
[F^(a+b/(c+d*x)^3)*(c+d*x)^m,x,1,1/3*F^a*(c+d*x)^(1+m)*GAMMA(1/3*(-1-m),-b*log(F)/(c+d*x)^3)*(-b*log(F)/(c+d*x)^3)^(1/3*(1+m))/d],
[F^(a+b/(c+d*x)^3)*(c+d*x)^14,x,1,-1/3*b^5*F^a*GAMMA(-5,-b*log(F)/(c+d*x)^3)*log(F)^5/d],
[F^(a+b/(c+d*x)^3)*(c+d*x)^11,x,1,1/3*b^4*F^a*GAMMA(-4,-b*log(F)/(c+d*x)^3)*log(F)^4/d],
[F^(a+b/(c+d*x)^3)*(c+d*x)^8,x,4,1/9*F^(a+b/(c+d*x)^3)*(c+d*x)^9/d+1/18*b*F^(a+b/(c+d*x)^3)*(c+d*x)^6*log(F)/d+1/18*b^2*F^(a+b/(c+d*x)^3)*(c+d*x)^3*log(F)^2/d-1/18*b^3*F^a*Ei(b*log(F)/(c+d*x)^3)*log(F)^3/d],
[F^(a+b/(c+d*x)^3)*(c+d*x)^5,x,3,1/6*F^(a+b/(c+d*x)^3)*(c+d*x)^6/d+1/6*b*F^(a+b/(c+d*x)^3)*(c+d*x)^3*log(F)/d-1/6*b^2*F^a*Ei(b*log(F)/(c+d*x)^3)*log(F)^2/d],
[F^(a+b/(c+d*x)^3)*(c+d*x)^2,x,2,1/3*F^(a+b/(c+d*x)^3)*(c+d*x)^3/d-1/3*b*F^a*Ei(b*log(F)/(c+d*x)^3)*log(F)/d],
[F^(a+b/(c+d*x)^3)/(c+d*x),x,1,-1/3*F^a*Ei(b*log(F)/(c+d*x)^3)/d],
[F^(a+b/(c+d*x)^3)/(c+d*x)^4,x,1,-1/3*F^(a+b/(c+d*x)^3)/(b*d*log(F))],
[F^(a+b/(c+d*x)^3)/(c+d*x)^7,x,2,1/3*F^(a+b/(c+d*x)^3)/(b^2*d*log(F)^2)-1/3*F^(a+b/(c+d*x)^3)/(b*d*(c+d*x)^3*log(F))],
[F^(a+b/(c+d*x)^3)/(c+d*x)^10,x,3,-2/3*F^(a+b/(c+d*x)^3)/(b^3*d*log(F)^3)+2/3*F^(a+b/(c+d*x)^3)/(b^2*d*(c+d*x)^3*log(F)^2)-1/3*F^(a+b/(c+d*x)^3)/(b*d*(c+d*x)^6*log(F))],
[F^(a+b/(c+d*x)^3)/(c+d*x)^13,x,4,2*F^(a+b/(c+d*x)^3)/(b^4*d*log(F)^4)-2*F^(a+b/(c+d*x)^3)/(b^3*d*(c+d*x)^3*log(F)^3)+F^(a+b/(c+d*x)^3)/(b^2*d*(c+d*x)^6*log(F)^2)-1/3*F^(a+b/(c+d*x)^3)/(b*d*(c+d*x)^9*log(F))],
[F^(a+b/(c+d*x)^3)/(c+d*x)^16,x,1,-1/3*F^(a+b/(c+d*x)^3)*(24*(c+d*x)^12-24*b*(c+d*x)^9*log(F)+12*b^2*(c+d*x)^6*log(F)^2-4*b^3*(c+d*x)^3*log(F)^3+b^4*log(F)^4)/(b^5*d*(c+d*x)^12*log(F)^5)],
[F^(a+b/(c+d*x)^3)/(c+d*x)^19,x,1,1/3*F^(a+b/(c+d*x)^3)*(120*(c+d*x)^15-120*b*(c+d*x)^12*log(F)+60*b^2*(c+d*x)^9*log(F)^2-20*b^3*(c+d*x)^6*log(F)^3+5*b^4*(c+d*x)^3*log(F)^4-b^5*log(F)^5)/(b^6*d*(c+d*x)^15*log(F)^6)],
[F^(a+b/(c+d*x)^3)*(c+d*x)^3,x,1,1/3*F^a*(c+d*x)^4*GAMMA(-4/3,-b*log(F)/(c+d*x)^3)*(-b*log(F)/(c+d*x)^3)^(4/3)/d],
[F^(a+b/(c+d*x)^3)*(c+d*x),x,1,1/3*F^a*(c+d*x)^2*GAMMA(-2/3,-b*log(F)/(c+d*x)^3)*(-b*log(F)/(c+d*x)^3)^(2/3)/d],
[F^(a+b/(c+d*x)^3),x,1,1/3*F^a*(c+d*x)*GAMMA(-1/3,-b*log(F)/(c+d*x)^3)*(-b*log(F)/(c+d*x)^3)^(1/3)/d],
[F^(a+b/(c+d*x)^3)/(c+d*x)^2,x,1,1/3*F^a*GAMMA(1/3,-b*log(F)/(c+d*x)^3)/(d*(c+d*x)*(-b*log(F)/(c+d*x)^3)^(1/3))],
[F^(a+b/(c+d*x)^3)/(c+d*x)^3,x,1,1/3*F^a*GAMMA(2/3,-b*log(F)/(c+d*x)^3)/(d*(c+d*x)^2*(-b*log(F)/(c+d*x)^3)^(2/3))],
[F^(a+b/(c+d*x)^3)/(c+d*x)^5,x,1,1/3*F^a*GAMMA(4/3,-b*log(F)/(c+d*x)^3)/(d*(c+d*x)^4*(-b*log(F)/(c+d*x)^3)^(4/3))],

# n symbolic
[F^(a+b*(c+d*x)^n)*(c+d*x)^m,x,1,-F^a*(c+d*x)^(1+m)*GAMMA((1+m)/n,-b*(c+d*x)^n*log(F))/(d*n*(-b*(c+d*x)^n*log(F))^((1+m)/n))],
[F^(a+b*(c+d*x)^n)*(c+d*x)^3,x,1,-F^a*(c+d*x)^4*GAMMA(4/n,-b*(c+d*x)^n*log(F))/(d*n*(-b*(c+d*x)^n*log(F))^(4/n))],
[F^(a+b*(c+d*x)^n)*(c+d*x)^2,x,1,-F^a*(c+d*x)^3*GAMMA(3/n,-b*(c+d*x)^n*log(F))/(d*n*(-b*(c+d*x)^n*log(F))^(3/n))],
[F^(a+b*(c+d*x)^n)*(c+d*x),x,1,-F^a*(c+d*x)^2*GAMMA(2/n,-b*(c+d*x)^n*log(F))/(d*n*(-b*(c+d*x)^n*log(F))^(2/n))],
[F^(a+b*(c+d*x)^n),x,1,-F^a*(c+d*x)*GAMMA(1/n,-b*(c+d*x)^n*log(F))/(d*n*(-b*(c+d*x)^n*log(F))^(1/n))],
[F^(a+b*(c+d*x)^n)/(c+d*x),x,1,F^a*Ei(b*(c+d*x)^n*log(F))/(d*n)],
[F^(a+b*(c+d*x)^n)/(c+d*x)^2,x,1,-F^a*GAMMA((-1)/n,-b*(c+d*x)^n*log(F))*(-b*(c+d*x)^n*log(F))^(1/n)/(d*n*(c+d*x))],
[F^(a+b*(c+d*x)^n)/(c+d*x)^3,x,1,-F^a*GAMMA((-2)/n,-b*(c+d*x)^n*log(F))*(-b*(c+d*x)^n*log(F))^(2/n)/(d*n*(c+d*x)^2)],
[F^(a+b*(c+d*x)^n)/(c+d*x)^4,x,1,-F^a*GAMMA((-3)/n,-b*(c+d*x)^n*log(F))*(-b*(c+d*x)^n*log(F))^(3/n)/(d*n*(c+d*x)^3)],
[F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+6*n),x,1,-F^(a+b*(c+d*x)^n)*(120-120*b*(c+d*x)^n*log(F)+60*b^2*(c+d*x)^(2*n)*log(F)^2-20*b^3*(c+d*x)^(3*n)*log(F)^3+5*b^4*(c+d*x)^(4*n)*log(F)^4-b^5*(c+d*x)^(5*n)*log(F)^5)/(b^6*d*n*log(F)^6)],
[F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+5*n),x,1,F^(a+b*(c+d*x)^n)*(24-24*b*(c+d*x)^n*log(F)+12*b^2*(c+d*x)^(2*n)*log(F)^2-4*b^3*(c+d*x)^(3*n)*log(F)^3+b^4*(c+d*x)^(4*n)*log(F)^4)/(b^5*d*n*log(F)^5)],
[F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+4*n),x,4,-6*F^(a+b*(c+d*x)^n)/(b^4*d*n*log(F)^4)+6*F^(a+b*(c+d*x)^n)*(c+d*x)^n/(b^3*d*n*log(F)^3)-3*F^(a+b*(c+d*x)^n)*(c+d*x)^(2*n)/(b^2*d*n*log(F)^2)+F^(a+b*(c+d*x)^n)*(c+d*x)^(3*n)/(b*d*n*log(F))],
[F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+3*n),x,3,2*F^(a+b*(c+d*x)^n)/(b^3*d*n*log(F)^3)-2*F^(a+b*(c+d*x)^n)*(c+d*x)^n/(b^2*d*n*log(F)^2)+F^(a+b*(c+d*x)^n)*(c+d*x)^(2*n)/(b*d*n*log(F))],
[F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+2*n),x,2,-F^(a+b*(c+d*x)^n)/(b^2*d*n*log(F)^2)+F^(a+b*(c+d*x)^n)*(c+d*x)^n/(b*d*n*log(F))],
[F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+n),x,1,F^(a+b*(c+d*x)^n)/(b*d*n*log(F))],
[F^(a+b*(c+d*x)^n)/(c+d*x),x,1,F^a*Ei(b*(c+d*x)^n*log(F))/(d*n)],
[F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-n),x,2,-F^(a+b*(c+d*x)^n)/(d*n*(c+d*x)^n)+b*F^a*Ei(b*(c+d*x)^n*log(F))*log(F)/(d*n)],
[F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-2*n),x,3,-1/2*F^(a+b*(c+d*x)^n)/(d*n*(c+d*x)^(2*n))-1/2*b*F^(a+b*(c+d*x)^n)*log(F)/(d*n*(c+d*x)^n)+1/2*b^2*F^a*Ei(b*(c+d*x)^n*log(F))*log(F)^2/(d*n)],
[F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-3*n),x,4,-1/3*F^(a+b*(c+d*x)^n)/(d*n*(c+d*x)^(3*n))-1/6*b*F^(a+b*(c+d*x)^n)*log(F)/(d*n*(c+d*x)^(2*n))-1/6*b^2*F^(a+b*(c+d*x)^n)*log(F)^2/(d*n*(c+d*x)^n)+1/6*b^3*F^a*Ei(b*(c+d*x)^n*log(F))*log(F)^3/(d*n)],
[F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-4*n),x,1,-b^4*F^a*GAMMA(-4,-b*(c+d*x)^n*log(F))*log(F)^4/(d*n)],
[F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-5*n),x,1,b^5*F^a*GAMMA(-5,-b*(c+d*x)^n*log(F))*log(F)^5/(d*n)],
[F^(c*(a+b*x)^n)*(a+b*x)^(-1+1/2*n),x,2,erfi((a+b*x)^(1/2*n)*sqrt(c)*sqrt(log(F)))*sqrt(Pi)/(b*n*sqrt(c)*sqrt(log(F)))],
[(a+b*x)^(-1+1/2*n)/F^(c*(a+b*x)^n),x,2,erf((a+b*x)^(1/2*n)*sqrt(c)*sqrt(log(F)))*sqrt(Pi)/(b*n*sqrt(c)*sqrt(log(F)))],

# Integrands of the form (e+f x)^m F^(a+b (c+d x)^n)

# n>0
[F^(a+b*(c+d*x)^2)*(e+f*x)^5,x,14,f^5*F^(a+b*(c+d*x)^2)/(b^3*d^6*log(F)^3)-5*f^3*(d*e-c*f)^2*F^(a+b*(c+d*x)^2)/(b^2*d^6*log(F)^2)-15/4*f^4*(d*e-c*f)*F^(a+b*(c+d*x)^2)*(c+d*x)/(b^2*d^6*log(F)^2)-f^5*F^(a+b*(c+d*x)^2)*(c+d*x)^2/(b^2*d^6*log(F)^2)+5/2*f*(d*e-c*f)^4*F^(a+b*(c+d*x)^2)/(b*d^6*log(F))+5*f^2*(d*e-c*f)^3*F^(a+b*(c+d*x)^2)*(c+d*x)/(b*d^6*log(F))+5*f^3*(d*e-c*f)^2*F^(a+b*(c+d*x)^2)*(c+d*x)^2/(b*d^6*log(F))+5/2*f^4*(d*e-c*f)*F^(a+b*(c+d*x)^2)*(c+d*x)^3/(b*d^6*log(F))+1/2*f^5*F^(a+b*(c+d*x)^2)*(c+d*x)^4/(b*d^6*log(F))+15/8*f^4*(d*e-c*f)*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(b^(5/2)*d^6*log(F)^(5/2))-5/2*f^2*(d*e-c*f)^3*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(b^(3/2)*d^6*log(F)^(3/2))+1/2*(d*e-c*f)^5*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(d^6*sqrt(b)*sqrt(log(F)))],
[F^(a+b*(c+d*x)^2)*(e+f*x)^4,x,11,-2*f^3*(d*e-c*f)*F^(a+b*(c+d*x)^2)/(b^2*d^5*log(F)^2)-3/4*f^4*F^(a+b*(c+d*x)^2)*(c+d*x)/(b^2*d^5*log(F)^2)+2*f*(d*e-c*f)^3*F^(a+b*(c+d*x)^2)/(b*d^5*log(F))+3*f^2*(d*e-c*f)^2*F^(a+b*(c+d*x)^2)*(c+d*x)/(b*d^5*log(F))+2*f^3*(d*e-c*f)*F^(a+b*(c+d*x)^2)*(c+d*x)^2/(b*d^5*log(F))+1/2*f^4*F^(a+b*(c+d*x)^2)*(c+d*x)^3/(b*d^5*log(F))+3/8*f^4*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(b^(5/2)*d^5*log(F)^(5/2))-3/2*f^2*(d*e-c*f)^2*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(b^(3/2)*d^5*log(F)^(3/2))+1/2*(d*e-c*f)^4*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(d^5*sqrt(b)*sqrt(log(F)))],
[F^(a+b*(c+d*x)^2)*(e+f*x)^3,x,8,-1/2*f^3*F^(a+b*(c+d*x)^2)/(b^2*d^4*log(F)^2)+3/2*f*(d*e-c*f)^2*F^(a+b*(c+d*x)^2)/(b*d^4*log(F))+3/2*f^2*(d*e-c*f)*F^(a+b*(c+d*x)^2)*(c+d*x)/(b*d^4*log(F))+1/2*f^3*F^(a+b*(c+d*x)^2)*(c+d*x)^2/(b*d^4*log(F))-3/4*f^2*(d*e-c*f)*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(b^(3/2)*d^4*log(F)^(3/2))+1/2*(d*e-c*f)^3*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(d^4*sqrt(b)*sqrt(log(F)))],
[F^(a+b*(c+d*x)^2)*(e+f*x)^2,x,6,f*(d*e-c*f)*F^(a+b*(c+d*x)^2)/(b*d^3*log(F))+1/2*f^2*F^(a+b*(c+d*x)^2)*(c+d*x)/(b*d^3*log(F))-1/4*f^2*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(b^(3/2)*d^3*log(F)^(3/2))+1/2*(d*e-c*f)^2*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(d^3*sqrt(b)*sqrt(log(F)))],
[F^(a+b*(c+d*x)^2)*(e+f*x),x,4,1/2*f*F^(a+b*(c+d*x)^2)/(b*d^2*log(F))+1/2*(d*e-c*f)*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(d^2*sqrt(b)*sqrt(log(F)))],
[F^(a+b*(c+d*x)^2),x,1,1/2*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(Pi)/(d*sqrt(b)*sqrt(log(F)))],
[F^(a+b*(c+d*x)^2)/(e+f*x),x,0,Unintegrable(F^(a+b*(c+d*x)^2)/(e+f*x),x)],
[F^(a+b*(c+d*x)^2)/(e+f*x)^2,x,2,-F^(a+b*(c+d*x)^2)/(f*(e+f*x))+d*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*sqrt(b)*sqrt(Pi)*sqrt(log(F))/f^2-2*b*d*(d*e-c*f)*log(F)*Unintegrable(F^(a+b*(c+d*x)^2)/(e+f*x),x)/f^2],
[F^(a+b*(c+d*x)^2)/(e+f*x)^3,x,3,-1/2*F^(a+b*(c+d*x)^2)/(f*(e+f*x)^2)+b*d*(d*e-c*f)*F^(a+b*(c+d*x)^2)*log(F)/(f^3*(e+f*x))-b^(3/2)*d^2*(d*e-c*f)*F^a*erfi((c+d*x)*sqrt(b)*sqrt(log(F)))*log(F)^(3/2)*sqrt(Pi)/f^4+b*d^2*log(F)*Unintegrable(F^(a+b*(c+d*x)^2)/(e+f*x),x)/f^2+2*b^2*d^2*(d*e-c*f)^2*log(F)^2*Unintegrable(F^(a+b*(c+d*x)^2)/(e+f*x),x)/f^4],
[exp(e*(c+d*x)^3)*(a+b*x)^3,x,6,-b^2*(b*c-a*d)*exp(e*(c+d*x)^3)/(d^4*e)+1/3*(b*c-a*d)^3*(c+d*x)*GAMMA(1/3,-e*(c+d*x)^3)/(d^4*(-e*(c+d*x)^3)^(1/3))-b*(b*c-a*d)^2*(c+d*x)^2*GAMMA(2/3,-e*(c+d*x)^3)/(d^4*(-e*(c+d*x)^3)^(2/3))-1/3*b^3*(c+d*x)^4*GAMMA(4/3,-e*(c+d*x)^3)/(d^4*(-e*(c+d*x)^3)^(4/3))],
[exp(e*(c+d*x)^3)*(a+b*x)^2,x,5,1/3*b^2*exp(e*(c+d*x)^3)/(d^3*e)-1/3*(b*c-a*d)^2*(c+d*x)*GAMMA(1/3,-e*(c+d*x)^3)/(d^3*(-e*(c+d*x)^3)^(1/3))+2/3*b*(b*c-a*d)*(c+d*x)^2*GAMMA(2/3,-e*(c+d*x)^3)/(d^3*(-e*(c+d*x)^3)^(2/3))],
[exp(e*(c+d*x)^3)*(a+b*x),x,4,1/3*(b*c-a*d)*(c+d*x)*GAMMA(1/3,-e*(c+d*x)^3)/(d^2*(-e*(c+d*x)^3)^(1/3))-1/3*b*(c+d*x)^2*GAMMA(2/3,-e*(c+d*x)^3)/(d^2*(-e*(c+d*x)^3)^(2/3))],
[exp(e*(c+d*x)^3),x,1,-1/3*(c+d*x)*GAMMA(1/3,-e*(c+d*x)^3)/(d*(-e*(c+d*x)^3)^(1/3))],
[exp(e*(c+d*x)^3)/(a+b*x),x,0,Unintegrable(exp(e*(c+d*x)^3)/(a+b*x),x)],
[exp(e*(c+d*x)^3)/(a+b*x)^2,x,5,-exp(e*(c+d*x)^3)/(b*(a+b*x))-d*(b*c-a*d)*e*(c+d*x)*GAMMA(1/3,-e*(c+d*x)^3)/(b^3*(-e*(c+d*x)^3)^(1/3))-d*e*(c+d*x)^2*GAMMA(2/3,-e*(c+d*x)^3)/(b^2*(-e*(c+d*x)^3)^(2/3))+3*d*(b*c-a*d)^2*e*Unintegrable(exp(e*(c+d*x)^3)/(a+b*x),x)/b^3],

# n<0
[F^(a+b/(c+d*x))/(e+f*x),x,4,-F^a*Ei(b*log(F)/(c+d*x))/f+F^(a-b*f/(d*e-c*f))*Ei(b*d*(e+f*x)*log(F)/((d*e-c*f)*(c+d*x)))/f],
[F^(a+b/(c+d*x))/(e+f*x)^2,x,9,d*F^(a+b/(c+d*x))/(f*(d*e-c*f))-F^(a+b/(c+d*x))/(f*(e+f*x))-b*d*F^(a-b*f/(d*e-c*f))*Ei(b*d*(e+f*x)*log(F)/((d*e-c*f)*(c+d*x)))*log(F)/(d*e-c*f)^2],
[F^(a+b/(c+d*x))/(e+f*x)^3,x,18,1/2*d^2*F^(a+b/(c+d*x))/(f*(d*e-c*f)^2)-1/2*F^(a+b/(c+d*x))/(f*(e+f*x)^2)-1/2*b*d^2*F^(a+b/(c+d*x))*log(F)/(d*e-c*f)^3+1/2*b*d*F^(a+b/(c+d*x))*log(F)/((d*e-c*f)^2*(e+f*x))-b*d^2*F^(a-b*f/(d*e-c*f))*Ei(b*d*(e+f*x)*log(F)/((d*e-c*f)*(c+d*x)))*log(F)/(d*e-c*f)^3+1/2*b^2*d^2*f*F^(a-b*f/(d*e-c*f))*Ei(b*d*(e+f*x)*log(F)/((d*e-c*f)*(c+d*x)))*log(F)^2/(d*e-c*f)^4],
[F^(a+b/(c+d*x))/(e+f*x)^4,x,36,1/3*d^3*F^(a+b/(c+d*x))/(f*(d*e-c*f)^3)-1/3*F^(a+b/(c+d*x))/(f*(e+f*x)^3)-5/6*b*d^3*F^(a+b/(c+d*x))*log(F)/(d*e-c*f)^4+1/6*b*d*F^(a+b/(c+d*x))*log(F)/((d*e-c*f)^2*(e+f*x)^2)+2/3*b*d^2*F^(a+b/(c+d*x))*log(F)/((d*e-c*f)^3*(e+f*x))-b*d^3*F^(a-b*f/(d*e-c*f))*Ei(b*d*(e+f*x)*log(F)/((d*e-c*f)*(c+d*x)))*log(F)/(d*e-c*f)^4+1/6*b^2*d^3*f*F^(a+b/(c+d*x))*log(F)^2/(d*e-c*f)^5-1/6*b^2*d^2*f*F^(a+b/(c+d*x))*log(F)^2/((d*e-c*f)^4*(e+f*x))+b^2*d^3*f*F^(a-b*f/(d*e-c*f))*Ei(b*d*(e+f*x)*log(F)/((d*e-c*f)*(c+d*x)))*log(F)^2/(d*e-c*f)^5-1/6*b^3*d^3*f^2*F^(a-b*f/(d*e-c*f))*Ei(b*d*(e+f*x)*log(F)/((d*e-c*f)*(c+d*x)))*log(F)^3/(d*e-c*f)^6],
[exp(e/(c+d*x))*(a+b*x)^4,x,13,(b*c-a*d)^4*exp(e/(c+d*x))*(c+d*x)/d^5-2*b*(b*c-a*d)^3*e*exp(e/(c+d*x))*(c+d*x)/d^5+b^2*(b*c-a*d)^2*e^2*exp(e/(c+d*x))*(c+d*x)/d^5-2*b*(b*c-a*d)^3*exp(e/(c+d*x))*(c+d*x)^2/d^5+b^2*(b*c-a*d)^2*e*exp(e/(c+d*x))*(c+d*x)^2/d^5+2*b^2*(b*c-a*d)^2*exp(e/(c+d*x))*(c+d*x)^3/d^5-(b*c-a*d)^4*e*Ei(e/(c+d*x))/d^5+2*b*(b*c-a*d)^3*e^2*Ei(e/(c+d*x))/d^5-b^2*(b*c-a*d)^2*e^3*Ei(e/(c+d*x))/d^5-b^4*e^5*GAMMA(-5,-e/(c+d*x))/d^5-4*b^3*(b*c-a*d)*e^4*GAMMA(-4,-e/(c+d*x))/d^5],
[exp(e/(c+d*x))*(a+b*x)^3,x,12,-(b*c-a*d)^3*exp(e/(c+d*x))*(c+d*x)/d^4+3/2*b*(b*c-a*d)^2*e*exp(e/(c+d*x))*(c+d*x)/d^4-1/2*b^2*(b*c-a*d)*e^2*exp(e/(c+d*x))*(c+d*x)/d^4+3/2*b*(b*c-a*d)^2*exp(e/(c+d*x))*(c+d*x)^2/d^4-1/2*b^2*(b*c-a*d)*e*exp(e/(c+d*x))*(c+d*x)^2/d^4-b^2*(b*c-a*d)*exp(e/(c+d*x))*(c+d*x)^3/d^4+(b*c-a*d)^3*e*Ei(e/(c+d*x))/d^4-3/2*b*(b*c-a*d)^2*e^2*Ei(e/(c+d*x))/d^4+1/2*b^2*(b*c-a*d)*e^3*Ei(e/(c+d*x))/d^4+b^3*e^4*GAMMA(-4,-e/(c+d*x))/d^4],
[exp(e/(c+d*x))*(a+b*x)^2,x,11,(b*c-a*d)^2*exp(e/(c+d*x))*(c+d*x)/d^3-b*(b*c-a*d)*e*exp(e/(c+d*x))*(c+d*x)/d^3+1/6*b^2*e^2*exp(e/(c+d*x))*(c+d*x)/d^3-b*(b*c-a*d)*exp(e/(c+d*x))*(c+d*x)^2/d^3+1/6*b^2*e*exp(e/(c+d*x))*(c+d*x)^2/d^3+1/3*b^2*exp(e/(c+d*x))*(c+d*x)^3/d^3-(b*c-a*d)^2*e*Ei(e/(c+d*x))/d^3+b*(b*c-a*d)*e^2*Ei(e/(c+d*x))/d^3-1/6*b^2*e^3*Ei(e/(c+d*x))/d^3],
[exp(e/(c+d*x))*(a+b*x),x,7,-(b*c-a*d)*exp(e/(c+d*x))*(c+d*x)/d^2+1/2*b*e*exp(e/(c+d*x))*(c+d*x)/d^2+1/2*b*exp(e/(c+d*x))*(c+d*x)^2/d^2+(b*c-a*d)*e*Ei(e/(c+d*x))/d^2-1/2*b*e^2*Ei(e/(c+d*x))/d^2],
[exp(e/(c+d*x)),x,2,exp(e/(c+d*x))*(c+d*x)/d-e*Ei(e/(c+d*x))/d],
[exp(e/(c+d*x))/(a+b*x),x,4,-Ei(e/(c+d*x))/b+exp(b*e/(b*c-a*d))*Ei(-d*e*(a+b*x)/((b*c-a*d)*(c+d*x)))/b],
[exp(e/(c+d*x))/(a+b*x)^2,x,9,-d*exp(e/(c+d*x))/(b*(b*c-a*d))-exp(e/(c+d*x))/(b*(a+b*x))-d*e*exp(b*e/(b*c-a*d))*Ei(-d*e*(a+b*x)/((b*c-a*d)*(c+d*x)))/(b*c-a*d)^2],
[exp(e/(c+d*x))/(a+b*x)^3,x,18,1/2*d^2*exp(e/(c+d*x))/(b*(b*c-a*d)^2)+1/2*d^2*e*exp(e/(c+d*x))/(b*c-a*d)^3-1/2*exp(e/(c+d*x))/(b*(a+b*x)^2)+1/2*d*e*exp(e/(c+d*x))/((b*c-a*d)^2*(a+b*x))+d^2*e*exp(b*e/(b*c-a*d))*Ei(-d*e*(a+b*x)/((b*c-a*d)*(c+d*x)))/(b*c-a*d)^3+1/2*b*d^2*e^2*exp(b*e/(b*c-a*d))*Ei(-d*e*(a+b*x)/((b*c-a*d)*(c+d*x)))/(b*c-a*d)^4],
[exp(e/(c+d*x)^2)*(a+b*x)^3,x,14,-(b*c-a*d)^3*exp(e/(c+d*x)^2)*(c+d*x)/d^4-2*b^2*(b*c-a*d)*e*exp(e/(c+d*x)^2)*(c+d*x)/d^4+3/2*b*(b*c-a*d)^2*exp(e/(c+d*x)^2)*(c+d*x)^2/d^4+1/4*b^3*e*exp(e/(c+d*x)^2)*(c+d*x)^2/d^4-b^2*(b*c-a*d)*exp(e/(c+d*x)^2)*(c+d*x)^3/d^4+1/4*b^3*exp(e/(c+d*x)^2)*(c+d*x)^4/d^4-3/2*b*(b*c-a*d)^2*e*Ei(e/(c+d*x)^2)/d^4-1/4*b^3*e^2*Ei(e/(c+d*x)^2)/d^4+2*b^2*(b*c-a*d)*e^(3/2)*erfi(sqrt(e)/(c+d*x))*sqrt(Pi)/d^4+(b*c-a*d)^3*erfi(sqrt(e)/(c+d*x))*sqrt(e)*sqrt(Pi)/d^4],
[exp(e/(c+d*x)^2)*(a+b*x)^2,x,11,(b*c-a*d)^2*exp(e/(c+d*x)^2)*(c+d*x)/d^3+2/3*b^2*e*exp(e/(c+d*x)^2)*(c+d*x)/d^3-b*(b*c-a*d)*exp(e/(c+d*x)^2)*(c+d*x)^2/d^3+1/3*b^2*exp(e/(c+d*x)^2)*(c+d*x)^3/d^3+b*(b*c-a*d)*e*Ei(e/(c+d*x)^2)/d^3-2/3*b^2*e^(3/2)*erfi(sqrt(e)/(c+d*x))*sqrt(Pi)/d^3-(b*c-a*d)^2*erfi(sqrt(e)/(c+d*x))*sqrt(e)*sqrt(Pi)/d^3],
[exp(e/(c+d*x)^2)*(a+b*x),x,7,-(b*c-a*d)*exp(e/(c+d*x)^2)*(c+d*x)/d^2+1/2*b*exp(e/(c+d*x)^2)*(c+d*x)^2/d^2-1/2*b*e*Ei(e/(c+d*x)^2)/d^2+(b*c-a*d)*erfi(sqrt(e)/(c+d*x))*sqrt(e)*sqrt(Pi)/d^2],
[exp(e/(c+d*x)^2),x,3,exp(e/(c+d*x)^2)*(c+d*x)/d-erfi(sqrt(e)/(c+d*x))*sqrt(e)*sqrt(Pi)/d],
[exp(e/(c+d*x)^2)/(a+b*x),x,0,Unintegrable(exp(e/(c+d*x)^2)/(a+b*x),x)],
[exp(e/(c+d*x)^2)/(a+b*x)^2,x,0,CannotIntegrate(exp(e/(c+d*x)^2)/(a+b*x)^2,x)],
[exp(e/(c+d*x)^2)/(a+b*x)^3,x,0,CannotIntegrate(exp(e/(c+d*x)^2)/(a+b*x)^3,x)],
[exp(e/(c+d*x)^3)*(a+b*x)^3,x,7,-b^2*(b*c-a*d)*exp(e/(c+d*x)^3)*(c+d*x)^3/d^4+b^2*(b*c-a*d)*e*Ei(e/(c+d*x)^3)/d^4+1/3*b^3*(-e/(c+d*x)^3)^(4/3)*(c+d*x)^4*GAMMA(-4/3,-e/(c+d*x)^3)/d^4+b*(b*c-a*d)^2*(-e/(c+d*x)^3)^(2/3)*(c+d*x)^2*GAMMA(-2/3,-e/(c+d*x)^3)/d^4-1/3*(b*c-a*d)^3*(-e/(c+d*x)^3)^(1/3)*(c+d*x)*GAMMA(-1/3,-e/(c+d*x)^3)/d^4],
[exp(e/(c+d*x)^3)*(a+b*x)^2,x,6,1/3*b^2*exp(e/(c+d*x)^3)*(c+d*x)^3/d^3-1/3*b^2*e*Ei(e/(c+d*x)^3)/d^3-2/3*b*(b*c-a*d)*(-e/(c+d*x)^3)^(2/3)*(c+d*x)^2*GAMMA(-2/3,-e/(c+d*x)^3)/d^3+1/3*(b*c-a*d)^2*(-e/(c+d*x)^3)^(1/3)*(c+d*x)*GAMMA(-1/3,-e/(c+d*x)^3)/d^3],
[exp(e/(c+d*x)^3)*(a+b*x),x,4,1/3*b*(-e/(c+d*x)^3)^(2/3)*(c+d*x)^2*GAMMA(-2/3,-e/(c+d*x)^3)/d^2-1/3*(b*c-a*d)*(-e/(c+d*x)^3)^(1/3)*(c+d*x)*GAMMA(-1/3,-e/(c+d*x)^3)/d^2],
[exp(e/(c+d*x)^3),x,1,1/3*(-e/(c+d*x)^3)^(1/3)*(c+d*x)*GAMMA(-1/3,-e/(c+d*x)^3)/d],
[exp(e/(c+d*x)^3)/(a+b*x),x,0,Unintegrable(exp(e/(c+d*x)^3)/(a+b*x),x)],
[exp(e/(c+d*x)^3)/(a+b*x)^2,x,0,CannotIntegrate(exp(e/(c+d*x)^3)/(a+b*x)^2,x)],

# Integrands of the form (g+h x)^m F^(e+f (a+b x)/(c+d x))
[F^(e+f*(a+b*x)/(c+d*x))/(g+h*x),x,5,-F^(e+b*f/d)*Ei(-(b*c-a*d)*f*log(F)/(d*(c+d*x)))/h+F^(e+f*(b*g-a*h)/(d*g-c*h))*Ei(-(b*c-a*d)*f*(g+h*x)*log(F)/((d*g-c*h)*(c+d*x)))/h],
[F^(e+f*(a+b*x)/(c+d*x))/(g+h*x)^2,x,12,d*F^(e+b*f/d-(b*c-a*d)*f/(d*(c+d*x)))/(h*(d*g-c*h))-F^(e+f*(a+b*x)/(c+d*x))/(h*(g+h*x))+(b*c-a*d)*f*F^(e+f*(b*g-a*h)/(d*g-c*h))*Ei(-(b*c-a*d)*f*(g+h*x)*log(F)/((d*g-c*h)*(c+d*x)))*log(F)/(d*g-c*h)^2],
[F^(e+f*(a+b*x)/(c+d*x))/(g+h*x)^3,x,24,1/2*d^2*F^(e+b*f/d-(b*c-a*d)*f/(d*(c+d*x)))/(h*(d*g-c*h)^2)-1/2*F^(e+f*(a+b*x)/(c+d*x))/(h*(g+h*x)^2)+1/2*d*(b*c-a*d)*f*F^(e+b*f/d-(b*c-a*d)*f/(d*(c+d*x)))*log(F)/(d*g-c*h)^3-1/2*(b*c-a*d)*f*F^(e+f*(a+b*x)/(c+d*x))*log(F)/((d*g-c*h)^2*(g+h*x))+d*(b*c-a*d)*f*F^(e+f*(b*g-a*h)/(d*g-c*h))*Ei(-(b*c-a*d)*f*(g+h*x)*log(F)/((d*g-c*h)*(c+d*x)))*log(F)/(d*g-c*h)^3+1/2*(b*c-a*d)^2*f^2*F^(e+f*(b*g-a*h)/(d*g-c*h))*h*Ei(-(b*c-a*d)*f*(g+h*x)*log(F)/((d*g-c*h)*(c+d*x)))*log(F)^2/(d*g-c*h)^4],
[F^(e+f*(a+b*x)/(c+d*x))/(g+h*x)^4,x,48,1/3*d^3*F^(e+b*f/d-(b*c-a*d)*f/(d*(c+d*x)))/(h*(d*g-c*h)^3)-1/3*F^(e+f*(a+b*x)/(c+d*x))/(h*(g+h*x)^3)+5/6*d^2*(b*c-a*d)*f*F^(e+b*f/d-(b*c-a*d)*f/(d*(c+d*x)))*log(F)/(d*g-c*h)^4-1/6*(b*c-a*d)*f*F^(e+f*(a+b*x)/(c+d*x))*log(F)/((d*g-c*h)^2*(g+h*x)^2)-2/3*d*(b*c-a*d)*f*F^(e+f*(a+b*x)/(c+d*x))*log(F)/((d*g-c*h)^3*(g+h*x))+d^2*(b*c-a*d)*f*F^(e+f*(b*g-a*h)/(d*g-c*h))*Ei(-(b*c-a*d)*f*(g+h*x)*log(F)/((d*g-c*h)*(c+d*x)))*log(F)/(d*g-c*h)^4+1/6*d*(b*c-a*d)^2*f^2*F^(e+b*f/d-(b*c-a*d)*f/(d*(c+d*x)))*h*log(F)^2/(d*g-c*h)^5-1/6*(b*c-a*d)^2*f^2*F^(e+f*(a+b*x)/(c+d*x))*h*log(F)^2/((d*g-c*h)^4*(g+h*x))+d*(b*c-a*d)^2*f^2*F^(e+f*(b*g-a*h)/(d*g-c*h))*h*Ei(-(b*c-a*d)*f*(g+h*x)*log(F)/((d*g-c*h)*(c+d*x)))*log(F)^2/(d*g-c*h)^5+1/6*(b*c-a*d)^3*f^3*F^(e+f*(b*g-a*h)/(d*g-c*h))*h^2*Ei(-(b*c-a*d)*f*(g+h*x)*log(F)/((d*g-c*h)*(c+d*x)))*log(F)^3/(d*g-c*h)^6],

# Integrands of the form x^m F^(a+b x+c x^2)
[f^(a+b*x+c*x^2)*x^3,x,10,-1/2*f^(a+b*x+c*x^2)/(c^2*log(f)^2)+1/8*b^2*f^(a+b*x+c*x^2)/(c^3*log(f))-1/4*b*f^(a+b*x+c*x^2)*x/(c^2*log(f))+1/2*f^(a+b*x+c*x^2)*x^2/(c*log(f))+3/8*b*f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(Pi)/(c^(5/2)*log(f)^(3/2))-1/16*b^3*f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(Pi)/(c^(7/2)*sqrt(log(f)))],
[f^(a+b*x+c*x^2)*x^2,x,6,-1/4*b*f^(a+b*x+c*x^2)/(c^2*log(f))+1/2*f^(a+b*x+c*x^2)*x/(c*log(f))-1/4*f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(Pi)/(c^(3/2)*log(f)^(3/2))+1/8*b^2*f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(Pi)/(c^(5/2)*sqrt(log(f)))],
[f^(a+b*x+c*x^2)*x,x,3,1/2*f^(a+b*x+c*x^2)/(c*log(f))-1/4*b*f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(Pi)/(c^(3/2)*sqrt(log(f)))],
[f^(a+b*x+c*x^2),x,2,1/2*f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(Pi)/(sqrt(c)*sqrt(log(f)))],
[f^(a+b*x+c*x^2)/x,x,0,Unintegrable(f^(a+b*x+c*x^2)/x,x)],
[f^(a+b*x+c*x^2)/x^2,x,3,-f^(a+b*x+c*x^2)/x+f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(c)*sqrt(Pi)*sqrt(log(f))+b*log(f)*Unintegrable(f^(a+b*x+c*x^2)/x,x)],
[exp(a+b*x-c*x^2)*x^3,x,10,-1/8*b^2*exp(a+b*x-c*x^2)/c^3-1/2*exp(a+b*x-c*x^2)/c^2-1/4*b*exp(a+b*x-c*x^2)*x/c^2-1/2*exp(a+b*x-c*x^2)*x^2/c-1/16*b^3*exp(a+1/4*b^2/c)*erf(1/2*(b-2*c*x)/sqrt(c))*sqrt(Pi)/c^(7/2)-3/8*b*exp(a+1/4*b^2/c)*erf(1/2*(b-2*c*x)/sqrt(c))*sqrt(Pi)/c^(5/2)],
[exp(a+b*x-c*x^2)*x^2,x,6,-1/4*b*exp(a+b*x-c*x^2)/c^2-1/2*exp(a+b*x-c*x^2)*x/c-1/8*b^2*exp(a+1/4*b^2/c)*erf(1/2*(b-2*c*x)/sqrt(c))*sqrt(Pi)/c^(5/2)-1/4*exp(a+1/4*b^2/c)*erf(1/2*(b-2*c*x)/sqrt(c))*sqrt(Pi)/c^(3/2)],
[exp(a+b*x-c*x^2)*x,x,3,-1/2*exp(a+b*x-c*x^2)/c-1/4*b*exp(a+1/4*b^2/c)*erf(1/2*(b-2*c*x)/sqrt(c))*sqrt(Pi)/c^(3/2)],
[exp(a+b*x-c*x^2),x,2,-1/2*exp(a+1/4*b^2/c)*erf(1/2*(b-2*c*x)/sqrt(c))*sqrt(Pi)/sqrt(c)],
[exp(a+b*x-c*x^2)/x,x,0,Unintegrable(exp(a+b*x-c*x^2)/x,x)],
[exp(a+b*x-c*x^2)/x^2,x,3,-exp(a+b*x-c*x^2)/x+exp(a+1/4*b^2/c)*erf(1/2*(b-2*c*x)/sqrt(c))*sqrt(c)*sqrt(Pi)+b*Unintegrable(exp(a+b*x-c*x^2)/x,x)],
[exp((a+b*x)*(c+d*x))*x^3,x,11,-1/2*exp(a*c+(b*c+a*d)*x+b*d*x^2)/(b^2*d^2)+1/8*(b*c+a*d)^2*exp(a*c+(b*c+a*d)*x+b*d*x^2)/(b^3*d^3)-1/4*(b*c+a*d)*exp(a*c+(b*c+a*d)*x+b*d*x^2)*x/(b^2*d^2)+1/2*exp(a*c+(b*c+a*d)*x+b*d*x^2)*x^2/(b*d)+3/8*(b*c+a*d)*erfi(1/2*(b*c+a*d+2*b*d*x)/(sqrt(b)*sqrt(d)))*sqrt(Pi)/(b^(5/2)*d^(5/2)*exp(1/4*(b*c-a*d)^2/(b*d)))-1/16*(b*c+a*d)^3*erfi(1/2*(b*c+a*d+2*b*d*x)/(sqrt(b)*sqrt(d)))*sqrt(Pi)/(b^(7/2)*d^(7/2)*exp(1/4*(b*c-a*d)^2/(b*d)))],
[exp((a+b*x)*(c+d*x))*x^2,x,7,-1/4*(b*c+a*d)*exp(a*c+(b*c+a*d)*x+b*d*x^2)/(b^2*d^2)+1/2*exp(a*c+(b*c+a*d)*x+b*d*x^2)*x/(b*d)-1/4*erfi(1/2*(b*c+a*d+2*b*d*x)/(sqrt(b)*sqrt(d)))*sqrt(Pi)/(b^(3/2)*d^(3/2)*exp(1/4*(b*c-a*d)^2/(b*d)))+1/8*(b*c+a*d)^2*erfi(1/2*(b*c+a*d+2*b*d*x)/(sqrt(b)*sqrt(d)))*sqrt(Pi)/(b^(5/2)*d^(5/2)*exp(1/4*(b*c-a*d)^2/(b*d)))],
[exp((a+b*x)*(c+d*x))*x,x,4,1/2*exp(a*c+(b*c+a*d)*x+b*d*x^2)/(b*d)-1/4*(b*c+a*d)*erfi(1/2*(b*c+a*d+2*b*d*x)/(sqrt(b)*sqrt(d)))*sqrt(Pi)/(b^(3/2)*d^(3/2)*exp(1/4*(b*c-a*d)^2/(b*d)))],
[exp((a+b*x)*(c+d*x)),x,3,1/2*erfi(1/2*(b*c+a*d+2*b*d*x)/(sqrt(b)*sqrt(d)))*sqrt(Pi)/(exp(1/4*(b*c-a*d)^2/(b*d))*sqrt(b)*sqrt(d))],
[exp((a+b*x)*(c+d*x))/x,x,1,Unintegrable(exp(a*c+(b*c+a*d)*x+b*d*x^2)/x,x)],
[exp((a+b*x)*(c+d*x))/x^2,x,4,-exp(a*c+(b*c+a*d)*x+b*d*x^2)/x+erfi(1/2*(b*c+a*d+2*b*d*x)/(sqrt(b)*sqrt(d)))*sqrt(b)*sqrt(d)*sqrt(Pi)/exp(1/4*(b*c-a*d)^2/(b*d))+(b*c+a*d)*Unintegrable(exp(a*c+(b*c+a*d)*x+b*d*x^2)/x,x)],

# Integrands of the form (d+e x)^m F^(a+b x+c x^2)
[f^(a+b*x+c*x^2)*(d+e*x)^3,x,10,-1/2*e^3*f^(a+b*x+c*x^2)/(c^2*log(f)^2)+1/8*e*(2*c*d-b*e)^2*f^(a+b*x+c*x^2)/(c^3*log(f))+1/4*e*(2*c*d-b*e)*f^(a+b*x+c*x^2)*(d+e*x)/(c^2*log(f))+1/2*e*f^(a+b*x+c*x^2)*(d+e*x)^2/(c*log(f))-3/8*e^2*(2*c*d-b*e)*f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(Pi)/(c^(5/2)*log(f)^(3/2))+1/16*(2*c*d-b*e)^3*f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(Pi)/(c^(7/2)*sqrt(log(f)))],
[f^(a+b*x+c*x^2)*(d+e*x)^2,x,6,1/4*e*(2*c*d-b*e)*f^(a+b*x+c*x^2)/(c^2*log(f))+1/2*e*f^(a+b*x+c*x^2)*(d+e*x)/(c*log(f))-1/4*e^2*f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(Pi)/(c^(3/2)*log(f)^(3/2))+1/8*(2*c*d-b*e)^2*f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(Pi)/(c^(5/2)*sqrt(log(f)))],
[f^(a+b*x+c*x^2)*(d+e*x),x,3,1/2*e*f^(a+b*x+c*x^2)/(c*log(f))+1/4*(2*c*d-b*e)*f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(Pi)/(c^(3/2)*sqrt(log(f)))],
[f^(a+b*x+c*x^2)/(d+e*x),x,0,Unintegrable(f^(a+b*x+c*x^2)/(d+e*x),x)],
[f^(a+b*x+c*x^2)/(d+e*x)^2,x,3,-f^(a+b*x+c*x^2)/(e*(d+e*x))+f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(c)*sqrt(Pi)*sqrt(log(f))/e^2-(2*c*d-b*e)*log(f)*Unintegrable(f^(a+b*x+c*x^2)/(d+e*x),x)/e^2],
[f^(a+b*x+c*x^2)/(d+e*x)^3,x,4,-1/2*f^(a+b*x+c*x^2)/(e*(d+e*x)^2)+1/2*(2*c*d-b*e)*f^(a+b*x+c*x^2)*log(f)/(e^3*(d+e*x))-1/2*(2*c*d-b*e)*f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*log(f)^(3/2)*sqrt(c)*sqrt(Pi)/e^4+c*log(f)*Unintegrable(f^(a+b*x+c*x^2)/(d+e*x),x)/e^2+1/2*(2*c*d-b*e)^2*log(f)^2*Unintegrable(f^(a+b*x+c*x^2)/(d+e*x),x)/e^4],
[f^(a+b*x+c*x^2)*(b+2*c*x)^3,x,2,-4*c*f^(a+b*x+c*x^2)/log(f)^2+f^(a+b*x+c*x^2)*(b+2*c*x)^2/log(f)],
[f^(a+b*x+c*x^2)*(b+2*c*x)^2,x,3,f^(a+b*x+c*x^2)*(b+2*c*x)/log(f)-f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(c)*sqrt(Pi)/log(f)^(3/2)],
[f^(a+b*x+c*x^2)*(b+2*c*x),x,1,f^(a+b*x+c*x^2)/log(f)],
[f^(a+b*x+c*x^2)/(b+2*c*x),x,1,1/4*f^(a-1/4*b^2/c)*Ei(1/4*(b+2*c*x)^2*log(f)/c)/c],
[f^(a+b*x+c*x^2)/(b+2*c*x)^2,x,3,-1/2*f^(a+b*x+c*x^2)/(c*(b+2*c*x))+1/4*f^(a-1/4*b^2/c)*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(Pi)*sqrt(log(f))/c^(3/2)],
[f^(a+b*x+c*x^2)/(b+2*c*x)^3,x,2,-1/4*f^(a+b*x+c*x^2)/(c*(b+2*c*x)^2)+1/16*f^(a-1/4*b^2/c)*Ei(1/4*(b+2*c*x)^2*log(f)/c)*log(f)/c^2],
[f^(b*x+c*x^2)*(b+2*c*x)^3,x,2,-4*c*f^(b*x+c*x^2)/log(f)^2+f^(b*x+c*x^2)*(b+2*c*x)^2/log(f)],
[f^(b*x+c*x^2)*(b+2*c*x)^2,x,3,f^(b*x+c*x^2)*(b+2*c*x)/log(f)-erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(c)*sqrt(Pi)/(f^(1/4*b^2/c)*log(f)^(3/2))],
[f^(b*x+c*x^2)*(b+2*c*x),x,1,f^(b*x+c*x^2)/log(f)],
[f^(b*x+c*x^2)/(b+2*c*x),x,1,1/4*Ei(1/4*(b+2*c*x)^2*log(f)/c)/(c*f^(1/4*b^2/c))],
[f^(b*x+c*x^2)/(b+2*c*x)^2,x,3,-1/2*f^(b*x+c*x^2)/(c*(b+2*c*x))+1/4*erfi(1/2*(b+2*c*x)*sqrt(log(f))/sqrt(c))*sqrt(Pi)*sqrt(log(f))/(c^(3/2)*f^(1/4*b^2/c))],
[f^(b*x+c*x^2)/(b+2*c*x)^3,x,2,-1/4*f^(b*x+c*x^2)/(c*(b+2*c*x)^2)+1/16*Ei(1/4*(b+2*c*x)^2*log(f)/c)*log(f)/(c^2*f^(1/4*b^2/c))],

# Integrands of the form x^m F^(d+e x)^n (a+b x+c x^2)^p
[exp(a+b*x)/(x^2*(c+d*x^2)),x,8,-exp(a+b*x)/(c*x)+b*exp(a)*Ei(b*x)/c+1/2*exp(a+b*sqrt(-c)/sqrt(d))*Ei(-b*(sqrt(-c)-x*sqrt(d))/sqrt(d))*sqrt(d)/(-c)^(3/2)-1/2*exp(a-b*sqrt(-c)/sqrt(d))*Ei(b*(sqrt(-c)+x*sqrt(d))/sqrt(d))*sqrt(d)/(-c)^(3/2)],
[exp(a+b*x)/(x*(c+d*x^2)),x,7,exp(a)*Ei(b*x)/c-1/2*exp(a+b*sqrt(-c)/sqrt(d))*Ei(-b*(sqrt(-c)-x*sqrt(d))/sqrt(d))/c-1/2*exp(a-b*sqrt(-c)/sqrt(d))*Ei(b*(sqrt(-c)+x*sqrt(d))/sqrt(d))/c],
[exp(a+b*x)/(c+d*x^2),x,4,1/2*exp(a+b*sqrt(-c)/sqrt(d))*Ei(-b*(sqrt(-c)-x*sqrt(d))/sqrt(d))/(sqrt(-c)*sqrt(d))-1/2*exp(a-b*sqrt(-c)/sqrt(d))*Ei(b*(sqrt(-c)+x*sqrt(d))/sqrt(d))/(sqrt(-c)*sqrt(d))],
[exp(a+b*x)*x/(c+d*x^2),x,4,1/2*exp(a+b*sqrt(-c)/sqrt(d))*Ei(-b*(sqrt(-c)-x*sqrt(d))/sqrt(d))/d+1/2*exp(a-b*sqrt(-c)/sqrt(d))*Ei(b*(sqrt(-c)+x*sqrt(d))/sqrt(d))/d],
[exp(a+b*x)*x^2/(c+d*x^2),x,7,exp(a+b*x)/(b*d)+1/2*exp(a+b*sqrt(-c)/sqrt(d))*Ei(-b*(sqrt(-c)-x*sqrt(d))/sqrt(d))*sqrt(-c)/d^(3/2)-1/2*exp(a-b*sqrt(-c)/sqrt(d))*Ei(b*(sqrt(-c)+x*sqrt(d))/sqrt(d))*sqrt(-c)/d^(3/2)],
[exp(d+e*x)/(x^2*(a+b*x+c*x^2)),x,9,-exp(d+e*x)/(a*x)-b*exp(d)*Ei(e*x)/a^2+e*exp(d)*Ei(e*x)/a+1/2*exp(d-1/2*e*(b+sqrt(b^2-4*a*c))/c)*Ei(1/2*e*(b+2*c*x+sqrt(b^2-4*a*c))/c)*(b+(-b^2+2*a*c)/sqrt(b^2-4*a*c))/a^2+1/2*exp(d-1/2*e*(b-sqrt(b^2-4*a*c))/c)*Ei(1/2*e*(b+2*c*x-sqrt(b^2-4*a*c))/c)*(b+(b^2-2*a*c)/sqrt(b^2-4*a*c))/a^2],
[exp(d+e*x)/(x*(a+b*x+c*x^2)),x,7,exp(d)*Ei(e*x)/a-1/2*exp(d-1/2*e*(b+sqrt(b^2-4*a*c))/c)*Ei(1/2*e*(b+2*c*x+sqrt(b^2-4*a*c))/c)*(1-b/sqrt(b^2-4*a*c))/a-1/2*exp(d-1/2*e*(b-sqrt(b^2-4*a*c))/c)*Ei(1/2*e*(b+2*c*x-sqrt(b^2-4*a*c))/c)*(1+b/sqrt(b^2-4*a*c))/a],
[exp(d+e*x)/(a+b*x+c*x^2),x,4,exp(d-1/2*e*(b-sqrt(b^2-4*a*c))/c)*Ei(1/2*e*(b+2*c*x-sqrt(b^2-4*a*c))/c)/sqrt(b^2-4*a*c)-exp(d-1/2*e*(b+sqrt(b^2-4*a*c))/c)*Ei(1/2*e*(b+2*c*x+sqrt(b^2-4*a*c))/c)/sqrt(b^2-4*a*c)],
[exp(d+e*x)*x/(a+b*x+c*x^2),x,4,1/2*exp(d-1/2*e*(b-sqrt(b^2-4*a*c))/c)*Ei(1/2*e*(b+2*c*x-sqrt(b^2-4*a*c))/c)*(1-b/sqrt(b^2-4*a*c))/c+1/2*exp(d-1/2*e*(b+sqrt(b^2-4*a*c))/c)*Ei(1/2*e*(b+2*c*x+sqrt(b^2-4*a*c))/c)*(1+b/sqrt(b^2-4*a*c))/c],
[exp(d+e*x)*x^2/(a+b*x+c*x^2),x,7,exp(d+e*x)/(c*e)-1/2*exp(d-1/2*e*(b-sqrt(b^2-4*a*c))/c)*Ei(1/2*e*(b+2*c*x-sqrt(b^2-4*a*c))/c)*(b+(-b^2+2*a*c)/sqrt(b^2-4*a*c))/c^2-1/2*exp(d-1/2*e*(b+sqrt(b^2-4*a*c))/c)*Ei(1/2*e*(b+2*c*x+sqrt(b^2-4*a*c))/c)*(b+(b^2-2*a*c)/sqrt(b^2-4*a*c))/c^2],
[exp(d+e*x)*x^3/(a+b*x+c*x^2),x,9,-exp(d+e*x)/(c*e^2)-b*exp(d+e*x)/(c^2*e)+exp(d+e*x)*x/(c*e)+1/2*exp(d-1/2*e*(b-sqrt(b^2-4*a*c))/c)*Ei(1/2*e*(b+2*c*x-sqrt(b^2-4*a*c))/c)*(b^2-a*c-b*(b^2-3*a*c)/sqrt(b^2-4*a*c))/c^3+1/2*exp(d-1/2*e*(b+sqrt(b^2-4*a*c))/c)*Ei(1/2*e*(b+2*c*x+sqrt(b^2-4*a*c))/c)*(b^2-a*c+b*(b^2-3*a*c)/sqrt(b^2-4*a*c))/c^3],

# Integrands of the form f^x / (a+b g^x)
[4^x/(a+2^x*b),x,3,2^x/(b*log(2))-a*log(a+2^x*b)/(b^2*log(2))],
[2^(2*x)/(a+2^x*b),x,3,2^x/(b*log(2))-a*log(a+2^x*b)/(b^2*log(2))],
[4^x/(a-2^x*b),x,3,-2^x/(b*log(2))-a*log(a-2^x*b)/(b^2*log(2))],
[2^(2*x)/(a-2^x*b),x,3,-2^x/(b*log(2))-a*log(a-2^x*b)/(b^2*log(2))],
[4^x/(a+b/2^x),x,3,b^2*x/a^3+2^(-1+2*x)/(a*log(2))-2^x*b/(a^2*log(2))+b^2*log(a+b/2^x)/(a^3*log(2))],
[2^(2*x)/(a+b/2^x),x,3,b^2*x/a^3+2^(-1+2*x)/(a*log(2))-2^x*b/(a^2*log(2))+b^2*log(a+b/2^x)/(a^3*log(2))],
[4^x/(a-b/2^x),x,3,b^2*x/a^3+2^(-1+2*x)/(a*log(2))+2^x*b/(a^2*log(2))+b^2*log(a-b/2^x)/(a^3*log(2))],
[2^(2*x)/(a-b/2^x),x,3,b^2*x/a^3+2^(-1+2*x)/(a*log(2))+2^x*b/(a^2*log(2))+b^2*log(a-b/2^x)/(a^3*log(2))],
[2^x/(a+4^x*b),x,2,arctan(2^x*sqrt(b)/sqrt(a))/(log(2)*sqrt(a)*sqrt(b))],
[2^x/(a+2^(2*x)*b),x,2,arctan(2^x*sqrt(b)/sqrt(a))/(log(2)*sqrt(a)*sqrt(b))],
[2^x/(a-4^x*b),x,2,arctanh(2^x*sqrt(b)/sqrt(a))/(log(2)*sqrt(a)*sqrt(b))],
[2^x/(a-2^(2*x)*b),x,2,arctanh(2^x*sqrt(b)/sqrt(a))/(log(2)*sqrt(a)*sqrt(b))],
[2^x/(a+b/4^x),x,4,2^x/(a*log(2))-arctan(2^x*sqrt(a)/sqrt(b))*sqrt(b)/(a^(3/2)*log(2))],
[2^x/(a+b/2^(2*x)),x,4,2^x/(a*log(2))-arctan(2^x*sqrt(a)/sqrt(b))*sqrt(b)/(a^(3/2)*log(2))],
[2^x/(a-b/4^x),x,4,2^x/(a*log(2))-arctanh(2^x*sqrt(a)/sqrt(b))*sqrt(b)/(a^(3/2)*log(2))],
[2^x/(a-b/2^(2*x)),x,4,2^x/(a*log(2))-arctanh(2^x*sqrt(a)/sqrt(b))*sqrt(b)/(a^(3/2)*log(2))],

# Integrands of the form f^x / Sqrt[a+b g^x]

#  Contributed by Robert Israel in sci.math.symbolic 
[2^x/sqrt(a+4^x*b),x,3,arctanh(2^x*sqrt(b)/sqrt(a+4^x*b))/(log(2)*sqrt(b))],
[2^x/sqrt(a+2^(2*x)*b),x,3,arctanh(2^x*sqrt(b)/sqrt(a+4^x*b))/(log(2)*sqrt(b))],
[2^x/sqrt(a-4^x*b),x,3,arctan(2^x*sqrt(b)/sqrt(a-4^x*b))/(log(2)*sqrt(b))],
[2^x/sqrt(a-2^(2*x)*b),x,3,arctan(2^x*sqrt(b)/sqrt(a-4^x*b))/(log(2)*sqrt(b))],
[2^x/sqrt(a+b/4^x),x,2,2^x*sqrt(a+b/2^(2*x))/(a*log(2))],
[2^x/sqrt(a+b/2^(2*x)),x,2,2^x*sqrt(a+b/2^(2*x))/(a*log(2))],
[2^x/sqrt(a-b/4^x),x,2,2^x*sqrt(a-b/2^(2*x))/(a*log(2))],
[2^x/sqrt(a-b/2^(2*x)),x,2,2^x*sqrt(a-b/2^(2*x))/(a*log(2))],
[4^x/sqrt(a+2^x*b),x,3,2/3*(a+2^x*b)^(3/2)/(b^2*log(2))-2*a*sqrt(a+2^x*b)/(b^2*log(2))],
[2^(2*x)/sqrt(a+2^x*b),x,3,2/3*(a+2^x*b)^(3/2)/(b^2*log(2))-2*a*sqrt(a+2^x*b)/(b^2*log(2))],
[4^x/sqrt(a-2^x*b),x,3,2/3*(a-2^x*b)^(3/2)/(b^2*log(2))-2*a*sqrt(a-2^x*b)/(b^2*log(2))],
[2^(2*x)/sqrt(a-2^x*b),x,3,2/3*(a-2^x*b)^(3/2)/(b^2*log(2))-2*a*sqrt(a-2^x*b)/(b^2*log(2))],
[4^x/sqrt(a+b/2^x),x,5,3/4*b^2*arctanh(sqrt(a+b/2^x)/sqrt(a))/(a^(5/2)*log(2))+2^(-1+2*x)*sqrt(a+b/2^x)/(a*log(2))-3*2^(-2+x)*b*sqrt(a+b/2^x)/(a^2*log(2))],
[2^(2*x)/sqrt(a+b/2^x),x,5,3/4*b^2*arctanh(sqrt(a+b/2^x)/sqrt(a))/(a^(5/2)*log(2))+2^(-1+2*x)*sqrt(a+b/2^x)/(a*log(2))-3*2^(-2+x)*b*sqrt(a+b/2^x)/(a^2*log(2))],
[4^x/sqrt(a-b/2^x),x,5,3/4*b^2*arctanh(sqrt(a-b/2^x)/sqrt(a))/(a^(5/2)*log(2))+2^(-1+2*x)*sqrt(a-b/2^x)/(a*log(2))+3*2^(-2+x)*b*sqrt(a-b/2^x)/(a^2*log(2))],
[2^(2*x)/sqrt(a-b/2^x),x,5,3/4*b^2*arctanh(sqrt(a-b/2^x)/sqrt(a))/(a^(5/2)*log(2))+2^(-1+2*x)*sqrt(a-b/2^x)/(a*log(2))+3*2^(-2+x)*b*sqrt(a-b/2^x)/(a^2*log(2))],

# Integrands of the form x^m (a+b f^(d+e x)+c f^(2 (d+e x)))^n
[1/(1+2*exp(x)+exp(2*x)),x,3,1/(1+exp(x))+x-log(1+exp(x))],
[1/(2+3*exp(x)+exp(2*x)),x,6,1/2*x-log(1+exp(x))+1/2*log(2+exp(x))],
[1/(-1+exp(x)+exp(2*x)),x,6,-x+1/10*log(1+2*exp(x)+sqrt(5))*(5-sqrt(5))+1/10*log(1+2*exp(x)-sqrt(5))*(5+sqrt(5))],
[1/(3+3*exp(x)+exp(2*x)),x,7,1/3*x-1/6*log(3+3*exp(x)+exp(2*x))-arctan((3+2*exp(x))/sqrt(3))/sqrt(3)],
[1/(a+b*exp(x)+c*exp(2*x)),x,7,x/a-1/2*log(a+b*exp(x)+c*exp(2*x))/a+b*arctanh((b+2*c*exp(x))/sqrt(b^2-4*a*c))/(a*sqrt(b^2-4*a*c))],
[x/(1+2*exp(x)+exp(2*x)),x,11,-x+x/(1+exp(x))+1/2*x^2+log(1+exp(x))-x*log(1+exp(x))-polylog(2,-exp(x))],
[x/(2+3*exp(x)+exp(2*x)),x,9,1/4*x^2+1/2*x*log(1+1/2*exp(x))-x*log(1+exp(x))-polylog(2,-exp(x))+1/2*polylog(2,-1/2*exp(x))],
[x/(-1+exp(x)+exp(2*x)),x,9,x^2/((1-sqrt(5))*sqrt(5))-2*x*log(1+2*exp(x)/(1-sqrt(5)))/((1-sqrt(5))*sqrt(5))-2*polylog(2,-2*exp(x)/(1-sqrt(5)))/((1-sqrt(5))*sqrt(5))-x^2/(sqrt(5)*(1+sqrt(5)))+2*x*log(1+2*exp(x)/(1+sqrt(5)))/(sqrt(5)*(1+sqrt(5)))+2*polylog(2,-2*exp(x)/(1+sqrt(5)))/(sqrt(5)*(1+sqrt(5)))],
[x/(3+3*exp(x)+exp(2*x)),x,9,-x^2/((3*I-sqrt(3))*sqrt(3))+2*x*log(1+2*exp(x)/(3+I*sqrt(3)))/((3*I-sqrt(3))*sqrt(3))+2*polylog(2,-2*exp(x)/(3+I*sqrt(3)))/((3*I-sqrt(3))*sqrt(3))+x^2/(sqrt(3)*(3*I+sqrt(3)))-2*x*log(1+2*exp(x)/(3-I*sqrt(3)))/(sqrt(3)*(3*I+sqrt(3)))-2*polylog(2,-2*exp(x)/(3-I*sqrt(3)))/(sqrt(3)*(3*I+sqrt(3)))],
[x/(a+b*exp(x)+c*exp(2*x)),x,9,-c*x^2/(b^2-4*a*c-b*sqrt(b^2-4*a*c))+2*c*x*log(1+2*c*exp(x)/(b-sqrt(b^2-4*a*c)))/(b^2-4*a*c-b*sqrt(b^2-4*a*c))+2*c*polylog(2,-2*c*exp(x)/(b-sqrt(b^2-4*a*c)))/(b^2-4*a*c-b*sqrt(b^2-4*a*c))-c*x^2/(b^2-4*a*c+b*sqrt(b^2-4*a*c))+2*c*x*log(1+2*c*exp(x)/(b+sqrt(b^2-4*a*c)))/(b^2-4*a*c+b*sqrt(b^2-4*a*c))+2*c*polylog(2,-2*c*exp(x)/(b+sqrt(b^2-4*a*c)))/(b^2-4*a*c+b*sqrt(b^2-4*a*c))],
[x^2/(1+2*exp(x)+exp(2*x)),x,12,-x^2+x^2/(1+exp(x))+1/3*x^3+2*x*log(1+exp(x))-x^2*log(1+exp(x))+2*polylog(2,-exp(x))-2*x*polylog(2,-exp(x))+2*polylog(3,-exp(x))],
[x^2/(2+3*exp(x)+exp(2*x)),x,11,1/6*x^3+1/2*x^2*log(1+1/2*exp(x))-x^2*log(1+exp(x))-2*x*polylog(2,-exp(x))+x*polylog(2,-1/2*exp(x))+2*polylog(3,-exp(x))-polylog(3,-1/2*exp(x))],
[x^2/(-1+exp(x)+exp(2*x)),x,11,2/3*x^3/((1-sqrt(5))*sqrt(5))-2*x^2*log(1+2*exp(x)/(1-sqrt(5)))/((1-sqrt(5))*sqrt(5))-4*x*polylog(2,-2*exp(x)/(1-sqrt(5)))/((1-sqrt(5))*sqrt(5))+4*polylog(3,-2*exp(x)/(1-sqrt(5)))/((1-sqrt(5))*sqrt(5))-2/3*x^3/(sqrt(5)*(1+sqrt(5)))+2*x^2*log(1+2*exp(x)/(1+sqrt(5)))/(sqrt(5)*(1+sqrt(5)))+4*x*polylog(2,-2*exp(x)/(1+sqrt(5)))/(sqrt(5)*(1+sqrt(5)))-4*polylog(3,-2*exp(x)/(1+sqrt(5)))/(sqrt(5)*(1+sqrt(5)))],
[x^2/(3+3*exp(x)+exp(2*x)),x,11,-2/3*x^3/((3*I-sqrt(3))*sqrt(3))+2*x^2*log(1+2*exp(x)/(3+I*sqrt(3)))/((3*I-sqrt(3))*sqrt(3))+4*x*polylog(2,-2*exp(x)/(3+I*sqrt(3)))/((3*I-sqrt(3))*sqrt(3))-4*polylog(3,-2*exp(x)/(3+I*sqrt(3)))/((3*I-sqrt(3))*sqrt(3))+2/3*x^3/(sqrt(3)*(3*I+sqrt(3)))-2*x^2*log(1+2*exp(x)/(3-I*sqrt(3)))/(sqrt(3)*(3*I+sqrt(3)))-4*x*polylog(2,-2*exp(x)/(3-I*sqrt(3)))/(sqrt(3)*(3*I+sqrt(3)))+4*polylog(3,-2*exp(x)/(3-I*sqrt(3)))/(sqrt(3)*(3*I+sqrt(3)))],
[x^2/(a+b*exp(x)+c*exp(2*x)),x,11,-2/3*c*x^3/(b^2-4*a*c-b*sqrt(b^2-4*a*c))+2*c*x^2*log(1+2*c*exp(x)/(b-sqrt(b^2-4*a*c)))/(b^2-4*a*c-b*sqrt(b^2-4*a*c))+4*c*x*polylog(2,-2*c*exp(x)/(b-sqrt(b^2-4*a*c)))/(b^2-4*a*c-b*sqrt(b^2-4*a*c))-4*c*polylog(3,-2*c*exp(x)/(b-sqrt(b^2-4*a*c)))/(b^2-4*a*c-b*sqrt(b^2-4*a*c))-2/3*c*x^3/(b^2-4*a*c+b*sqrt(b^2-4*a*c))+2*c*x^2*log(1+2*c*exp(x)/(b+sqrt(b^2-4*a*c)))/(b^2-4*a*c+b*sqrt(b^2-4*a*c))+4*c*x*polylog(2,-2*c*exp(x)/(b+sqrt(b^2-4*a*c)))/(b^2-4*a*c+b*sqrt(b^2-4*a*c))-4*c*polylog(3,-2*c*exp(x)/(b+sqrt(b^2-4*a*c)))/(b^2-4*a*c+b*sqrt(b^2-4*a*c))],
[1/(1+2*f^(c+d*x)+f^(2*c+2*d*x)),x,3,x+1/(d*(1+f^(c+d*x))*log(f))-log(1+f^(c+d*x))/(d*log(f))],
[1/(a+b*f^(c+d*x)+c*f^(2*c+2*d*x)),x,7,x/a-1/2*log(a+b*f^(c+d*x)+c*f^(2*c+2*d*x))/(a*d*log(f))+b*arctanh((b+2*c*f^(c+d*x))/sqrt(b^2-4*a*c))/(a*d*log(f)*sqrt(b^2-4*a*c))],
[1/(a+b*f^(g+h*x)+c*f^(2*(g+h*x))),x,7,x/a-1/2*log(a+b*f^(g+h*x)+c*f^(2*g+2*h*x))/(a*h*log(f))+b*arctanh((b+2*c*f^(g+h*x))/sqrt(b^2-4*a*c))/(a*h*log(f)*sqrt(b^2-4*a*c))],
[x/(1+2*f^(c+d*x)+f^(2*c+2*d*x)),x,11,1/2*x^2-x/(d*log(f))+x/(d*(1+f^(c+d*x))*log(f))+log(1+f^(c+d*x))/(d^2*log(f)^2)-x*log(1+f^(c+d*x))/(d*log(f))-polylog(2,-f^(c+d*x))/(d^2*log(f)^2)],
[x/(a+b*f^(c+d*x)+c*f^(2*c+2*d*x)),x,9,-2*c*x*log(1+2*c*f^(c+d*x)/(b-sqrt(b^2-4*a*c)))/(d*log(f)*(b-sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c))-2*c*polylog(2,-2*c*f^(c+d*x)/(b-sqrt(b^2-4*a*c)))/(d^2*log(f)^2*(b-sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c))+2*c*x*log(1+2*c*f^(c+d*x)/(b+sqrt(b^2-4*a*c)))/(d*log(f)*sqrt(b^2-4*a*c)*(b+sqrt(b^2-4*a*c)))+2*c*polylog(2,-2*c*f^(c+d*x)/(b+sqrt(b^2-4*a*c)))/(d^2*log(f)^2*sqrt(b^2-4*a*c)*(b+sqrt(b^2-4*a*c)))-c*x^2/(b^2-4*a*c-b*sqrt(b^2-4*a*c))-c*x^2/(b^2-4*a*c+b*sqrt(b^2-4*a*c))],
[x^2/(1+2*f^(c+d*x)+f^(2*c+2*d*x)),x,12,1/3*x^3-x^2/(d*log(f))+x^2/(d*(1+f^(c+d*x))*log(f))+2*x*log(1+f^(c+d*x))/(d^2*log(f)^2)-x^2*log(1+f^(c+d*x))/(d*log(f))+2*polylog(2,-f^(c+d*x))/(d^3*log(f)^3)-2*x*polylog(2,-f^(c+d*x))/(d^2*log(f)^2)+2*polylog(3,-f^(c+d*x))/(d^3*log(f)^3)],
[x^2/(a+b*f^(c+d*x)+c*f^(2*c+2*d*x)),x,11,-2*c*x^2*log(1+2*c*f^(c+d*x)/(b-sqrt(b^2-4*a*c)))/(d*log(f)*(b-sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c))-4*c*x*polylog(2,-2*c*f^(c+d*x)/(b-sqrt(b^2-4*a*c)))/(d^2*log(f)^2*(b-sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c))+4*c*polylog(3,-2*c*f^(c+d*x)/(b-sqrt(b^2-4*a*c)))/(d^3*log(f)^3*(b-sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c))+2*c*x^2*log(1+2*c*f^(c+d*x)/(b+sqrt(b^2-4*a*c)))/(d*log(f)*sqrt(b^2-4*a*c)*(b+sqrt(b^2-4*a*c)))+4*c*x*polylog(2,-2*c*f^(c+d*x)/(b+sqrt(b^2-4*a*c)))/(d^2*log(f)^2*sqrt(b^2-4*a*c)*(b+sqrt(b^2-4*a*c)))-4*c*polylog(3,-2*c*f^(c+d*x)/(b+sqrt(b^2-4*a*c)))/(d^3*log(f)^3*sqrt(b^2-4*a*c)*(b+sqrt(b^2-4*a*c)))-2/3*c*x^3/(b^2-4*a*c-b*sqrt(b^2-4*a*c))-2/3*c*x^3/(b^2-4*a*c+b*sqrt(b^2-4*a*c))],
[(d+e*f^(g+h*x))/(a+b*f^(g+h*x)+c*f^(2*g+2*h*x)),x,7,d*x/a-1/2*d*log(a+b*f^(g+h*x)+c*f^(2*g+2*h*x))/(a*h*log(f))+(b*d-2*a*e)*arctanh((b+2*c*f^(g+h*x))/sqrt(b^2-4*a*c))/(a*h*log(f)*sqrt(b^2-4*a*c))],
[(d+e*f^(g+h*x))/(a+b*f^(g+h*x)+c*f^(2*(g+h*x))),x,7,d*x/a-1/2*d*log(a+b*f^(g+h*x)+c*f^(2*g+2*h*x))/(a*h*log(f))+(b*d-2*a*e)*arctanh((b+2*c*f^(g+h*x))/sqrt(b^2-4*a*c))/(a*h*log(f)*sqrt(b^2-4*a*c))],
[1/(2+exp(-x)+exp(x)),x,2,(-1)/(1+exp(x))],
[x/(2+exp(-x)+exp(x)),x,7,x-x/(1+exp(x))-log(1+exp(x))],
[x^2/(2+exp(-x)+exp(x)),x,7,x^2-x^2/(1+exp(x))-2*x*log(1+exp(x))-2*polylog(2,-exp(x))],
[1/(2+f^(-c-d*x)+f^(c+d*x)),x,2,(-1)/(d*(1+f^(c+d*x))*log(f))],
[x/(2+f^(-c-d*x)+f^(c+d*x)),x,7,x/(d*log(f))-x/(d*(1+f^(c+d*x))*log(f))-log(1+f^(c+d*x))/(d^2*log(f)^2)],
[x^2/(2+f^(-c-d*x)+f^(c+d*x)),x,7,x^2/(d*log(f))-x^2/(d*(1+f^(c+d*x))*log(f))-2*x*log(1+f^(c+d*x))/(d^2*log(f)^2)-2*polylog(2,-f^(c+d*x))/(d^3*log(f)^3)],
[1/(2+1/3^x+3^x),x,2,(-1)/((1+3^x)*log(3))],
[1/(1+(-1)/exp(x)+2*exp(x)),x,4,1/3*log(1-2*exp(x))-1/3*log(1+exp(x))],
[1/(a+b/exp(x)+c*exp(x)),x,4,-2*arctanh((a+2*c*exp(x))/sqrt(a^2-4*b*c))/sqrt(a^2-4*b*c)],
[x/(a+b/exp(x)+c*exp(x)),x,8,x*log(1+2*c*exp(x)/(a-sqrt(a^2-4*b*c)))/sqrt(a^2-4*b*c)-x*log(1+2*c*exp(x)/(a+sqrt(a^2-4*b*c)))/sqrt(a^2-4*b*c)+polylog(2,-2*c*exp(x)/(a-sqrt(a^2-4*b*c)))/sqrt(a^2-4*b*c)-polylog(2,-2*c*exp(x)/(a+sqrt(a^2-4*b*c)))/sqrt(a^2-4*b*c)],
[x^2/(a+b/exp(x)+c*exp(x)),x,10,x^2*log(1+2*c*exp(x)/(a-sqrt(a^2-4*b*c)))/sqrt(a^2-4*b*c)-x^2*log(1+2*c*exp(x)/(a+sqrt(a^2-4*b*c)))/sqrt(a^2-4*b*c)+2*x*polylog(2,-2*c*exp(x)/(a-sqrt(a^2-4*b*c)))/sqrt(a^2-4*b*c)-2*x*polylog(2,-2*c*exp(x)/(a+sqrt(a^2-4*b*c)))/sqrt(a^2-4*b*c)-2*polylog(3,-2*c*exp(x)/(a-sqrt(a^2-4*b*c)))/sqrt(a^2-4*b*c)+2*polylog(3,-2*c*exp(x)/(a+sqrt(a^2-4*b*c)))/sqrt(a^2-4*b*c)],
[1/(a+b*f^(-c-d*x)+c*f^(c+d*x)),x,4,-2*arctanh((a+2*c*f^(c+d*x))/sqrt(a^2-4*b*c))/(d*log(f)*sqrt(a^2-4*b*c))],
[x/(a+b*f^(-c-d*x)+c*f^(c+d*x)),x,8,x*log(1+2*c*f^(c+d*x)/(a-sqrt(a^2-4*b*c)))/(d*log(f)*sqrt(a^2-4*b*c))-x*log(1+2*c*f^(c+d*x)/(a+sqrt(a^2-4*b*c)))/(d*log(f)*sqrt(a^2-4*b*c))+polylog(2,-2*c*f^(c+d*x)/(a-sqrt(a^2-4*b*c)))/(d^2*log(f)^2*sqrt(a^2-4*b*c))-polylog(2,-2*c*f^(c+d*x)/(a+sqrt(a^2-4*b*c)))/(d^2*log(f)^2*sqrt(a^2-4*b*c))],
[x^2/(a+b*f^(-c-d*x)+c*f^(c+d*x)),x,10,x^2*log(1+2*c*f^(c+d*x)/(a-sqrt(a^2-4*b*c)))/(d*log(f)*sqrt(a^2-4*b*c))-x^2*log(1+2*c*f^(c+d*x)/(a+sqrt(a^2-4*b*c)))/(d*log(f)*sqrt(a^2-4*b*c))+2*x*polylog(2,-2*c*f^(c+d*x)/(a-sqrt(a^2-4*b*c)))/(d^2*log(f)^2*sqrt(a^2-4*b*c))-2*x*polylog(2,-2*c*f^(c+d*x)/(a+sqrt(a^2-4*b*c)))/(d^2*log(f)^2*sqrt(a^2-4*b*c))-2*polylog(3,-2*c*f^(c+d*x)/(a-sqrt(a^2-4*b*c)))/(d^3*log(f)^3*sqrt(a^2-4*b*c))+2*polylog(3,-2*c*f^(c+d*x)/(a+sqrt(a^2-4*b*c)))/(d^3*log(f)^3*sqrt(a^2-4*b*c))],

# Integrands of the form u^m (a+b F^(c Sqrt[d+e x]/Sqrt[f+g x]))^n
[(a+b*F^(c*sqrt(d+e*x)/sqrt(f+g*x)))^n/(d*f+(e*f+d*g)*x+e*g*x^2),x,0,Unintegrable((a+b*F^(c*sqrt(d+e*x)/sqrt(f+g*x)))^n/(d*f+(e*f+d*g)*x+e*g*x^2),x)],
[(a+b*F^(c*sqrt(d+e*x)/sqrt(f+g*x)))^3/(d*f+(e*f+d*g)*x+e*g*x^2),x,6,6*a^2*b*Ei(c*log(F)*sqrt(d+e*x)/sqrt(f+g*x))/(e*f-d*g)+6*a*b^2*Ei(2*c*log(F)*sqrt(d+e*x)/sqrt(f+g*x))/(e*f-d*g)+2*b^3*Ei(3*c*log(F)*sqrt(d+e*x)/sqrt(f+g*x))/(e*f-d*g)+2*a^3*log(sqrt(d+e*x)/sqrt(f+g*x))/(e*f-d*g)],
[(a+b*F^(c*sqrt(d+e*x)/sqrt(f+g*x)))^2/(d*f+(e*f+d*g)*x+e*g*x^2),x,5,4*a*b*Ei(c*log(F)*sqrt(d+e*x)/sqrt(f+g*x))/(e*f-d*g)+2*b^2*Ei(2*c*log(F)*sqrt(d+e*x)/sqrt(f+g*x))/(e*f-d*g)+2*a^2*log(sqrt(d+e*x)/sqrt(f+g*x))/(e*f-d*g)],
[(a+b*F^(c*sqrt(d+e*x)/sqrt(f+g*x)))/(d*f+(e*f+d*g)*x+e*g*x^2),x,4,2*b*Ei(c*log(F)*sqrt(d+e*x)/sqrt(f+g*x))/(e*f-d*g)+2*a*log(sqrt(d+e*x)/sqrt(f+g*x))/(e*f-d*g)],
[1/(d*f+(e*f+d*g)*x+e*g*x^2),x,3,log(d+e*x)/(e*f-d*g)-log(f+g*x)/(e*f-d*g)],
[1/((a+b*F^(c*sqrt(d+e*x)/sqrt(f+g*x)))*(d*f+(e*f+d*g)*x+e*g*x^2)),x,0,Unintegrable(1/((a+b*F^(c*sqrt(d+e*x)/sqrt(f+g*x)))*(d*f+(e*f+d*g)*x+e*g*x^2)),x)],
[1/((a+b*F^(c*sqrt(d+e*x)/sqrt(f+g*x)))^2*(d*f+(e*f+d*g)*x+e*g*x^2)),x,0,Unintegrable(1/((a+b*F^(c*sqrt(d+e*x)/sqrt(f+g*x)))^2*(d*f+(e*f+d*g)*x+e*g*x^2)),x)],
[(a+b*F^(c*sqrt(d+e*x)/sqrt(d*f-e*f*x)))^n/(d^2-e^2*x^2),x,0,Unintegrable((a+b*F^(c*sqrt(d+e*x)/sqrt(d*f-e*f*x)))^n/(d^2-e^2*x^2),x)],
[(a+b*F^(c*sqrt(d+e*x)/sqrt(d*f-e*f*x)))^3/(d^2-e^2*x^2),x,6,3*a^2*b*Ei(c*log(F)*sqrt(d+e*x)/sqrt(d*f-e*f*x))/(d*e)+3*a*b^2*Ei(2*c*log(F)*sqrt(d+e*x)/sqrt(d*f-e*f*x))/(d*e)+b^3*Ei(3*c*log(F)*sqrt(d+e*x)/sqrt(d*f-e*f*x))/(d*e)+a^3*log(sqrt(d+e*x)/sqrt(d*f-e*f*x))/(d*e)],
[(a+b*F^(c*sqrt(d+e*x)/sqrt(d*f-e*f*x)))^2/(d^2-e^2*x^2),x,5,2*a*b*Ei(c*log(F)*sqrt(d+e*x)/sqrt(d*f-e*f*x))/(d*e)+b^2*Ei(2*c*log(F)*sqrt(d+e*x)/sqrt(d*f-e*f*x))/(d*e)+a^2*log(sqrt(d+e*x)/sqrt(d*f-e*f*x))/(d*e)],
[(a+b*F^(c*sqrt(d+e*x)/sqrt(d*f-e*f*x)))/(d^2-e^2*x^2),x,4,b*Ei(c*log(F)*sqrt(d+e*x)/sqrt(d*f-e*f*x))/(d*e)+a*log(sqrt(d+e*x)/sqrt(d*f-e*f*x))/(d*e)],
[1/(d^2-e^2*x^2),x,1,arctanh(e*x/d)/(d*e)],
[1/((a+b*F^(c*sqrt(d+e*x)/sqrt(d*f-e*f*x)))*(d^2-e^2*x^2)),x,0,Unintegrable(1/((a+b*F^(c*sqrt(d+e*x)/sqrt(d*f-e*f*x)))*(d^2-e^2*x^2)),x)],
[1/((a+b*F^(c*sqrt(d+e*x)/sqrt(d*f-e*f*x)))^2*(d^2-e^2*x^2)),x,0,Unintegrable(1/((a+b*F^(c*sqrt(d+e*x)/sqrt(d*f-e*f*x)))^2*(d^2-e^2*x^2)),x)],
[(F^(sqrt(1-a*x)/sqrt(1+a*x)))^n/(1-a^2*x^2),x,3,-(F^(sqrt(1-a*x)/sqrt(1+a*x)))^n*Ei(n*log(F)*sqrt(1-a*x)/sqrt(1+a*x))/(a*F^(n*sqrt(1-a*x)/sqrt(1+a*x)))],
[F^(3*sqrt(1-a*x)/sqrt(1+a*x))/(1-a^2*x^2),x,2,-Ei(3*log(F)*sqrt(1-a*x)/sqrt(1+a*x))/a],
[F^(2*sqrt(1-a*x)/sqrt(1+a*x))/(1-a^2*x^2),x,2,-Ei(2*log(F)*sqrt(1-a*x)/sqrt(1+a*x))/a],
[F^(sqrt(1-a*x)/sqrt(1+a*x))/(1-a^2*x^2),x,2,-Ei(log(F)*sqrt(1-a*x)/sqrt(1+a*x))/a],
[1/(F^(sqrt(1-a*x)/sqrt(1+a*x))*(1-a^2*x^2)),x,2,-Ei(-log(F)*sqrt(1-a*x)/sqrt(1+a*x))/a],
[1/(F^(2*sqrt(1-a*x)/sqrt(1+a*x))*(1-a^2*x^2)),x,2,-Ei(-2*log(F)*sqrt(1-a*x)/sqrt(1+a*x))/a],

# Integrands of the form x^m F^(a+b x) G^(c+d x)
[a^x*b^x*x^2,x,4,2*a^x*b^x/(log(a)+log(b))^3-2*a^x*b^x*x/(log(a)+log(b))^2+a^x*b^x*x^2/(log(a)+log(b))],
[a^x*b^x*x,x,3,-a^x*b^x/(log(a)+log(b))^2+a^x*b^x*x/(log(a)+log(b))],
[a^x*b^x,x,2,a^x*b^x/(log(a)+log(b))],
[a^x*b^x/x,x,2,Ei(x*(log(a)+log(b)))],
[a^x*b^x/x^2,x,3,-a^x*b^x/x+Ei(x*(log(a)+log(b)))*(log(a)+log(b))],
[a^x*b^x/x^3,x,4,-1/2*a^x*b^x/x^2-1/2*a^x*b^x*(log(a)+log(b))/x+1/2*Ei(x*(log(a)+log(b)))*(log(a)+log(b))^2],
[a^x*b^x*c^x,x,3,a^x*b^x*c^x/(log(a)+log(b)+log(c))],
[a^x/b^x,x,2,a^x/(b^x*(log(a)-log(b)))],
[a^x*x^2/b^x,x,4,2*a^x/(b^x*(log(a)-log(b))^3)-2*a^x*x/(b^x*(log(a)-log(b))^2)+a^x*x^2/(b^x*(log(a)-log(b)))],

# Integrands of the form (f+g x)^m (d+e F^(h+i x)) (a+b F^(h+i x)+c F^(2 h+2 i x))^n
[(d+e*exp(h+i*x))*(f+g*x)^3/(a+b*exp(h+i*x)+c*exp(2*h+2*i*x)),x,13,1/4*(f+g*x)^4*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(g*(b-sqrt(b^2-4*a*c)))-(f+g*x)^3*log(1+2*c*exp(h+i*x)/(b-sqrt(b^2-4*a*c)))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(i*(b-sqrt(b^2-4*a*c)))-3*g*(f+g*x)^2*polylog(2,-2*c*exp(h+i*x)/(b-sqrt(b^2-4*a*c)))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(i^2*(b-sqrt(b^2-4*a*c)))+6*g^2*(f+g*x)*polylog(3,-2*c*exp(h+i*x)/(b-sqrt(b^2-4*a*c)))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(i^3*(b-sqrt(b^2-4*a*c)))-6*g^3*polylog(4,-2*c*exp(h+i*x)/(b-sqrt(b^2-4*a*c)))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(i^4*(b-sqrt(b^2-4*a*c)))+1/4*(f+g*x)^4*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(g*(b+sqrt(b^2-4*a*c)))-(f+g*x)^3*log(1+2*c*exp(h+i*x)/(b+sqrt(b^2-4*a*c)))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(i*(b+sqrt(b^2-4*a*c)))-3*g*(f+g*x)^2*polylog(2,-2*c*exp(h+i*x)/(b+sqrt(b^2-4*a*c)))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(i^2*(b+sqrt(b^2-4*a*c)))+6*g^2*(f+g*x)*polylog(3,-2*c*exp(h+i*x)/(b+sqrt(b^2-4*a*c)))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(i^3*(b+sqrt(b^2-4*a*c)))-6*g^3*polylog(4,-2*c*exp(h+i*x)/(b+sqrt(b^2-4*a*c)))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(i^4*(b+sqrt(b^2-4*a*c)))],
[(d+e*exp(h+i*x))*(f+g*x)^2/(a+b*exp(h+i*x)+c*exp(2*h+2*i*x)),x,11,1/3*(f+g*x)^3*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(g*(b-sqrt(b^2-4*a*c)))-(f+g*x)^2*log(1+2*c*exp(h+i*x)/(b-sqrt(b^2-4*a*c)))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(i*(b-sqrt(b^2-4*a*c)))-2*g*(f+g*x)*polylog(2,-2*c*exp(h+i*x)/(b-sqrt(b^2-4*a*c)))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(i^2*(b-sqrt(b^2-4*a*c)))+2*g^2*polylog(3,-2*c*exp(h+i*x)/(b-sqrt(b^2-4*a*c)))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(i^3*(b-sqrt(b^2-4*a*c)))+1/3*(f+g*x)^3*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(g*(b+sqrt(b^2-4*a*c)))-(f+g*x)^2*log(1+2*c*exp(h+i*x)/(b+sqrt(b^2-4*a*c)))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(i*(b+sqrt(b^2-4*a*c)))-2*g*(f+g*x)*polylog(2,-2*c*exp(h+i*x)/(b+sqrt(b^2-4*a*c)))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(i^2*(b+sqrt(b^2-4*a*c)))+2*g^2*polylog(3,-2*c*exp(h+i*x)/(b+sqrt(b^2-4*a*c)))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(i^3*(b+sqrt(b^2-4*a*c)))],
[(d+e*exp(h+i*x))*(f+g*x)/(a+b*exp(h+i*x)+c*exp(2*h+2*i*x)),x,9,1/2*(f+g*x)^2*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(g*(b-sqrt(b^2-4*a*c)))-(f+g*x)*log(1+2*c*exp(h+i*x)/(b-sqrt(b^2-4*a*c)))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(i*(b-sqrt(b^2-4*a*c)))-g*polylog(2,-2*c*exp(h+i*x)/(b-sqrt(b^2-4*a*c)))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(i^2*(b-sqrt(b^2-4*a*c)))+1/2*(f+g*x)^2*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(g*(b+sqrt(b^2-4*a*c)))-(f+g*x)*log(1+2*c*exp(h+i*x)/(b+sqrt(b^2-4*a*c)))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(i*(b+sqrt(b^2-4*a*c)))-g*polylog(2,-2*c*exp(h+i*x)/(b+sqrt(b^2-4*a*c)))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(i^2*(b+sqrt(b^2-4*a*c)))],
[(d+e*exp(h+i*x))/(a+b*exp(h+i*x)+c*exp(2*h+2*i*x)),x,7,d*x/a-1/2*d*log(a+b*exp(h+i*x)+c*exp(2*h+2*i*x))/(a*i)+(b*d-2*a*e)*arctanh((b+2*c*exp(h+i*x))/sqrt(b^2-4*a*c))/(a*i*sqrt(b^2-4*a*c))],
[(d+e*exp(h+i*x))/((a+b*exp(h+i*x)+c*exp(2*h+2*i*x))*(f+g*x)),x,2,d*CannotIntegrate(1/((a+b*exp(h+i*x)+c*exp(2*h+2*i*x))*(f+g*x)),x)+e*CannotIntegrate(exp(h+i*x)/((a+b*exp(h+i*x)+c*exp(2*h+2*i*x))*(f+g*x)),x)],
[(d+e*exp(h+i*x))/((a+b*exp(h+i*x)+c*exp(2*h+2*i*x))*(f+g*x)^2),x,2,d*CannotIntegrate(1/((a+b*exp(h+i*x)+c*exp(2*h+2*i*x))*(f+g*x)^2),x)+e*CannotIntegrate(exp(h+i*x)/((a+b*exp(h+i*x)+c*exp(2*h+2*i*x))*(f+g*x)^2),x)],
[(b*e-a*e*exp(c+d*x))*x/(b*e-2*a*e*exp(c+d*x)-b*e*exp(2*(c+d*x))),x,9,1/2*x^2-1/2*x*log(1+b*exp(c+d*x)/(a-sqrt(a^2+b^2)))/d-1/2*x*log(1+b*exp(c+d*x)/(a+sqrt(a^2+b^2)))/d-1/2*polylog(2,-b*exp(c+d*x)/(a-sqrt(a^2+b^2)))/d^2-1/2*polylog(2,-b*exp(c+d*x)/(a+sqrt(a^2+b^2)))/d^2],

# Integrands of the form (d x)^m F^(a+b Log[c+d x^n])
[F^(a+b*log(c+d*x^n))*x^2,x,4,1/3*F^a*x^3*(c+d*x^n)^(b*log(F))*hypergeom([3/n,-b*log(F)],[(3+n)/n],-d*x^n/c)/(1+d*x^n/c)^(b*log(F))],
[F^(a+b*log(c+d*x^n))*x,x,4,1/2*F^a*x^2*(c+d*x^n)^(b*log(F))*hypergeom([2/n,-b*log(F)],[(2+n)/n],-d*x^n/c)/(1+d*x^n/c)^(b*log(F))],
[F^(a+b*log(c+d*x^n)),x,4,F^a*x*(c+d*x^n)^(b*log(F))*hypergeom([1/n,-b*log(F)],[1+1/n],-d*x^n/c)/(1+d*x^n/c)^(b*log(F))],
[F^(a+b*log(c+d*x^n))/x,x,4,-F^a*(c+d*x^n)^(1+b*log(F))*hypergeom([1,1+b*log(F)],[2+b*log(F)],1+d*x^n/c)/(c*n*(1+b*log(F)))],
[F^(a+b*log(c+d*x^n))/x^2,x,4,-F^a*(c+d*x^n)^(b*log(F))*hypergeom([(-1)/n,-b*log(F)],[(-1+n)/n],-d*x^n/c)/(x*(1+d*x^n/c)^(b*log(F)))],
[F^(a+b*log(c+d*x^n))/x^3,x,4,-1/2*F^a*(c+d*x^n)^(b*log(F))*hypergeom([(-2)/n,-b*log(F)],[(-2+n)/n],-d*x^n/c)/(x^2*(1+d*x^n/c)^(b*log(F)))],
[F^(a+b*log(c+d*x^n))*(d*x)^m,x,4,F^a*(d*x)^(1+m)*(c+d*x^n)^(b*log(F))*hypergeom([(1+m)/n,-b*log(F)],[(1+m+n)/n],-d*x^n/c)/(d*(1+m)*(1+d*x^n/c)^(b*log(F)))],

# Integrands of the form (g+h x)^m F^(f (a+b Log[c (d+e x)^n]^2))

# Integrands of the form (g+h x)^m F^(f (a+b Log[c (d+e x)^n]^2)) when e g-d h=0
[exp(log((d+e*x)^n)^2)*(d+e*x)^m,x,3,1/2*(d+e*x)^(1+m)*erfi(1/2*(1+m+2*n*log((d+e*x)^n))/n)*sqrt(Pi)/(e*exp(1/4*(1+m)^2/n^2)*n*((d+e*x)^n)^((1+m)/n))],
[F^(f*(a+b*log(c*(d+e*x)^n)^2))*(d*g+e*g*x)^m,x,3,1/2*F^(a*f)*(d*g+e*g*x)^(1+m)*erfi(1/2*(1+m+2*b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e*exp(1/4*(1+m)^2/(b*f*n^2*log(F)))*g*n*(c*(d+e*x)^n)^((1+m)/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n)^2))*(d*g+e*g*x)^2,x,3,1/2*F^(a*f)*g^2*(d+e*x)^3*erfi(1/2*(3+2*b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e*exp(9/4/(b*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(3/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n)^2))*(d*g+e*g*x),x,3,1/2*F^(a*f)*g*(d+e*x)^2*erfi((1+b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e*exp(1/(b*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(2/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n)^2)),x,3,1/2*F^(a*f)*(d+e*x)*erfi(1/2*(1+2*b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e*exp(1/4/(b*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(1/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n)^2))/(d*g+e*g*x),x,2,1/2*F^(a*f)*erfi(log(c*(d+e*x)^n)*sqrt(b)*sqrt(f)*sqrt(log(F)))*sqrt(Pi)/(e*g*n*sqrt(b)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n)^2))/(d*g+e*g*x)^2,x,3,1/2*F^(a*f)*(c*(d+e*x)^n)^(1/n)*erfi(1/2*(-1+2*b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e*exp(1/4/(b*f*n^2*log(F)))*g^2*n*(d+e*x)*sqrt(b)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n)^2))/(d*g+e*g*x)^3,x,3,1/2*F^(a*f)*(c*(d+e*x)^n)^(2/n)*erfi((-1+b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e*exp(1/(b*f*n^2*log(F)))*g^3*n*(d+e*x)^2*sqrt(b)*sqrt(f)*sqrt(log(F)))],

# Integrands of the form (g+h x)^m F^(f (a+b Log[c (d+e x)^n]^2))
[F^(f*(a+b*log(c*(d+e*x)^n)^2))*(g+h*x)^m,x,0,Unintegrable(F^(f*(a+b*log(c*(d+e*x)^n)^2))*(g+h*x)^m,x)],
[F^(f*(a+b*log(c*(d+e*x)^n)^2))*(g+h*x)^3,x,14,3/2*F^(a*f)*h*(e*g-d*h)^2*(d+e*x)^2*erfi((1+b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e^4*exp(1/(b*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(2/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))+1/2*F^(a*f)*h^3*(d+e*x)^4*erfi((2+b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e^4*exp(4/(b*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(4/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))+1/2*F^(a*f)*(e*g-d*h)^3*(d+e*x)*erfi(1/2*(1+2*b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e^4*exp(1/4/(b*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(1/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))+3/2*F^(a*f)*h^2*(e*g-d*h)*(d+e*x)^3*erfi(1/2*(3+2*b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e^4*exp(9/4/(b*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(3/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n)^2))*(g+h*x)^2,x,11,F^(a*f)*h*(e*g-d*h)*(d+e*x)^2*erfi((1+b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e^3*exp(1/(b*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(2/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))+1/2*F^(a*f)*(e*g-d*h)^2*(d+e*x)*erfi(1/2*(1+2*b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e^3*exp(1/4/(b*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(1/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))+1/2*F^(a*f)*h^2*(d+e*x)^3*erfi(1/2*(3+2*b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e^3*exp(9/4/(b*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(3/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n)^2))*(g+h*x),x,8,1/2*F^(a*f)*h*(d+e*x)^2*erfi((1+b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e^2*exp(1/(b*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(2/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))+1/2*F^(a*f)*(e*g-d*h)*(d+e*x)*erfi(1/2*(1+2*b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e^2*exp(1/4/(b*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(1/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n)^2)),x,3,1/2*F^(a*f)*(d+e*x)*erfi(1/2*(1+2*b*f*n*log(F)*log(c*(d+e*x)^n))/(n*sqrt(b)*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(e*exp(1/4/(b*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(1/n)*sqrt(b)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n)^2))/(g+h*x),x,0,Unintegrable(F^(f*(a+b*log(c*(d+e*x)^n)^2))/(g+h*x),x)],
[F^(f*(a+b*log(c*(d+e*x)^n)^2))/(g+h*x)^2,x,0,Unintegrable(F^(f*(a+b*log(c*(d+e*x)^n)^2))/(g+h*x)^2,x)],
[F^(f*(a+b*log(c*(d+e*x)^n)^2))/(g+h*x)^3,x,0,Unintegrable(F^(f*(a+b*log(c*(d+e*x)^n)^2))/(g+h*x)^3,x)],

# Integrands of the form (g+h x)^m F^(f (a+b Log[c (d+e x)^n])^2)

# Integrands of the form (g+h x)^m F^(f (a+b Log[c (d+e x)^n])^2) when e g-d h=0
[F^(f*(a+b*log(c*(d+e*x)^n))^2)*(d*g+e*g*x)^m,x,4,1/2*F^(a^2*f)*(d+e*x)*(d*g+e*g*x)^m*erfi(1/2*(1+m+2*a*b*f*n*log(F)+2*b^2*f*n*log(F)*log(c*(d+e*x)^n))/(b*n*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e*exp(1/4*(1+m+2*a*b*f*n*log(F))^2/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^((1+m)/n)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n))^2)*(d*g+e*g*x)^2,x,4,1/2*g^2*(d+e*x)^3*erfi(1/2*(3/n+2*a*b*f*log(F)+2*b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e*exp(3/4*(3+4*a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(3/n)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n))^2)*(d*g+e*g*x),x,4,1/2*g*(d+e*x)^2*erfi((1/n+a*b*f*log(F)+b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e*exp((1+2*a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(2/n)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n))^2),x,4,1/2*(d+e*x)*erfi(1/2*(1/n+2*a*b*f*log(F)+2*b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e*exp(1/4*(1+4*a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(1/n)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n))^2)/(d*g+e*g*x),x,4,1/2*erfi(a*sqrt(f)*sqrt(log(F))+b*log(c*(d+e*x)^n)*sqrt(f)*sqrt(log(F)))*sqrt(Pi)/(b*e*g*n*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n))^2)/(d*g+e*g*x)^2,x,4,1/2*exp(a/(b*n)+(-1/4)/(b^2*f*n^2*log(F)))*(c*(d+e*x)^n)^(1/n)*erfi(1/2*((-1)/n+2*a*b*f*log(F)+2*b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e*g^2*n*(d+e*x)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n))^2)/(d*g+e*g*x)^3,x,4,1/2*(c*(d+e*x)^n)^(2/n)*erfi(((-1)/n+a*b*f*log(F)+b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e*exp((1-2*a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*g^3*n*(d+e*x)^2*sqrt(f)*sqrt(log(F)))],

# Integrands of the form (g+h x)^m F^(f (a+b Log[c (d+e x)^n])^2)
[F^(f*(a+b*log(c*(d+e*x)^n))^2)*(g+h*x)^m,x,0,Unintegrable(F^(f*(a+b*log(c*(d+e*x)^n))^2)*(g+h*x)^m,x)],
[F^(f*(a+b*log(c*(d+e*x)^n))^2)*(g+h*x)^3,x,18,3/2*h*(e*g-d*h)^2*(d+e*x)^2*erfi((1/n+a*b*f*log(F)+b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e^4*exp((1+2*a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(2/n)*sqrt(f)*sqrt(log(F)))+1/2*h^3*(d+e*x)^4*erfi((2/n+a*b*f*log(F)+b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e^4*exp(4*(1+a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(4/n)*sqrt(f)*sqrt(log(F)))+1/2*(e*g-d*h)^3*(d+e*x)*erfi(1/2*(1/n+2*a*b*f*log(F)+2*b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e^4*exp(1/4*(1+4*a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(1/n)*sqrt(f)*sqrt(log(F)))+3/2*h^2*(e*g-d*h)*(d+e*x)^3*erfi(1/2*(3/n+2*a*b*f*log(F)+2*b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e^4*exp(3/4*(3+4*a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(3/n)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n))^2)*(g+h*x)^2,x,14,h*(e*g-d*h)*(d+e*x)^2*erfi((1/n+a*b*f*log(F)+b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e^3*exp((1+2*a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(2/n)*sqrt(f)*sqrt(log(F)))+1/2*(e*g-d*h)^2*(d+e*x)*erfi(1/2*(1/n+2*a*b*f*log(F)+2*b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e^3*exp(1/4*(1+4*a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(1/n)*sqrt(f)*sqrt(log(F)))+1/2*h^2*(d+e*x)^3*erfi(1/2*(3/n+2*a*b*f*log(F)+2*b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e^3*exp(3/4*(3+4*a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(3/n)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n))^2)*(g+h*x),x,10,1/2*h*(d+e*x)^2*erfi((1/n+a*b*f*log(F)+b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e^2*exp((1+2*a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(2/n)*sqrt(f)*sqrt(log(F)))+1/2*(e*g-d*h)*(d+e*x)*erfi(1/2*(1/n+2*a*b*f*log(F)+2*b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e^2*exp(1/4*(1+4*a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(1/n)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n))^2),x,4,1/2*(d+e*x)*erfi(1/2*(1/n+2*a*b*f*log(F)+2*b^2*f*log(F)*log(c*(d+e*x)^n))/(b*sqrt(f)*sqrt(log(F))))*sqrt(Pi)/(b*e*exp(1/4*(1+4*a*b*f*n*log(F))/(b^2*f*n^2*log(F)))*n*(c*(d+e*x)^n)^(1/n)*sqrt(f)*sqrt(log(F)))],
[F^(f*(a+b*log(c*(d+e*x)^n))^2)/(g+h*x),x,0,Unintegrable(F^(f*(a+b*log(c*(d+e*x)^n))^2)/(g+h*x),x)],
[F^(f*(a+b*log(c*(d+e*x)^n))^2)/(g+h*x)^2,x,0,Unintegrable(F^(f*(a+b*log(c*(d+e*x)^n))^2)/(g+h*x)^2,x)],
[F^(f*(a+b*log(c*(d+e*x)^n))^2)/(g+h*x)^3,x,0,Unintegrable(F^(f*(a+b*log(c*(d+e*x)^n))^2)/(g+h*x)^3,x)],

# Integrands of the form u F^v D[v,x]
[F^(a+b*x+c*x^3)*(b+3*c*x^2),x,1,F^(a+b*x+c*x^3)/log(F)],
[F^(1/(a+b*x+c*x^2))*(b+2*c*x)/(a+b*x+c*x^2)^2,x,1,-F^(1/(a+b*x+c*x^2))/log(F)],
[exp(a+b*x+c*x^2)*(b+2*c*x)*(a+b*x+c*x^2)^m,x,2,(a+b*x+c*x^2)^m*GAMMA(1+m,-a-b*x-c*x^2)/(-a-b*x-c*x^2)^m],
[exp(a+b*x+c*x^2)*(b+2*c*x)*(a+b*x+c*x^2)^3,x,5,-6*exp(a+b*x+c*x^2)+6*exp(a+b*x+c*x^2)*(a+b*x+c*x^2)-3*exp(a+b*x+c*x^2)*(a+b*x+c*x^2)^2+exp(a+b*x+c*x^2)*(a+b*x+c*x^2)^3],
[exp(a+b*x+c*x^2)*(b+2*c*x)*(a+b*x+c*x^2)^2,x,4,2*exp(a+b*x+c*x^2)-2*exp(a+b*x+c*x^2)*(a+b*x+c*x^2)+exp(a+b*x+c*x^2)*(a+b*x+c*x^2)^2],
[exp(a+b*x+c*x^2)*(b+2*c*x)*(a+b*x+c*x^2),x,3,-exp(a+b*x+c*x^2)+exp(a+b*x+c*x^2)*(a+b*x+c*x^2)],
[exp(a+b*x+c*x^2)*(b+2*c*x),x,1,exp(a+b*x+c*x^2)],
[exp(a+b*x+c*x^2)*(b+2*c*x)/(a+b*x+c*x^2),x,2,Ei(a+b*x+c*x^2)],
[exp(a+b*x+c*x^2)*(b+2*c*x)/(a+b*x+c*x^2)^2,x,3,-exp(a+b*x+c*x^2)/(a+b*x+c*x^2)+Ei(a+b*x+c*x^2)],
[exp(a+b*x+c*x^2)*(b+2*c*x)/(a+b*x+c*x^2)^3,x,4,-1/2*exp(a+b*x+c*x^2)/(a+b*x+c*x^2)^2-1/2*exp(a+b*x+c*x^2)/(a+b*x+c*x^2)+1/2*Ei(a+b*x+c*x^2)],
[exp(a+b*x+c*x^2)*(b+2*c*x)*(a+b*x+c*x^2)^(7/2),x,7,35/4*exp(a+b*x+c*x^2)*(a+b*x+c*x^2)^(3/2)-7/2*exp(a+b*x+c*x^2)*(a+b*x+c*x^2)^(5/2)+exp(a+b*x+c*x^2)*(a+b*x+c*x^2)^(7/2)+105/16*erfi(sqrt(a+b*x+c*x^2))*sqrt(Pi)-105/8*exp(a+b*x+c*x^2)*sqrt(a+b*x+c*x^2)],
[exp(a+b*x+c*x^2)*(b+2*c*x)*(a+b*x+c*x^2)^(5/2),x,6,-5/2*exp(a+b*x+c*x^2)*(a+b*x+c*x^2)^(3/2)+exp(a+b*x+c*x^2)*(a+b*x+c*x^2)^(5/2)-15/8*erfi(sqrt(a+b*x+c*x^2))*sqrt(Pi)+15/4*exp(a+b*x+c*x^2)*sqrt(a+b*x+c*x^2)],
[exp(a+b*x+c*x^2)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2),x,5,exp(a+b*x+c*x^2)*(a+b*x+c*x^2)^(3/2)+3/4*erfi(sqrt(a+b*x+c*x^2))*sqrt(Pi)-3/2*exp(a+b*x+c*x^2)*sqrt(a+b*x+c*x^2)],
[exp(a+b*x+c*x^2)*(b+2*c*x)*(a+b*x+c*x^2)^(1/2),x,4,-1/2*erfi(sqrt(a+b*x+c*x^2))*sqrt(Pi)+exp(a+b*x+c*x^2)*sqrt(a+b*x+c*x^2)],
[exp(a+b*x+c*x^2)*(b+2*c*x)/(a+b*x+c*x^2)^(1/2),x,3,erfi(sqrt(a+b*x+c*x^2))*sqrt(Pi)],
[exp(a+b*x+c*x^2)*(b+2*c*x)/(a+b*x+c*x^2)^(3/2),x,4,2*erfi(sqrt(a+b*x+c*x^2))*sqrt(Pi)-2*exp(a+b*x+c*x^2)/sqrt(a+b*x+c*x^2)],
[exp(a+b*x+c*x^2)*(b+2*c*x)/(a+b*x+c*x^2)^(5/2),x,5,-2/3*exp(a+b*x+c*x^2)/(a+b*x+c*x^2)^(3/2)+4/3*erfi(sqrt(a+b*x+c*x^2))*sqrt(Pi)-4/3*exp(a+b*x+c*x^2)/sqrt(a+b*x+c*x^2)],
[exp(a+b*x+c*x^2)*(b+2*c*x)/(a+b*x+c*x^2)^(7/2),x,6,-2/5*exp(a+b*x+c*x^2)/(a+b*x+c*x^2)^(5/2)-4/15*exp(a+b*x+c*x^2)/(a+b*x+c*x^2)^(3/2)+8/15*erfi(sqrt(a+b*x+c*x^2))*sqrt(Pi)-8/15*exp(a+b*x+c*x^2)/sqrt(a+b*x+c*x^2)],
[exp(a+b*x+c*x^2)*(b+2*c*x)/(a+b*x+c*x^2)^(9/2),x,7,-2/7*exp(a+b*x+c*x^2)/(a+b*x+c*x^2)^(7/2)-4/35*exp(a+b*x+c*x^2)/(a+b*x+c*x^2)^(5/2)-8/105*exp(a+b*x+c*x^2)/(a+b*x+c*x^2)^(3/2)+16/105*erfi(sqrt(a+b*x+c*x^2))*sqrt(Pi)-16/105*exp(a+b*x+c*x^2)/sqrt(a+b*x+c*x^2)],

# Problems from Calculus textbooks

# Anton Calculus, 4th Edition
[1/(exp(x)*sqrt(1+(-1)/exp(2*x))),x,2,-arcsin(exp(-x))],
[exp(x)/(4+exp(2*x)),x,2,1/2*arctan(1/2*exp(x))],
[exp(x)/(1-exp(2*x)),x,2,arctanh(exp(x))],
[exp(x)/(3-4*exp(2*x)),x,2,1/2*arctanh(2*exp(x)/sqrt(3))/sqrt(3)],
[exp(x)*sqrt(3-4*exp(2*x)),x,3,3/4*arcsin(2*exp(x)/sqrt(3))+1/2*exp(x)*sqrt(3-4*exp(2*x))],
[exp(x^2)*x^3,x,2,-1/2*exp(x^2)+1/2*exp(x^2)*x^2],
[exp(x)*sqrt(1-exp(2*x)),x,3,1/2*arcsin(exp(x))+1/2*exp(x)*sqrt(1-exp(2*x))],
[exp(x)/sqrt(1+exp(x)+exp(2*x)),x,3,arcsinh((1+2*exp(x))/sqrt(3))],
[exp(x)/(-4+exp(2*x)),x,2,-1/2*arctanh(1/2*exp(x))],

# Ayres Calculus, 1964 edition
[exp(2-x^2)*x,x,1,-1/2*exp(2-x^2)],
[exp(x)-x^E,x,2,exp(x)-x^(1+E)/(1+E)],
[(-1+exp(2*x))/(3+exp(2*x)),x,3,-1/3*x+2/3*log(3+exp(2*x))],
[exp(x)/sqrt(1-exp(2*x)),x,2,arcsin(exp(x))],
[exp(2*x)/(1+exp(4*x)),x,2,1/2*arctan(exp(2*x))],
[1/(-3*exp(x)+exp(2*x)),x,3,1/3/exp(x)-1/9*x+1/9*log(3-exp(x))],
[exp(x)*(-2+exp(x))/(1+exp(x)),x,3,exp(x)-3*log(1+exp(x))],

# Edwards and Penney Calculus
[exp(x)/(-1+exp(2*x)),x,2,-arctanh(exp(x))],
[exp(x)/(1+exp(2*x)),x,2,arctan(exp(x))],
[(exp(-x)+exp(x))/((-1)/exp(x)+exp(x)),x,4,log(exp(-x)-exp(x)),-x+log(1-exp(2*x))],
[((-1)/exp(x)+exp(x))/(exp(-x)+exp(x)),x,4,log(exp(-x)+exp(x)),-x+log(1+exp(2*x))],
[(exp(-2*x)+exp(2*x))/((-1)/exp(2*x)+exp(2*x)),x,4,-x+1/2*log(1-exp(4*x))],
[exp(x)/sqrt(1+exp(2*x)),x,2,arcsinh(exp(x))],
[exp(sqrt(4+x))/sqrt(4+x),x,1,2*exp(sqrt(4+x))],
[x/sqrt(-1+exp(2*x^2)),x,4,1/2*arctan(sqrt(-1+exp(2*x^2)))],
[exp(x)*sqrt(9+exp(2*x)),x,3,9/2*arcsinh(1/3*exp(x))+1/2*exp(x)*sqrt(9+exp(2*x))],
[exp(x)*sqrt(1+exp(2*x)),x,3,1/2*arcsinh(exp(x))+1/2*exp(x)*sqrt(1+exp(2*x))],
[exp(x^2)*x/(1+exp(2*x^2)),x,3,1/2*arctan(exp(x^2))],
[exp(x^(3/2))*x^2,x,3,-2/3*exp(x^(3/2))+2/3*exp(x^(3/2))*x^(3/2)],

# Grossman Calculus
[exp(x)/sqrt(-3+exp(2*x)),x,3,arctanh(exp(x)/sqrt(-3+exp(2*x)))],
[exp(x)/(16-exp(2*x)),x,2,1/4*arctanh(1/4*exp(x))],
[exp(5*x)/(1+exp(10*x)),x,2,1/5*arctan(exp(5*x))],
[exp(4*x)/sqrt(16+exp(8*x)),x,2,1/4*arcsinh(1/4*exp(4*x))],
[exp(4*x^3)*x^2*cos(7*x^3),x,2,4/195*exp(4*x^3)*cos(7*x^3)+7/195*exp(4*x^3)*sin(7*x^3)],

# Hughes, Hallet, Gleason, et al Calculus, 2nd Edition
[exp(1+x^2)*x,x,1,1/2*exp(1+x^2)],
[exp(1+x^3)*x^2,x,1,1/3*exp(1+x^3)],
[exp(sqrt(x))/sqrt(x),x,1,2*exp(sqrt(x))],
[exp(x^(1/3))/x^(2/3),x,1,3*exp(x^(1/3))],
[exp(3*x)*(-8+2*x^3+x^5),x,13,-724/243*exp(3*x)+76/81*exp(3*x)*x-38/27*exp(3*x)*x^2+38/27*exp(3*x)*x^3-5/9*exp(3*x)*x^4+1/3*exp(3*x)*x^5],
[(exp(x)+x)^2,x,5,-2*exp(x)+1/2*exp(2*x)+2*exp(x)*x+1/3*x^3],

# Spivak Calculus
[(exp(x)+exp(2*x)+exp(3*x))/exp(4*x),x,3,(-1/3)/exp(3*x)+(-1/2)/exp(2*x)+(-1)/exp(x)],
[exp(x)/(1+2*exp(x)+exp(2*x)),x,2,(-1)/(1+exp(x))],

# Stewart Calculus
[cos(3*x)/exp(x),x,1,-1/10*cos(3*x)/exp(x)+3/10*sin(3*x)/exp(x)],
[exp(2*x)/(2+3*exp(x)+exp(2*x)),x,4,-log(1+exp(x))+2*log(2+exp(x))],
[exp(2*x)/(1+exp(x)),x,3,exp(x)-log(1+exp(x))],
[exp(3*x)*cos(5*x),x,1,3/34*exp(3*x)*cos(5*x)+5/34*exp(3*x)*sin(5*x)],
[exp(x)*sech(exp(x)),x,2,arctan(sinh(exp(x)))],
[1/(exp(x)*(1+2*exp(x))),x,3,(-1)/exp(x)-2*x+2*log(1+2*exp(x))],
[exp(x)*cos(4+3*x),x,1,1/10*exp(x)*cos(4+3*x)+3/10*exp(x)*sin(4+3*x)],

# Thomas Calculus, 8th Edition
[exp(x)*sec(1-exp(x))^3,x,3,-1/2*arctanh(sin(1-exp(x)))-1/2*sec(1-exp(x))*tan(1-exp(x))],
[(exp(-x)+exp(x))*x,x,6,(-1)/exp(x)-exp(x)-x/exp(x)+exp(x)*x],
[exp(x)/(2+3*exp(x)+exp(2*x)),x,4,log(1+exp(x))-log(2+exp(x))],
[exp(2*x)/(1+exp(x))^(1/3),x,3,-3/2*(1+exp(x))^(2/3)+3/5*(1+exp(x))^(5/3)],
[exp(2*x)/(1+exp(x))^(1/4),x,3,-4/3*(1+exp(x))^(3/4)+4/7*(1+exp(x))^(7/4)],
[(-exp(x)+2*exp(2*x))/sqrt(-1-6*exp(x)+3*exp(2*x)),x,4,-arctanh((1-exp(x))*sqrt(3)/sqrt(-1-6*exp(x)+3*exp(2*x)))/sqrt(3)+2/3*sqrt(-1-6*exp(x)+3*exp(2*x))],

# Problems from integration competitions

# MIT Integration Competition
[exp(x)*(-5*x+x^2),x,8,7*exp(x)-7*exp(x)*x+exp(x)*x^2],
[exp(3*x)*(-x+x^2),x,8,5/27*exp(3*x)-5/9*exp(3*x)*x+1/3*exp(3*x)*x^2],

# University of Wisconsin Integration Competition
[exp(x^x)*x^(2*x)*(1+log(x)),x,-2,exp(x^x)*(-1+x^x)],
[(exp(5*x)+exp(7*x))/(exp(-x)+exp(x)),x,2,1/6*exp(6*x)],
[x^(-2+(-1)/x)*(1-log(x)),x,-2,(-1)/x^(1/x)],

# Miscellaneous problems

#  Note: Apart should NOT be used to expand integrands of this form! 
[(a+b*exp(x))^2,x,3,2*a*b*exp(x)+1/2*b^2*exp(2*x)+a^2*x],
[(a+b*exp(x))^3,x,3,3*a^2*b*exp(x)+3/2*a*b^2*exp(2*x)+1/3*b^3*exp(3*x)+a^3*x],
[(a+b*exp(x))^4,x,3,4*a^3*b*exp(x)+3*a^2*b^2*exp(2*x)+4/3*a*b^3*exp(3*x)+1/4*b^4*exp(4*x)+a^4*x],
[1/sqrt(a+b*exp(c+d*x)),x,3,-2*arctanh(sqrt(a+b*exp(c+d*x))/sqrt(a))/(d*sqrt(a))],
[1/sqrt(-a+b*exp(c+d*x)),x,3,2*arctan(sqrt(-a+b*exp(c+d*x))/sqrt(a))/(d*sqrt(a))],
[sqrt(a+b*exp(c+d*x)),x,4,-2*arctanh(sqrt(a+b*exp(c+d*x))/sqrt(a))*sqrt(a)/d+2*sqrt(a+b*exp(c+d*x))/d],
[sqrt(-a+b*exp(c+d*x)),x,4,-2*arctan(sqrt(-a+b*exp(c+d*x))/sqrt(a))*sqrt(a)/d+2*sqrt(-a+b*exp(c+d*x))/d],
[exp(6*x)*sin(3*x),x,1,-1/15*exp(6*x)*cos(3*x)+2/15*exp(6*x)*sin(3*x)],
[exp(3*x)/(1+exp(2*x)),x,3,exp(x)-arctan(exp(x))],
[exp(3*x)/(-1+exp(2*x)),x,3,exp(x)-arctanh(exp(x))],
[1/(exp(x)*sqrt(1+exp(2*x))),x,2,-sqrt(1+exp(2*x))/exp(x)],
[exp(x)/(-1-8*exp(x)+exp(2*x)),x,3,arctanh((4-exp(x))/sqrt(17))/sqrt(17)],
[exp(7*x)*x^3,x,4,-6/2401*exp(7*x)+6/343*exp(7*x)*x-3/49*exp(7*x)*x^2+1/7*exp(7*x)*x^3],
[exp(8-2*x)*x^3,x,4,-3/8*exp(8-2*x)-3/4*exp(8-2*x)*x-3/4*exp(8-2*x)*x^2-1/2*exp(8-2*x)*x^3],
[exp(x)*sqrt(9-exp(2*x)),x,3,9/2*arcsin(1/3*exp(x))+1/2*exp(x)*sqrt(9-exp(2*x))],
[exp(6*x)*sqrt(9-exp(2*x)),x,3,-27*(9-exp(2*x))^(3/2)+18/5*(9-exp(2*x))^(5/2)-1/7*(9-exp(2*x))^(7/2)],
[exp(6*x)/(9-exp(x))^(5/2),x,3,39366/(9-exp(x))^(3/2)+540*(9-exp(x))^(3/2)-18*(9-exp(x))^(5/2)+2/7*(9-exp(x))^(7/2)+(-65610)/sqrt(9-exp(x))-14580*sqrt(9-exp(x))],
[(2-7*exp(x^4))^5*x^3,x,4,-140*exp(x^4)+490*exp(2*x^4)-3430/3*exp(3*x^4)+12005/8*exp(4*x^4)-16807/20*exp(5*x^4)+8*x^4],
[exp(x^2)*x*sqrt(1-exp(2*x^2)),x,4,1/4*arcsin(exp(x^2))+1/4*exp(x^2)*sqrt(1-exp(2*x^2))],
[exp(x^3)*(1-exp(4*x^3))^2*x^2,x,4,1/3*exp(x^3)-2/15*exp(5*x^3)+1/27*exp(9*x^3)],
[exp(exp(x)+x),x,2,exp(exp(x))],
[exp(exp(exp(x))+exp(x)+x),x,3,exp(exp(exp(x)))],
[(exp(-x)+exp(x))^2,x,4,(-1/2)/exp(2*x)+1/2*exp(2*x)+2*x],
[1/(exp(-x)+exp(x)),x,2,arctan(exp(x))],
[1/(exp(-x)+exp(x))^2,x,2,(-1/2)/(1+exp(2*x))],
[1/((-1)/exp(x)+exp(x)),x,2,-arctanh(exp(x))],
[1/((-1)/exp(x)+exp(x))^2,x,2,1/2/(1-exp(2*x))],
[exp(x)*((-1)/exp(x)+exp(x))^2,x,3,(-1)/exp(x)-2*exp(x)+1/3*exp(3*x)],
[exp(x)*((-1)/exp(x)+exp(x))^3,x,4,1/2/exp(2*x)-3/2*exp(2*x)+1/4*exp(4*x)+3*x],
[(1+4^x)/(1+2^x),x,3,x+2^x/log(2)-2*log(1+2^x)/log(2)],
[(1+4^x)/(1+1/2^x),x,3,-2^x/log(2)+2^(-1+2*x)/log(2)+2*log(1+2^x)/log(2)],
[exp((a+x)^2)/x^2-2*a*exp((a+x)^2)/x,x,3,-exp((a+x)^2)/x+erfi(a+x)*sqrt(Pi)],
[(x^4+x^6+x^8)/exp(x^2),x,15,-147/16*x/exp(x^2)-49/8*x^3/exp(x^2)-9/4*x^5/exp(x^2)-1/2*x^7/exp(x^2)+147/32*erf(x)*sqrt(Pi)],
[1/(-exp(x)+exp(3*x)),x,3,exp(-x)-arctanh(exp(x))],
[exp(x)*(-5+x+x^2)/(-1+x)^2,x,6,exp(x)-3*exp(x)/(1-x)],
[exp(x^2)*x^3/(1+x^2)^2,x,1,1/2*exp(x^2)/(1+x^2)],
[exp(3*x)/sqrt(25+16*exp(2*x)),x,3,-25/128*arcsinh(4/5*exp(x))+1/32*exp(x)*sqrt(25+16*exp(2*x))],

#  {E^(a + b*x + c*x^2)/(d + e*x)^2, x, 0} 
[(1+exp(x))/sqrt(exp(x)+x),x,1,2*sqrt(exp(x)+x)],
[(1+exp(x))/(exp(x)+x),x,1,log(exp(x)+x)],
[exp(x^2)/x^2,x,2,-exp(x^2)/x+erfi(x)*sqrt(Pi)],
[exp(x^2)*(1+4*x^4)/x^2,x,6,-exp(x^2)/x+2*exp(x^2)*x],
[(a+b*x)^2*sqrt(f^x),x,3,16*b^2*sqrt(f^x)/log(f)^3-8*b*(a+b*x)*sqrt(f^x)/log(f)^2+2*(a+b*x)^2*sqrt(f^x)/log(f)],
[3^(1+x^2)*x,x,1,1/2*3^(1+x^2)/log(3)],
[2^sqrt(x)/sqrt(x),x,1,2^(1+sqrt(x))/log(2)],
[2^(1/x)/x^2,x,1,-2^(1/x)/log(2)],
[1/2^x+2^x,x,3,(-1)/(2^x*log(2))+2^x/log(2)],
[(2-3*x+x^2)/exp(4*x),x,8,(-11/32)/exp(4*x)+5/8*x/exp(4*x)-1/4*x^2/exp(4*x)],
[k^(1/2*x)+x^sqrt(k),x,2,2*k^(1/2*x)/log(k)+x^(1+sqrt(k))/(1+sqrt(k))],
[10^sqrt(x)/sqrt(x),x,1,2^(1+sqrt(x))*5^sqrt(x)/log(10)],

#  Problems requiring simplification of irreducible integrands 
[exp(x)/(exp(x)+x)^(1/2)+1/sqrt(exp(x)+x),x,2,2*sqrt(exp(x)+x)],
[(1+exp(x))*x/sqrt(exp(x)+x)+2*sqrt(exp(x)+x),x,6,2*x*sqrt(exp(x)+x)],
[x/sqrt(exp(x)+x)+exp(x)*x/sqrt(exp(x)+x)+2*sqrt(exp(x)+x),x,4,2*x*sqrt(exp(x)+x)],
[(1+exp(x))*x/sqrt(exp(x)+x),x,5,-2*CannotIntegrate(sqrt(exp(x)+x),x)+2*x*sqrt(exp(x)+x)],
[x/sqrt(exp(x)+x)+exp(x)*x/sqrt(exp(x)+x),x,4,-2*CannotIntegrate(sqrt(exp(x)+x),x)+2*x*sqrt(exp(x)+x)],
[exp(x)*x/sqrt(exp(x)+x),x,2,-CannotIntegrate(1/sqrt(exp(x)+x),x)-3*CannotIntegrate(sqrt(exp(x)+x),x)+2*sqrt(exp(x)+x)+2*x*sqrt(exp(x)+x)],
[1/5*x^2*(5*exp(x)+3*x^2)/sqrt(5*exp(x)+x^3)+4/5*x*sqrt(5*exp(x)+x^3),x,4,2/5*x^2*sqrt(5*exp(x)+x^3)],
[exp(x)*x^2/sqrt(5*exp(x)+x^3),x,1,-3/5*CannotIntegrate(x^4/sqrt(5*exp(x)+x^3),x)-4/5*CannotIntegrate(x*sqrt(5*exp(x)+x^3),x)+2/5*x^2*sqrt(5*exp(x)+x^3)],
[(-1-exp(x))/(exp(x)+x)^(1/3),x,1,-3/2*(exp(x)+x)^(2/3)],
[(-1)/(exp(x)+x)^(1/3)+x/(exp(x)+x)^(1/3)-(exp(x)+x)^(2/3),x,2,-3/2*(exp(x)+x)^(2/3)],
[x/(exp(x)+x)^(1/3),x,1,-3/2*(exp(x)+x)^(2/3)+CannotIntegrate(1/(exp(x)+x)^(1/3),x)+CannotIntegrate((exp(x)+x)^(2/3),x)],
[(5*x+exp(x)*(3+2*x))/(exp(x)+x)^(1/3),x,8,3*x*(exp(x)+x)^(2/3)],
[2*x/(exp(x)+x)^(1/3)+2*exp(x)*x/(exp(x)+x)^(1/3)+3*(exp(x)+x)^(2/3),x,4,3*x*(exp(x)+x)^(2/3)],
[exp(x)*((-1)/exp(x)+exp(x))*(exp(-x)+exp(x))^2,x,3,1/2/exp(2*x)+1/2*exp(2*x)+1/4*exp(4*x)-x],

#  Unwise expansion leads to infinite recursion 
[x/(exp(x)+x),x,0,CannotIntegrate(x/(exp(x)+x),x)],
[x^2/sqrt(exp(x)+x),x,0,CannotIntegrate(x^2/sqrt(exp(x)+x),x)],
[exp(x)/(exp(x)+x),x,0,CannotIntegrate(exp(x)/(exp(x)+x),x)],
[exp(x)/(exp(x)+x^2),x,0,CannotIntegrate(exp(x)/(exp(x)+x^2),x)],
[F0(x)/(x+F0(x)),x,2,x-CannotIntegrate(x/(x+F0(x)),x)],
[F0(x)/(x^2+F0(x)),x,2,x-CannotIntegrate(x^2/(x^2+F0(x)),x)],
[F0(x)/(x+F0(x))^2,x,2,-CannotIntegrate(x/(x+F0(x))^2,x)+CannotIntegrate(1/(x+F0(x)),x)],
[F0(x)/(x^2+F0(x))^2,x,2,-CannotIntegrate(x^2/(x^2+F0(x))^2,x)+CannotIntegrate(1/(x^2+F0(x)),x)],
[(a*F^(c+d*x))^m*(b*F^(e+f*x))^n,x,4,(a*F^(c+d*x))^m*(b*F^(e+f*x))^n/((d*m+f*n)*log(F))],
[exp(a+c+b*x^n+d*x^n),x,2,-exp(a+c)*x*GAMMA(1/n,-(b+d)*x^n)/(n*(-(b+d)*x^n)^(1/n))],
[f^(a+b*x^n)*g^(c+d*x^n),x,2,-f^a*g^c*x*GAMMA(1/n,-x^n*(b*log(f)+d*log(g)))/(n*(-x^n*(b*log(f)+d*log(g)))^(1/n))],
[exp(x^n)*x^m,x,1,-x^(1+m)*GAMMA((1+m)/n,-x^n)/(n*(-x^n)^((1+m)/n))],
[f^(x^n)*x^m,x,1,-x^(1+m)*GAMMA((1+m)/n,-x^n*log(f))/(n*(-x^n*log(f))^((1+m)/n))],
[exp((a+b*x)^n)*(a+b*x)^m,x,1,-(a+b*x)^(1+m)*GAMMA((1+m)/n,-(a+b*x)^n)/(b*n*(-(a+b*x)^n)^((1+m)/n))],
[f^((a+b*x)^n)*(a+b*x)^m,x,1,-(a+b*x)^(1+m)*GAMMA((1+m)/n,-(a+b*x)^n*log(f))/(b*n*(-(a+b*x)^n*log(f))^((1+m)/n))],

#  Contributed by Oleg Marichev, Wolfram Research 
[exp((a+b*x)^3)*x,x,4,1/3*a*(a+b*x)*GAMMA(1/3,-(a+b*x)^3)/(b^2*(-(a+b*x)^3)^(1/3))-1/3*(a+b*x)^2*GAMMA(2/3,-(a+b*x)^3)/(b^2*(-(a+b*x)^3)^(2/3))],

#  Problem posted on Maple Primes on 1 June 2017 
[(5*x^2+3*(exp(x)+x)^(1/3)+exp(x)*(3*x+2*x^2))/(x*(exp(x)+x)^(1/3)),x,8,3*x*(exp(x)+x)^(2/3)+3*log(x)]]:
