# Maple integration test file: "6 Hyperbolic functions\6.7 Miscellaneous\6.7.1 Hyperbolic functions.txt"

lst:=[

# Integration Problems Involving Hyperbolic Functions

# Rectification problems

#  Following integrands are equal. 
[2/(-1+3*cosh(4+6*x)),x,3,1/3*arctan(sqrt(2)*tanh(2+3*x))/sqrt(2)],
[1/(cosh(2+3*x)^2+2*sinh(2+3*x)^2),x,2,1/3*arctan(sqrt(2)*tanh(2+3*x))/sqrt(2)],
[sech(2+3*x)^2/(1+2*tanh(2+3*x)^2),x,2,1/3*arctan(sqrt(2)*tanh(2+3*x))/sqrt(2)],
[csch(2+3*x)^2/(2+coth(2+3*x)^2),x,2,1/3*arctan(sqrt(2)*tanh(2+3*x))/sqrt(2)],
[csch(2+3*x)^2/(2-coth(2+3*x)^2),x,2,-1/3*arctanh(sqrt(2)*tanh(2+3*x))/sqrt(2)],
[csch(2+3*x)^2/(1+2*coth(2+3*x)^2),x,2,1/3*arctan(tanh(2+3*x)/sqrt(2))/sqrt(2)],
[csch(2+3*x)^2/(1-2*coth(2+3*x)^2),x,2,-1/3*arctanh(tanh(2+3*x)/sqrt(2))/sqrt(2)],

# Integrands of the form Hyper[a+b x]^n Hyper[c+d x]^p

# Integrands of the form Hyper[a+b x]^m Hyper[a+b x]^n

# Integrands of the form Cosh[a+b x]^m Sinh[a+b x]^n
[cosh(a+b*x)*sinh(a+b*x),x,2,1/2*sinh(a+b*x)^2/b],
[cosh(a+b*x)*sinh(a+b*x)^n,x,2,sinh(a+b*x)^(1+n)/(b*(1+n))],
[cosh(a+b*x)^3*sinh(a+b*x)^n,x,3,sinh(a+b*x)^(1+n)/(b*(1+n))+sinh(a+b*x)^(3+n)/(b*(3+n))],
[cosh(a+b*x)^5*sinh(a+b*x)^n,x,3,sinh(a+b*x)^(1+n)/(b*(1+n))+2*sinh(a+b*x)^(3+n)/(b*(3+n))+sinh(a+b*x)^(5+n)/(b*(5+n))],
[cosh(a+b*x)^m*sinh(a+b*x),x,2,cosh(a+b*x)^(1+m)/(b*(1+m))],
[cosh(a+b*x)^m*sinh(a+b*x)^3,x,3,-cosh(a+b*x)^(1+m)/(b*(1+m))+cosh(a+b*x)^(3+m)/(b*(3+m))],
[cosh(a+b*x)^m*sinh(a+b*x)^5,x,3,cosh(a+b*x)^(1+m)/(b*(1+m))-2*cosh(a+b*x)^(3+m)/(b*(3+m))+cosh(a+b*x)^(5+m)/(b*(5+m))],
[cosh(a+b*x)^2*sinh(a+b*x)^2,x,3,-1/8*x-1/8*cosh(a+b*x)*sinh(a+b*x)/b+1/4*cosh(a+b*x)^3*sinh(a+b*x)/b],
[cosh(a+b*x)^2*sinh(a+b*x)^4,x,4,1/16*x+1/16*cosh(a+b*x)*sinh(a+b*x)/b-1/8*cosh(a+b*x)^3*sinh(a+b*x)/b+1/6*cosh(a+b*x)^3*sinh(a+b*x)^3/b],
[cosh(a+b*x)^2*sinh(a+b*x)^6,x,5,-5/128*x-5/128*cosh(a+b*x)*sinh(a+b*x)/b+5/64*cosh(a+b*x)^3*sinh(a+b*x)/b-5/48*cosh(a+b*x)^3*sinh(a+b*x)^3/b+1/8*cosh(a+b*x)^3*sinh(a+b*x)^5/b],
[cosh(a+b*x)^4*sinh(a+b*x)^2,x,4,-1/16*x-1/16*cosh(a+b*x)*sinh(a+b*x)/b-1/24*cosh(a+b*x)^3*sinh(a+b*x)/b+1/6*cosh(a+b*x)^5*sinh(a+b*x)/b],
[cosh(a+b*x)^4*sinh(a+b*x)^4,x,5,3/128*x+3/128*cosh(a+b*x)*sinh(a+b*x)/b+1/64*cosh(a+b*x)^3*sinh(a+b*x)/b-1/16*cosh(a+b*x)^5*sinh(a+b*x)/b+1/8*cosh(a+b*x)^5*sinh(a+b*x)^3/b],
[cosh(a+b*x)^4*sinh(a+b*x)^6,x,6,-3/256*x-3/256*cosh(a+b*x)*sinh(a+b*x)/b-1/128*cosh(a+b*x)^3*sinh(a+b*x)/b+1/32*cosh(a+b*x)^5*sinh(a+b*x)/b-1/16*cosh(a+b*x)^5*sinh(a+b*x)^3/b+1/10*cosh(a+b*x)^5*sinh(a+b*x)^5/b],
[cosh(a+b*x)^6*sinh(a+b*x)^2,x,5,-5/128*x-5/128*cosh(a+b*x)*sinh(a+b*x)/b-5/192*cosh(a+b*x)^3*sinh(a+b*x)/b-1/48*cosh(a+b*x)^5*sinh(a+b*x)/b+1/8*cosh(a+b*x)^7*sinh(a+b*x)/b],
[cosh(a+b*x)^6*sinh(a+b*x)^4,x,6,3/256*x+3/256*cosh(a+b*x)*sinh(a+b*x)/b+1/128*cosh(a+b*x)^3*sinh(a+b*x)/b+1/160*cosh(a+b*x)^5*sinh(a+b*x)/b-3/80*cosh(a+b*x)^7*sinh(a+b*x)/b+1/10*cosh(a+b*x)^7*sinh(a+b*x)^3/b],
[cosh(a+b*x)^6*sinh(a+b*x)^6,x,7,-5/1024*x-5/1024*cosh(a+b*x)*sinh(a+b*x)/b-5/1536*cosh(a+b*x)^3*sinh(a+b*x)/b-1/384*cosh(a+b*x)^5*sinh(a+b*x)/b+1/64*cosh(a+b*x)^7*sinh(a+b*x)/b-1/24*cosh(a+b*x)^7*sinh(a+b*x)^3/b+1/12*cosh(a+b*x)^7*sinh(a+b*x)^5/b],
[csch(a+b*x)*sech(a+b*x),x,2,log(tanh(a+b*x))/b],
[csch(a+b*x)*sech(a+b*x)^2,x,3,-arctanh(cosh(a+b*x))/b+sech(a+b*x)/b],
[csch(a+b*x)*sech(a+b*x)^3,x,3,log(tanh(a+b*x))/b-1/2*tanh(a+b*x)^2/b],
[csch(a+b*x)*sech(a+b*x)^4,x,4,-arctanh(cosh(a+b*x))/b+sech(a+b*x)/b+1/3*sech(a+b*x)^3/b],
[csch(a+b*x)*sech(a+b*x)^5,x,4,log(tanh(a+b*x))/b-tanh(a+b*x)^2/b+1/4*tanh(a+b*x)^4/b],
[csch(a+b*x)^2*sech(a+b*x),x,3,-arctan(sinh(a+b*x))/b-csch(a+b*x)/b],
[csch(a+b*x)^2*sech(a+b*x)^2,x,3,-coth(a+b*x)/b-tanh(a+b*x)/b],
[csch(a+b*x)^2*sech(a+b*x)^3,x,4,-3/2*arctan(sinh(a+b*x))/b-3/2*csch(a+b*x)/b+1/2*csch(a+b*x)*sech(a+b*x)^2/b],
[csch(a+b*x)^2*sech(a+b*x)^4,x,3,-coth(a+b*x)/b-2*tanh(a+b*x)/b+1/3*tanh(a+b*x)^3/b],
[csch(a+b*x)^2*sech(a+b*x)^5,x,5,-15/8*arctan(sinh(a+b*x))/b-15/8*csch(a+b*x)/b+5/8*csch(a+b*x)*sech(a+b*x)^2/b+1/4*csch(a+b*x)*sech(a+b*x)^4/b],
[csch(a+b*x)^3*sech(a+b*x),x,3,-1/2*coth(a+b*x)^2/b-log(tanh(a+b*x))/b],
[csch(a+b*x)^3*sech(a+b*x)^2,x,4,3/2*arctanh(cosh(a+b*x))/b-3/2*sech(a+b*x)/b-1/2*csch(a+b*x)^2*sech(a+b*x)/b],
[csch(a+b*x)^3*sech(a+b*x)^3,x,4,-1/2*coth(a+b*x)^2/b-2*log(tanh(a+b*x))/b+1/2*tanh(a+b*x)^2/b],
[csch(a+b*x)^3*sech(a+b*x)^4,x,5,5/2*arctanh(cosh(a+b*x))/b-5/2*sech(a+b*x)/b-5/6*sech(a+b*x)^3/b-1/2*csch(a+b*x)^2*sech(a+b*x)^3/b],
[csch(a+b*x)^3*sech(a+b*x)^5,x,4,-1/2*coth(a+b*x)^2/b-3*log(tanh(a+b*x))/b+3/2*tanh(a+b*x)^2/b-1/4*tanh(a+b*x)^4/b],
[csch(a+b*x)^4*sech(a+b*x),x,4,arctan(sinh(a+b*x))/b+csch(a+b*x)/b-1/3*csch(a+b*x)^3/b],
[csch(a+b*x)^4*sech(a+b*x)^2,x,3,2*coth(a+b*x)/b-1/3*coth(a+b*x)^3/b+tanh(a+b*x)/b],
[csch(a+b*x)^4*sech(a+b*x)^3,x,5,5/2*arctan(sinh(a+b*x))/b+5/2*csch(a+b*x)/b-5/6*csch(a+b*x)^3/b+1/2*csch(a+b*x)^3*sech(a+b*x)^2/b],
[csch(a+b*x)^4*sech(a+b*x)^4,x,3,3*coth(a+b*x)/b-1/3*coth(a+b*x)^3/b+3*tanh(a+b*x)/b-1/3*tanh(a+b*x)^3/b],
[csch(a+b*x)^4*sech(a+b*x)^5,x,6,35/8*arctan(sinh(a+b*x))/b+35/8*csch(a+b*x)/b-35/24*csch(a+b*x)^3/b+7/8*csch(a+b*x)^3*sech(a+b*x)^2/b+1/4*csch(a+b*x)^3*sech(a+b*x)^4/b],
[csch(a+b*x)^5*sech(a+b*x),x,4,coth(a+b*x)^2/b-1/4*coth(a+b*x)^4/b+log(tanh(a+b*x))/b],
[csch(a+b*x)^5*sech(a+b*x)^2,x,5,-15/8*arctanh(cosh(a+b*x))/b+15/8*sech(a+b*x)/b+5/8*csch(a+b*x)^2*sech(a+b*x)/b-1/4*csch(a+b*x)^4*sech(a+b*x)/b],
[csch(a+b*x)^5*sech(a+b*x)^3,x,4,3/2*coth(a+b*x)^2/b-1/4*coth(a+b*x)^4/b+3*log(tanh(a+b*x))/b-1/2*tanh(a+b*x)^2/b],
[csch(a+b*x)^5*sech(a+b*x)^4,x,6,-35/8*arctanh(cosh(a+b*x))/b+35/8*sech(a+b*x)/b+35/24*sech(a+b*x)^3/b+7/8*csch(a+b*x)^2*sech(a+b*x)^3/b-1/4*csch(a+b*x)^4*sech(a+b*x)^3/b],
[csch(a+b*x)^5*sech(a+b*x)^5,x,4,2*coth(a+b*x)^2/b-1/4*coth(a+b*x)^4/b+6*log(tanh(a+b*x))/b-2*tanh(a+b*x)^2/b+1/4*tanh(a+b*x)^4/b],
[sinh(a+b*x)^(7/2)/cosh(a+b*x)^(7/2),x,6,-arctan(sqrt(cosh(a+b*x))/sqrt(sinh(a+b*x)))/b+arctanh(sqrt(cosh(a+b*x))/sqrt(sinh(a+b*x)))/b-2/5*sinh(a+b*x)^(5/2)/(b*cosh(a+b*x)^(5/2))-2*sqrt(sinh(a+b*x))/(b*sqrt(cosh(a+b*x)))],
[sinh(a+b*x)^(5/2)/cosh(a+b*x)^(5/2),x,5,-arctan(sqrt(sinh(a+b*x))/sqrt(cosh(a+b*x)))/b+arctanh(sqrt(sinh(a+b*x))/sqrt(cosh(a+b*x)))/b-2/3*sinh(a+b*x)^(3/2)/(b*cosh(a+b*x)^(3/2))],
[sinh(a+b*x)^(3/2)/cosh(a+b*x)^(3/2),x,5,-arctan(sqrt(cosh(a+b*x))/sqrt(sinh(a+b*x)))/b+arctanh(sqrt(cosh(a+b*x))/sqrt(sinh(a+b*x)))/b-2*sqrt(sinh(a+b*x))/(b*sqrt(cosh(a+b*x)))],
[sinh(a+b*x)^(1/2)/cosh(a+b*x)^(1/2),x,4,-arctan(sqrt(sinh(a+b*x))/sqrt(cosh(a+b*x)))/b+arctanh(sqrt(sinh(a+b*x))/sqrt(cosh(a+b*x)))/b],
[cosh(a+b*x)^(1/2)/sinh(a+b*x)^(1/2),x,4,-arctan(sqrt(cosh(a+b*x))/sqrt(sinh(a+b*x)))/b+arctanh(sqrt(cosh(a+b*x))/sqrt(sinh(a+b*x)))/b],
[cosh(a+b*x)^(3/2)/sinh(a+b*x)^(3/2),x,5,-arctan(sqrt(sinh(a+b*x))/sqrt(cosh(a+b*x)))/b+arctanh(sqrt(sinh(a+b*x))/sqrt(cosh(a+b*x)))/b-2*sqrt(cosh(a+b*x))/(b*sqrt(sinh(a+b*x)))],
[cosh(a+b*x)^(5/2)/sinh(a+b*x)^(5/2),x,5,-arctan(sqrt(cosh(a+b*x))/sqrt(sinh(a+b*x)))/b+arctanh(sqrt(cosh(a+b*x))/sqrt(sinh(a+b*x)))/b-2/3*cosh(a+b*x)^(3/2)/(b*sinh(a+b*x)^(3/2))],
[cosh(a+b*x)^(7/2)/sinh(a+b*x)^(7/2),x,6,-arctan(sqrt(sinh(a+b*x))/sqrt(cosh(a+b*x)))/b+arctanh(sqrt(sinh(a+b*x))/sqrt(cosh(a+b*x)))/b-2/5*cosh(a+b*x)^(5/2)/(b*sinh(a+b*x)^(5/2))-2*sqrt(cosh(a+b*x))/(b*sqrt(sinh(a+b*x)))],
[sinh(a+b*x)^(7/3)/cosh(a+b*x)^(7/3),x,9,-1/2*log(1-sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))/b+1/4*log(1+sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3)+sinh(a+b*x)^(4/3)/cosh(a+b*x)^(4/3))/b-3/4*sinh(a+b*x)^(4/3)/(b*cosh(a+b*x)^(4/3))-1/2*arctan((1+2*sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))/sqrt(3))*sqrt(3)/b],
[sinh(a+b*x)^(5/3)/cosh(a+b*x)^(5/3),x,9,-1/2*log(1-cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/b+1/4*log(1+cosh(a+b*x)^(4/3)/sinh(a+b*x)^(4/3)+cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/b-3/2*sinh(a+b*x)^(2/3)/(b*cosh(a+b*x)^(2/3))-1/2*arctan((1+2*cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/sqrt(3))*sqrt(3)/b],
[sinh(a+b*x)^(4/3)/cosh(a+b*x)^(4/3),x,12,arctanh(cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3))/b-1/4*log(1+cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3)-cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3))/b+1/4*log(1+cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3)+cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3))/b-3*sinh(a+b*x)^(1/3)/(b*cosh(a+b*x)^(1/3))+1/2*arctan((1-2*cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3))/sqrt(3))*sqrt(3)/b-1/2*arctan((1+2*cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3))/sqrt(3))*sqrt(3)/b],
[sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3),x,11,arctanh(sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3))/b-1/4*log(1-sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3)+sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))/b+1/4*log(1+sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3)+sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))/b+1/2*arctan((1-2*sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3))/sqrt(3))*sqrt(3)/b-1/2*arctan((1+2*sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3))/sqrt(3))*sqrt(3)/b],
[sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3),x,8,-1/2*log(1-sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))/b+1/4*log(1+sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3)+sinh(a+b*x)^(4/3)/cosh(a+b*x)^(4/3))/b-1/2*arctan((1+2*sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))/sqrt(3))*sqrt(3)/b],
[cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3),x,8,-1/2*log(1-cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/b+1/4*log(1+cosh(a+b*x)^(4/3)/sinh(a+b*x)^(4/3)+cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/b-1/2*arctan((1+2*cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/sqrt(3))*sqrt(3)/b],
[cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3),x,11,arctanh(cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3))/b-1/4*log(1+cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3)-cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3))/b+1/4*log(1+cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3)+cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3))/b+1/2*arctan((1-2*cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3))/sqrt(3))*sqrt(3)/b-1/2*arctan((1+2*cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3))/sqrt(3))*sqrt(3)/b],
[cosh(a+b*x)^(4/3)/sinh(a+b*x)^(4/3),x,12,arctanh(sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3))/b-1/4*log(1-sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3)+sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))/b+1/4*log(1+sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3)+sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))/b-3*cosh(a+b*x)^(1/3)/(b*sinh(a+b*x)^(1/3))+1/2*arctan((1-2*sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3))/sqrt(3))*sqrt(3)/b-1/2*arctan((1+2*sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3))/sqrt(3))*sqrt(3)/b],
[cosh(a+b*x)^(5/3)/sinh(a+b*x)^(5/3),x,9,-1/2*log(1-sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))/b+1/4*log(1+sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3)+sinh(a+b*x)^(4/3)/cosh(a+b*x)^(4/3))/b-3/2*cosh(a+b*x)^(2/3)/(b*sinh(a+b*x)^(2/3))-1/2*arctan((1+2*sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))/sqrt(3))*sqrt(3)/b],
[cosh(a+b*x)^(7/3)/sinh(a+b*x)^(7/3),x,9,-1/2*log(1-cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/b+1/4*log(1+cosh(a+b*x)^(4/3)/sinh(a+b*x)^(4/3)+cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/b-3/4*cosh(a+b*x)^(4/3)/(b*sinh(a+b*x)^(4/3))-1/2*arctan((1+2*cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/sqrt(3))*sqrt(3)/b],
[cosh(x)^(2/3)/sinh(x)^(8/3),x,1,-3/5*cosh(x)^(5/3)/sinh(x)^(5/3)],
[sinh(x)^(2/3)/cosh(x)^(8/3),x,1,3/5*sinh(x)^(5/3)/cosh(x)^(5/3)],
[cosh(x)*csch(x)^(7/3),x,2,-3/4*csch(x)^(4/3)],

# Integrands of the form Hyper[a+b x]^m Tanh[a+b x]^n
[sinh(a+b*x)*tanh(a+b*x),x,3,-arctan(sinh(a+b*x))/b+sinh(a+b*x)/b],
[sinh(a+b*x)*tanh(a+b*x)^2,x,3,cosh(a+b*x)/b+sech(a+b*x)/b],
[sinh(a+b*x)*tanh(a+b*x)^3,x,4,-3/2*arctan(sinh(a+b*x))/b+3/2*sinh(a+b*x)/b-1/2*sinh(a+b*x)*tanh(a+b*x)^2/b],
[sinh(a+b*x)*tanh(a+b*x)^4,x,3,cosh(a+b*x)/b+2*sech(a+b*x)/b-1/3*sech(a+b*x)^3/b],
[sinh(a+b*x)^2*tanh(a+b*x),x,3,1/2*cosh(a+b*x)^2/b-log(cosh(a+b*x))/b],
[sinh(a+b*x)^2*tanh(a+b*x)^2,x,4,-3/2*x+3/2*tanh(a+b*x)/b+1/2*sinh(a+b*x)^2*tanh(a+b*x)/b],
[sinh(a+b*x)^2*tanh(a+b*x)^3,x,4,1/2*cosh(a+b*x)^2/b-2*log(cosh(a+b*x))/b-1/2*sech(a+b*x)^2/b],
[sinh(a+b*x)^3*tanh(a+b*x),x,4,arctan(sinh(a+b*x))/b-sinh(a+b*x)/b+1/3*sinh(a+b*x)^3/b],
[sinh(a+b*x)^3*tanh(a+b*x)^2,x,3,-2*cosh(a+b*x)/b+1/3*cosh(a+b*x)^3/b-sech(a+b*x)/b],
[sinh(a+b*x)^3*tanh(a+b*x)^3,x,5,5/2*arctan(sinh(a+b*x))/b-5/2*sinh(a+b*x)/b+5/6*sinh(a+b*x)^3/b-1/2*sinh(a+b*x)^3*tanh(a+b*x)^2/b],
[sinh(a+b*x)^4*tanh(a+b*x),x,4,-cosh(a+b*x)^2/b+1/4*cosh(a+b*x)^4/b+log(cosh(a+b*x))/b],
[sech(a+b*x)*tanh(a+b*x),x,2,-sech(a+b*x)/b],
[sech(a+b*x)^2*tanh(a+b*x),x,2,-1/2*sech(a+b*x)^2/b],
[sech(a+b*x)^n*tanh(a+b*x),x,2,-sech(a+b*x)^n/(b*n)],
[sech(a+b*x)^2*tanh(a+b*x)^2,x,2,1/3*tanh(a+b*x)^3/b],
[sech(a+b*x)^2*tanh(a+b*x)^3,x,2,1/4*tanh(a+b*x)^4/b],
[sech(a+b*x)^2*tanh(a+b*x)^n,x,2,tanh(a+b*x)^(1+n)/(b*(1+n))],
[sech(a+b*x)*tanh(a+b*x)^3,x,2,-sech(a+b*x)/b+1/3*sech(a+b*x)^3/b],
[sech(a+b*x)^3*tanh(a+b*x)^3,x,3,-1/3*sech(a+b*x)^3/b+1/5*sech(a+b*x)^5/b],
[sech(a+b*x)^n*tanh(a+b*x)^3,x,3,-sech(a+b*x)^n/(b*n)+sech(a+b*x)^(2+n)/(b*(2+n))],
[sech(a+b*x)^4*tanh(a+b*x)^2,x,3,1/3*tanh(a+b*x)^3/b-1/5*tanh(a+b*x)^5/b],
[sech(a+b*x)^4*sqrt(tanh(a+b*x)),x,3,2/3*tanh(a+b*x)^(3/2)/b-2/7*tanh(a+b*x)^(7/2)/b],
[sech(a+b*x)^4*tanh(a+b*x)^n,x,3,tanh(a+b*x)^(1+n)/(b*(1+n))-tanh(a+b*x)^(3+n)/(b*(3+n))],
[sech(a+b*x)*tanh(a+b*x)^2,x,2,1/2*arctan(sinh(a+b*x))/b-1/2*sech(a+b*x)*tanh(a+b*x)/b],
[sech(a+b*x)*tanh(a+b*x)^4,x,3,3/8*arctan(sinh(a+b*x))/b-3/8*sech(a+b*x)*tanh(a+b*x)/b-1/4*sech(a+b*x)*tanh(a+b*x)^3/b],
[sech(a+b*x)^3*tanh(a+b*x)^2,x,3,1/8*arctan(sinh(a+b*x))/b+1/8*sech(a+b*x)*tanh(a+b*x)/b-1/4*sech(a+b*x)^3*tanh(a+b*x)/b],
[sech(x)*tanh(x)^5,x,3,-sech(x)+2/3*sech(x)^3-1/5*sech(x)^5],
[sech(x)^7*tanh(x)^5,x,3,-1/7*sech(x)^7+2/9*sech(x)^9-1/11*sech(x)^11],
[sech(x)^3*tanh(x)^4,x,4,1/16*arctan(sinh(x))+1/16*sech(x)*tanh(x)-1/8*sech(x)^3*tanh(x)-1/6*sech(x)^3*tanh(x)^3],
[sech(x)^5*tanh(x)^2,x,4,1/16*arctan(sinh(x))+1/16*sech(x)*tanh(x)+1/24*sech(x)^3*tanh(x)-1/6*sech(x)^5*tanh(x)],
[sech(x)^8*tanh(x)^6,x,3,1/7*tanh(x)^7-1/3*tanh(x)^9+3/11*tanh(x)^11-1/13*tanh(x)^13],

# Integrands of the form Hyper[a+b x]^m Coth[a+b x]^n
[cosh(a+b*x)*coth(a+b*x),x,3,-arctanh(cosh(a+b*x))/b+cosh(a+b*x)/b],
[cosh(a+b*x)*coth(a+b*x)^2,x,3,-csch(a+b*x)/b+sinh(a+b*x)/b],
[cosh(a+b*x)*coth(a+b*x)^3,x,4,-3/2*arctanh(cosh(a+b*x))/b+3/2*cosh(a+b*x)/b-1/2*cosh(a+b*x)*coth(a+b*x)^2/b],
[cosh(a+b*x)*coth(a+b*x)^4,x,3,-2*csch(a+b*x)/b-1/3*csch(a+b*x)^3/b+sinh(a+b*x)/b],
[cosh(a+b*x)^2*coth(a+b*x),x,3,log(sinh(a+b*x))/b+1/2*sinh(a+b*x)^2/b],
[cosh(a+b*x)^2*coth(a+b*x)^2,x,4,3/2*x-3/2*coth(a+b*x)/b+1/2*cosh(a+b*x)^2*coth(a+b*x)/b],
[cosh(a+b*x)^2*coth(a+b*x)^3,x,4,-1/2*csch(a+b*x)^2/b+2*log(sinh(a+b*x))/b+1/2*sinh(a+b*x)^2/b],
[cosh(a+b*x)^3*coth(a+b*x),x,4,-arctanh(cosh(a+b*x))/b+cosh(a+b*x)/b+1/3*cosh(a+b*x)^3/b],
[cosh(a+b*x)^3*coth(a+b*x)^2,x,3,-csch(a+b*x)/b+2*sinh(a+b*x)/b+1/3*sinh(a+b*x)^3/b],
[cosh(a+b*x)^3*coth(a+b*x)^3,x,5,-5/2*arctanh(cosh(a+b*x))/b+5/2*cosh(a+b*x)/b+5/6*cosh(a+b*x)^3/b-1/2*cosh(a+b*x)^3*coth(a+b*x)^2/b],
[cosh(a+b*x)^4*coth(a+b*x),x,4,log(sinh(a+b*x))/b+sinh(a+b*x)^2/b+1/4*sinh(a+b*x)^4/b],
[coth(a+b*x)*csch(a+b*x),x,2,-csch(a+b*x)/b],
[coth(a+b*x)*csch(a+b*x)^2,x,2,-1/2*csch(a+b*x)^2/b],
[coth(a+b*x)*csch(a+b*x)^n,x,2,-csch(a+b*x)^n/(b*n)],
[coth(a+b*x)^2*csch(a+b*x)^2,x,2,-1/3*coth(a+b*x)^3/b],
[coth(a+b*x)^3*csch(a+b*x)^2,x,2,-1/4*coth(a+b*x)^4/b],
[coth(a+b*x)^n*csch(a+b*x)^2,x,2,-coth(a+b*x)^(1+n)/(b*(1+n))],
[coth(a+b*x)^3*csch(a+b*x),x,2,-csch(a+b*x)/b-1/3*csch(a+b*x)^3/b],
[coth(a+b*x)^3*csch(a+b*x)^3,x,3,-1/3*csch(a+b*x)^3/b-1/5*csch(a+b*x)^5/b],
[coth(a+b*x)^3*csch(a+b*x)^n,x,3,-csch(a+b*x)^n/(b*n)-csch(a+b*x)^(2+n)/(b*(2+n))],
[coth(a+b*x)^2*csch(a+b*x),x,2,-1/2*arctanh(cosh(a+b*x))/b-1/2*coth(a+b*x)*csch(a+b*x)/b],
[coth(a+b*x)^2*csch(a+b*x)^3,x,3,1/8*arctanh(cosh(a+b*x))/b-1/8*coth(a+b*x)*csch(a+b*x)/b-1/4*coth(a+b*x)*csch(a+b*x)^3/b],
[coth(a+b*x)^4*csch(a+b*x),x,3,-3/8*arctanh(cosh(a+b*x))/b-3/8*coth(a+b*x)*csch(a+b*x)/b-1/4*coth(a+b*x)^3*csch(a+b*x)/b],
[coth(x)^2*csch(x)^4,x,3,1/3*coth(x)^3-1/5*coth(x)^5],
[coth(x)^3*csch(x)^4,x,3,-1/4*csch(x)^4-1/6*csch(x)^6],
[coth(x)^n*csch(x)^4,x,3,coth(x)^(1+n)/(1+n)-coth(x)^(3+n)/(3+n)],
[coth(x)^4*csch(x)^3,x,4,1/16*arctanh(cosh(x))-1/16*coth(x)*csch(x)-1/8*coth(x)*csch(x)^3-1/6*coth(x)^3*csch(x)^3],
[coth(x)^4*csch(x)^6,x,3,-1/5*coth(x)^5+2/7*coth(x)^7-1/9*coth(x)^9],
[coth(6*x)^5*csch(6*x),x,3,-1/6*csch(6*x)-1/9*csch(6*x)^3-1/30*csch(6*x)^5],
[coth(x)^7*csch(x)^3,x,3,-1/3*csch(x)^3-3/5*csch(x)^5-3/7*csch(x)^7-1/9*csch(x)^9],

# Integrands of the form Hyper[a+b x] Hyper[c+d x] when b^2-d^2=0
[sinh(a+b*x)*sinh(c+b*x),x,3,-1/2*x*cosh(a-c)+1/4*sinh(a+c+2*b*x)/b],
[sinh(c-b*x)*sinh(a+b*x),x,3,1/2*x*cosh(a+c)-1/4*sinh(a-c+2*b*x)/b],
[cosh(a+b*x)*cosh(c+b*x),x,3,1/2*x*cosh(a-c)+1/4*sinh(a+c+2*b*x)/b],
[cosh(c-b*x)*cosh(a+b*x),x,3,1/2*x*cosh(a+c)+1/4*sinh(a-c+2*b*x)/b],
[tanh(a+b*x)*tanh(c+b*x),x,4,x-coth(a-c)*log(cosh(a+b*x))/b+coth(a-c)*log(cosh(c+b*x))/b],
[tanh(c-b*x)*tanh(a+b*x),x,4,-x-coth(a+c)*log(cosh(c-b*x))/b+coth(a+c)*log(cosh(a+b*x))/b],
[coth(a+b*x)*coth(c+b*x),x,4,x-coth(a-c)*log(sinh(a+b*x))/b+coth(a-c)*log(sinh(c+b*x))/b],
[coth(c-b*x)*coth(a+b*x),x,4,-x-coth(a+c)*log(sinh(c-b*x))/b+coth(a+c)*log(sinh(a+b*x))/b],
[sech(a+b*x)*sech(c+b*x),x,3,csch(a-c)*log(cosh(a+b*x))/b-csch(a-c)*log(cosh(c+b*x))/b],
[sech(c-b*x)*sech(a+b*x),x,3,-csch(a+c)*log(cosh(c-b*x))/b+csch(a+c)*log(cosh(a+b*x))/b],
[csch(a+b*x)*csch(c+b*x),x,3,-csch(a-c)*log(sinh(a+b*x))/b+csch(a-c)*log(sinh(c+b*x))/b],
[csch(c-b*x)*csch(a+b*x),x,3,-csch(a+c)*log(sinh(c-b*x))/b+csch(a+c)*log(sinh(a+b*x))/b],
[sinh(a+b*x)*tanh(c+b*x),x,3,-arctan(sinh(c+b*x))*cosh(a-c)/b+sinh(a+b*x)/b],
[sinh(a+b*x)*tanh(c+b*x)^2,x,6,cosh(a+b*x)/b+cosh(a-c)*sech(c+b*x)/b-arctan(sinh(c+b*x))*sinh(a-c)/b],
[sinh(a+b*x)*tanh(c+b*x)^3,x,9,-3/2*arctan(sinh(c+b*x))*cosh(a-c)/b+sech(c+b*x)*sinh(a-c)/b+sinh(a+b*x)/b+1/2*cosh(a-c)*sech(c+b*x)*tanh(c+b*x)/b],
[coth(c+b*x)*sinh(a+b*x),x,3,-arctanh(cosh(c+b*x))*sinh(a-c)/b+sinh(a+b*x)/b],
[coth(c+b*x)^2*sinh(a+b*x),x,6,-arctanh(cosh(c+b*x))*cosh(a-c)/b+cosh(a+b*x)/b-csch(c+b*x)*sinh(a-c)/b],
[coth(c+b*x)^3*sinh(a+b*x),x,9,-cosh(a-c)*csch(c+b*x)/b-3/2*arctanh(cosh(c+b*x))*sinh(a-c)/b-1/2*coth(c+b*x)*csch(c+b*x)*sinh(a-c)/b+sinh(a+b*x)/b],
[sech(c+b*x)*sinh(a+b*x),x,3,cosh(a-c)*log(cosh(c+b*x))/b+x*sinh(a-c)],
[sech(c+b*x)^2*sinh(a+b*x),x,4,-cosh(a-c)*sech(c+b*x)/b+arctan(sinh(c+b*x))*sinh(a-c)/b],
[sech(c+b*x)^3*sinh(a+b*x),x,5,-1/2*cosh(a-c)*sech(c+b*x)^2/b+sinh(a-c)*tanh(c+b*x)/b],
[csch(c+b*x)*sinh(a+b*x),x,3,x*cosh(a-c)+log(sinh(c+b*x))*sinh(a-c)/b],
[csch(c+b*x)^2*sinh(a+b*x),x,4,-arctanh(cosh(c+b*x))*cosh(a-c)/b-csch(c+b*x)*sinh(a-c)/b],
[csch(c+b*x)^3*sinh(a+b*x),x,5,-cosh(a-c)*coth(c+b*x)/b-1/2*csch(c+b*x)^2*sinh(a-c)/b],
[cosh(a+b*x)*tanh(c+b*x),x,3,cosh(a+b*x)/b-arctan(sinh(c+b*x))*sinh(a-c)/b],
[cosh(a+b*x)*tanh(c+b*x)^2,x,6,-arctan(sinh(c+b*x))*cosh(a-c)/b+sech(c+b*x)*sinh(a-c)/b+sinh(a+b*x)/b],
[cosh(a+b*x)*tanh(c+b*x)^3,x,9,cosh(a+b*x)/b+cosh(a-c)*sech(c+b*x)/b-3/2*arctan(sinh(c+b*x))*sinh(a-c)/b+1/2*sech(c+b*x)*sinh(a-c)*tanh(c+b*x)/b],
[cosh(a+b*x)*coth(c+b*x),x,3,-arctanh(cosh(c+b*x))*cosh(a-c)/b+cosh(a+b*x)/b],
[cosh(a+b*x)*coth(c+b*x)^2,x,6,-cosh(a-c)*csch(c+b*x)/b-arctanh(cosh(c+b*x))*sinh(a-c)/b+sinh(a+b*x)/b],
[cosh(a+b*x)*coth(c+b*x)^3,x,9,-3/2*arctanh(cosh(c+b*x))*cosh(a-c)/b+cosh(a+b*x)/b-1/2*cosh(a-c)*coth(c+b*x)*csch(c+b*x)/b-csch(c+b*x)*sinh(a-c)/b],
[cosh(a+b*x)*sech(c+b*x),x,3,x*cosh(a-c)+log(cosh(c+b*x))*sinh(a-c)/b],
[cosh(a+b*x)*sech(c+b*x)^2,x,4,arctan(sinh(c+b*x))*cosh(a-c)/b-sech(c+b*x)*sinh(a-c)/b],
[cosh(a+b*x)*sech(c+b*x)^3,x,5,-1/2*sech(c+b*x)^2*sinh(a-c)/b+cosh(a-c)*tanh(c+b*x)/b],
[cosh(a+b*x)*csch(c+b*x),x,3,cosh(a-c)*log(sinh(c+b*x))/b+x*sinh(a-c)],
[cosh(a+b*x)*csch(c+b*x)^2,x,4,-cosh(a-c)*csch(c+b*x)/b-arctanh(cosh(c+b*x))*sinh(a-c)/b],
[cosh(a+b*x)*csch(c+b*x)^3,x,5,-1/2*cosh(a-c)*csch(c+b*x)^2/b-coth(c+b*x)*sinh(a-c)/b],

# Integrands of the form Hyper[a+b x]^m Hyper[c+d x]^n
[sinh(a+b*x)*sinh(c+d*x),x,4,-1/2*sinh(a-c+(b-d)*x)/(b-d)+1/2*sinh(a+c+(b+d)*x)/(b+d)],
[sinh(a+b*x)*sinh(c+d*x)^2,x,5,-1/2*cosh(a+b*x)/b+1/4*cosh(a-2*c+(b-2*d)*x)/(b-2*d)+1/4*cosh(a+2*c+(b+2*d)*x)/(b+2*d)],
[sinh(a+b*x)*sinh(c+d*x)^3,x,6,-1/8*sinh(a-3*c+(b-3*d)*x)/(b-3*d)+3/8*sinh(a-c+(b-d)*x)/(b-d)-3/8*sinh(a+c+(b+d)*x)/(b+d)+1/8*sinh(a+3*c+(b+3*d)*x)/(b+3*d)],
[sinh(a+b*x)^2*sinh(c+d*x)^2,x,6,1/4*x-1/8*sinh(2*a+2*b*x)/b+1/16*sinh(2*(a-c)+2*(b-d)*x)/(b-d)-1/8*sinh(2*c+2*d*x)/d+1/16*sinh(2*(a+c)+2*(b+d)*x)/(b+d)],
[sinh(a+b*x)^2*sinh(c+d*x)^3,x,8,-1/16*cosh(2*a-3*c+(2*b-3*d)*x)/(2*b-3*d)+3/16*cosh(2*a-c+(2*b-d)*x)/(2*b-d)+3/8*cosh(c+d*x)/d-1/24*cosh(3*c+3*d*x)/d-3/16*cosh(2*a+c+(2*b+d)*x)/(2*b+d)+1/16*cosh(2*a+3*c+(2*b+3*d)*x)/(2*b+3*d)],
[sinh(a+b*x)^3*sinh(c+d*x)^3,x,10,3/32*sinh(a-3*c+(b-3*d)*x)/(b-3*d)-9/32*sinh(a-c+(b-d)*x)/(b-d)-1/96*sinh(3*(a-c)+3*(b-d)*x)/(b-d)+3/32*sinh(3*a-c+(3*b-d)*x)/(3*b-d)+9/32*sinh(a+c+(b+d)*x)/(b+d)+1/96*sinh(3*(a+c)+3*(b+d)*x)/(b+d)-3/32*sinh(3*a+c+(3*b+d)*x)/(3*b+d)-3/32*sinh(a+3*c+(b+3*d)*x)/(b+3*d)],
[cosh(a+b*x)*cosh(c+d*x),x,4,1/2*sinh(a-c+(b-d)*x)/(b-d)+1/2*sinh(a+c+(b+d)*x)/(b+d)],
[cosh(a+b*x)*cosh(c+d*x)^2,x,5,1/2*sinh(a+b*x)/b+1/4*sinh(a-2*c+(b-2*d)*x)/(b-2*d)+1/4*sinh(a+2*c+(b+2*d)*x)/(b+2*d)],
[cosh(a+b*x)*cosh(c+d*x)^3,x,6,1/8*sinh(a-3*c+(b-3*d)*x)/(b-3*d)+3/8*sinh(a-c+(b-d)*x)/(b-d)+3/8*sinh(a+c+(b+d)*x)/(b+d)+1/8*sinh(a+3*c+(b+3*d)*x)/(b+3*d)],
[cosh(a+b*x)^2*cosh(c+d*x)^2,x,6,1/4*x+1/8*sinh(2*a+2*b*x)/b+1/16*sinh(2*(a-c)+2*(b-d)*x)/(b-d)+1/8*sinh(2*c+2*d*x)/d+1/16*sinh(2*(a+c)+2*(b+d)*x)/(b+d)],
[cosh(a+b*x)^2*cosh(c+d*x)^3,x,8,1/16*sinh(2*a-3*c+(2*b-3*d)*x)/(2*b-3*d)+3/16*sinh(2*a-c+(2*b-d)*x)/(2*b-d)+3/8*sinh(c+d*x)/d+1/24*sinh(3*c+3*d*x)/d+3/16*sinh(2*a+c+(2*b+d)*x)/(2*b+d)+1/16*sinh(2*a+3*c+(2*b+3*d)*x)/(2*b+3*d)],
[cosh(a+b*x)^3*cosh(c+d*x)^3,x,10,3/32*sinh(a-3*c+(b-3*d)*x)/(b-3*d)+9/32*sinh(a-c+(b-d)*x)/(b-d)+1/96*sinh(3*(a-c)+3*(b-d)*x)/(b-d)+3/32*sinh(3*a-c+(3*b-d)*x)/(3*b-d)+9/32*sinh(a+c+(b+d)*x)/(b+d)+1/96*sinh(3*(a+c)+3*(b+d)*x)/(b+d)+3/32*sinh(3*a+c+(3*b+d)*x)/(3*b+d)+3/32*sinh(a+3*c+(b+3*d)*x)/(b+3*d)],
[cosh(c+d*x)*sinh(a+b*x),x,4,1/2*cosh(a-c+(b-d)*x)/(b-d)+1/2*cosh(a+c+(b+d)*x)/(b+d)],
[cosh(c+d*x)^2*sinh(a+b*x),x,5,1/2*cosh(a+b*x)/b+1/4*cosh(a-2*c+(b-2*d)*x)/(b-2*d)+1/4*cosh(a+2*c+(b+2*d)*x)/(b+2*d)],
[cosh(c+d*x)^3*sinh(a+b*x),x,6,1/8*cosh(a-3*c+(b-3*d)*x)/(b-3*d)+3/8*cosh(a-c+(b-d)*x)/(b-d)+3/8*cosh(a+c+(b+d)*x)/(b+d)+1/8*cosh(a+3*c+(b+3*d)*x)/(b+3*d)],
[cosh(c+d*x)*sinh(a+b*x)^2,x,5,1/4*sinh(2*a-c+(2*b-d)*x)/(2*b-d)-1/2*sinh(c+d*x)/d+1/4*sinh(2*a+c+(2*b+d)*x)/(2*b+d)],
[cosh(c+d*x)^2*sinh(a+b*x)^2,x,6,-1/4*x+1/8*sinh(2*a+2*b*x)/b+1/16*sinh(2*(a-c)+2*(b-d)*x)/(b-d)-1/8*sinh(2*c+2*d*x)/d+1/16*sinh(2*(a+c)+2*(b+d)*x)/(b+d)],
[cosh(c+d*x)^3*sinh(a+b*x)^2,x,8,1/16*sinh(2*a-3*c+(2*b-3*d)*x)/(2*b-3*d)+3/16*sinh(2*a-c+(2*b-d)*x)/(2*b-d)-3/8*sinh(c+d*x)/d-1/24*sinh(3*c+3*d*x)/d+3/16*sinh(2*a+c+(2*b+d)*x)/(2*b+d)+1/16*sinh(2*a+3*c+(2*b+3*d)*x)/(2*b+3*d)],
[cosh(c+d*x)*sinh(a+b*x)^3,x,6,-3/8*cosh(a-c+(b-d)*x)/(b-d)+1/8*cosh(3*a-c+(3*b-d)*x)/(3*b-d)-3/8*cosh(a+c+(b+d)*x)/(b+d)+1/8*cosh(3*a+c+(3*b+d)*x)/(3*b+d)],
[cosh(c+d*x)^2*sinh(a+b*x)^3,x,8,-3/8*cosh(a+b*x)/b+1/24*cosh(3*a+3*b*x)/b-3/16*cosh(a-2*c+(b-2*d)*x)/(b-2*d)+1/16*cosh(3*a-2*c+(3*b-2*d)*x)/(3*b-2*d)-3/16*cosh(a+2*c+(b+2*d)*x)/(b+2*d)+1/16*cosh(3*a+2*c+(3*b+2*d)*x)/(3*b+2*d)],
[cosh(c+d*x)^3*sinh(a+b*x)^3,x,10,-3/32*cosh(a-3*c+(b-3*d)*x)/(b-3*d)-9/32*cosh(a-c+(b-d)*x)/(b-d)+1/96*cosh(3*(a-c)+3*(b-d)*x)/(b-d)+3/32*cosh(3*a-c+(3*b-d)*x)/(3*b-d)-9/32*cosh(a+c+(b+d)*x)/(b+d)+1/96*cosh(3*(a+c)+3*(b+d)*x)/(b+d)+3/32*cosh(3*a+c+(3*b+d)*x)/(3*b+d)-3/32*cosh(a+3*c+(b+3*d)*x)/(b+3*d)],
[sinh(a+b*x)*tanh(c+d*x),x,6,1/2*exp(-a-b*x)/b+1/2*exp(a+b*x)/b-exp(-a-b*x)*hypergeom([1,-1/2*b/d],[1-1/2*b/d],-exp(2*(c+d*x)))/b-exp(a+b*x)*hypergeom([1,1/2*b/d],[1+1/2*b/d],-exp(2*(c+d*x)))/b],
[coth(c+d*x)*sinh(a+b*x),x,6,1/2*exp(-a-b*x)/b+1/2*exp(a+b*x)/b-exp(-a-b*x)*hypergeom([1,-1/2*b/d],[1-1/2*b/d],exp(2*(c+d*x)))/b-exp(a+b*x)*hypergeom([1,1/2*b/d],[1+1/2*b/d],exp(2*(c+d*x)))/b],
[cosh(a+b*x)*coth(c+d*x),x,6,-1/2*exp(-a-b*x)/b+1/2*exp(a+b*x)/b+exp(-a-b*x)*hypergeom([1,-1/2*b/d],[1-1/2*b/d],exp(2*(c+d*x)))/b-exp(a+b*x)*hypergeom([1,1/2*b/d],[1+1/2*b/d],exp(2*(c+d*x)))/b],
[cosh(a+b*x)*tanh(c+d*x),x,6,-1/2*exp(-a-b*x)/b+1/2*exp(a+b*x)/b+exp(-a-b*x)*hypergeom([1,-1/2*b/d],[1-1/2*b/d],-exp(2*(c+d*x)))/b-exp(a+b*x)*hypergeom([1,1/2*b/d],[1+1/2*b/d],-exp(2*(c+d*x)))/b],

# Integrands of the form Hyper[m x] Hyper[n x]

# Integrands of the form Hyper[m x] Sinh[n x]
[sinh(x)*sinh(2*x),x,1,2/3*sinh(x)^3,-1/2*sinh(x)+1/6*sinh(3*x)],
[sinh(x)*sinh(3*x),x,1,-1/4*sinh(2*x)+1/8*sinh(4*x)],
[sinh(x)*sinh(4*x),x,1,-1/6*sinh(3*x)+1/10*sinh(5*x)],
[sinh(x)*sinh(m*x),x,4,-1/2*sinh((1-m)*x)/(1-m)+1/2*sinh((1+m)*x)/(1+m)],
[cosh(2*x)*sinh(x),x,1,-1/2*cosh(x)+1/6*cosh(3*x)],
[cosh(3*x)*sinh(x),x,1,-1/4*cosh(2*x)+1/8*cosh(4*x)],
[cosh(4*x)*sinh(x),x,1,-1/6*cosh(3*x)+1/10*cosh(5*x)],
[cosh(m*x)*sinh(x),x,4,1/2*cosh((1-m)*x)/(1-m)+1/2*cosh((1+m)*x)/(1+m)],
[sinh(x)*tanh(2*x),x,4,sinh(x)-arctan(sinh(x)*sqrt(2))/sqrt(2)],
[sinh(x)*tanh(3*x),x,5,-1/3*arctan(sinh(x))-1/3*arctan(2*sinh(x))+sinh(x)],
[sinh(x)*tanh(4*x),x,6,sinh(x)-1/4*arctan(2*sinh(x)/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-1/4*arctan(2*sinh(x)/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))],
[sinh(x)*tanh(5*x),x,9,-1/5*arctan(sinh(x))+sinh(x)-1/5*arctan(sinh(x)*sqrt(2*(3+sqrt(5))))*sqrt(1/2*(3-sqrt(5)))-1/5*arctan(2*sinh(x)*sqrt(2/(3+sqrt(5))))*sqrt(1/2*(3+sqrt(5)))],
[sinh(x)*tanh(6*x),x,10,sinh(x)-1/3*arctan(sinh(x)*sqrt(2))/sqrt(2)-1/6*arctan(2*sinh(x)/sqrt(2-sqrt(3)))*sqrt(2-sqrt(3))-1/6*arctan(2*sinh(x)/sqrt(2+sqrt(3)))*sqrt(2+sqrt(3))],
[sinh(x)*tanh(n*x),x,6,1/2/exp(x)+1/2*exp(x)-hypergeom([1,(-1/2)/n],[1+(-1/2)/n],-exp(2*n*x))/exp(x)-exp(x)*hypergeom([1,1/2/n],[1/2*(2+1/n)],-exp(2*n*x))],
[coth(2*x)*sinh(x),x,3,-1/2*arctan(sinh(x))+sinh(x)],
[coth(3*x)*sinh(x),x,3,sinh(x)-arctan(2*sinh(x)/sqrt(3))/sqrt(3)],
[coth(4*x)*sinh(x),x,6,-1/4*arctan(sinh(x))+sinh(x)-1/2*arctan(sinh(x)*sqrt(2))/sqrt(2)],
[coth(5*x)*sinh(x),x,6,sinh(x)-1/5*arctan(sinh(x)*sqrt(2/5*(5+sqrt(5))))*sqrt(1/2*(5-sqrt(5)))-1/5*arctan(2*sinh(x)*sqrt(2/(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5)))],
[coth(6*x)*sinh(x),x,7,-1/6*arctan(sinh(x))-1/6*arctan(2*sinh(x))+sinh(x)-1/2*arctan(2*sinh(x)/sqrt(3))/sqrt(3)],
[sech(2*x)*sinh(x),x,2,-arctanh(cosh(x)*sqrt(2))/sqrt(2)],
[sech(3*x)*sinh(x),x,5,-1/3*log(cosh(x))+1/6*log(3-4*cosh(x)^2)],
[sech(4*x)*sinh(x),x,4,1/2*arctanh(2*cosh(x)/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-1/2*arctanh(2*cosh(x)/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))],
[sech(5*x)*sinh(x),x,7,1/5*log(cosh(x))-1/20*log(5-8*cosh(x)^2+sqrt(5))*(1-sqrt(5))-1/20*log(5-8*cosh(x)^2-sqrt(5))*(1+sqrt(5))],
[sech(6*x)*sinh(x),x,7,1/3*arctanh(cosh(x)*sqrt(2))/sqrt(2)-1/6*arctanh(2*cosh(x)/sqrt(2-sqrt(3)))/sqrt(2-sqrt(3))-1/6*arctanh(2*cosh(x)/sqrt(2+sqrt(3)))/sqrt(2+sqrt(3))],
[csch(2*x)*sinh(x),x,2,1/2*arctan(sinh(x))],
[csch(3*x)*sinh(x),x,2,arctan(tanh(x)/sqrt(3))/sqrt(3)],
[csch(4*x)*sinh(x),x,4,-1/4*arctan(sinh(x))+1/2*arctan(sinh(x)*sqrt(2))/sqrt(2)],
[csch(5*x)*sinh(x),x,4,1/5*arctan(tanh(x)/sqrt(5-2*sqrt(5)))*sqrt(1/2*(5-sqrt(5)))-1/5*arctan(tanh(x)/sqrt(5+2*sqrt(5)))*sqrt(1/2*(5+sqrt(5)))],
[csch(6*x)*sinh(x),x,7,1/6*arctan(sinh(x))+1/6*arctan(2*sinh(x))-1/2*arctan(2*sinh(x)/sqrt(3))/sqrt(3)],

# Integrands of the form Hyper[m x] Cosh[n x]
[cosh(x)*sinh(2*x),x,1,2/3*cosh(x)^3,1/2*cosh(x)+1/6*cosh(3*x)],
[cosh(x)*sinh(3*x),x,1,1/4*cosh(2*x)+1/8*cosh(4*x)],
[cosh(x)*sinh(4*x),x,1,1/6*cosh(3*x)+1/10*cosh(5*x)],
[cosh(x)*sinh(m*x),x,4,-1/2*cosh((1-m)*x)/(1-m)+1/2*cosh((1+m)*x)/(1+m)],
[cosh(x)*cosh(2*x),x,1,1/2*sinh(x)+1/6*sinh(3*x)],
[cosh(x)*cosh(3*x),x,1,1/4*sinh(2*x)+1/8*sinh(4*x)],
[cosh(x)*cosh(4*x),x,1,1/6*sinh(3*x)+1/10*sinh(5*x)],
[cosh(x)*cosh(m*x),x,4,1/2*sinh((1-m)*x)/(1-m)+1/2*sinh((1+m)*x)/(1+m)],
[cosh(x)*tanh(2*x),x,4,cosh(x)-arctanh(cosh(x)*sqrt(2))/sqrt(2)],
[cosh(x)*tanh(3*x),x,3,cosh(x)-arctanh(2*cosh(x)/sqrt(3))/sqrt(3)],
[cosh(x)*tanh(4*x),x,6,cosh(x)-1/4*arctanh(2*cosh(x)/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-1/4*arctanh(2*cosh(x)/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))],
[cosh(x)*tanh(5*x),x,6,cosh(x)-1/5*arctanh(cosh(x)*sqrt(2/5*(5+sqrt(5))))*sqrt(1/2*(5-sqrt(5)))-1/5*arctanh(2*cosh(x)*sqrt(2/(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5)))],
[cosh(x)*tanh(6*x),x,10,cosh(x)-1/3*arctanh(cosh(x)*sqrt(2))/sqrt(2)-1/6*arctanh(2*cosh(x)/sqrt(2-sqrt(3)))*sqrt(2-sqrt(3))-1/6*arctanh(2*cosh(x)/sqrt(2+sqrt(3)))*sqrt(2+sqrt(3))],
[cosh(x)*coth(2*x),x,4,-1/2*arctanh(cosh(x))+cosh(x)],
[cosh(x)*coth(3*x),x,9,cosh(x)+1/6*log(1-2*cosh(x))+1/6*log(1-cosh(x))-1/6*log(1+cosh(x))-1/6*log(1+2*cosh(x))],
[cosh(x)*coth(4*x),x,6,-1/4*arctanh(cosh(x))+cosh(x)-1/2*arctanh(cosh(x)*sqrt(2))/sqrt(2)],
[cosh(x)*coth(5*x),x,10,-1/5*arctanh(cosh(x))+cosh(x)+1/20*log(1-4*cosh(x)-sqrt(5))*(1-sqrt(5))-1/20*log(1+4*cosh(x)-sqrt(5))*(1-sqrt(5))+1/20*log(1-4*cosh(x)+sqrt(5))*(1+sqrt(5))-1/20*log(1+4*cosh(x)+sqrt(5))*(1+sqrt(5))],
[cosh(x)*coth(6*x),x,7,-1/6*arctanh(cosh(x))-1/6*arctanh(2*cosh(x))+cosh(x)-1/2*arctanh(2*cosh(x)/sqrt(3))/sqrt(3)],
[cosh(x)*coth(n*x),x,6,(-1/2)/exp(x)+1/2*exp(x)+hypergeom([1,(-1/2)/n],[1+(-1/2)/n],exp(2*n*x))/exp(x)-exp(x)*hypergeom([1,1/2/n],[1/2*(2+1/n)],exp(2*n*x))],
[cosh(x)*sech(2*x),x,2,arctan(sinh(x)*sqrt(2))/sqrt(2)],
[cosh(x)*sech(3*x),x,2,arctan(sqrt(3)*tanh(x))/sqrt(3)],
[cosh(x)*sech(4*x),x,4,1/2*arctan(2*sinh(x)/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-1/2*arctan(2*sinh(x)/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))],
[cosh(x)*sech(5*x),x,4,-1/5*arctan(sqrt(5-2*sqrt(5))*tanh(x))*sqrt(1/2*(5-sqrt(5)))+1/5*arctan(sqrt(5+2*sqrt(5))*tanh(x))*sqrt(1/2*(5+sqrt(5)))],
[cosh(x)*sech(6*x),x,7,-1/3*arctan(sinh(x)*sqrt(2))/sqrt(2)+1/6*arctan(2*sinh(x)/sqrt(2-sqrt(3)))/sqrt(2-sqrt(3))+1/6*arctan(2*sinh(x)/sqrt(2+sqrt(3)))/sqrt(2+sqrt(3))],
[cosh(x)*csch(2*x),x,2,-1/2*arctanh(cosh(x))],
[cosh(x)*csch(3*x),x,5,1/3*log(sinh(x))-1/6*log(3+4*sinh(x)^2)],
[cosh(x)*csch(4*x),x,4,-1/4*arctanh(cosh(x))+1/2*arctanh(cosh(x)*sqrt(2))/sqrt(2)],
[cosh(x)*csch(5*x),x,7,1/5*log(sinh(x))-1/20*log(5+8*sinh(x)^2+sqrt(5))*(1-sqrt(5))-1/20*log(5+8*sinh(x)^2-sqrt(5))*(1+sqrt(5))],
[cosh(x)*csch(6*x),x,7,-1/6*arctanh(cosh(x))-1/6*arctanh(2*cosh(x))+1/2*arctanh(2*cosh(x)/sqrt(3))/sqrt(3)],

# Integrands of the form x^m Hyper[a+b x]^n Hyper[a+b x]^p

# Integrands of the form x^m Cosh[a+b x]^n Sinh[a+b x]^p

# p=1
[x^m*cosh(a+b*x)*sinh(a+b*x),x,5,2^(-3-m)*exp(2*a)*x^m*GAMMA(1+m,-2*b*x)/(b*(-b*x)^m)+2^(-3-m)*x^m*GAMMA(1+m,2*b*x)/(b*exp(2*a)*(b*x)^m)],
[x^3*cosh(a+b*x)*sinh(a+b*x),x,5,3/8*x/b^3+1/4*x^3/b-3/8*cosh(a+b*x)*sinh(a+b*x)/b^4-3/4*x^2*cosh(a+b*x)*sinh(a+b*x)/b^2+3/4*x*sinh(a+b*x)^2/b^3+1/2*x^3*sinh(a+b*x)^2/b],
[x^2*cosh(a+b*x)*sinh(a+b*x),x,3,1/4*x^2/b-1/2*x*cosh(a+b*x)*sinh(a+b*x)/b^2+1/4*sinh(a+b*x)^2/b^3+1/2*x^2*sinh(a+b*x)^2/b],
[x*cosh(a+b*x)*sinh(a+b*x),x,3,1/4*x/b-1/4*cosh(a+b*x)*sinh(a+b*x)/b^2+1/2*x*sinh(a+b*x)^2/b],
[cosh(a+b*x)*sinh(a+b*x),x,2,1/2*sinh(a+b*x)^2/b],
[cosh(a+b*x)*sinh(a+b*x)/x,x,5,1/2*cosh(2*a)*Shi(2*b*x)+1/2*Chi(2*b*x)*sinh(2*a)],
[cosh(a+b*x)*sinh(a+b*x)/x^2,x,6,b*Chi(2*b*x)*cosh(2*a)+b*Shi(2*b*x)*sinh(2*a)-1/2*sinh(2*a+2*b*x)/x],
[cosh(a+b*x)*sinh(a+b*x)/x^3,x,7,-1/2*b*cosh(2*a+2*b*x)/x+b^2*cosh(2*a)*Shi(2*b*x)+b^2*Chi(2*b*x)*sinh(2*a)-1/4*sinh(2*a+2*b*x)/x^2],
[cosh(a+b*x)*sinh(a+b*x)/x^4,x,8,2/3*b^3*Chi(2*b*x)*cosh(2*a)-1/6*b*cosh(2*a+2*b*x)/x^2+2/3*b^3*Shi(2*b*x)*sinh(2*a)-1/6*sinh(2*a+2*b*x)/x^3-1/3*b^2*sinh(2*a+2*b*x)/x],
[x^m*cosh(a+b*x)^2*sinh(a+b*x),x,8,1/8*3^(-1-m)*exp(3*a)*x^m*GAMMA(1+m,-3*b*x)/(b*(-b*x)^m)+1/8*exp(a)*x^m*GAMMA(1+m,-b*x)/(b*(-b*x)^m)+1/8*x^m*GAMMA(1+m,b*x)/(b*exp(a)*(b*x)^m)+1/8*3^(-1-m)*x^m*GAMMA(1+m,3*b*x)/(b*exp(3*a)*(b*x)^m)],
[x^3*cosh(a+b*x)^2*sinh(a+b*x),x,7,4/3*x*cosh(a+b*x)/b^3+2/9*x*cosh(a+b*x)^3/b^3+1/3*x^3*cosh(a+b*x)^3/b-14/9*sinh(a+b*x)/b^4-2/3*x^2*sinh(a+b*x)/b^2-1/3*x^2*cosh(a+b*x)^2*sinh(a+b*x)/b^2-2/27*sinh(a+b*x)^3/b^4],
[x^2*cosh(a+b*x)^2*sinh(a+b*x),x,4,4/9*cosh(a+b*x)/b^3+2/27*cosh(a+b*x)^3/b^3+1/3*x^2*cosh(a+b*x)^3/b-4/9*x*sinh(a+b*x)/b^2-2/9*x*cosh(a+b*x)^2*sinh(a+b*x)/b^2],
[x*cosh(a+b*x)^2*sinh(a+b*x),x,3,1/3*x*cosh(a+b*x)^3/b-1/3*sinh(a+b*x)/b^2-1/9*sinh(a+b*x)^3/b^2],
[cosh(a+b*x)^2*sinh(a+b*x),x,2,1/3*cosh(a+b*x)^3/b],
[cosh(a+b*x)^2*sinh(a+b*x)/x,x,8,1/4*cosh(a)*Shi(b*x)+1/4*cosh(3*a)*Shi(3*b*x)+1/4*Chi(b*x)*sinh(a)+1/4*Chi(3*b*x)*sinh(3*a)],
[cosh(a+b*x)^2*sinh(a+b*x)/x^2,x,10,1/4*b*Chi(b*x)*cosh(a)+3/4*b*Chi(3*b*x)*cosh(3*a)+1/4*b*Shi(b*x)*sinh(a)+3/4*b*Shi(3*b*x)*sinh(3*a)-1/4*sinh(a+b*x)/x-1/4*sinh(3*a+3*b*x)/x],
[cosh(a+b*x)^2*sinh(a+b*x)/x^3,x,12,-1/8*b*cosh(a+b*x)/x-3/8*b*cosh(3*a+3*b*x)/x+1/8*b^2*cosh(a)*Shi(b*x)+9/8*b^2*cosh(3*a)*Shi(3*b*x)+1/8*b^2*Chi(b*x)*sinh(a)+9/8*b^2*Chi(3*b*x)*sinh(3*a)-1/8*sinh(a+b*x)/x^2-1/8*sinh(3*a+3*b*x)/x^2],
[cosh(a+b*x)^2*sinh(a+b*x)/x^4,x,14,1/24*b^3*Chi(b*x)*cosh(a)+9/8*b^3*Chi(3*b*x)*cosh(3*a)-1/24*b*cosh(a+b*x)/x^2-1/8*b*cosh(3*a+3*b*x)/x^2+1/24*b^3*Shi(b*x)*sinh(a)+9/8*b^3*Shi(3*b*x)*sinh(3*a)-1/12*sinh(a+b*x)/x^3-1/24*b^2*sinh(a+b*x)/x-1/12*sinh(3*a+3*b*x)/x^3-3/8*b^2*sinh(3*a+3*b*x)/x],
[x^m*cosh(a+b*x)^3*sinh(a+b*x),x,8,exp(4*a)*x^m*GAMMA(1+m,-4*b*x)/(2^(2*(3+m))*b*(-b*x)^m)+2^(-4-m)*exp(2*a)*x^m*GAMMA(1+m,-2*b*x)/(b*(-b*x)^m)+2^(-4-m)*x^m*GAMMA(1+m,2*b*x)/(b*exp(2*a)*(b*x)^m)+x^m*GAMMA(1+m,4*b*x)/(2^(2*(3+m))*b*exp(4*a)*(b*x)^m)],
[x^3*cosh(a+b*x)^3*sinh(a+b*x),x,9,-45/256*x/b^3-3/32*x^3/b+9/32*x*cosh(a+b*x)^2/b^3+3/32*x*cosh(a+b*x)^4/b^3+1/4*x^3*cosh(a+b*x)^4/b-45/256*cosh(a+b*x)*sinh(a+b*x)/b^4-9/32*x^2*cosh(a+b*x)*sinh(a+b*x)/b^2-3/128*cosh(a+b*x)^3*sinh(a+b*x)/b^4-3/16*x^2*cosh(a+b*x)^3*sinh(a+b*x)/b^2],
[x^2*cosh(a+b*x)^3*sinh(a+b*x),x,4,-3/32*x^2/b+3/32*cosh(a+b*x)^2/b^3+1/32*cosh(a+b*x)^4/b^3+1/4*x^2*cosh(a+b*x)^4/b-3/16*x*cosh(a+b*x)*sinh(a+b*x)/b^2-1/8*x*cosh(a+b*x)^3*sinh(a+b*x)/b^2],
[x*cosh(a+b*x)^3*sinh(a+b*x),x,4,-3/32*x/b+1/4*x*cosh(a+b*x)^4/b-3/32*cosh(a+b*x)*sinh(a+b*x)/b^2-1/16*cosh(a+b*x)^3*sinh(a+b*x)/b^2],
[cosh(a+b*x)^3*sinh(a+b*x),x,2,1/4*cosh(a+b*x)^4/b],
[cosh(a+b*x)^3*sinh(a+b*x)/x,x,8,1/4*cosh(2*a)*Shi(2*b*x)+1/8*cosh(4*a)*Shi(4*b*x)+1/4*Chi(2*b*x)*sinh(2*a)+1/8*Chi(4*b*x)*sinh(4*a)],
[cosh(a+b*x)^3*sinh(a+b*x)/x^2,x,10,1/2*b*Chi(2*b*x)*cosh(2*a)+1/2*b*Chi(4*b*x)*cosh(4*a)+1/2*b*Shi(2*b*x)*sinh(2*a)+1/2*b*Shi(4*b*x)*sinh(4*a)-1/4*sinh(2*a+2*b*x)/x-1/8*sinh(4*a+4*b*x)/x],
[cosh(a+b*x)^3*sinh(a+b*x)/x^3,x,12,-1/4*b*cosh(2*a+2*b*x)/x-1/4*b*cosh(4*a+4*b*x)/x+1/2*b^2*cosh(2*a)*Shi(2*b*x)+b^2*cosh(4*a)*Shi(4*b*x)+1/2*b^2*Chi(2*b*x)*sinh(2*a)+b^2*Chi(4*b*x)*sinh(4*a)-1/8*sinh(2*a+2*b*x)/x^2-1/16*sinh(4*a+4*b*x)/x^2],
[cosh(a+b*x)^3*sinh(a+b*x)/x^4,x,14,1/3*b^3*Chi(2*b*x)*cosh(2*a)+4/3*b^3*Chi(4*b*x)*cosh(4*a)-1/12*b*cosh(2*a+2*b*x)/x^2-1/12*b*cosh(4*a+4*b*x)/x^2+1/3*b^3*Shi(2*b*x)*sinh(2*a)+4/3*b^3*Shi(4*b*x)*sinh(4*a)-1/12*sinh(2*a+2*b*x)/x^3-1/6*b^2*sinh(2*a+2*b*x)/x-1/24*sinh(4*a+4*b*x)/x^3-1/3*b^2*sinh(4*a+4*b*x)/x],
[cosh(x)*sinh(x)/x,x,3,1/2*Shi(2*x)],
[cosh(x)*sinh(x)/x^2,x,4,Chi(2*x)-1/2*sinh(2*x)/x],
[cosh(x)*sinh(x)/x^3,x,5,-1/2*cosh(2*x)/x+Shi(2*x)-1/4*sinh(2*x)/x^2],

# p=2
[x^m*cosh(a+b*x)*sinh(a+b*x)^2,x,8,1/8*3^(-1-m)*exp(3*a)*x^m*GAMMA(1+m,-3*b*x)/(b*(-b*x)^m)-1/8*exp(a)*x^m*GAMMA(1+m,-b*x)/(b*(-b*x)^m)+1/8*x^m*GAMMA(1+m,b*x)/(b*exp(a)*(b*x)^m)-1/8*3^(-1-m)*x^m*GAMMA(1+m,3*b*x)/(b*exp(3*a)*(b*x)^m)],
[x^3*cosh(a+b*x)*sinh(a+b*x)^2,x,7,14/9*cosh(a+b*x)/b^4+2/3*x^2*cosh(a+b*x)/b^2-2/27*cosh(a+b*x)^3/b^4-4/3*x*sinh(a+b*x)/b^3-1/3*x^2*cosh(a+b*x)*sinh(a+b*x)^2/b^2+2/9*x*sinh(a+b*x)^3/b^3+1/3*x^3*sinh(a+b*x)^3/b],
[x^2*cosh(a+b*x)*sinh(a+b*x)^2,x,4,4/9*x*cosh(a+b*x)/b^2-4/9*sinh(a+b*x)/b^3-2/9*x*cosh(a+b*x)*sinh(a+b*x)^2/b^2+2/27*sinh(a+b*x)^3/b^3+1/3*x^2*sinh(a+b*x)^3/b],
[x*cosh(a+b*x)*sinh(a+b*x)^2,x,3,1/3*cosh(a+b*x)/b^2-1/9*cosh(a+b*x)^3/b^2+1/3*x*sinh(a+b*x)^3/b],
[cosh(a+b*x)*sinh(a+b*x)^2,x,2,1/3*sinh(a+b*x)^3/b],
[cosh(a+b*x)*sinh(a+b*x)^2/x,x,8,-1/4*Chi(b*x)*cosh(a)+1/4*Chi(3*b*x)*cosh(3*a)-1/4*Shi(b*x)*sinh(a)+1/4*Shi(3*b*x)*sinh(3*a)],
[cosh(a+b*x)*sinh(a+b*x)^2/x^2,x,10,1/4*cosh(a+b*x)/x-1/4*cosh(3*a+3*b*x)/x-1/4*b*cosh(a)*Shi(b*x)+3/4*b*cosh(3*a)*Shi(3*b*x)-1/4*b*Chi(b*x)*sinh(a)+3/4*b*Chi(3*b*x)*sinh(3*a)],
[cosh(a+b*x)*sinh(a+b*x)^2/x^3,x,12,-1/8*b^2*Chi(b*x)*cosh(a)+9/8*b^2*Chi(3*b*x)*cosh(3*a)+1/8*cosh(a+b*x)/x^2-1/8*cosh(3*a+3*b*x)/x^2-1/8*b^2*Shi(b*x)*sinh(a)+9/8*b^2*Shi(3*b*x)*sinh(3*a)+1/8*b*sinh(a+b*x)/x-3/8*b*sinh(3*a+3*b*x)/x],
[cosh(a+b*x)*sinh(a+b*x)^2/x^4,x,14,1/12*cosh(a+b*x)/x^3+1/24*b^2*cosh(a+b*x)/x-1/12*cosh(3*a+3*b*x)/x^3-3/8*b^2*cosh(3*a+3*b*x)/x-1/24*b^3*cosh(a)*Shi(b*x)+9/8*b^3*cosh(3*a)*Shi(3*b*x)-1/24*b^3*Chi(b*x)*sinh(a)+9/8*b^3*Chi(3*b*x)*sinh(3*a)+1/24*b*sinh(a+b*x)/x^2-1/8*b*sinh(3*a+3*b*x)/x^2],
[x^m*cosh(a+b*x)^2*sinh(a+b*x)^2,x,5,-1/8*x^(1+m)/(1+m)+exp(4*a)*x^m*GAMMA(1+m,-4*b*x)/(2^(2*(3+m))*b*(-b*x)^m)-x^m*GAMMA(1+m,4*b*x)/(2^(2*(3+m))*b*exp(4*a)*(b*x)^m)],
[x^3*cosh(a+b*x)^2*sinh(a+b*x)^2,x,6,-1/32*x^4-3/1024*cosh(4*a+4*b*x)/b^4-3/128*x^2*cosh(4*a+4*b*x)/b^2+3/256*x*sinh(4*a+4*b*x)/b^3+1/32*x^3*sinh(4*a+4*b*x)/b],
[x^2*cosh(a+b*x)^2*sinh(a+b*x)^2,x,5,-1/24*x^3-1/64*x*cosh(4*a+4*b*x)/b^2+1/256*sinh(4*a+4*b*x)/b^3+1/32*x^2*sinh(4*a+4*b*x)/b],
[x*cosh(a+b*x)^2*sinh(a+b*x)^2,x,4,-1/16*x^2-1/128*cosh(4*a+4*b*x)/b^2+1/32*x*sinh(4*a+4*b*x)/b],
[cosh(a+b*x)^2*sinh(a+b*x)^2,x,3,-1/8*x-1/8*cosh(a+b*x)*sinh(a+b*x)/b+1/4*cosh(a+b*x)^3*sinh(a+b*x)/b],
[cosh(a+b*x)^2*sinh(a+b*x)^2/x,x,5,1/8*Chi(4*b*x)*cosh(4*a)-1/8*log(x)+1/8*Shi(4*b*x)*sinh(4*a)],
[cosh(a+b*x)^2*sinh(a+b*x)^2/x^2,x,6,1/8/x-1/8*cosh(4*a+4*b*x)/x+1/2*b*cosh(4*a)*Shi(4*b*x)+1/2*b*Chi(4*b*x)*sinh(4*a)],
[cosh(a+b*x)^2*sinh(a+b*x)^2/x^3,x,7,1/16/x^2+b^2*Chi(4*b*x)*cosh(4*a)-1/16*cosh(4*a+4*b*x)/x^2+b^2*Shi(4*b*x)*sinh(4*a)-1/4*b*sinh(4*a+4*b*x)/x],
[cosh(a+b*x)^2*sinh(a+b*x)^2/x^4,x,8,1/24/x^3-1/24*cosh(4*a+4*b*x)/x^3-1/3*b^2*cosh(4*a+4*b*x)/x+4/3*b^3*cosh(4*a)*Shi(4*b*x)+4/3*b^3*Chi(4*b*x)*sinh(4*a)-1/12*b*sinh(4*a+4*b*x)/x^2],
[x^m*cosh(a+b*x)^3*sinh(a+b*x)^2,x,11,1/32*5^(-1-m)*exp(5*a)*x^m*GAMMA(1+m,-5*b*x)/(b*(-b*x)^m)+1/32*3^(-1-m)*exp(3*a)*x^m*GAMMA(1+m,-3*b*x)/(b*(-b*x)^m)-1/16*exp(a)*x^m*GAMMA(1+m,-b*x)/(b*(-b*x)^m)+1/16*x^m*GAMMA(1+m,b*x)/(b*exp(a)*(b*x)^m)-1/32*3^(-1-m)*x^m*GAMMA(1+m,3*b*x)/(b*exp(3*a)*(b*x)^m)-1/32*5^(-1-m)*x^m*GAMMA(1+m,5*b*x)/(b*exp(5*a)*(b*x)^m)],
[x^3*cosh(a+b*x)^3*sinh(a+b*x)^2,x,14,3/4*cosh(a+b*x)/b^4+3/8*x^2*cosh(a+b*x)/b^2-1/216*cosh(3*a+3*b*x)/b^4-1/48*x^2*cosh(3*a+3*b*x)/b^2-3/5000*cosh(5*a+5*b*x)/b^4-3/400*x^2*cosh(5*a+5*b*x)/b^2-3/4*x*sinh(a+b*x)/b^3-1/8*x^3*sinh(a+b*x)/b+1/72*x*sinh(3*a+3*b*x)/b^3+1/48*x^3*sinh(3*a+3*b*x)/b+3/1000*x*sinh(5*a+5*b*x)/b^3+1/80*x^3*sinh(5*a+5*b*x)/b],
[x^2*cosh(a+b*x)^3*sinh(a+b*x)^2,x,11,1/4*x*cosh(a+b*x)/b^2-1/72*x*cosh(3*a+3*b*x)/b^2-1/200*x*cosh(5*a+5*b*x)/b^2-1/4*sinh(a+b*x)/b^3-1/8*x^2*sinh(a+b*x)/b+1/216*sinh(3*a+3*b*x)/b^3+1/48*x^2*sinh(3*a+3*b*x)/b+1/1000*sinh(5*a+5*b*x)/b^3+1/80*x^2*sinh(5*a+5*b*x)/b],
[x*cosh(a+b*x)^3*sinh(a+b*x)^2,x,8,1/8*cosh(a+b*x)/b^2-1/144*cosh(3*a+3*b*x)/b^2-1/400*cosh(5*a+5*b*x)/b^2-1/8*x*sinh(a+b*x)/b+1/48*x*sinh(3*a+3*b*x)/b+1/80*x*sinh(5*a+5*b*x)/b],
[cosh(a+b*x)^3*sinh(a+b*x)^2,x,3,1/3*sinh(a+b*x)^3/b+1/5*sinh(a+b*x)^5/b],
[cosh(a+b*x)^3*sinh(a+b*x)^2/x,x,11,-1/8*Chi(b*x)*cosh(a)+1/16*Chi(3*b*x)*cosh(3*a)+1/16*Chi(5*b*x)*cosh(5*a)-1/8*Shi(b*x)*sinh(a)+1/16*Shi(3*b*x)*sinh(3*a)+1/16*Shi(5*b*x)*sinh(5*a)],
[cosh(a+b*x)^3*sinh(a+b*x)^2/x^2,x,14,1/8*cosh(a+b*x)/x-1/16*cosh(3*a+3*b*x)/x-1/16*cosh(5*a+5*b*x)/x-1/8*b*cosh(a)*Shi(b*x)+3/16*b*cosh(3*a)*Shi(3*b*x)+5/16*b*cosh(5*a)*Shi(5*b*x)-1/8*b*Chi(b*x)*sinh(a)+3/16*b*Chi(3*b*x)*sinh(3*a)+5/16*b*Chi(5*b*x)*sinh(5*a)],
[cosh(a+b*x)^3*sinh(a+b*x)^2/x^3,x,17,-1/16*b^2*Chi(b*x)*cosh(a)+9/32*b^2*Chi(3*b*x)*cosh(3*a)+25/32*b^2*Chi(5*b*x)*cosh(5*a)+1/16*cosh(a+b*x)/x^2-1/32*cosh(3*a+3*b*x)/x^2-1/32*cosh(5*a+5*b*x)/x^2-1/16*b^2*Shi(b*x)*sinh(a)+9/32*b^2*Shi(3*b*x)*sinh(3*a)+25/32*b^2*Shi(5*b*x)*sinh(5*a)+1/16*b*sinh(a+b*x)/x-3/32*b*sinh(3*a+3*b*x)/x-5/32*b*sinh(5*a+5*b*x)/x],
[cosh(a+b*x)^3*sinh(a+b*x)^2/x^4,x,20,1/24*cosh(a+b*x)/x^3+1/48*b^2*cosh(a+b*x)/x-1/48*cosh(3*a+3*b*x)/x^3-3/32*b^2*cosh(3*a+3*b*x)/x-1/48*cosh(5*a+5*b*x)/x^3-25/96*b^2*cosh(5*a+5*b*x)/x-1/48*b^3*cosh(a)*Shi(b*x)+9/32*b^3*cosh(3*a)*Shi(3*b*x)+125/96*b^3*cosh(5*a)*Shi(5*b*x)-1/48*b^3*Chi(b*x)*sinh(a)+9/32*b^3*Chi(3*b*x)*sinh(3*a)+125/96*b^3*Chi(5*b*x)*sinh(5*a)+1/48*b*sinh(a+b*x)/x^2-1/32*b*sinh(3*a+3*b*x)/x^2-5/96*b*sinh(5*a+5*b*x)/x^2],

# p=3
[x^m*cosh(a+b*x)*sinh(a+b*x)^3,x,8,exp(4*a)*x^m*GAMMA(1+m,-4*b*x)/(2^(2*(3+m))*b*(-b*x)^m)-2^(-4-m)*exp(2*a)*x^m*GAMMA(1+m,-2*b*x)/(b*(-b*x)^m)-2^(-4-m)*x^m*GAMMA(1+m,2*b*x)/(b*exp(2*a)*(b*x)^m)+x^m*GAMMA(1+m,4*b*x)/(2^(2*(3+m))*b*exp(4*a)*(b*x)^m)],
[x^3*cosh(a+b*x)*sinh(a+b*x)^3,x,9,-45/256*x/b^3-3/32*x^3/b+45/256*cosh(a+b*x)*sinh(a+b*x)/b^4+9/32*x^2*cosh(a+b*x)*sinh(a+b*x)/b^2-9/32*x*sinh(a+b*x)^2/b^3-3/128*cosh(a+b*x)*sinh(a+b*x)^3/b^4-3/16*x^2*cosh(a+b*x)*sinh(a+b*x)^3/b^2+3/32*x*sinh(a+b*x)^4/b^3+1/4*x^3*sinh(a+b*x)^4/b],
[x^2*cosh(a+b*x)*sinh(a+b*x)^3,x,4,-3/32*x^2/b+3/16*x*cosh(a+b*x)*sinh(a+b*x)/b^2-3/32*sinh(a+b*x)^2/b^3-1/8*x*cosh(a+b*x)*sinh(a+b*x)^3/b^2+1/32*sinh(a+b*x)^4/b^3+1/4*x^2*sinh(a+b*x)^4/b],
[x*cosh(a+b*x)*sinh(a+b*x)^3,x,4,-3/32*x/b+3/32*cosh(a+b*x)*sinh(a+b*x)/b^2-1/16*cosh(a+b*x)*sinh(a+b*x)^3/b^2+1/4*x*sinh(a+b*x)^4/b],
[cosh(a+b*x)*sinh(a+b*x)^3,x,2,1/4*sinh(a+b*x)^4/b],
[cosh(a+b*x)*sinh(a+b*x)^3/x,x,8,-1/4*cosh(2*a)*Shi(2*b*x)+1/8*cosh(4*a)*Shi(4*b*x)-1/4*Chi(2*b*x)*sinh(2*a)+1/8*Chi(4*b*x)*sinh(4*a)],
[cosh(a+b*x)*sinh(a+b*x)^3/x^2,x,10,-1/2*b*Chi(2*b*x)*cosh(2*a)+1/2*b*Chi(4*b*x)*cosh(4*a)-1/2*b*Shi(2*b*x)*sinh(2*a)+1/2*b*Shi(4*b*x)*sinh(4*a)+1/4*sinh(2*a+2*b*x)/x-1/8*sinh(4*a+4*b*x)/x],
[cosh(a+b*x)*sinh(a+b*x)^3/x^3,x,12,1/4*b*cosh(2*a+2*b*x)/x-1/4*b*cosh(4*a+4*b*x)/x-1/2*b^2*cosh(2*a)*Shi(2*b*x)+b^2*cosh(4*a)*Shi(4*b*x)-1/2*b^2*Chi(2*b*x)*sinh(2*a)+b^2*Chi(4*b*x)*sinh(4*a)+1/8*sinh(2*a+2*b*x)/x^2-1/16*sinh(4*a+4*b*x)/x^2],
[cosh(a+b*x)*sinh(a+b*x)^3/x^4,x,14,-1/3*b^3*Chi(2*b*x)*cosh(2*a)+4/3*b^3*Chi(4*b*x)*cosh(4*a)+1/12*b*cosh(2*a+2*b*x)/x^2-1/12*b*cosh(4*a+4*b*x)/x^2-1/3*b^3*Shi(2*b*x)*sinh(2*a)+4/3*b^3*Shi(4*b*x)*sinh(4*a)+1/12*sinh(2*a+2*b*x)/x^3+1/6*b^2*sinh(2*a+2*b*x)/x-1/24*sinh(4*a+4*b*x)/x^3-1/3*b^2*sinh(4*a+4*b*x)/x],
[x^m*cosh(a+b*x)^2*sinh(a+b*x)^3,x,11,1/32*5^(-1-m)*exp(5*a)*x^m*GAMMA(1+m,-5*b*x)/(b*(-b*x)^m)-1/32*3^(-1-m)*exp(3*a)*x^m*GAMMA(1+m,-3*b*x)/(b*(-b*x)^m)-1/16*exp(a)*x^m*GAMMA(1+m,-b*x)/(b*(-b*x)^m)-1/16*x^m*GAMMA(1+m,b*x)/(b*exp(a)*(b*x)^m)-1/32*3^(-1-m)*x^m*GAMMA(1+m,3*b*x)/(b*exp(3*a)*(b*x)^m)+1/32*5^(-1-m)*x^m*GAMMA(1+m,5*b*x)/(b*exp(5*a)*(b*x)^m)],
[x^3*cosh(a+b*x)^2*sinh(a+b*x)^3,x,14,-3/4*x*cosh(a+b*x)/b^3-1/8*x^3*cosh(a+b*x)/b-1/72*x*cosh(3*a+3*b*x)/b^3-1/48*x^3*cosh(3*a+3*b*x)/b+3/1000*x*cosh(5*a+5*b*x)/b^3+1/80*x^3*cosh(5*a+5*b*x)/b+3/4*sinh(a+b*x)/b^4+3/8*x^2*sinh(a+b*x)/b^2+1/216*sinh(3*a+3*b*x)/b^4+1/48*x^2*sinh(3*a+3*b*x)/b^2-3/5000*sinh(5*a+5*b*x)/b^4-3/400*x^2*sinh(5*a+5*b*x)/b^2],
[x^2*cosh(a+b*x)^2*sinh(a+b*x)^3,x,11,-1/4*cosh(a+b*x)/b^3-1/8*x^2*cosh(a+b*x)/b-1/216*cosh(3*a+3*b*x)/b^3-1/48*x^2*cosh(3*a+3*b*x)/b+1/1000*cosh(5*a+5*b*x)/b^3+1/80*x^2*cosh(5*a+5*b*x)/b+1/4*x*sinh(a+b*x)/b^2+1/72*x*sinh(3*a+3*b*x)/b^2-1/200*x*sinh(5*a+5*b*x)/b^2],
[x*cosh(a+b*x)^2*sinh(a+b*x)^3,x,8,-1/8*x*cosh(a+b*x)/b-1/48*x*cosh(3*a+3*b*x)/b+1/80*x*cosh(5*a+5*b*x)/b+1/8*sinh(a+b*x)/b^2+1/144*sinh(3*a+3*b*x)/b^2-1/400*sinh(5*a+5*b*x)/b^2],
[cosh(a+b*x)^2*sinh(a+b*x)^3,x,3,-1/3*cosh(a+b*x)^3/b+1/5*cosh(a+b*x)^5/b],
[cosh(a+b*x)^2*sinh(a+b*x)^3/x,x,11,-1/8*cosh(a)*Shi(b*x)-1/16*cosh(3*a)*Shi(3*b*x)+1/16*cosh(5*a)*Shi(5*b*x)-1/8*Chi(b*x)*sinh(a)-1/16*Chi(3*b*x)*sinh(3*a)+1/16*Chi(5*b*x)*sinh(5*a)],
[cosh(a+b*x)^2*sinh(a+b*x)^3/x^2,x,14,-1/8*b*Chi(b*x)*cosh(a)-3/16*b*Chi(3*b*x)*cosh(3*a)+5/16*b*Chi(5*b*x)*cosh(5*a)-1/8*b*Shi(b*x)*sinh(a)-3/16*b*Shi(3*b*x)*sinh(3*a)+5/16*b*Shi(5*b*x)*sinh(5*a)+1/8*sinh(a+b*x)/x+1/16*sinh(3*a+3*b*x)/x-1/16*sinh(5*a+5*b*x)/x],
[cosh(a+b*x)^2*sinh(a+b*x)^3/x^3,x,17,1/16*b*cosh(a+b*x)/x+3/32*b*cosh(3*a+3*b*x)/x-5/32*b*cosh(5*a+5*b*x)/x-1/16*b^2*cosh(a)*Shi(b*x)-9/32*b^2*cosh(3*a)*Shi(3*b*x)+25/32*b^2*cosh(5*a)*Shi(5*b*x)-1/16*b^2*Chi(b*x)*sinh(a)-9/32*b^2*Chi(3*b*x)*sinh(3*a)+25/32*b^2*Chi(5*b*x)*sinh(5*a)+1/16*sinh(a+b*x)/x^2+1/32*sinh(3*a+3*b*x)/x^2-1/32*sinh(5*a+5*b*x)/x^2],
[cosh(a+b*x)^2*sinh(a+b*x)^3/x^4,x,20,-1/48*b^3*Chi(b*x)*cosh(a)-9/32*b^3*Chi(3*b*x)*cosh(3*a)+125/96*b^3*Chi(5*b*x)*cosh(5*a)+1/48*b*cosh(a+b*x)/x^2+1/32*b*cosh(3*a+3*b*x)/x^2-5/96*b*cosh(5*a+5*b*x)/x^2-1/48*b^3*Shi(b*x)*sinh(a)-9/32*b^3*Shi(3*b*x)*sinh(3*a)+125/96*b^3*Shi(5*b*x)*sinh(5*a)+1/24*sinh(a+b*x)/x^3+1/48*b^2*sinh(a+b*x)/x+1/48*sinh(3*a+3*b*x)/x^3+3/32*b^2*sinh(3*a+3*b*x)/x-1/48*sinh(5*a+5*b*x)/x^3-25/96*b^2*sinh(5*a+5*b*x)/x],
[x^m*cosh(a+b*x)^3*sinh(a+b*x)^3,x,8,2^(-7-m)*3^(-1-m)*exp(6*a)*x^m*GAMMA(1+m,-6*b*x)/(b*(-b*x)^m)-3*2^(-7-m)*exp(2*a)*x^m*GAMMA(1+m,-2*b*x)/(b*(-b*x)^m)-3*2^(-7-m)*x^m*GAMMA(1+m,2*b*x)/(b*exp(2*a)*(b*x)^m)+2^(-7-m)*3^(-1-m)*x^m*GAMMA(1+m,6*b*x)/(b*exp(6*a)*(b*x)^m)],
[x^3*cosh(a+b*x)^3*sinh(a+b*x)^3,x,10,-9/128*x*cosh(2*a+2*b*x)/b^3-3/64*x^3*cosh(2*a+2*b*x)/b+1/1152*x*cosh(6*a+6*b*x)/b^3+1/192*x^3*cosh(6*a+6*b*x)/b+9/256*sinh(2*a+2*b*x)/b^4+9/128*x^2*sinh(2*a+2*b*x)/b^2-1/6912*sinh(6*a+6*b*x)/b^4-1/384*x^2*sinh(6*a+6*b*x)/b^2],
[x^2*cosh(a+b*x)^3*sinh(a+b*x)^3,x,8,-3/128*cosh(2*a+2*b*x)/b^3-3/64*x^2*cosh(2*a+2*b*x)/b+1/3456*cosh(6*a+6*b*x)/b^3+1/192*x^2*cosh(6*a+6*b*x)/b+3/64*x*sinh(2*a+2*b*x)/b^2-1/576*x*sinh(6*a+6*b*x)/b^2],
[x*cosh(a+b*x)^3*sinh(a+b*x)^3,x,6,-3/64*x*cosh(2*a+2*b*x)/b+1/192*x*cosh(6*a+6*b*x)/b+3/128*sinh(2*a+2*b*x)/b^2-1/1152*sinh(6*a+6*b*x)/b^2],
[cosh(a+b*x)^3*sinh(a+b*x)^3,x,3,1/4*sinh(a+b*x)^4/b+1/6*sinh(a+b*x)^6/b],
[cosh(a+b*x)^3*sinh(a+b*x)^3/x,x,8,-3/32*cosh(2*a)*Shi(2*b*x)+1/32*cosh(6*a)*Shi(6*b*x)-3/32*Chi(2*b*x)*sinh(2*a)+1/32*Chi(6*b*x)*sinh(6*a)],
[cosh(a+b*x)^3*sinh(a+b*x)^3/x^2,x,10,-3/16*b*Chi(2*b*x)*cosh(2*a)+3/16*b*Chi(6*b*x)*cosh(6*a)-3/16*b*Shi(2*b*x)*sinh(2*a)+3/16*b*Shi(6*b*x)*sinh(6*a)+3/32*sinh(2*a+2*b*x)/x-1/32*sinh(6*a+6*b*x)/x],
[cosh(a+b*x)^3*sinh(a+b*x)^3/x^3,x,12,3/32*b*cosh(2*a+2*b*x)/x-3/32*b*cosh(6*a+6*b*x)/x-3/16*b^2*cosh(2*a)*Shi(2*b*x)+9/16*b^2*cosh(6*a)*Shi(6*b*x)-3/16*b^2*Chi(2*b*x)*sinh(2*a)+9/16*b^2*Chi(6*b*x)*sinh(6*a)+3/64*sinh(2*a+2*b*x)/x^2-1/64*sinh(6*a+6*b*x)/x^2],
[cosh(a+b*x)^3*sinh(a+b*x)^3/x^4,x,14,-1/8*b^3*Chi(2*b*x)*cosh(2*a)+9/8*b^3*Chi(6*b*x)*cosh(6*a)+1/32*b*cosh(2*a+2*b*x)/x^2-1/32*b*cosh(6*a+6*b*x)/x^2-1/8*b^3*Shi(2*b*x)*sinh(2*a)+9/8*b^3*Shi(6*b*x)*sinh(6*a)+1/32*sinh(2*a+2*b*x)/x^3+1/16*b^2*sinh(2*a+2*b*x)/x-1/96*sinh(6*a+6*b*x)/x^3-3/16*b^2*sinh(6*a+6*b*x)/x],

# Integrands of the form x^m Sech[a+b x]^n Sinh[a+b x]^p

# p=1
[x^m*sech(a+b*x)*sinh(a+b*x),x,0,Unintegrable(x^m*tanh(a+b*x),x)],
[x^3*sech(a+b*x)*sinh(a+b*x),x,6,-1/4*x^4+x^3*log(1+exp(2*(a+b*x)))/b+3/2*x^2*polylog(2,-exp(2*(a+b*x)))/b^2-3/2*x*polylog(3,-exp(2*(a+b*x)))/b^3+3/4*polylog(4,-exp(2*(a+b*x)))/b^4],
[x^2*sech(a+b*x)*sinh(a+b*x),x,5,-1/3*x^3+x^2*log(1+exp(2*(a+b*x)))/b+x*polylog(2,-exp(2*(a+b*x)))/b^2-1/2*polylog(3,-exp(2*(a+b*x)))/b^3],
[x*sech(a+b*x)*sinh(a+b*x),x,4,-1/2*x^2+x*log(1+exp(2*(a+b*x)))/b+1/2*polylog(2,-exp(2*(a+b*x)))/b^2],
[sech(a+b*x)*sinh(a+b*x),x,1,log(cosh(a+b*x))/b],
[sech(a+b*x)*sinh(a+b*x)/x,x,0,Unintegrable(tanh(a+b*x)/x,x)],
[sech(a+b*x)*sinh(a+b*x)/x^2,x,0,Unintegrable(tanh(a+b*x)/x^2,x)],
[x^m*sech(a+b*x)^2*sinh(a+b*x),x,0,CannotIntegrate(x^m*sech(a+b*x)*tanh(a+b*x),x)],
[x^3*sech(a+b*x)^2*sinh(a+b*x),x,8,6*x^2*arctan(exp(a+b*x))/b^2-6*I*x*polylog(2,-I*exp(a+b*x))/b^3+6*I*x*polylog(2,I*exp(a+b*x))/b^3+6*I*polylog(3,-I*exp(a+b*x))/b^4-6*I*polylog(3,I*exp(a+b*x))/b^4-x^3*sech(a+b*x)/b],
[x^2*sech(a+b*x)^2*sinh(a+b*x),x,6,4*x*arctan(exp(a+b*x))/b^2-2*I*polylog(2,-I*exp(a+b*x))/b^3+2*I*polylog(2,I*exp(a+b*x))/b^3-x^2*sech(a+b*x)/b],
[x*sech(a+b*x)^2*sinh(a+b*x),x,2,arctan(sinh(a+b*x))/b^2-x*sech(a+b*x)/b],
[sech(a+b*x)^2*sinh(a+b*x),x,2,-sech(a+b*x)/b],
[sech(a+b*x)^2*sinh(a+b*x)/x,x,0,CannotIntegrate(sech(a+b*x)*tanh(a+b*x)/x,x)],
[sech(a+b*x)^2*sinh(a+b*x)/x^2,x,0,CannotIntegrate(sech(a+b*x)*tanh(a+b*x)/x^2,x)],
[x^m*sech(a+b*x)^3*sinh(a+b*x),x,0,CannotIntegrate(x^m*sech(a+b*x)^2*tanh(a+b*x),x)],
[x^3*sech(a+b*x)^3*sinh(a+b*x),x,6,3/2*x^2/b^2-3*x*log(1+exp(2*(a+b*x)))/b^3-3/2*polylog(2,-exp(2*(a+b*x)))/b^4-1/2*x^3*sech(a+b*x)^2/b+3/2*x^2*tanh(a+b*x)/b^2],
[x^2*sech(a+b*x)^3*sinh(a+b*x),x,3,-log(cosh(a+b*x))/b^3-1/2*x^2*sech(a+b*x)^2/b+x*tanh(a+b*x)/b^2],
[x*sech(a+b*x)^3*sinh(a+b*x),x,3,-1/2*x*sech(a+b*x)^2/b+1/2*tanh(a+b*x)/b^2],
[sech(a+b*x)^3*sinh(a+b*x),x,2,-1/2*sech(a+b*x)^2/b],
[sech(a+b*x)^3*sinh(a+b*x)/x,x,0,CannotIntegrate(sech(a+b*x)^2*tanh(a+b*x)/x,x)],
[sech(a+b*x)^3*sinh(a+b*x)/x^2,x,0,CannotIntegrate(sech(a+b*x)^2*tanh(a+b*x)/x^2,x)],

# p=2
[x^m*sech(a+b*x)*sinh(a+b*x)^2,x,4,1/2*exp(a)*x^m*GAMMA(1+m,-b*x)/(b*(-b*x)^m)-1/2*x^m*GAMMA(1+m,b*x)/(b*exp(a)*(b*x)^m)-Unintegrable(x^m*sech(a+b*x),x)],
[x^3*sech(a+b*x)*sinh(a+b*x)^2,x,14,-2*x^3*arctan(exp(a+b*x))/b-6*cosh(a+b*x)/b^4-3*x^2*cosh(a+b*x)/b^2+3*I*x^2*polylog(2,-I*exp(a+b*x))/b^2-3*I*x^2*polylog(2,I*exp(a+b*x))/b^2-6*I*x*polylog(3,-I*exp(a+b*x))/b^3+6*I*x*polylog(3,I*exp(a+b*x))/b^3+6*I*polylog(4,-I*exp(a+b*x))/b^4-6*I*polylog(4,I*exp(a+b*x))/b^4+6*x*sinh(a+b*x)/b^3+x^3*sinh(a+b*x)/b],
[x^2*sech(a+b*x)*sinh(a+b*x)^2,x,11,-2*x^2*arctan(exp(a+b*x))/b-2*x*cosh(a+b*x)/b^2+2*I*x*polylog(2,-I*exp(a+b*x))/b^2-2*I*x*polylog(2,I*exp(a+b*x))/b^2-2*I*polylog(3,-I*exp(a+b*x))/b^3+2*I*polylog(3,I*exp(a+b*x))/b^3+2*sinh(a+b*x)/b^3+x^2*sinh(a+b*x)/b],
[x*sech(a+b*x)*sinh(a+b*x)^2,x,8,-2*x*arctan(exp(a+b*x))/b-cosh(a+b*x)/b^2+I*polylog(2,-I*exp(a+b*x))/b^2-I*polylog(2,I*exp(a+b*x))/b^2+x*sinh(a+b*x)/b],
[sech(a+b*x)*sinh(a+b*x)^2,x,3,-arctan(sinh(a+b*x))/b+sinh(a+b*x)/b],
[sech(a+b*x)*sinh(a+b*x)^2/x,x,4,Chi(b*x)*cosh(a)+Shi(b*x)*sinh(a)-Unintegrable(sech(a+b*x)/x,x)],
[sech(a+b*x)*sinh(a+b*x)^2/x^2,x,5,-cosh(a+b*x)/x+b*cosh(a)*Shi(b*x)+b*Chi(b*x)*sinh(a)-Unintegrable(sech(a+b*x)/x^2,x)],
[x^m*sech(a+b*x)^2*sinh(a+b*x)^2,x,0,Unintegrable(x^m*tanh(a+b*x)^2,x)],
[x^3*sech(a+b*x)^2*sinh(a+b*x)^2,x,7,-x^3/b+1/4*x^4+3*x^2*log(1+exp(2*(a+b*x)))/b^2+3*x*polylog(2,-exp(2*(a+b*x)))/b^3-3/2*polylog(3,-exp(2*(a+b*x)))/b^4-x^3*tanh(a+b*x)/b],
[x^2*sech(a+b*x)^2*sinh(a+b*x)^2,x,6,-x^2/b+1/3*x^3+2*x*log(1+exp(2*(a+b*x)))/b^2+polylog(2,-exp(2*(a+b*x)))/b^3-x^2*tanh(a+b*x)/b],
[x*sech(a+b*x)^2*sinh(a+b*x)^2,x,3,1/2*x^2+log(cosh(a+b*x))/b^2-x*tanh(a+b*x)/b],
[sech(a+b*x)^2*sinh(a+b*x)^2,x,2,x-tanh(a+b*x)/b],
[sech(a+b*x)^2*sinh(a+b*x)^2/x,x,0,Unintegrable(tanh(a+b*x)^2/x,x)],
[sech(a+b*x)^2*sinh(a+b*x)^2/x^2,x,0,Unintegrable(tanh(a+b*x)^2/x^2,x)],
[x^m*sech(a+b*x)^3*sinh(a+b*x)^2,x,1,Unintegrable(x^m*sech(a+b*x),x)-Unintegrable(x^m*sech(a+b*x)^3,x)],
[x^3*sech(a+b*x)^3*sinh(a+b*x)^2,x,25,6*x*arctan(exp(a+b*x))/b^3+x^3*arctan(exp(a+b*x))/b-3*I*polylog(2,-I*exp(a+b*x))/b^4-3/2*I*x^2*polylog(2,-I*exp(a+b*x))/b^2+3*I*polylog(2,I*exp(a+b*x))/b^4+3/2*I*x^2*polylog(2,I*exp(a+b*x))/b^2+3*I*x*polylog(3,-I*exp(a+b*x))/b^3-3*I*x*polylog(3,I*exp(a+b*x))/b^3-3*I*polylog(4,-I*exp(a+b*x))/b^4+3*I*polylog(4,I*exp(a+b*x))/b^4-3/2*x^2*sech(a+b*x)/b^2-1/2*x^3*sech(a+b*x)*tanh(a+b*x)/b],
[x^2*sech(a+b*x)^3*sinh(a+b*x)^2,x,17,x^2*arctan(exp(a+b*x))/b+arctan(sinh(a+b*x))/b^3-I*x*polylog(2,-I*exp(a+b*x))/b^2+I*x*polylog(2,I*exp(a+b*x))/b^2+I*polylog(3,-I*exp(a+b*x))/b^3-I*polylog(3,I*exp(a+b*x))/b^3-x*sech(a+b*x)/b^2-1/2*x^2*sech(a+b*x)*tanh(a+b*x)/b],
[x*sech(a+b*x)^3*sinh(a+b*x)^2,x,12,x*arctan(exp(a+b*x))/b-1/2*I*polylog(2,-I*exp(a+b*x))/b^2+1/2*I*polylog(2,I*exp(a+b*x))/b^2-1/2*sech(a+b*x)/b^2-1/2*x*sech(a+b*x)*tanh(a+b*x)/b],
[sech(a+b*x)^3*sinh(a+b*x)^2,x,2,1/2*arctan(sinh(a+b*x))/b-1/2*sech(a+b*x)*tanh(a+b*x)/b],
[sech(a+b*x)^3*sinh(a+b*x)^2/x,x,1,Unintegrable(sech(a+b*x)/x,x)-Unintegrable(sech(a+b*x)^3/x,x)],
[sech(a+b*x)^3*sinh(a+b*x)^2/x^2,x,1,Unintegrable(sech(a+b*x)/x^2,x)-Unintegrable(sech(a+b*x)^3/x^2,x)],

# p=3
[x^m*sech(a+b*x)*sinh(a+b*x)^3,x,6,2^(-3-m)*exp(2*a)*x^m*GAMMA(1+m,-2*b*x)/(b*(-b*x)^m)+2^(-3-m)*x^m*GAMMA(1+m,2*b*x)/(b*exp(2*a)*(b*x)^m)-Unintegrable(x^m*tanh(a+b*x),x)],
[x^3*sech(a+b*x)*sinh(a+b*x)^3,x,12,3/8*x/b^3+1/4*x^3/b+1/4*x^4-x^3*log(1+exp(2*(a+b*x)))/b-3/2*x^2*polylog(2,-exp(2*(a+b*x)))/b^2+3/2*x*polylog(3,-exp(2*(a+b*x)))/b^3-3/4*polylog(4,-exp(2*(a+b*x)))/b^4-3/8*cosh(a+b*x)*sinh(a+b*x)/b^4-3/4*x^2*cosh(a+b*x)*sinh(a+b*x)/b^2+3/4*x*sinh(a+b*x)^2/b^3+1/2*x^3*sinh(a+b*x)^2/b],
[x^2*sech(a+b*x)*sinh(a+b*x)^3,x,9,1/4*x^2/b+1/3*x^3-x^2*log(1+exp(2*(a+b*x)))/b-x*polylog(2,-exp(2*(a+b*x)))/b^2+1/2*polylog(3,-exp(2*(a+b*x)))/b^3-1/2*x*cosh(a+b*x)*sinh(a+b*x)/b^2+1/4*sinh(a+b*x)^2/b^3+1/2*x^2*sinh(a+b*x)^2/b],
[x*sech(a+b*x)*sinh(a+b*x)^3,x,8,1/4*x/b+1/2*x^2-x*log(1+exp(2*(a+b*x)))/b-1/2*polylog(2,-exp(2*(a+b*x)))/b^2-1/4*cosh(a+b*x)*sinh(a+b*x)/b^2+1/2*x*sinh(a+b*x)^2/b],
[sech(a+b*x)*sinh(a+b*x)^3,x,3,1/2*cosh(a+b*x)^2/b-log(cosh(a+b*x))/b],
[sech(a+b*x)*sinh(a+b*x)^3/x,x,6,1/2*cosh(2*a)*Shi(2*b*x)+1/2*Chi(2*b*x)*sinh(2*a)-Unintegrable(tanh(a+b*x)/x,x)],
[sech(a+b*x)*sinh(a+b*x)^3/x^2,x,7,b*Chi(2*b*x)*cosh(2*a)+b*Shi(2*b*x)*sinh(2*a)-1/2*sinh(2*a+2*b*x)/x-Unintegrable(tanh(a+b*x)/x^2,x)],
[x^m*sech(a+b*x)^2*sinh(a+b*x)^3,x,4,-CannotIntegrate(x^m*sech(a+b*x)*tanh(a+b*x),x)+1/2*exp(a)*x^m*GAMMA(1+m,-b*x)/(b*(-b*x)^m)+1/2*x^m*GAMMA(1+m,b*x)/(b*exp(a)*(b*x)^m)],
[x^3*sech(a+b*x)^2*sinh(a+b*x)^3,x,13,-6*x^2*arctan(exp(a+b*x))/b^2+6*x*cosh(a+b*x)/b^3+x^3*cosh(a+b*x)/b+6*I*x*polylog(2,-I*exp(a+b*x))/b^3-6*I*x*polylog(2,I*exp(a+b*x))/b^3-6*I*polylog(3,-I*exp(a+b*x))/b^4+6*I*polylog(3,I*exp(a+b*x))/b^4+x^3*sech(a+b*x)/b-6*sinh(a+b*x)/b^4-3*x^2*sinh(a+b*x)/b^2],
[x^2*sech(a+b*x)^2*sinh(a+b*x)^3,x,10,-4*x*arctan(exp(a+b*x))/b^2+2*cosh(a+b*x)/b^3+x^2*cosh(a+b*x)/b+2*I*polylog(2,-I*exp(a+b*x))/b^3-2*I*polylog(2,I*exp(a+b*x))/b^3+x^2*sech(a+b*x)/b-2*x*sinh(a+b*x)/b^2],
[x*sech(a+b*x)^2*sinh(a+b*x)^3,x,5,-arctan(sinh(a+b*x))/b^2+x*cosh(a+b*x)/b+x*sech(a+b*x)/b-sinh(a+b*x)/b^2],
[sech(a+b*x)^2*sinh(a+b*x)^3,x,3,cosh(a+b*x)/b+sech(a+b*x)/b],
[sech(a+b*x)^2*sinh(a+b*x)^3/x,x,4,-CannotIntegrate(sech(a+b*x)*tanh(a+b*x)/x,x)+cosh(a)*Shi(b*x)+Chi(b*x)*sinh(a)],
[sech(a+b*x)^2*sinh(a+b*x)^3/x^2,x,5,-CannotIntegrate(sech(a+b*x)*tanh(a+b*x)/x^2,x)+b*Chi(b*x)*cosh(a)+b*Shi(b*x)*sinh(a)-sinh(a+b*x)/x],
[x^m*sech(a+b*x)^3*sinh(a+b*x)^3,x,0,Unintegrable(x^m*tanh(a+b*x)^3,x)],
[x^3*sech(a+b*x)^3*sinh(a+b*x)^3,x,13,-3/2*x^2/b^2+1/2*x^3/b-1/4*x^4+3*x*log(1+exp(2*(a+b*x)))/b^3+x^3*log(1+exp(2*(a+b*x)))/b+3/2*polylog(2,-exp(2*(a+b*x)))/b^4+3/2*x^2*polylog(2,-exp(2*(a+b*x)))/b^2-3/2*x*polylog(3,-exp(2*(a+b*x)))/b^3+3/4*polylog(4,-exp(2*(a+b*x)))/b^4-3/2*x^2*tanh(a+b*x)/b^2-1/2*x^3*tanh(a+b*x)^2/b],
[x^2*sech(a+b*x)^3*sinh(a+b*x)^3,x,9,1/2*x^2/b-1/3*x^3+x^2*log(1+exp(2*(a+b*x)))/b+log(cosh(a+b*x))/b^3+x*polylog(2,-exp(2*(a+b*x)))/b^2-1/2*polylog(3,-exp(2*(a+b*x)))/b^3-x*tanh(a+b*x)/b^2-1/2*x^2*tanh(a+b*x)^2/b],
[x*sech(a+b*x)^3*sinh(a+b*x)^3,x,7,1/2*x/b-1/2*x^2+x*log(1+exp(2*(a+b*x)))/b+1/2*polylog(2,-exp(2*(a+b*x)))/b^2-1/2*tanh(a+b*x)/b^2-1/2*x*tanh(a+b*x)^2/b],
[sech(a+b*x)^3*sinh(a+b*x)^3,x,2,log(cosh(a+b*x))/b-1/2*tanh(a+b*x)^2/b],
[sech(a+b*x)^3*sinh(a+b*x)^3/x,x,0,Unintegrable(tanh(a+b*x)^3/x,x)],
[sech(a+b*x)^3*sinh(a+b*x)^3/x^2,x,0,Unintegrable(tanh(a+b*x)^3/x^2,x)],

# Integrands of the form x^m Cosh[a+b x]^n Csch[a+b x]^p

# p=1
[x^m*cosh(a+b*x)*csch(a+b*x),x,0,Unintegrable(x^m*coth(a+b*x),x)],
[x^3*cosh(a+b*x)*csch(a+b*x),x,6,-1/4*x^4+x^3*log(1-exp(2*(a+b*x)))/b+3/2*x^2*polylog(2,exp(2*(a+b*x)))/b^2-3/2*x*polylog(3,exp(2*(a+b*x)))/b^3+3/4*polylog(4,exp(2*(a+b*x)))/b^4],
[x^2*cosh(a+b*x)*csch(a+b*x),x,5,-1/3*x^3+x^2*log(1-exp(2*(a+b*x)))/b+x*polylog(2,exp(2*(a+b*x)))/b^2-1/2*polylog(3,exp(2*(a+b*x)))/b^3],
[x*cosh(a+b*x)*csch(a+b*x),x,4,-1/2*x^2+x*log(1-exp(2*(a+b*x)))/b+1/2*polylog(2,exp(2*(a+b*x)))/b^2],
[cosh(a+b*x)*csch(a+b*x),x,1,log(sinh(a+b*x))/b],
[cosh(a+b*x)*csch(a+b*x)/x,x,0,Unintegrable(coth(a+b*x)/x,x)],
[cosh(a+b*x)*csch(a+b*x)/x^2,x,0,Unintegrable(coth(a+b*x)/x^2,x)],
[x^m*cosh(a+b*x)^2*csch(a+b*x),x,4,1/2*exp(a)*x^m*GAMMA(1+m,-b*x)/(b*(-b*x)^m)+1/2*x^m*GAMMA(1+m,b*x)/(b*exp(a)*(b*x)^m)+Unintegrable(x^m*csch(a+b*x),x)],
[x^3*cosh(a+b*x)^2*csch(a+b*x),x,14,-2*x^3*arctanh(exp(a+b*x))/b+6*x*cosh(a+b*x)/b^3+x^3*cosh(a+b*x)/b-3*x^2*polylog(2,-exp(a+b*x))/b^2+3*x^2*polylog(2,exp(a+b*x))/b^2+6*x*polylog(3,-exp(a+b*x))/b^3-6*x*polylog(3,exp(a+b*x))/b^3-6*polylog(4,-exp(a+b*x))/b^4+6*polylog(4,exp(a+b*x))/b^4-6*sinh(a+b*x)/b^4-3*x^2*sinh(a+b*x)/b^2],
[x^2*cosh(a+b*x)^2*csch(a+b*x),x,11,-2*x^2*arctanh(exp(a+b*x))/b+2*cosh(a+b*x)/b^3+x^2*cosh(a+b*x)/b-2*x*polylog(2,-exp(a+b*x))/b^2+2*x*polylog(2,exp(a+b*x))/b^2+2*polylog(3,-exp(a+b*x))/b^3-2*polylog(3,exp(a+b*x))/b^3-2*x*sinh(a+b*x)/b^2],
[x*cosh(a+b*x)^2*csch(a+b*x),x,8,-2*x*arctanh(exp(a+b*x))/b+x*cosh(a+b*x)/b-polylog(2,-exp(a+b*x))/b^2+polylog(2,exp(a+b*x))/b^2-sinh(a+b*x)/b^2],
[cosh(a+b*x)^2*csch(a+b*x),x,3,-arctanh(cosh(a+b*x))/b+cosh(a+b*x)/b],
[cosh(a+b*x)^2*csch(a+b*x)/x,x,4,cosh(a)*Shi(b*x)+Chi(b*x)*sinh(a)+Unintegrable(csch(a+b*x)/x,x)],
[cosh(a+b*x)^2*csch(a+b*x)/x^2,x,5,b*Chi(b*x)*cosh(a)+b*Shi(b*x)*sinh(a)-sinh(a+b*x)/x+Unintegrable(csch(a+b*x)/x^2,x)],
[x^m*cosh(a+b*x)^3*csch(a+b*x),x,6,2^(-3-m)*exp(2*a)*x^m*GAMMA(1+m,-2*b*x)/(b*(-b*x)^m)+2^(-3-m)*x^m*GAMMA(1+m,2*b*x)/(b*exp(2*a)*(b*x)^m)+Unintegrable(x^m*coth(a+b*x),x)],
[x^3*cosh(a+b*x)^3*csch(a+b*x),x,12,3/8*x/b^3+1/4*x^3/b-1/4*x^4+x^3*log(1-exp(2*(a+b*x)))/b+3/2*x^2*polylog(2,exp(2*(a+b*x)))/b^2-3/2*x*polylog(3,exp(2*(a+b*x)))/b^3+3/4*polylog(4,exp(2*(a+b*x)))/b^4-3/8*cosh(a+b*x)*sinh(a+b*x)/b^4-3/4*x^2*cosh(a+b*x)*sinh(a+b*x)/b^2+3/4*x*sinh(a+b*x)^2/b^3+1/2*x^3*sinh(a+b*x)^2/b],
[x^2*cosh(a+b*x)^3*csch(a+b*x),x,9,1/4*x^2/b-1/3*x^3+x^2*log(1-exp(2*(a+b*x)))/b+x*polylog(2,exp(2*(a+b*x)))/b^2-1/2*polylog(3,exp(2*(a+b*x)))/b^3-1/2*x*cosh(a+b*x)*sinh(a+b*x)/b^2+1/4*sinh(a+b*x)^2/b^3+1/2*x^2*sinh(a+b*x)^2/b],
[x*cosh(a+b*x)^3*csch(a+b*x),x,8,1/4*x/b-1/2*x^2+x*log(1-exp(2*(a+b*x)))/b+1/2*polylog(2,exp(2*(a+b*x)))/b^2-1/4*cosh(a+b*x)*sinh(a+b*x)/b^2+1/2*x*sinh(a+b*x)^2/b],
[cosh(a+b*x)^3*csch(a+b*x),x,3,log(sinh(a+b*x))/b+1/2*sinh(a+b*x)^2/b],
[cosh(a+b*x)^3*csch(a+b*x)/x,x,6,1/2*cosh(2*a)*Shi(2*b*x)+1/2*Chi(2*b*x)*sinh(2*a)+Unintegrable(coth(a+b*x)/x,x)],
[cosh(a+b*x)^3*csch(a+b*x)/x^2,x,7,b*Chi(2*b*x)*cosh(2*a)+b*Shi(2*b*x)*sinh(2*a)-1/2*sinh(2*a+2*b*x)/x+Unintegrable(coth(a+b*x)/x^2,x)],
[x*cosh(x)^2*coth(x)^2,x,6,3/4*x^2-1/4*cosh(x)^2-x*coth(x)+log(sinh(x))+1/2*x*cosh(x)*sinh(x)],
[x^2*cosh(x)^2*coth(x)^2,x,11,1/4*x-x^2+1/2*x^3-1/2*x*cosh(x)^2-x^2*coth(x)+2*x*log(1-exp(2*x))+polylog(2,exp(2*x))+1/4*cosh(x)*sinh(x)+1/2*x^2*cosh(x)*sinh(x)],
[x^3*cosh(x)^2*coth(x)^2,x,12,3/8*x^2-x^3+3/8*x^4-3/8*cosh(x)^2-3/4*x^2*cosh(x)^2-x^3*coth(x)+3*x^2*log(1-exp(2*x))+3*x*polylog(2,exp(2*x))-3/2*polylog(3,exp(2*x))+3/4*x*cosh(x)*sinh(x)+1/2*x^3*cosh(x)*sinh(x)],
[x*cosh(x)^2*coth(x)^3,x,16,3/4*x-x^2-1/2*coth(x)-1/2*x*coth(x)^2+2*x*log(1-exp(2*x))+polylog(2,exp(2*x))-1/4*cosh(x)*sinh(x)+1/2*x*sinh(x)^2],
[x^2*cosh(x)^2*coth(x)^3,x,19,3/4*x^2-2/3*x^3-x*coth(x)-1/2*x^2*coth(x)^2+2*x^2*log(1-exp(2*x))+log(sinh(x))+2*x*polylog(2,exp(2*x))-polylog(3,exp(2*x))-1/2*x*cosh(x)*sinh(x)+1/4*sinh(x)^2+1/2*x^2*sinh(x)^2],
[x^3*cosh(x)^2*coth(x)^3,x,26,3/8*x-3/2*x^2+3/4*x^3-1/2*x^4-3/2*x^2*coth(x)-1/2*x^3*coth(x)^2+3*x*log(1-exp(2*x))+2*x^3*log(1-exp(2*x))+3/2*polylog(2,exp(2*x))+3*x^2*polylog(2,exp(2*x))-3*x*polylog(3,exp(2*x))+3/2*polylog(4,exp(2*x))-3/8*cosh(x)*sinh(x)-3/4*x^2*cosh(x)*sinh(x)+3/4*x*sinh(x)^2+1/2*x^3*sinh(x)^2],

# p=2
[x^m*cosh(a+b*x)*csch(a+b*x)^2,x,0,CannotIntegrate(x^m*coth(a+b*x)*csch(a+b*x),x)],
[x^3*cosh(a+b*x)*csch(a+b*x)^2,x,8,-6*x^2*arctanh(exp(a+b*x))/b^2-x^3*csch(a+b*x)/b-6*x*polylog(2,-exp(a+b*x))/b^3+6*x*polylog(2,exp(a+b*x))/b^3+6*polylog(3,-exp(a+b*x))/b^4-6*polylog(3,exp(a+b*x))/b^4],
[x^2*cosh(a+b*x)*csch(a+b*x)^2,x,6,-4*x*arctanh(exp(a+b*x))/b^2-x^2*csch(a+b*x)/b-2*polylog(2,-exp(a+b*x))/b^3+2*polylog(2,exp(a+b*x))/b^3],
[x*cosh(a+b*x)*csch(a+b*x)^2,x,2,-arctanh(cosh(a+b*x))/b^2-x*csch(a+b*x)/b],
[cosh(a+b*x)*csch(a+b*x)^2,x,2,-csch(a+b*x)/b],
[cosh(a+b*x)*csch(a+b*x)^2/x,x,0,CannotIntegrate(coth(a+b*x)*csch(a+b*x)/x,x)],
[cosh(a+b*x)*csch(a+b*x)^2/x^2,x,0,CannotIntegrate(coth(a+b*x)*csch(a+b*x)/x^2,x)],
[x^m*cosh(a+b*x)^2*csch(a+b*x)^2,x,0,Unintegrable(x^m*coth(a+b*x)^2,x)],
[x^3*cosh(a+b*x)^2*csch(a+b*x)^2,x,7,-x^3/b+1/4*x^4-x^3*coth(a+b*x)/b+3*x^2*log(1-exp(2*(a+b*x)))/b^2+3*x*polylog(2,exp(2*(a+b*x)))/b^3-3/2*polylog(3,exp(2*(a+b*x)))/b^4],
[x^2*cosh(a+b*x)^2*csch(a+b*x)^2,x,6,-x^2/b+1/3*x^3-x^2*coth(a+b*x)/b+2*x*log(1-exp(2*(a+b*x)))/b^2+polylog(2,exp(2*(a+b*x)))/b^3],
[x*cosh(a+b*x)^2*csch(a+b*x)^2,x,3,1/2*x^2-x*coth(a+b*x)/b+log(sinh(a+b*x))/b^2],
[cosh(a+b*x)^2*csch(a+b*x)^2,x,2,x-coth(a+b*x)/b],
[cosh(a+b*x)^2*csch(a+b*x)^2/x,x,0,Unintegrable(coth(a+b*x)^2/x,x)],
[cosh(a+b*x)^2*csch(a+b*x)^2/x^2,x,0,Unintegrable(coth(a+b*x)^2/x^2,x)],
[x^m*cosh(a+b*x)^3*csch(a+b*x)^2,x,4,CannotIntegrate(x^m*coth(a+b*x)*csch(a+b*x),x)+1/2*exp(a)*x^m*GAMMA(1+m,-b*x)/(b*(-b*x)^m)-1/2*x^m*GAMMA(1+m,b*x)/(b*exp(a)*(b*x)^m)],
[x^3*cosh(a+b*x)^3*csch(a+b*x)^2,x,13,-6*x^2*arctanh(exp(a+b*x))/b^2-6*cosh(a+b*x)/b^4-3*x^2*cosh(a+b*x)/b^2-x^3*csch(a+b*x)/b-6*x*polylog(2,-exp(a+b*x))/b^3+6*x*polylog(2,exp(a+b*x))/b^3+6*polylog(3,-exp(a+b*x))/b^4-6*polylog(3,exp(a+b*x))/b^4+6*x*sinh(a+b*x)/b^3+x^3*sinh(a+b*x)/b],
[x^2*cosh(a+b*x)^3*csch(a+b*x)^2,x,10,-4*x*arctanh(exp(a+b*x))/b^2-2*x*cosh(a+b*x)/b^2-x^2*csch(a+b*x)/b-2*polylog(2,-exp(a+b*x))/b^3+2*polylog(2,exp(a+b*x))/b^3+2*sinh(a+b*x)/b^3+x^2*sinh(a+b*x)/b],
[x*cosh(a+b*x)^3*csch(a+b*x)^2,x,5,-arctanh(cosh(a+b*x))/b^2-cosh(a+b*x)/b^2-x*csch(a+b*x)/b+x*sinh(a+b*x)/b],
[cosh(a+b*x)^3*csch(a+b*x)^2,x,3,-csch(a+b*x)/b+sinh(a+b*x)/b],
[cosh(a+b*x)^3*csch(a+b*x)^2/x,x,4,CannotIntegrate(coth(a+b*x)*csch(a+b*x)/x,x)+Chi(b*x)*cosh(a)+Shi(b*x)*sinh(a)],
[cosh(a+b*x)^3*csch(a+b*x)^2/x^2,x,5,CannotIntegrate(coth(a+b*x)*csch(a+b*x)/x^2,x)-cosh(a+b*x)/x+b*cosh(a)*Shi(b*x)+b*Chi(b*x)*sinh(a)],

# p=3
[x^m*cosh(a+b*x)*csch(a+b*x)^3,x,0,CannotIntegrate(x^m*coth(a+b*x)*csch(a+b*x)^2,x)],
[x^3*cosh(a+b*x)*csch(a+b*x)^3,x,6,-3/2*x^2/b^2-3/2*x^2*coth(a+b*x)/b^2-1/2*x^3*csch(a+b*x)^2/b+3*x*log(1-exp(2*(a+b*x)))/b^3+3/2*polylog(2,exp(2*(a+b*x)))/b^4],
[x^2*cosh(a+b*x)*csch(a+b*x)^3,x,3,-x*coth(a+b*x)/b^2-1/2*x^2*csch(a+b*x)^2/b+log(sinh(a+b*x))/b^3],
[x*cosh(a+b*x)*csch(a+b*x)^3,x,3,-1/2*coth(a+b*x)/b^2-1/2*x*csch(a+b*x)^2/b],
[cosh(a+b*x)*csch(a+b*x)^3,x,2,-1/2*csch(a+b*x)^2/b],
[cosh(a+b*x)*csch(a+b*x)^3/x,x,0,CannotIntegrate(coth(a+b*x)*csch(a+b*x)^2/x,x)],
[cosh(a+b*x)*csch(a+b*x)^3/x^2,x,0,CannotIntegrate(coth(a+b*x)*csch(a+b*x)^2/x^2,x)],
[x^m*cosh(a+b*x)^2*csch(a+b*x)^3,x,1,Unintegrable(x^m*csch(a+b*x),x)+Unintegrable(x^m*csch(a+b*x)^3,x)],
[x^3*cosh(a+b*x)^2*csch(a+b*x)^3,x,25,-6*x*arctanh(exp(a+b*x))/b^3-x^3*arctanh(exp(a+b*x))/b-3/2*x^2*csch(a+b*x)/b^2-1/2*x^3*coth(a+b*x)*csch(a+b*x)/b-3*polylog(2,-exp(a+b*x))/b^4-3/2*x^2*polylog(2,-exp(a+b*x))/b^2+3*polylog(2,exp(a+b*x))/b^4+3/2*x^2*polylog(2,exp(a+b*x))/b^2+3*x*polylog(3,-exp(a+b*x))/b^3-3*x*polylog(3,exp(a+b*x))/b^3-3*polylog(4,-exp(a+b*x))/b^4+3*polylog(4,exp(a+b*x))/b^4],
[x^2*cosh(a+b*x)^2*csch(a+b*x)^3,x,17,-x^2*arctanh(exp(a+b*x))/b-arctanh(cosh(a+b*x))/b^3-x*csch(a+b*x)/b^2-1/2*x^2*coth(a+b*x)*csch(a+b*x)/b-x*polylog(2,-exp(a+b*x))/b^2+x*polylog(2,exp(a+b*x))/b^2+polylog(3,-exp(a+b*x))/b^3-polylog(3,exp(a+b*x))/b^3],
[x*cosh(a+b*x)^2*csch(a+b*x)^3,x,12,-x*arctanh(exp(a+b*x))/b-1/2*csch(a+b*x)/b^2-1/2*x*coth(a+b*x)*csch(a+b*x)/b-1/2*polylog(2,-exp(a+b*x))/b^2+1/2*polylog(2,exp(a+b*x))/b^2],
[cosh(a+b*x)^2*csch(a+b*x)^3,x,2,-1/2*arctanh(cosh(a+b*x))/b-1/2*coth(a+b*x)*csch(a+b*x)/b],
[cosh(a+b*x)^2*csch(a+b*x)^3/x,x,1,Unintegrable(csch(a+b*x)/x,x)+Unintegrable(csch(a+b*x)^3/x,x)],
[cosh(a+b*x)^2*csch(a+b*x)^3/x^2,x,1,Unintegrable(csch(a+b*x)/x^2,x)+Unintegrable(csch(a+b*x)^3/x^2,x)],
[x^m*cosh(a+b*x)^3*csch(a+b*x)^3,x,0,Unintegrable(x^m*coth(a+b*x)^3,x)],
[x^3*cosh(a+b*x)^3*csch(a+b*x)^3,x,13,-3/2*x^2/b^2+1/2*x^3/b-1/4*x^4-3/2*x^2*coth(a+b*x)/b^2-1/2*x^3*coth(a+b*x)^2/b+3*x*log(1-exp(2*(a+b*x)))/b^3+x^3*log(1-exp(2*(a+b*x)))/b+3/2*polylog(2,exp(2*(a+b*x)))/b^4+3/2*x^2*polylog(2,exp(2*(a+b*x)))/b^2-3/2*x*polylog(3,exp(2*(a+b*x)))/b^3+3/4*polylog(4,exp(2*(a+b*x)))/b^4],
[x^2*cosh(a+b*x)^3*csch(a+b*x)^3,x,9,1/2*x^2/b-1/3*x^3-x*coth(a+b*x)/b^2-1/2*x^2*coth(a+b*x)^2/b+x^2*log(1-exp(2*(a+b*x)))/b+log(sinh(a+b*x))/b^3+x*polylog(2,exp(2*(a+b*x)))/b^2-1/2*polylog(3,exp(2*(a+b*x)))/b^3],
[x*cosh(a+b*x)^3*csch(a+b*x)^3,x,7,1/2*x/b-1/2*x^2-1/2*coth(a+b*x)/b^2-1/2*x*coth(a+b*x)^2/b+x*log(1-exp(2*(a+b*x)))/b+1/2*polylog(2,exp(2*(a+b*x)))/b^2],
[cosh(a+b*x)^3*csch(a+b*x)^3,x,2,-1/2*coth(a+b*x)^2/b+log(sinh(a+b*x))/b],
[cosh(a+b*x)^3*csch(a+b*x)^3/x,x,0,Unintegrable(coth(a+b*x)^3/x,x)],
[cosh(a+b*x)^3*csch(a+b*x)^3/x^2,x,0,Unintegrable(coth(a+b*x)^3/x^2,x)],

# Integrands of the form x^m Sech[a+b x]^n Csch[a+b x]^p

# p=1
[x^m*csch(a+b*x)*sech(a+b*x),x,0,CannotIntegrate(x^m*csch(a+b*x)*sech(a+b*x),x)],
[x^3*csch(a+b*x)*sech(a+b*x),x,10,-2*x^3*arctanh(exp(2*a+2*b*x))/b-3/2*x^2*polylog(2,-exp(2*a+2*b*x))/b^2+3/2*x^2*polylog(2,exp(2*a+2*b*x))/b^2+3/2*x*polylog(3,-exp(2*a+2*b*x))/b^3-3/2*x*polylog(3,exp(2*a+2*b*x))/b^3-3/4*polylog(4,-exp(2*a+2*b*x))/b^4+3/4*polylog(4,exp(2*a+2*b*x))/b^4],
[x^2*csch(a+b*x)*sech(a+b*x),x,8,-2*x^2*arctanh(exp(2*a+2*b*x))/b-x*polylog(2,-exp(2*a+2*b*x))/b^2+x*polylog(2,exp(2*a+2*b*x))/b^2+1/2*polylog(3,-exp(2*a+2*b*x))/b^3-1/2*polylog(3,exp(2*a+2*b*x))/b^3],
[x*csch(a+b*x)*sech(a+b*x),x,6,-2*x*arctanh(exp(2*a+2*b*x))/b-1/2*polylog(2,-exp(2*a+2*b*x))/b^2+1/2*polylog(2,exp(2*a+2*b*x))/b^2],
[csch(a+b*x)*sech(a+b*x),x,2,log(tanh(a+b*x))/b],
[csch(a+b*x)*sech(a+b*x)/x,x,1,2*Unintegrable(csch(2*a+2*b*x)/x,x)],
[csch(a+b*x)*sech(a+b*x)/x^2,x,1,2*Unintegrable(csch(2*a+2*b*x)/x^2,x)],
[x^m*csch(a+b*x)*sech(a+b*x)^2,x,0,CannotIntegrate(x^m*csch(a+b*x)*sech(a+b*x)^2,x)],
[x^3*csch(a+b*x)*sech(a+b*x)^2,x,21,-6*x^2*arctan(exp(a+b*x))/b^2-2*x^3*arctanh(exp(a+b*x))/b-3*x^2*polylog(2,-exp(a+b*x))/b^2+6*I*x*polylog(2,-I*exp(a+b*x))/b^3-6*I*x*polylog(2,I*exp(a+b*x))/b^3+3*x^2*polylog(2,exp(a+b*x))/b^2+6*x*polylog(3,-exp(a+b*x))/b^3-6*I*polylog(3,-I*exp(a+b*x))/b^4+6*I*polylog(3,I*exp(a+b*x))/b^4-6*x*polylog(3,exp(a+b*x))/b^3-6*polylog(4,-exp(a+b*x))/b^4+6*polylog(4,exp(a+b*x))/b^4+x^3*sech(a+b*x)/b],
[x^2*csch(a+b*x)*sech(a+b*x)^2,x,17,-4*x*arctan(exp(a+b*x))/b^2-2*x^2*arctanh(exp(a+b*x))/b-2*x*polylog(2,-exp(a+b*x))/b^2+2*I*polylog(2,-I*exp(a+b*x))/b^3-2*I*polylog(2,I*exp(a+b*x))/b^3+2*x*polylog(2,exp(a+b*x))/b^2+2*polylog(3,-exp(a+b*x))/b^3-2*polylog(3,exp(a+b*x))/b^3+x^2*sech(a+b*x)/b],
[x*csch(a+b*x)*sech(a+b*x)^2,x,10,-arctan(sinh(a+b*x))/b^2-2*x*arctanh(exp(a+b*x))/b-polylog(2,-exp(a+b*x))/b^2+polylog(2,exp(a+b*x))/b^2+x*sech(a+b*x)/b],
[csch(a+b*x)*sech(a+b*x)^2,x,3,-arctanh(cosh(a+b*x))/b+sech(a+b*x)/b],
[csch(a+b*x)*sech(a+b*x)^2/x,x,0,CannotIntegrate(csch(a+b*x)*sech(a+b*x)^2/x,x)],
[csch(a+b*x)*sech(a+b*x)^2/x^2,x,0,CannotIntegrate(csch(a+b*x)*sech(a+b*x)^2/x^2,x)],
[x^m*csch(a+b*x)*sech(a+b*x)^3,x,0,CannotIntegrate(x^m*csch(a+b*x)*sech(a+b*x)^3,x)],
[x^3*csch(a+b*x)*sech(a+b*x)^3,x,20,-3/2*x^2/b^2+1/2*x^3/b-2*x^3*arctanh(exp(2*a+2*b*x))/b+3*x*log(1+exp(2*(a+b*x)))/b^3+3/2*polylog(2,-exp(2*(a+b*x)))/b^4-3/2*x^2*polylog(2,-exp(2*a+2*b*x))/b^2+3/2*x^2*polylog(2,exp(2*a+2*b*x))/b^2+3/2*x*polylog(3,-exp(2*a+2*b*x))/b^3-3/2*x*polylog(3,exp(2*a+2*b*x))/b^3-3/4*polylog(4,-exp(2*a+2*b*x))/b^4+3/4*polylog(4,exp(2*a+2*b*x))/b^4-3/2*x^2*tanh(a+b*x)/b^2-1/2*x^3*tanh(a+b*x)^2/b],
[x^2*csch(a+b*x)*sech(a+b*x)^3,x,15,1/2*x^2/b-2*x^2*arctanh(exp(2*a+2*b*x))/b+log(cosh(a+b*x))/b^3-x*polylog(2,-exp(2*a+2*b*x))/b^2+x*polylog(2,exp(2*a+2*b*x))/b^2+1/2*polylog(3,-exp(2*a+2*b*x))/b^3-1/2*polylog(3,exp(2*a+2*b*x))/b^3-x*tanh(a+b*x)/b^2-1/2*x^2*tanh(a+b*x)^2/b],
[x*csch(a+b*x)*sech(a+b*x)^3,x,11,1/2*x/b-2*x*arctanh(exp(2*a+2*b*x))/b-1/2*polylog(2,-exp(2*a+2*b*x))/b^2+1/2*polylog(2,exp(2*a+2*b*x))/b^2-1/2*tanh(a+b*x)/b^2-1/2*x*tanh(a+b*x)^2/b],
[csch(a+b*x)*sech(a+b*x)^3,x,3,log(tanh(a+b*x))/b-1/2*tanh(a+b*x)^2/b],
[csch(a+b*x)*sech(a+b*x)^3/x,x,0,CannotIntegrate(csch(a+b*x)*sech(a+b*x)^3/x,x)],
[csch(a+b*x)*sech(a+b*x)^3/x^2,x,0,CannotIntegrate(csch(a+b*x)*sech(a+b*x)^3/x^2,x)],

# p=2
[x^m*csch(a+b*x)^2*sech(a+b*x),x,0,CannotIntegrate(x^m*csch(a+b*x)^2*sech(a+b*x),x)],
[x^3*csch(a+b*x)^2*sech(a+b*x),x,21,-2*x^3*arctan(exp(a+b*x))/b-6*x^2*arctanh(exp(a+b*x))/b^2-x^3*csch(a+b*x)/b-6*x*polylog(2,-exp(a+b*x))/b^3+3*I*x^2*polylog(2,-I*exp(a+b*x))/b^2-3*I*x^2*polylog(2,I*exp(a+b*x))/b^2+6*x*polylog(2,exp(a+b*x))/b^3+6*polylog(3,-exp(a+b*x))/b^4-6*I*x*polylog(3,-I*exp(a+b*x))/b^3+6*I*x*polylog(3,I*exp(a+b*x))/b^3-6*polylog(3,exp(a+b*x))/b^4+6*I*polylog(4,-I*exp(a+b*x))/b^4-6*I*polylog(4,I*exp(a+b*x))/b^4],
[x^2*csch(a+b*x)^2*sech(a+b*x),x,17,-2*x^2*arctan(exp(a+b*x))/b-4*x*arctanh(exp(a+b*x))/b^2-x^2*csch(a+b*x)/b-2*polylog(2,-exp(a+b*x))/b^3+2*I*x*polylog(2,-I*exp(a+b*x))/b^2-2*I*x*polylog(2,I*exp(a+b*x))/b^2+2*polylog(2,exp(a+b*x))/b^3-2*I*polylog(3,-I*exp(a+b*x))/b^3+2*I*polylog(3,I*exp(a+b*x))/b^3],
[x*csch(a+b*x)^2*sech(a+b*x),x,10,-2*x*arctan(exp(a+b*x))/b-arctanh(cosh(a+b*x))/b^2-x*csch(a+b*x)/b+I*polylog(2,-I*exp(a+b*x))/b^2-I*polylog(2,I*exp(a+b*x))/b^2],
[csch(a+b*x)^2*sech(a+b*x),x,3,-arctan(sinh(a+b*x))/b-csch(a+b*x)/b],
[csch(a+b*x)^2*sech(a+b*x)/x,x,0,CannotIntegrate(csch(a+b*x)^2*sech(a+b*x)/x,x)],
[csch(a+b*x)^2*sech(a+b*x)/x^2,x,0,CannotIntegrate(csch(a+b*x)^2*sech(a+b*x)/x^2,x)],
[x^m*csch(a+b*x)^2*sech(a+b*x)^2,x,0,CannotIntegrate(x^m*csch(a+b*x)^2*sech(a+b*x)^2,x)],
[x^3*csch(a+b*x)^2*sech(a+b*x)^2,x,7,-2*x^3/b-2*x^3*coth(2*a+2*b*x)/b+3*x^2*log(1-exp(4*(a+b*x)))/b^2+3/2*x*polylog(2,exp(4*(a+b*x)))/b^3-3/8*polylog(3,exp(4*(a+b*x)))/b^4],
[x^2*csch(a+b*x)^2*sech(a+b*x)^2,x,6,-2*x^2/b-2*x^2*coth(2*a+2*b*x)/b+2*x*log(1-exp(4*(a+b*x)))/b^2+1/2*polylog(2,exp(4*(a+b*x)))/b^3],
[x*csch(a+b*x)^2*sech(a+b*x)^2,x,3,-2*x*coth(2*a+2*b*x)/b+log(sinh(2*a+2*b*x))/b^2],
[csch(a+b*x)^2*sech(a+b*x)^2,x,3,-coth(a+b*x)/b-tanh(a+b*x)/b],
[csch(a+b*x)^2*sech(a+b*x)^2/x,x,1,4*Unintegrable(csch(2*a+2*b*x)^2/x,x)],
[csch(a+b*x)^2*sech(a+b*x)^2/x^2,x,1,4*Unintegrable(csch(2*a+2*b*x)^2/x^2,x)],
[x^m*csch(a+b*x)^2*sech(a+b*x)^3,x,0,CannotIntegrate(x^m*csch(a+b*x)^2*sech(a+b*x)^3,x)],

#  {x^3*Sech[a + b*x]^3*Csch[a + b*x]^2, x, 35, (6*x*ArcTan[E^(a + b*x)])/b^3 - (3*x^3*ArcTan[E^(a + b*x)])/b - (6*x^2*ArcTanh[E^(a + b*x)])/b^2 - (6*x*PolyLog[2, -E^(a + b*x)])/b^3 - (3*I*PolyLog[2, (-I)*E^(a + b*x)])/b^4 + (9*I*x^2*PolyLog[2, (-I)*E^(a + b*x)])/(2*b^2) + (3*I*PolyLog[2, I*E^(a + b*x)])/b^4 - (9*I*x^2*PolyLog[2, I*E^(a + b*x)])/(2*b^2) + (6*x*PolyLog[2, E^(a + b*x)])/b^3 + (6*PolyLog[3, -E^(a + b*x)])/b^4 - (9*I*x*PolyLog[3, (-I)*E^(a + b*x)])/b^3 + (9*I*x*PolyLog[3, I*E^(a + b*x)])/b^3 - (6*PolyLog[3, E^(a + b*x)])/b^4 + (9*I*PolyLog[4, (-I)*E^(a + b*x)])/b^4 - (9*I*PolyLog[4, I*E^(a + b*x)])/b^4 - (3*x^2*Sech[a + b*x])/(2*b^2) - (x^3*Csch[a + b*x]*Sech[a + b*x]^2)/b - (3*x^3*Sech[a + b*x]*Tanh[a + b*x])/(2*b)} 
[x^2*csch(a+b*x)^2*sech(a+b*x)^3,x,29,-3*x^2*arctan(exp(a+b*x))/b+arctan(sinh(a+b*x))/b^3-4*x*arctanh(exp(a+b*x))/b^2-3/2*x^2*csch(a+b*x)/b-2*polylog(2,-exp(a+b*x))/b^3+3*I*x*polylog(2,-I*exp(a+b*x))/b^2-3*I*x*polylog(2,I*exp(a+b*x))/b^2+2*polylog(2,exp(a+b*x))/b^3-3*I*polylog(3,-I*exp(a+b*x))/b^3+3*I*polylog(3,I*exp(a+b*x))/b^3-x*sech(a+b*x)/b^2+1/2*x^2*csch(a+b*x)*sech(a+b*x)^2/b],
[x*csch(a+b*x)^2*sech(a+b*x)^3,x,13,-3*x*arctan(exp(a+b*x))/b-arctanh(cosh(a+b*x))/b^2-3/2*x*csch(a+b*x)/b+3/2*I*polylog(2,-I*exp(a+b*x))/b^2-3/2*I*polylog(2,I*exp(a+b*x))/b^2-1/2*sech(a+b*x)/b^2+1/2*x*csch(a+b*x)*sech(a+b*x)^2/b],
[csch(a+b*x)^2*sech(a+b*x)^3,x,4,-3/2*arctan(sinh(a+b*x))/b-3/2*csch(a+b*x)/b+1/2*csch(a+b*x)*sech(a+b*x)^2/b],
[csch(a+b*x)^2*sech(a+b*x)^3/x,x,0,CannotIntegrate(csch(a+b*x)^2*sech(a+b*x)^3/x,x)],
[csch(a+b*x)^2*sech(a+b*x)^3/x^2,x,0,CannotIntegrate(csch(a+b*x)^2*sech(a+b*x)^3/x^2,x)],

# p=3
[x^m*csch(a+b*x)^3*sech(a+b*x),x,0,CannotIntegrate(x^m*csch(a+b*x)^3*sech(a+b*x),x)],
[x^3*csch(a+b*x)^3*sech(a+b*x),x,20,-3/2*x^2/b^2+1/2*x^3/b+2*x^3*arctanh(exp(2*a+2*b*x))/b-3/2*x^2*coth(a+b*x)/b^2-1/2*x^3*coth(a+b*x)^2/b+3*x*log(1-exp(2*(a+b*x)))/b^3+3/2*polylog(2,exp(2*(a+b*x)))/b^4+3/2*x^2*polylog(2,-exp(2*a+2*b*x))/b^2-3/2*x^2*polylog(2,exp(2*a+2*b*x))/b^2-3/2*x*polylog(3,-exp(2*a+2*b*x))/b^3+3/2*x*polylog(3,exp(2*a+2*b*x))/b^3+3/4*polylog(4,-exp(2*a+2*b*x))/b^4-3/4*polylog(4,exp(2*a+2*b*x))/b^4],
[x^2*csch(a+b*x)^3*sech(a+b*x),x,15,1/2*x^2/b+2*x^2*arctanh(exp(2*a+2*b*x))/b-x*coth(a+b*x)/b^2-1/2*x^2*coth(a+b*x)^2/b+log(sinh(a+b*x))/b^3+x*polylog(2,-exp(2*a+2*b*x))/b^2-x*polylog(2,exp(2*a+2*b*x))/b^2-1/2*polylog(3,-exp(2*a+2*b*x))/b^3+1/2*polylog(3,exp(2*a+2*b*x))/b^3],
[x*csch(a+b*x)^3*sech(a+b*x),x,11,1/2*x/b+2*x*arctanh(exp(2*a+2*b*x))/b-1/2*coth(a+b*x)/b^2-1/2*x*coth(a+b*x)^2/b+1/2*polylog(2,-exp(2*a+2*b*x))/b^2-1/2*polylog(2,exp(2*a+2*b*x))/b^2],
[csch(a+b*x)^3*sech(a+b*x),x,3,-1/2*coth(a+b*x)^2/b-log(tanh(a+b*x))/b],
[csch(a+b*x)^3*sech(a+b*x)/x,x,0,CannotIntegrate(csch(a+b*x)^3*sech(a+b*x)/x,x)],
[csch(a+b*x)^3*sech(a+b*x)/x^2,x,0,CannotIntegrate(csch(a+b*x)^3*sech(a+b*x)/x^2,x)],
[x^m*csch(a+b*x)^3*sech(a+b*x)^2,x,0,CannotIntegrate(x^m*csch(a+b*x)^3*sech(a+b*x)^2,x)],
[x^3*csch(a+b*x)^3*sech(a+b*x)^2,x,40,6*x^2*arctan(exp(a+b*x))/b^2-6*x*arctanh(exp(a+b*x))/b^3+3*x^3*arctanh(exp(a+b*x))/b-3/2*x^2*csch(a+b*x)/b^2-3*polylog(2,-exp(a+b*x))/b^4+9/2*x^2*polylog(2,-exp(a+b*x))/b^2-6*I*x*polylog(2,-I*exp(a+b*x))/b^3+6*I*x*polylog(2,I*exp(a+b*x))/b^3+3*polylog(2,exp(a+b*x))/b^4-9/2*x^2*polylog(2,exp(a+b*x))/b^2-9*x*polylog(3,-exp(a+b*x))/b^3+6*I*polylog(3,-I*exp(a+b*x))/b^4-6*I*polylog(3,I*exp(a+b*x))/b^4+9*x*polylog(3,exp(a+b*x))/b^3+9*polylog(4,-exp(a+b*x))/b^4-9*polylog(4,exp(a+b*x))/b^4-3/2*x^3*sech(a+b*x)/b-1/2*x^3*csch(a+b*x)^2*sech(a+b*x)/b],
[x^2*csch(a+b*x)^3*sech(a+b*x)^2,x,29,4*x*arctan(exp(a+b*x))/b^2+3*x^2*arctanh(exp(a+b*x))/b-arctanh(cosh(a+b*x))/b^3-x*csch(a+b*x)/b^2+3*x*polylog(2,-exp(a+b*x))/b^2-2*I*polylog(2,-I*exp(a+b*x))/b^3+2*I*polylog(2,I*exp(a+b*x))/b^3-3*x*polylog(2,exp(a+b*x))/b^2-3*polylog(3,-exp(a+b*x))/b^3+3*polylog(3,exp(a+b*x))/b^3-3/2*x^2*sech(a+b*x)/b-1/2*x^2*csch(a+b*x)^2*sech(a+b*x)/b],
[x*csch(a+b*x)^3*sech(a+b*x)^2,x,13,arctan(sinh(a+b*x))/b^2+3*x*arctanh(exp(a+b*x))/b-1/2*csch(a+b*x)/b^2+3/2*polylog(2,-exp(a+b*x))/b^2-3/2*polylog(2,exp(a+b*x))/b^2-3/2*x*sech(a+b*x)/b-1/2*x*csch(a+b*x)^2*sech(a+b*x)/b],
[csch(a+b*x)^3*sech(a+b*x)^2,x,4,3/2*arctanh(cosh(a+b*x))/b-3/2*sech(a+b*x)/b-1/2*csch(a+b*x)^2*sech(a+b*x)/b],
[csch(a+b*x)^3*sech(a+b*x)^2/x,x,0,CannotIntegrate(csch(a+b*x)^3*sech(a+b*x)^2/x,x)],
[csch(a+b*x)^3*sech(a+b*x)^2/x^2,x,0,CannotIntegrate(csch(a+b*x)^3*sech(a+b*x)^2/x^2,x)],
[x^m*csch(a+b*x)^3*sech(a+b*x)^3,x,0,CannotIntegrate(x^m*csch(a+b*x)^3*sech(a+b*x)^3,x)],
[x^3*csch(a+b*x)^3*sech(a+b*x)^3,x,16,-6*x*arctanh(exp(2*a+2*b*x))/b^3+4*x^3*arctanh(exp(2*a+2*b*x))/b-3*x^2*csch(2*a+2*b*x)/b^2-2*x^3*coth(2*a+2*b*x)*csch(2*a+2*b*x)/b-3/2*polylog(2,-exp(2*a+2*b*x))/b^4+3*x^2*polylog(2,-exp(2*a+2*b*x))/b^2+3/2*polylog(2,exp(2*a+2*b*x))/b^4-3*x^2*polylog(2,exp(2*a+2*b*x))/b^2-3*x*polylog(3,-exp(2*a+2*b*x))/b^3+3*x*polylog(3,exp(2*a+2*b*x))/b^3+3/2*polylog(4,-exp(2*a+2*b*x))/b^4-3/2*polylog(4,exp(2*a+2*b*x))/b^4],
[x^2*csch(a+b*x)^3*sech(a+b*x)^3,x,10,4*x^2*arctanh(exp(2*a+2*b*x))/b-arctanh(cosh(2*a+2*b*x))/b^3-2*x*csch(2*a+2*b*x)/b^2-2*x^2*coth(2*a+2*b*x)*csch(2*a+2*b*x)/b+2*x*polylog(2,-exp(2*a+2*b*x))/b^2-2*x*polylog(2,exp(2*a+2*b*x))/b^2-polylog(3,-exp(2*a+2*b*x))/b^3+polylog(3,exp(2*a+2*b*x))/b^3],
[x*csch(a+b*x)^3*sech(a+b*x)^3,x,7,4*x*arctanh(exp(2*a+2*b*x))/b-csch(2*a+2*b*x)/b^2-2*x*coth(2*a+2*b*x)*csch(2*a+2*b*x)/b+polylog(2,-exp(2*a+2*b*x))/b^2-polylog(2,exp(2*a+2*b*x))/b^2],
[csch(a+b*x)^3*sech(a+b*x)^3,x,4,-1/2*coth(a+b*x)^2/b-2*log(tanh(a+b*x))/b+1/2*tanh(a+b*x)^2/b],
[csch(a+b*x)^3*sech(a+b*x)^3/x,x,1,8*Unintegrable(csch(2*a+2*b*x)^3/x,x)],
[csch(a+b*x)^3*sech(a+b*x)^3/x^2,x,1,8*Unintegrable(csch(2*a+2*b*x)^3/x^2,x)],

# Integrands of the form x^m Cosh[a+b x]^(n/2) Sinh[a+b x]^n
[x*cosh(a+b*x)^(5/2)*sinh(a+b*x),x,4,2/7*x*cosh(a+b*x)^(7/2)/b+20/147*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticF(sin(1/2*I*(a+b*x)),sqrt(2))/b^2-4/49*cosh(a+b*x)^(5/2)*sinh(a+b*x)/b^2-20/147*sinh(a+b*x)*sqrt(cosh(a+b*x))/b^2],
[x*cosh(a+b*x)^(3/2)*sinh(a+b*x),x,3,2/5*x*cosh(a+b*x)^(5/2)/b+12/25*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticE(sin(1/2*I*(a+b*x)),sqrt(2))/b^2-4/25*cosh(a+b*x)^(3/2)*sinh(a+b*x)/b^2],
[x*sinh(a+b*x)*sqrt(cosh(a+b*x)),x,3,2/3*x*cosh(a+b*x)^(3/2)/b+4/9*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticF(sin(1/2*I*(a+b*x)),sqrt(2))/b^2-4/9*sinh(a+b*x)*sqrt(cosh(a+b*x))/b^2],
[x*sinh(a+b*x)/sqrt(cosh(a+b*x)),x,2,4*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticE(sin(1/2*I*(a+b*x)),sqrt(2))/b^2+2*x*sqrt(cosh(a+b*x))/b],
[x*sinh(a+b*x)/cosh(a+b*x)^(3/2),x,2,-4*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticF(sin(1/2*I*(a+b*x)),sqrt(2))/b^2-2*x/(b*sqrt(cosh(a+b*x)))],
[x*sinh(a+b*x)/cosh(a+b*x)^(5/2),x,3,-2/3*x/(b*cosh(a+b*x)^(3/2))+4/3*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticE(sin(1/2*I*(a+b*x)),sqrt(2))/b^2+4/3*sinh(a+b*x)/(b^2*sqrt(cosh(a+b*x)))],
[x*sinh(a+b*x)/cosh(a+b*x)^(7/2),x,3,-2/5*x/(b*cosh(a+b*x)^(5/2))-4/15*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticF(sin(1/2*I*(a+b*x)),sqrt(2))/b^2+4/15*sinh(a+b*x)/(b^2*cosh(a+b*x)^(3/2))],
[x*sinh(a+b*x)/cosh(a+b*x)^(9/2),x,4,-2/7*x/(b*cosh(a+b*x)^(7/2))+12/35*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticE(sin(1/2*I*(a+b*x)),sqrt(2))/b^2+4/35*sinh(a+b*x)/(b^2*cosh(a+b*x)^(5/2))+12/35*sinh(a+b*x)/(b^2*sqrt(cosh(a+b*x)))],
[x*sech(a+b*x)^(9/2)*sinh(a+b*x),x,5,-2/7*x*sech(a+b*x)^(7/2)/b+4/35*sech(a+b*x)^(5/2)*sinh(a+b*x)/b^2+12/35*sinh(a+b*x)*sqrt(sech(a+b*x))/b^2+12/35*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticE(sin(1/2*I*(a+b*x)),sqrt(2))*sqrt(cosh(a+b*x))*sqrt(sech(a+b*x))/b^2],
[x*sech(a+b*x)^(7/2)*sinh(a+b*x),x,4,-2/5*x*sech(a+b*x)^(5/2)/b+4/15*sech(a+b*x)^(3/2)*sinh(a+b*x)/b^2-4/15*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticF(sin(1/2*I*(a+b*x)),sqrt(2))*sqrt(cosh(a+b*x))*sqrt(sech(a+b*x))/b^2],
[x*sech(a+b*x)^(5/2)*sinh(a+b*x),x,4,-2/3*x*sech(a+b*x)^(3/2)/b+4/3*sinh(a+b*x)*sqrt(sech(a+b*x))/b^2+4/3*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticE(sin(1/2*I*(a+b*x)),sqrt(2))*sqrt(cosh(a+b*x))*sqrt(sech(a+b*x))/b^2],
[x*sech(a+b*x)^(3/2)*sinh(a+b*x),x,3,-2*x*sqrt(sech(a+b*x))/b-4*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticF(sin(1/2*I*(a+b*x)),sqrt(2))*sqrt(cosh(a+b*x))*sqrt(sech(a+b*x))/b^2],
[x*sech(a+b*x)^(1/2)*sinh(a+b*x),x,3,2*x/(b*sqrt(sech(a+b*x)))+4*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticE(sin(1/2*I*(a+b*x)),sqrt(2))*sqrt(cosh(a+b*x))*sqrt(sech(a+b*x))/b^2],
[x*sinh(a+b*x)/sech(a+b*x)^(1/2),x,4,2/3*x/(b*sech(a+b*x)^(3/2))-4/9*sinh(a+b*x)/(b^2*sqrt(sech(a+b*x)))+4/9*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticF(sin(1/2*I*(a+b*x)),sqrt(2))*sqrt(cosh(a+b*x))*sqrt(sech(a+b*x))/b^2],
[x*sinh(a+b*x)/sech(a+b*x)^(3/2),x,4,2/5*x/(b*sech(a+b*x)^(5/2))-4/25*sinh(a+b*x)/(b^2*sech(a+b*x)^(3/2))+12/25*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticE(sin(1/2*I*(a+b*x)),sqrt(2))*sqrt(cosh(a+b*x))*sqrt(sech(a+b*x))/b^2],
[x*sinh(a+b*x)/sech(a+b*x)^(5/2),x,5,2/7*x/(b*sech(a+b*x)^(7/2))-4/49*sinh(a+b*x)/(b^2*sech(a+b*x)^(5/2))-20/147*sinh(a+b*x)/(b^2*sqrt(sech(a+b*x)))+20/147*I*sqrt(cos(1/2*I*(a+b*x))^2)/cos(1/2*I*(a+b*x))*EllipticF(sin(1/2*I*(a+b*x)),sqrt(2))*sqrt(cosh(a+b*x))*sqrt(sech(a+b*x))/b^2],

# Integrands of the form x^m Sinh[a+b x]^(n/2) Cosh[a+b x]^n
[x*cosh(a+b*x)*sinh(a+b*x)^(5/2),x,5,-4/49*cosh(a+b*x)*sinh(a+b*x)^(5/2)/b^2+2/7*x*sinh(a+b*x)^(7/2)/b+20/147*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticF(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))*sqrt(I*sinh(a+b*x))/(b^2*sqrt(sinh(a+b*x)))+20/147*cosh(a+b*x)*sqrt(sinh(a+b*x))/b^2],
[x*cosh(a+b*x)*sinh(a+b*x)^(3/2),x,4,-4/25*cosh(a+b*x)*sinh(a+b*x)^(3/2)/b^2+2/5*x*sinh(a+b*x)^(5/2)/b-12/25*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticE(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))*sqrt(sinh(a+b*x))/(b^2*sqrt(I*sinh(a+b*x)))],
[x*cosh(a+b*x)*sqrt(sinh(a+b*x)),x,4,2/3*x*sinh(a+b*x)^(3/2)/b-4/9*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticF(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))*sqrt(I*sinh(a+b*x))/(b^2*sqrt(sinh(a+b*x)))-4/9*cosh(a+b*x)*sqrt(sinh(a+b*x))/b^2],
[x*cosh(a+b*x)/sqrt(sinh(a+b*x)),x,3,2*x*sqrt(sinh(a+b*x))/b+4*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticE(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))*sqrt(sinh(a+b*x))/(b^2*sqrt(I*sinh(a+b*x)))],
[x*cosh(a+b*x)/sinh(a+b*x)^(3/2),x,3,-2*x/(b*sqrt(sinh(a+b*x)))-4*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticF(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))*sqrt(I*sinh(a+b*x))/(b^2*sqrt(sinh(a+b*x)))],
[x*cosh(a+b*x)/sinh(a+b*x)^(5/2),x,4,-2/3*x/(b*sinh(a+b*x)^(3/2))-4/3*cosh(a+b*x)/(b^2*sqrt(sinh(a+b*x)))-4/3*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticE(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))*sqrt(sinh(a+b*x))/(b^2*sqrt(I*sinh(a+b*x)))],
[x*cosh(a+b*x)/sinh(a+b*x)^(7/2),x,4,-2/5*x/(b*sinh(a+b*x)^(5/2))-4/15*cosh(a+b*x)/(b^2*sinh(a+b*x)^(3/2))+4/15*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticF(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))*sqrt(I*sinh(a+b*x))/(b^2*sqrt(sinh(a+b*x)))],
[x*cosh(a+b*x)/sinh(a+b*x)^(9/2),x,5,-2/7*x/(b*sinh(a+b*x)^(7/2))-4/35*cosh(a+b*x)/(b^2*sinh(a+b*x)^(5/2))+12/35*cosh(a+b*x)/(b^2*sqrt(sinh(a+b*x)))+12/35*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticE(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))*sqrt(sinh(a+b*x))/(b^2*sqrt(I*sinh(a+b*x)))],
[x*cosh(a+b*x)*csch(a+b*x)^(9/2),x,5,-4/35*cosh(a+b*x)*csch(a+b*x)^(5/2)/b^2-2/7*x*csch(a+b*x)^(7/2)/b+12/35*cosh(a+b*x)*sqrt(csch(a+b*x))/b^2+12/35*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticE(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))/(b^2*sqrt(csch(a+b*x))*sqrt(I*sinh(a+b*x)))],
[x*cosh(a+b*x)*csch(a+b*x)^(7/2),x,4,-4/15*cosh(a+b*x)*csch(a+b*x)^(3/2)/b^2-2/5*x*csch(a+b*x)^(5/2)/b+4/15*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticF(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))*sqrt(csch(a+b*x))*sqrt(I*sinh(a+b*x))/b^2],
[x*cosh(a+b*x)*csch(a+b*x)^(5/2),x,4,-2/3*x*csch(a+b*x)^(3/2)/b-4/3*cosh(a+b*x)*sqrt(csch(a+b*x))/b^2-4/3*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticE(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))/(b^2*sqrt(csch(a+b*x))*sqrt(I*sinh(a+b*x)))],
[x*cosh(a+b*x)*csch(a+b*x)^(3/2),x,3,-2*x*sqrt(csch(a+b*x))/b-4*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticF(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))*sqrt(csch(a+b*x))*sqrt(I*sinh(a+b*x))/b^2],
[x*cosh(a+b*x)*csch(a+b*x)^(1/2),x,3,2*x/(b*sqrt(csch(a+b*x)))+4*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticE(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))/(b^2*sqrt(csch(a+b*x))*sqrt(I*sinh(a+b*x)))],
[x*cosh(a+b*x)/csch(a+b*x)^(1/2),x,4,2/3*x/(b*csch(a+b*x)^(3/2))-4/9*cosh(a+b*x)/(b^2*sqrt(csch(a+b*x)))-4/9*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticF(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))*sqrt(csch(a+b*x))*sqrt(I*sinh(a+b*x))/b^2],
[x*cosh(a+b*x)/csch(a+b*x)^(3/2),x,4,2/5*x/(b*csch(a+b*x)^(5/2))-4/25*cosh(a+b*x)/(b^2*csch(a+b*x)^(3/2))-12/25*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticE(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))/(b^2*sqrt(csch(a+b*x))*sqrt(I*sinh(a+b*x)))],
[x*cosh(a+b*x)/csch(a+b*x)^(5/2),x,5,2/7*x/(b*csch(a+b*x)^(7/2))-4/49*cosh(a+b*x)/(b^2*csch(a+b*x)^(5/2))+20/147*cosh(a+b*x)/(b^2*sqrt(csch(a+b*x)))+20/147*I*sqrt(cos(1/2*(I*a-1/2*Pi+I*b*x))^2)/cos(1/2*(I*a-1/2*Pi+I*b*x))*EllipticF(sin(1/2*(I*a-1/2*Pi+I*b*x)),sqrt(2))*sqrt(csch(a+b*x))*sqrt(I*sinh(a+b*x))/b^2],

# Integrands of the form (Hyper[a+b x] Hyper[a+b x])^m
[(sinh(x)*tanh(x))^(1/2),x,3,2*coth(x)*sqrt(sinh(x)*tanh(x))],
[(sinh(x)*tanh(x))^(3/2),x,4,8/3*csch(x)*sqrt(sinh(x)*tanh(x))+2/3*sinh(x)*sqrt(sinh(x)*tanh(x))],
[(sinh(x)*tanh(x))^(5/2),x,5,-64/15*coth(x)*sqrt(sinh(x)*tanh(x))+16/15*sqrt(sinh(x)*tanh(x))*tanh(x)+2/5*sinh(x)^2*sqrt(sinh(x)*tanh(x))*tanh(x)],
[(cosh(x)*coth(x))^(1/2),x,3,2*sqrt(cosh(x)*coth(x))*tanh(x)],
[(cosh(x)*coth(x))^(3/2),x,4,2/3*cosh(x)*sqrt(cosh(x)*coth(x))-8/3*sech(x)*sqrt(cosh(x)*coth(x))],
[(cosh(x)*coth(x))^(5/2),x,5,-16/15*coth(x)*sqrt(cosh(x)*coth(x))+2/5*cosh(x)^2*coth(x)*sqrt(cosh(x)*coth(x))+64/15*sqrt(cosh(x)*coth(x))*tanh(x)],

# Integrands of the form x^m (a+b Hyper[x])^n (c+d Hyper[x])^p
[(b+c+cosh(x))/(a+b*sinh(x)),x,7,log(a+b*sinh(x))/b-2*(b+c)*arctanh((b-a*tanh(1/2*x))/sqrt(a^2+b^2))/sqrt(a^2+b^2)],
[(b+c+cosh(x))/(a-b*sinh(x)),x,7,-log(a-b*sinh(x))/b+2*(b+c)*arctanh((b+a*tanh(1/2*x))/sqrt(a^2+b^2))/sqrt(a^2+b^2)],
[(b+c+sinh(x))/(a+b*cosh(x)),x,6,log(a+b*cosh(x))/b+2*(b+c)*arctanh(sqrt(a-b)*tanh(1/2*x)/sqrt(a+b))/(sqrt(a-b)*sqrt(a+b))],
[(b+c+sinh(x))/(a-b*cosh(x)),x,6,-log(a-b*cosh(x))/b+2*(b+c)*arctanh(sqrt(a+b)*tanh(1/2*x)/sqrt(a-b))/(sqrt(a-b)*sqrt(a+b))],
[x*(b-a*sinh(x))/(a+b*sinh(x))^2,x,3,log(a+b*sinh(x))/b-x*cosh(x)/(a+b*sinh(x))],
[x*(b+a*cosh(x))/(a+b*cosh(x))^2,x,3,-log(a+b*cosh(x))/b+x*sinh(x)/(a+b*cosh(x))],
[(a+b*sech(x))/(c+d*cosh(x)),x,5,b*arctan(sinh(x))/c+2*(a*c-b*d)*arctanh(sqrt(c-d)*tanh(1/2*x)/sqrt(c+d))/(c*sqrt(c-d)*sqrt(c+d))],
[(a+b*csch(x))/(c+d*sinh(x)),x,6,-b*arctanh(cosh(x))/c-2*(a*c-b*d)*arctanh((d-c*tanh(1/2*x))/sqrt(c^2+d^2))/(c*sqrt(c^2+d^2))],

# Integrands of the form x^m (a+b Hyper[x])^n (c+d Hyper[x]^2)^p
[(1+sinh(x)^2)/(1-sinh(x)^2),x,3,-x+arctanh(sqrt(2)*tanh(x))*sqrt(2)],
[(1-sinh(x)^2)/(1+sinh(x)^2),x,4,-x+2*tanh(x)],
[(1+cosh(x)^2)/(1-cosh(x)^2),x,4,-x+2*coth(x)],
[(1-cosh(x)^2)/(1+cosh(x)^2),x,3,-x+arctanh(tanh(x)/sqrt(2))*sqrt(2)],
[(a+b*sech(x)^2)/(c+d*cosh(x)),x,6,-b*d*arctan(sinh(x))/c^2+2*(a*c^2+b*d^2)*arctanh(sqrt(c-d)*tanh(1/2*x)/sqrt(c+d))/(c^2*sqrt(c-d)*sqrt(c+d))+b*tanh(x)/c],
[(a+b*csch(x)^2)/(c+d*sinh(x)),x,7,b*d*arctanh(cosh(x))/c^2-b*coth(x)/c-2*(a*c^2+b*d^2)*arctanh((d-c*tanh(1/2*x))/sqrt(c^2+d^2))/(c^2*sqrt(c^2+d^2))],

# Integrands of the form u (a Hyper[c+d x] + b Hyper[c+d x])^p

# Integrands of the form (a Hyper[c+d x] + b Hyper[c+d x])^p

# Integrands of the form (a Cosh[c+d x] + b Sinh[c+d x])^n
[a*cosh(x)+b*sinh(x),x,3,b*cosh(x)+a*sinh(x)],
[(a*cosh(x)+b*sinh(x))^2,x,2,1/2*(a^2-b^2)*x+1/2*(b*cosh(x)+a*sinh(x))*(a*cosh(x)+b*sinh(x))],
[(a*cosh(x)+b*sinh(x))^3,x,2,(a^2-b^2)*(b*cosh(x)+a*sinh(x))+1/3*(b*cosh(x)+a*sinh(x))^3],
[(a*cosh(x)+b*sinh(x))^4,x,3,3/8*(a^2-b^2)^2*x+3/8*(a^2-b^2)*(b*cosh(x)+a*sinh(x))*(a*cosh(x)+b*sinh(x))+1/4*(b*cosh(x)+a*sinh(x))*(a*cosh(x)+b*sinh(x))^3],
[(a*cosh(x)+b*sinh(x))^5,x,3,(a^2-b^2)^2*(b*cosh(x)+a*sinh(x))+2/3*(a^2-b^2)*(b*cosh(x)+a*sinh(x))^3+1/5*(b*cosh(x)+a*sinh(x))^5],
[1/(a*cosh(x)+b*sinh(x)),x,2,arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/sqrt(a^2-b^2)],
[1/(a*cosh(x)+b*sinh(x))^2,x,1,sinh(x)/(a*(a*cosh(x)+b*sinh(x)))],
[1/(a*cosh(x)+b*sinh(x))^3,x,3,1/2*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(3/2)+1/2*(b*cosh(x)+a*sinh(x))/((a^2-b^2)*(a*cosh(x)+b*sinh(x))^2)],
[1/(a*cosh(x)+b*sinh(x))^4,x,2,1/3*(b*cosh(x)+a*sinh(x))/((a^2-b^2)*(a*cosh(x)+b*sinh(x))^3)+2/3*sinh(x)/(a*(a^2-b^2)*(a*cosh(x)+b*sinh(x)))],
[1/(a*cosh(x)+b*sinh(x))^5,x,4,3/8*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)+1/4*(b*cosh(x)+a*sinh(x))/((a^2-b^2)*(a*cosh(x)+b*sinh(x))^4)+3/8*(b*cosh(x)+a*sinh(x))/((a^2-b^2)^2*(a*cosh(x)+b*sinh(x))^2)],
[(a*cosh(x)+b*sinh(x))^(1/2),x,2,-2*I*sqrt(cos(1/2*(I*x-arctan(a,-I*b)))^2)/cos(1/2*(I*x-arctan(a,-I*b)))*EllipticE(sin(1/2*(I*x-arctan(a,-I*b))),sqrt(2))*sqrt(a*cosh(x)+b*sinh(x))/sqrt((a*cosh(x)+b*sinh(x))/sqrt(a^2-b^2))],
[(a*cosh(x)+b*sinh(x))^(3/2),x,3,2/3*(b*cosh(x)+a*sinh(x))*sqrt(a*cosh(x)+b*sinh(x))-2/3*I*(a^2-b^2)*sqrt(cos(1/2*(I*x-arctan(a,-I*b)))^2)/cos(1/2*(I*x-arctan(a,-I*b)))*EllipticF(sin(1/2*(I*x-arctan(a,-I*b))),sqrt(2))*sqrt((a*cosh(x)+b*sinh(x))/sqrt(a^2-b^2))/sqrt(a*cosh(x)+b*sinh(x))],
[(a*cosh(x)+b*sinh(x))^(5/2),x,3,2/5*(b*cosh(x)+a*sinh(x))*(a*cosh(x)+b*sinh(x))^(3/2)-6/5*I*(a^2-b^2)*sqrt(cos(1/2*(I*x-arctan(a,-I*b)))^2)/cos(1/2*(I*x-arctan(a,-I*b)))*EllipticE(sin(1/2*(I*x-arctan(a,-I*b))),sqrt(2))*sqrt(a*cosh(x)+b*sinh(x))/sqrt((a*cosh(x)+b*sinh(x))/sqrt(a^2-b^2))],
[1/(a*cosh(x)+b*sinh(x))^(1/2),x,2,-2*I*sqrt(cos(1/2*(I*x-arctan(a,-I*b)))^2)/cos(1/2*(I*x-arctan(a,-I*b)))*EllipticF(sin(1/2*(I*x-arctan(a,-I*b))),sqrt(2))*sqrt((a*cosh(x)+b*sinh(x))/sqrt(a^2-b^2))/sqrt(a*cosh(x)+b*sinh(x))],
[1/(a*cosh(x)+b*sinh(x))^(3/2),x,3,2*(b*cosh(x)+a*sinh(x))/((a^2-b^2)*sqrt(a*cosh(x)+b*sinh(x)))+2*I*sqrt(cos(1/2*(I*x-arctan(a,-I*b)))^2)/cos(1/2*(I*x-arctan(a,-I*b)))*EllipticE(sin(1/2*(I*x-arctan(a,-I*b))),sqrt(2))*sqrt(a*cosh(x)+b*sinh(x))/((a^2-b^2)*sqrt((a*cosh(x)+b*sinh(x))/sqrt(a^2-b^2)))],
[1/(a*cosh(x)+b*sinh(x))^(5/2),x,3,2/3*(b*cosh(x)+a*sinh(x))/((a^2-b^2)*(a*cosh(x)+b*sinh(x))^(3/2))-2/3*I*sqrt(cos(1/2*(I*x-arctan(a,-I*b)))^2)/cos(1/2*(I*x-arctan(a,-I*b)))*EllipticF(sin(1/2*(I*x-arctan(a,-I*b))),sqrt(2))*sqrt((a*cosh(x)+b*sinh(x))/sqrt(a^2-b^2))/((a^2-b^2)*sqrt(a*cosh(x)+b*sinh(x)))],
[a*cosh(c+d*x)+a*sinh(c+d*x),x,3,a*cosh(c+d*x)/d+a*sinh(c+d*x)/d],
[(a*cosh(c+d*x)+a*sinh(c+d*x))^2,x,1,1/2*(a*cosh(c+d*x)+a*sinh(c+d*x))^2/d],
[(a*cosh(c+d*x)+a*sinh(c+d*x))^3,x,1,1/3*(a*cosh(c+d*x)+a*sinh(c+d*x))^3/d],
[(a*cosh(c+d*x)+a*sinh(c+d*x))^n,x,1,(a*cosh(c+d*x)+a*sinh(c+d*x))^n/(d*n)],
[1/(a*cosh(c+d*x)+a*sinh(c+d*x)),x,1,(-1)/(d*(a*cosh(c+d*x)+a*sinh(c+d*x)))],
[1/(a*cosh(c+d*x)+a*sinh(c+d*x))^2,x,1,(-1/2)/(d*(a*cosh(c+d*x)+a*sinh(c+d*x))^2)],
[1/(a*cosh(c+d*x)+a*sinh(c+d*x))^3,x,1,(-1/3)/(d*(a*cosh(c+d*x)+a*sinh(c+d*x))^3)],
[sqrt(a*cosh(c+d*x)+a*sinh(c+d*x)),x,1,2*sqrt(a*cosh(c+d*x)+a*sinh(c+d*x))/d],
[1/sqrt(a*cosh(c+d*x)+a*sinh(c+d*x)),x,1,(-2)/(d*sqrt(a*cosh(c+d*x)+a*sinh(c+d*x)))],
[a*cosh(c+d*x)-a*sinh(c+d*x),x,3,-a*cosh(c+d*x)/d+a*sinh(c+d*x)/d],
[(a*cosh(c+d*x)-a*sinh(c+d*x))^2,x,1,-1/2*(a*cosh(c+d*x)-a*sinh(c+d*x))^2/d],
[(a*cosh(c+d*x)-a*sinh(c+d*x))^3,x,1,-1/3*(a*cosh(c+d*x)-a*sinh(c+d*x))^3/d],
[(a*cosh(c+d*x)-a*sinh(c+d*x))^n,x,1,-(a*cosh(c+d*x)-a*sinh(c+d*x))^n/(d*n)],
[1/(a*cosh(c+d*x)-a*sinh(c+d*x)),x,1,1/(d*(a*cosh(c+d*x)-a*sinh(c+d*x)))],
[1/(a*cosh(c+d*x)-a*sinh(c+d*x))^2,x,1,1/2/(d*(a*cosh(c+d*x)-a*sinh(c+d*x))^2)],
[1/(a*cosh(c+d*x)-a*sinh(c+d*x))^3,x,1,1/3/(d*(a*cosh(c+d*x)-a*sinh(c+d*x))^3)],
[sqrt(a*cosh(c+d*x)-a*sinh(c+d*x)),x,1,-2*sqrt(a*cosh(c+d*x)-a*sinh(c+d*x))/d],
[1/sqrt(a*cosh(c+d*x)-a*sinh(c+d*x)),x,1,2/(d*sqrt(a*cosh(c+d*x)-a*sinh(c+d*x)))],

# Integrands of the form (a Sech[c+d x] + b Tanh[c+d x])^n
[(a*sech(x)+b*tanh(x))^5,x,8,1/8*a*(3*a^4+10*a^2*b^2+15*b^4)*arctan(sinh(x))+b^5*log(cosh(x))-1/8*a*b^2*(3*a^2+7*b^2)*sinh(x)-1/4*sech(x)^4*(b-a*sinh(x))*(a+b*sinh(x))^4-1/8*sech(x)^2*(a+b*sinh(x))^2*(2*b*(a^2+2*b^2)-a*(3*a^2+5*b^2)*sinh(x))],
[(a*sech(x)+b*tanh(x))^4,x,4,b^4*x-4/3*a*b*(a^2+2*b^2)*cosh(x)-1/3*b^2*(2*a^2+3*b^2)*cosh(x)*sinh(x)-1/3*sech(x)^3*(b-a*sinh(x))*(a+b*sinh(x))^3+1/3*sech(x)*(a+b*sinh(x))^2*(a*b+(2*a^2+3*b^2)*sinh(x))],
[(a*sech(x)+b*tanh(x))^3,x,7,1/2*a*(a^2+3*b^2)*arctan(sinh(x))+b^3*log(cosh(x))-1/2*a*b^2*sinh(x)-1/2*sech(x)^2*(b-a*sinh(x))*(a+b*sinh(x))^2],
[(a*sech(x)+b*tanh(x))^2,x,4,b^2*x-a*b*cosh(x)-sech(x)*(b-a*sinh(x))*(a+b*sinh(x))],
[a*sech(x)+b*tanh(x),x,3,a*arctan(sinh(x))+b*log(cosh(x))],
[1/(a*sech(x)+b*tanh(x)),x,3,log(a+b*sinh(x))/b],
[1/(a*sech(x)+b*tanh(x))^2,x,6,x/b^2-cosh(x)/(b*(a+b*sinh(x)))+2*a*arctanh((b-a*tanh(1/2*x))/sqrt(a^2+b^2))/(b^2*sqrt(a^2+b^2))],
[1/(a*sech(x)+b*tanh(x))^3,x,4,log(a+b*sinh(x))/b^3+1/2*(-a^2-b^2)/(b^3*(a+b*sinh(x))^2)+2*a/(b^3*(a+b*sinh(x)))],
[1/(a*sech(x)+b*tanh(x))^4,x,8,x/b^4+a*(2*a^2+3*b^2)*arctanh((b-a*tanh(1/2*x))/sqrt(a^2+b^2))/(b^4*(a^2+b^2)^(3/2))-1/3*cosh(x)^3/(b*(a+b*sinh(x))^3)+1/2*a*cosh(x)^3/(b*(a^2+b^2)*(a+b*sinh(x))^2)-1/2*cosh(x)*(2*(a^2+b^2)+a*b*sinh(x))/(b^3*(a^2+b^2)*(a+b*sinh(x)))],
[1/(a*sech(x)+b*tanh(x))^5,x,4,log(a+b*sinh(x))/b^5-1/4*(a^2+b^2)^2/(b^5*(a+b*sinh(x))^4)+4/3*a*(a^2+b^2)/(b^5*(a+b*sinh(x))^3)+(-3*a^2-b^2)/(b^5*(a+b*sinh(x))^2)+4*a/(b^5*(a+b*sinh(x)))],
[(sech(x)+I*tanh(x))^5,x,4,I*log(I+sinh(x))+(-2*I)/(1-I*sinh(x))^2+4*I/(1-I*sinh(x))],
[(sech(x)+I*tanh(x))^4,x,5,x-2/3*I*cosh(x)^3/(1-I*sinh(x))^3+2*I*cosh(x)/(1-I*sinh(x))],
[(sech(x)+I*tanh(x))^3,x,4,-I*log(I+sinh(x))+(-2*I)/(1-I*sinh(x))],
[(sech(x)+I*tanh(x))^2,x,4,-x-2*I*cosh(x)/(1-I*sinh(x))],
[sech(x)+I*tanh(x),x,3,arctan(sinh(x))+I*log(cosh(x))],
[1/(sech(x)+I*tanh(x)),x,3,-I*log(I-sinh(x))],
[1/(sech(x)+I*tanh(x))^2,x,3,-x+2*I*cosh(x)/(1+I*sinh(x))],
[1/(sech(x)+I*tanh(x))^3,x,4,I*log(I-sinh(x))+2*I/(1+I*sinh(x))],
[1/(sech(x)+I*tanh(x))^4,x,4,x+2/3*I*cosh(x)^3/(1+I*sinh(x))^3-2*I*cosh(x)/(1+I*sinh(x))],
[1/(sech(x)+I*tanh(x))^5,x,4,-I*log(I-sinh(x))+2*I/(1+I*sinh(x))^2+(-4*I)/(1+I*sinh(x))],
[(sech(x)-I*tanh(x))^5,x,4,-I*log(I-sinh(x))+2*I/(1+I*sinh(x))^2+(-4*I)/(1+I*sinh(x))],
[(sech(x)-I*tanh(x))^4,x,5,x+2/3*I*cosh(x)^3/(1+I*sinh(x))^3-2*I*cosh(x)/(1+I*sinh(x))],
[(sech(x)-I*tanh(x))^3,x,4,I*log(I-sinh(x))+2*I/(1+I*sinh(x))],
[(sech(x)-I*tanh(x))^2,x,4,-x+2*I*cosh(x)/(1+I*sinh(x))],
[sech(x)-I*tanh(x),x,3,arctan(sinh(x))-I*log(cosh(x))],
[1/(sech(x)-I*tanh(x)),x,3,I*log(I+sinh(x))],
[1/(sech(x)-I*tanh(x))^2,x,3,-x-2*I*cosh(x)/(1-I*sinh(x))],
[1/(sech(x)-I*tanh(x))^3,x,4,-I*log(I+sinh(x))+(-2*I)/(1-I*sinh(x))],
[1/(sech(x)-I*tanh(x))^4,x,4,x-2/3*I*cosh(x)^3/(1-I*sinh(x))^3+2*I*cosh(x)/(1-I*sinh(x))],
[1/(sech(x)-I*tanh(x))^5,x,4,I*log(I+sinh(x))+(-2*I)/(1-I*sinh(x))^2+4*I/(1-I*sinh(x))],

# Integrands of the form (a Coth[c+d x] + b Csch[c+d x])^n
[(a*coth(x)+b*csch(x))^5,x,8,-1/8*b*(15*a^4-10*a^2*b^2+3*b^4)*arctanh(cosh(x))+1/8*a^2*b*(7*a^2-3*b^2)*cosh(x)-1/8*(b+a*cosh(x))^2*(2*a*(2*a^2-b^2)+b*(5*a^2-3*b^2)*cosh(x))*csch(x)^2-1/4*(b+a*cosh(x))^4*(a+b*cosh(x))*csch(x)^4+a^5*log(sinh(x))],
[(a*coth(x)+b*csch(x))^4,x,4,a^4*x-1/3*(b+a*cosh(x))^2*(a*b+(3*a^2-2*b^2)*cosh(x))*csch(x)-1/3*(b+a*cosh(x))^3*(a+b*cosh(x))*csch(x)^3+4/3*a*b*(2*a^2-b^2)*sinh(x)+1/3*a^2*(3*a^2-2*b^2)*cosh(x)*sinh(x)],
[(a*coth(x)+b*csch(x))^3,x,7,-1/2*b*(3*a^2-b^2)*arctanh(cosh(x))+1/2*a^2*b*cosh(x)-1/2*(b+a*cosh(x))^2*(a+b*cosh(x))*csch(x)^2+a^3*log(sinh(x))],
[(a*coth(x)+b*csch(x))^2,x,4,a^2*x-(b+a*cosh(x))*(a+b*cosh(x))*csch(x)+a*b*sinh(x)],
[a*coth(x)+b*csch(x),x,3,-b*arctanh(cosh(x))+a*log(sinh(x))],
[1/(a*coth(x)+b*csch(x)),x,3,log(b+a*cosh(x))/a],
[1/(a*coth(x)+b*csch(x))^2,x,5,x/a^2-sinh(x)/(a*(b+a*cosh(x)))-2*b*arctan(sqrt(a-b)*tanh(1/2*x)/sqrt(a+b))/(a^2*sqrt(a-b)*sqrt(a+b))],
[1/(a*coth(x)+b*csch(x))^3,x,4,1/2*(a^2-b^2)/(a^3*(b+a*cosh(x))^2)+2*b/(a^3*(b+a*cosh(x)))+log(b+a*cosh(x))/a^3],
[1/(a*coth(x)+b*csch(x))^4,x,7,x/a^4-b*(3*a^2-2*b^2)*arctan(sqrt(a-b)*tanh(1/2*x)/sqrt(a+b))/(a^4*(a-b)^(3/2)*(a+b)^(3/2))-1/2*(2*(a^2-b^2)-a*b*cosh(x))*sinh(x)/(a^3*(a^2-b^2)*(b+a*cosh(x)))-1/3*sinh(x)^3/(a*(b+a*cosh(x))^3)-1/2*b*sinh(x)^3/(a*(a^2-b^2)*(b+a*cosh(x))^2)],
[1/(a*coth(x)+b*csch(x))^5,x,4,-1/4*(a^2-b^2)^2/(a^5*(b+a*cosh(x))^4)-4/3*b*(a^2-b^2)/(a^5*(b+a*cosh(x))^3)+(a^2-3*b^2)/(a^5*(b+a*cosh(x))^2)+4*b/(a^5*(b+a*cosh(x)))+log(b+a*cosh(x))/a^5],
[(coth(x)+csch(x))^5,x,4,(-2)/(1-cosh(x))^2+4/(1-cosh(x))+log(1-cosh(x))],
[(coth(x)+csch(x))^4,x,5,x+2*sinh(x)/(1-cosh(x))+2/3*sinh(x)^3/(1-cosh(x))^3],
[(coth(x)+csch(x))^3,x,4,2/(1-cosh(x))+log(1-cosh(x))],
[(coth(x)+csch(x))^2,x,4,x+2*sinh(x)/(1-cosh(x))],
[coth(x)+csch(x),x,3,-arctanh(cosh(x))+log(sinh(x))],
[1/(coth(x)+csch(x)),x,3,log(1+cosh(x))],
[1/(coth(x)+csch(x))^2,x,3,x-2*sinh(x)/(1+cosh(x))],
[1/(coth(x)+csch(x))^3,x,4,2/(1+cosh(x))+log(1+cosh(x))],
[1/(coth(x)+csch(x))^4,x,4,x-2*sinh(x)/(1+cosh(x))-2/3*sinh(x)^3/(1+cosh(x))^3],
[1/(coth(x)+csch(x))^5,x,4,(-2)/(1+cosh(x))^2+4/(1+cosh(x))+log(1+cosh(x))],
[(-coth(x)+csch(x))^5,x,4,2/(1+cosh(x))^2+(-4)/(1+cosh(x))-log(1+cosh(x))],
[(-coth(x)+csch(x))^4,x,5,x-2*sinh(x)/(1+cosh(x))-2/3*sinh(x)^3/(1+cosh(x))^3],
[(-coth(x)+csch(x))^3,x,4,(-2)/(1+cosh(x))-log(1+cosh(x))],
[(-coth(x)+csch(x))^2,x,4,x-2*sinh(x)/(1+cosh(x))],
[-coth(x)+csch(x),x,3,-arctanh(cosh(x))-log(sinh(x))],
[1/(-coth(x)+csch(x)),x,3,-log(1-cosh(x))],
[1/(-coth(x)+csch(x))^2,x,3,x+2*sinh(x)/(1-cosh(x))],
[1/(-coth(x)+csch(x))^3,x,4,(-2)/(1-cosh(x))-log(1-cosh(x))],
[1/(-coth(x)+csch(x))^4,x,4,x+2*sinh(x)/(1-cosh(x))+2/3*sinh(x)^3/(1-cosh(x))^3],
[1/(-coth(x)+csch(x))^5,x,4,2/(1-cosh(x))^2+(-4)/(1-cosh(x))-log(1-cosh(x))],

# Integrands of the form (a Csch[c+d x] + b Sinh[c+d x])^n

#  Note that Csch[x]+Sinh[x] == Cosh[x]*Coth[x] 
[csch(x)+sinh(x),x,3,-arctanh(cosh(x))+cosh(x)],
[(csch(x)+sinh(x))^2,x,4,3/2*x-3/2*coth(x)+1/2*cosh(x)^2*coth(x)],
[(csch(x)+sinh(x))^3,x,6,-5/2*arctanh(cosh(x))+5/2*cosh(x)+5/6*cosh(x)^3-1/2*cosh(x)^3*coth(x)^2],
[(csch(x)+sinh(x))^(1/2),x,4,2*sqrt(cosh(x)*coth(x))*tanh(x)],
[(csch(x)+sinh(x))^(3/2),x,5,2/3*cosh(x)*sqrt(cosh(x)*coth(x))-8/3*sech(x)*sqrt(cosh(x)*coth(x))],
[(csch(x)+sinh(x))^(5/2),x,6,-16/15*coth(x)*sqrt(cosh(x)*coth(x))+2/5*cosh(x)^2*coth(x)*sqrt(cosh(x)*coth(x))+64/15*sqrt(cosh(x)*coth(x))*tanh(x)],

# Integrands of the form (a Sech[c+d x] + b Cosh[c+d x])^n

#  Note that Sech[x]-Cosh[x] == -Sinh[x]*Tanh[x] 
[-cosh(x)+sech(x),x,3,arctan(sinh(x))-sinh(x)],
[(-cosh(x)+sech(x))^2,x,4,-3/2*x+3/2*tanh(x)+1/2*sinh(x)^2*tanh(x)],
[(-cosh(x)+sech(x))^3,x,6,-5/2*arctan(sinh(x))+5/2*sinh(x)-5/6*sinh(x)^3+1/2*sinh(x)^3*tanh(x)^2],
[(-cosh(x)+sech(x))^(1/2),x,3,2*coth(x)*sqrt(-sinh(x)*tanh(x))],
[(-cosh(x)+sech(x))^(3/2),x,4,-8/3*csch(x)*sqrt(-sinh(x)*tanh(x))-2/3*sinh(x)*sqrt(-sinh(x)*tanh(x))],
[(-cosh(x)+sech(x))^(5/2),x,5,-64/15*coth(x)*sqrt(-sinh(x)*tanh(x))+16/15*sqrt(-sinh(x)*tanh(x))*tanh(x)+2/5*sinh(x)^2*sqrt(-sinh(x)*tanh(x))*tanh(x)],

# Integrands of the form (a Sinh[c+d x] + b Tanh[c+d x])^n
[1/(sinh(x)+tanh(x)),x,6,-1/2*arctanh(cosh(x))+(-1/2)/(1+cosh(x)),-1/2*arctanh(cosh(x))-1/2*coth(x)*csch(x)+1/2*csch(x)^2],
[1/(sinh(x)-tanh(x)),x,6,-1/2*arctanh(cosh(x))+1/2/(1-cosh(x)),-1/2*arctanh(cosh(x))-1/2*coth(x)*csch(x)-1/2*csch(x)^2],

# Integrands of the form Hyper[x]^m / (a Hyper[x] + b Hyper[x])

# Integrands of the form Hyper[x]^m / (a Cosh[x] + b Sinh[x])
[sinh(x)/(a*cosh(x)+b*sinh(x)),x,2,-b*x/(a^2-b^2)+a*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)],
[sinh(x)^2/(a*cosh(x)+b*sinh(x)),x,4,-a^2*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(3/2)-b*cosh(x)/(a^2-b^2)+a*sinh(x)/(a^2-b^2)],
[sinh(x)^3/(a*cosh(x)+b*sinh(x)),x,5,a^2*b*x/(a^2-b^2)^2+1/2*b*x/(a^2-b^2)-a^3*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2-1/2*b*cosh(x)*sinh(x)/(a^2-b^2)+1/2*a*sinh(x)^2/(a^2-b^2)],
[cosh(x)/(a*cosh(x)+b*sinh(x)),x,2,a*x/(a^2-b^2)-b*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)],
[cosh(x)^2/(a*cosh(x)+b*sinh(x)),x,4,-b^2*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(3/2)-b*cosh(x)/(a^2-b^2)+a*sinh(x)/(a^2-b^2)],
[cosh(x)^3/(a*cosh(x)+b*sinh(x)),x,5,-a*b^2*x/(a^2-b^2)^2+1/2*a*x/(a^2-b^2)-1/2*b*cosh(x)^2/(a^2-b^2)+b^3*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2+1/2*a*cosh(x)*sinh(x)/(a^2-b^2)],
[tanh(x)/(b*cosh(x)+a*sinh(x)),x,5,arctan(sinh(x))/a+b*arctanh((a*cosh(x)+b*sinh(x))/sqrt(a^2-b^2))/(a*sqrt(a^2-b^2))],
[coth(x)/(b*cosh(x)+a*sinh(x)),x,5,-arctanh(cosh(x))/b+a*arctanh((a*cosh(x)+b*sinh(x))/sqrt(a^2-b^2))/(b*sqrt(a^2-b^2))],

# Integrands of the form Hyper[x]^m / (a Sech[x] + b Tanh[x])

# Integrands of the form Hyper[x]^m / (a Csch[x] + b Coth[x])

# Integrands of the form Hyper[x]^m / (a Hyper[x] + b Hyper[x])^2
[sinh(x)/(a*cosh(x)+b*sinh(x))^2,x,3,-b*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(3/2)-a/((a^2-b^2)*(a*cosh(x)+b*sinh(x)))],
[sinh(x)^2/(a*cosh(x)+b*sinh(x))^2,x,4,(a^2+b^2)*x/(a^2-b^2)^2-a/((a^2-b^2)*(b+a*coth(x)))-2*a*b*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2],
[sinh(x)^3/(a*cosh(x)+b*sinh(x))^2,x,16,3*a^2*b*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)+(2*a^2+b^2)*cosh(x)/(-a^2*b^2+b^4)+a*(a^2+2*b^2)*sinh(x)/(b^3*(a^2-b^2))-a^3/(b^3*(a+b)^2*(1-tanh(1/2*x)))+a^3/((a-b)^2*b^3*(1+tanh(1/2*x)))+2*a^2*(a+b*tanh(1/2*x))/((a^2-b^2)^2*(a+2*b*tanh(1/2*x)+a*tanh(1/2*x)^2)),-3*a^2*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(b*(a^2-b^2)^(3/2))+2*a^2*b*arctan((b+a*tanh(1/2*x))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)+2*a^2*(3*a^2-b^2)*arctan((b+a*tanh(1/2*x))/sqrt(a^2-b^2))/(b*(a^2-b^2)^(5/2))+cosh(x)/b^2-3*a^2*cosh(x)/(b^2*(a^2-b^2))-2*a*sinh(x)/b^3+3*a^3*sinh(x)/(b^3*(a^2-b^2))-a^3/(b^3*(a+b)^2*(1-tanh(1/2*x)))+a^3/((a-b)^2*b^3*(1+tanh(1/2*x)))+2*a^2*(a+b*tanh(1/2*x))/((a^2-b^2)^2*(a+2*b*tanh(1/2*x)+a*tanh(1/2*x)^2))],
[cosh(x)/(a*cosh(x)+b*sinh(x))^2,x,3,a*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(3/2)+b/((a^2-b^2)*(a*cosh(x)+b*sinh(x)))],
[cosh(x)^2/(a*cosh(x)+b*sinh(x))^2,x,4,(a^2+b^2)*x/(a^2-b^2)^2-2*a*b*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2+b/((a^2-b^2)*(a+b*tanh(x)))],
[cosh(x)^3/(a*cosh(x)+b*sinh(x))^2,x,8,-3*a*b^2*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)+1/((a+b)^2*(1-tanh(1/2*x)))+(-1)/((a-b)^2*(1+tanh(1/2*x)))-2*b^3*(a+b*tanh(1/2*x))/(a*(a^2-b^2)^2*(a+2*b*tanh(1/2*x)+a*tanh(1/2*x)^2)),-2*b^4*arctan((b+a*tanh(1/2*x))/sqrt(a^2-b^2))/(a*(a^2-b^2)^(5/2))-2*b^2*(3*a^2-b^2)*arctan((b+a*tanh(1/2*x))/sqrt(a^2-b^2))/(a*(a^2-b^2)^(5/2))+1/((a+b)^2*(1-tanh(1/2*x)))+(-1)/((a-b)^2*(1+tanh(1/2*x)))-2*b^3*(a+b*tanh(1/2*x))/(a*(a^2-b^2)^2*(a+2*b*tanh(1/2*x)+a*tanh(1/2*x)^2))],

# Integrands of the form Hyper[x]^m / (a Hyper[x] + b Hyper[x])^3
[sinh(x)/(a*cosh(x)+b*sinh(x))^3,x,2,1/2*tanh(x)^2/(a*(a+b*tanh(x))^2)],

#  {Sinh[x]^2/(a*Cosh[x] + b*Sinh[x])^3, x, 0, -(((a^2 - 2*b^2)*ArcTanh[(-b + a*Tan[x/2])/Sqrt[a^2 + b^2]])/(a^2 + b^2)^(5/2)) + (a*(3*a*b*Cosh[x] + (a^2 + 4*b^2)*Sinh[x]))/(2*(a^2 + b^2)^2*(a*Cosh[x] + b*Sinh[x])^2)} 
[sinh(x)^3/(a*cosh(x)+b*sinh(x))^3,x,5,-b*(3*a^2+b^2)*x/(a^2-b^2)^3-1/2*a/((a^2-b^2)*(b+a*coth(x))^2)+2*a*b/((a^2-b^2)^2*(b+a*coth(x)))+a*(a^2+3*b^2)*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^3],
[cosh(x)/(a*cosh(x)+b*sinh(x))^3,x,2,-1/2*coth(x)^2/(b*(b+a*coth(x))^2)],

#  {Cosh[x]^2/(a*Cosh[x] + b*Sinh[x])^3, x, 0, ((2*a^2 - b^2)*ArcTanh[(-b + a*Tan[x/2])/Sqrt[a^2 + b^2]])/(a^2 + b^2)^(5/2) - (b*((4*a^2 + b^2)*Cosh[x] + 3*a*b*Sinh[x]))/(2*(a^2 + b^2)^2*(a*Cosh[x] + b*Sinh[x])^2)} 
[cosh(x)^3/(a*cosh(x)+b*sinh(x))^3,x,5,a*(a^2+3*b^2)*x/(a^2-b^2)^3-b*(3*a^2+b^2)*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^3+1/2*b/((a^2-b^2)*(a+b*tanh(x))^2)+2*a*b/((a^2-b^2)^2*(a+b*tanh(x)))],

# Integrands of the form Hyper[x]^m Hyper[x]^n (a Hyper[x] + b Hyper[x])^p
[cosh(x)*sinh(x)/(a*cosh(x)+b*sinh(x)),x,5,a*b*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(3/2)+a*cosh(x)/(a^2-b^2)-b*sinh(x)/(a^2-b^2)],
[cosh(x)*sinh(x)^2/(a*cosh(x)+b*sinh(x)),x,7,-a*b^2*x/(a^2-b^2)^2-1/2*a*x/(a^2-b^2)+a^2*b*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2+1/2*a*cosh(x)*sinh(x)/(a^2-b^2)-1/2*b*sinh(x)^2/(a^2-b^2)],
[cosh(x)*sinh(x)^3/(a*cosh(x)+b*sinh(x)),x,9,-a^3*b*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)-a*b^2*cosh(x)/(a^2-b^2)^2-a*cosh(x)/(a^2-b^2)+1/3*a*cosh(x)^3/(a^2-b^2)+a^2*b*sinh(x)/(a^2-b^2)^2-1/3*b*sinh(x)^3/(a^2-b^2)],
[cosh(x)^2*sinh(x)/(a*cosh(x)+b*sinh(x)),x,7,a^2*b*x/(a^2-b^2)^2-1/2*b*x/(a^2-b^2)-a*b^2*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2-1/2*b*cosh(x)*sinh(x)/(a^2-b^2)+1/2*a*sinh(x)^2/(a^2-b^2)],
[cosh(x)^2*sinh(x)^2/(a*cosh(x)+b*sinh(x)),x,10,a^2*b^2*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)+a^2*b*cosh(x)/(a^2-b^2)^2-1/3*b*cosh(x)^3/(a^2-b^2)-a*b^2*sinh(x)/(a^2-b^2)^2+1/3*a*sinh(x)^3/(a^2-b^2)],
[cosh(x)^2*sinh(x)^3/(a*cosh(x)+b*sinh(x)),x,13,-a^2*b^3*x/(a^2-b^2)^3-1/2*a^2*b*x/(a^2-b^2)^2+1/8*b*x/(a^2-b^2)+a^3*b^2*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^3+1/2*a^2*b*cosh(x)*sinh(x)/(a^2-b^2)^2+1/8*b*cosh(x)*sinh(x)/(a^2-b^2)-1/4*b*cosh(x)^3*sinh(x)/(a^2-b^2)-1/2*a*b^2*sinh(x)^2/(a^2-b^2)^2+1/4*a*sinh(x)^4/(a^2-b^2)],
[cosh(x)^3*sinh(x)/(a*cosh(x)+b*sinh(x)),x,9,-a*b^3*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)-a*b^2*cosh(x)/(a^2-b^2)^2+1/3*a*cosh(x)^3/(a^2-b^2)+a^2*b*sinh(x)/(a^2-b^2)^2-b*sinh(x)/(a^2-b^2)-1/3*b*sinh(x)^3/(a^2-b^2)],
[cosh(x)^3*sinh(x)^2/(a*cosh(x)+b*sinh(x)),x,13,a^3*b^2*x/(a^2-b^2)^3-1/2*a*b^2*x/(a^2-b^2)^2-1/8*a*x/(a^2-b^2)-1/4*b*cosh(x)^4/(a^2-b^2)-a^2*b^3*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^3-1/2*a*b^2*cosh(x)*sinh(x)/(a^2-b^2)^2-1/8*a*cosh(x)*sinh(x)/(a^2-b^2)+1/4*a*cosh(x)^3*sinh(x)/(a^2-b^2)+1/2*a^2*b*sinh(x)^2/(a^2-b^2)^2],
[cosh(x)^3*sinh(x)^3/(a*cosh(x)+b*sinh(x)),x,17,a^3*b^3*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)+a^3*b^2*cosh(x)/(a^2-b^2)^3-1/3*a*b^2*cosh(x)^3/(a^2-b^2)^2-1/3*a*cosh(x)^3/(a^2-b^2)+1/5*a*cosh(x)^5/(a^2-b^2)-a^2*b^3*sinh(x)/(a^2-b^2)^3+1/3*a^2*b*sinh(x)^3/(a^2-b^2)^2-1/3*b*sinh(x)^3/(a^2-b^2)-1/5*b*sinh(x)^5/(a^2-b^2)],
[cosh(x)*sinh(x)/(a*cosh(x)+b*sinh(x))^2,x,6,-2*a*b*x/(a^2-b^2)^2+a^2*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2+b^2*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2+b*sinh(x)/((a^2-b^2)*(a*cosh(x)+b*sinh(x)))],
[cosh(x)*sinh(x)^2/(a*cosh(x)+b*sinh(x))^2,x,13,-a^3*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)-2*a*b^2*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)-2*a*b*cosh(x)/(a^2-b^2)^2+a^2*sinh(x)/(a^2-b^2)^2+b^2*sinh(x)/(a^2-b^2)^2-a^2*b/((a^2-b^2)^2*(a*cosh(x)+b*sinh(x)))],
[cosh(x)*sinh(x)^3/(a*cosh(x)+b*sinh(x))^2,x,17,a^3*b*x/(a^2-b^2)^3+a*b^3*x/(a^2-b^2)^3+a*b*x/(a^2-b^2)^2+a*b*(a^2+b^2)*x/(a^2-b^2)^3-a^2*b/((a^2-b^2)^2*(b+a*coth(x)))-a^4*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^3-3*a^2*b^2*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^3-a*b*cosh(x)*sinh(x)/(a^2-b^2)^2+1/2*a^2*sinh(x)^2/(a^2-b^2)^2+1/2*b^2*sinh(x)^2/(a^2-b^2)^2],
[cosh(x)^2*sinh(x)/(a*cosh(x)+b*sinh(x))^2,x,13,2*a^2*b*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)+b^3*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(5/2)+a^2*cosh(x)/(a^2-b^2)^2+b^2*cosh(x)/(a^2-b^2)^2-2*a*b*sinh(x)/(a^2-b^2)^2+a*b^2/((a^2-b^2)^2*(a*cosh(x)+b*sinh(x)))],
[cosh(x)^2*sinh(x)^2/(a*cosh(x)+b*sinh(x))^2,x,21,-4*a^2*b^2*x/(a^2-b^2)^3-1/2*a^2*x/(a^2-b^2)^2+1/2*b^2*x/(a^2-b^2)^2+2*a^3*b*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^3+2*a*b^3*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^3+1/2*a^2*cosh(x)*sinh(x)/(a^2-b^2)^2+1/2*b^2*cosh(x)*sinh(x)/(a^2-b^2)^2-a*b*sinh(x)^2/(a^2-b^2)^2+a*b^2*sinh(x)/((a^2-b^2)^2*(a*cosh(x)+b*sinh(x)))],
[cosh(x)^2*sinh(x)^3/(a*cosh(x)+b*sinh(x))^2,x,33,-2*a^4*b*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)-3*a^2*b^3*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)-4*a^2*b^2*cosh(x)/(a^2-b^2)^3-a^2*cosh(x)/(a^2-b^2)^2+1/3*a^2*cosh(x)^3/(a^2-b^2)^2+1/3*b^2*cosh(x)^3/(a^2-b^2)^2+2*a^3*b*sinh(x)/(a^2-b^2)^3+2*a*b^3*sinh(x)/(a^2-b^2)^3-2/3*a*b*sinh(x)^3/(a^2-b^2)^2-a^3*b^2/((a^2-b^2)^3*(a*cosh(x)+b*sinh(x)))],
[cosh(x)^3*sinh(x)/(a*cosh(x)+b*sinh(x))^2,x,17,a^3*b*x/(a^2-b^2)^3+a*b^3*x/(a^2-b^2)^3-a*b*x/(a^2-b^2)^2+a*b*(a^2+b^2)*x/(a^2-b^2)^3+1/2*b^2*cosh(x)^2/(a^2-b^2)^2-3*a^2*b^2*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^3-b^4*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^3-a*b*cosh(x)*sinh(x)/(a^2-b^2)^2+1/2*a^2*sinh(x)^2/(a^2-b^2)^2+a*b^2/((a^2-b^2)^2*(a+b*tanh(x)))],
[cosh(x)^3*sinh(x)^2/(a*cosh(x)+b*sinh(x))^2,x,33,3*a^3*b^2*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)+2*a*b^4*arctan((b*cosh(x)+a*sinh(x))/sqrt(a^2-b^2))/(a^2-b^2)^(7/2)+2*a^3*b*cosh(x)/(a^2-b^2)^3+2*a*b^3*cosh(x)/(a^2-b^2)^3-2/3*a*b*cosh(x)^3/(a^2-b^2)^2-4*a^2*b^2*sinh(x)/(a^2-b^2)^3+b^2*sinh(x)/(a^2-b^2)^2+1/3*a^2*sinh(x)^3/(a^2-b^2)^2+1/3*b^2*sinh(x)^3/(a^2-b^2)^2+a^2*b^3/((a^2-b^2)^3*(a*cosh(x)+b*sinh(x)))],
[cosh(x)^3*sinh(x)^3/(a*cosh(x)+b*sinh(x))^2,x,48,-6*a^3*b^3*x/(a^2-b^2)^4-a^3*b*x/(a^2-b^2)^3+a*b^3*x/(a^2-b^2)^3+1/4*a*b*x/(a^2-b^2)^2+1/4*b^2*cosh(x)^4/(a^2-b^2)^2+3*a^4*b^2*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^4+3*a^2*b^4*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^4+a^3*b*cosh(x)*sinh(x)/(a^2-b^2)^3+a*b^3*cosh(x)*sinh(x)/(a^2-b^2)^3+1/4*a*b*cosh(x)*sinh(x)/(a^2-b^2)^2-1/2*a*b*cosh(x)^3*sinh(x)/(a^2-b^2)^2-2*a^2*b^2*sinh(x)^2/(a^2-b^2)^3+1/4*a^2*sinh(x)^4/(a^2-b^2)^2+a^2*b^3*sinh(x)/((a^2-b^2)^3*(a*cosh(x)+b*sinh(x)))],

# Integrands of the form (A + B Hyper[x]) / (a Hyper[x] + b Hyper[x])
[(A+C*sinh(x))/(b*cosh(x)+c*sinh(x)),x,3,-c*C*x/(b^2-c^2)+b*C*log(b*cosh(x)+c*sinh(x))/(b^2-c^2)+A*arctan((c*cosh(x)+b*sinh(x))/sqrt(b^2-c^2))/sqrt(b^2-c^2)],
[(A+C*sinh(x))/(b*cosh(x)+c*sinh(x))^2,x,3,-c*C*arctan((c*cosh(x)+b*sinh(x))/sqrt(b^2-c^2))/(b^2-c^2)^(3/2)+(-b*C+A*c*cosh(x)+A*b*sinh(x))/((b^2-c^2)*(b*cosh(x)+c*sinh(x)))],
[(A+C*sinh(x))/(b*cosh(x)+c*sinh(x))^3,x,4,1/2*A*arctan((c*cosh(x)+b*sinh(x))/sqrt(b^2-c^2))/(b^2-c^2)^(3/2)+1/2*(-b*C+A*c*cosh(x)+A*b*sinh(x))/((b^2-c^2)*(b*cosh(x)+c*sinh(x))^2)+(-c^2*C*cosh(x)-b*c*C*sinh(x))/((b^2-c^2)^2*(b*cosh(x)+c*sinh(x)))],
[(A+B*cosh(x))/(b*cosh(x)+c*sinh(x)),x,3,b*B*x/(b^2-c^2)-B*c*log(b*cosh(x)+c*sinh(x))/(b^2-c^2)+A*arctan((c*cosh(x)+b*sinh(x))/sqrt(b^2-c^2))/sqrt(b^2-c^2)],
[(A+B*cosh(x))/(b*cosh(x)+c*sinh(x))^2,x,3,b*B*arctan((c*cosh(x)+b*sinh(x))/sqrt(b^2-c^2))/(b^2-c^2)^(3/2)+(B*c+A*c*cosh(x)+A*b*sinh(x))/((b^2-c^2)*(b*cosh(x)+c*sinh(x)))],
[(A+B*cosh(x))/(b*cosh(x)+c*sinh(x))^3,x,4,1/2*A*arctan((c*cosh(x)+b*sinh(x))/sqrt(b^2-c^2))/(b^2-c^2)^(3/2)+1/2*(B*c+A*c*cosh(x)+A*b*sinh(x))/((b^2-c^2)*(b*cosh(x)+c*sinh(x))^2)+(b*B*c*cosh(x)+b^2*B*sinh(x))/((b^2-c^2)^2*(b*cosh(x)+c*sinh(x)))],

# Integrands of the form (A + B Hyper[x]+C Hyper[x]) / (a Hyper[x]+b Hyper[x])
[(cosh(x)+sinh(x))/(cosh(x)-sinh(x)),x,1,1/2*(cosh(x)+sinh(x))^2],
[(cosh(x)-sinh(x))/(cosh(x)+sinh(x)),x,1,(-1/2)/(cosh(x)+sinh(x))^2],
[(cosh(x)-I*sinh(x))/(cosh(x)+I*sinh(x)),x,1,-I*log(cosh(x)+I*sinh(x))],
[(B*cosh(x)+C*sinh(x))/(b*cosh(x)+c*sinh(x)),x,1,(b*B-c*C)*x/(b^2-c^2)-(B*c-b*C)*log(b*cosh(x)+c*sinh(x))/(b^2-c^2)],
[(B*cosh(x)+C*sinh(x))/(b*cosh(x)+c*sinh(x))^2,x,3,(b*B-c*C)*arctan((c*cosh(x)+b*sinh(x))/sqrt(b^2-c^2))/(b^2-c^2)^(3/2)+(B*c-b*C)/((b^2-c^2)*(b*cosh(x)+c*sinh(x)))],
[(B*cosh(x)+C*sinh(x))/(b*cosh(x)+c*sinh(x))^3,x,3,1/2*(B*c-b*C)/((b^2-c^2)*(b*cosh(x)+c*sinh(x))^2)+(b*B-c*C)*sinh(x)/(b*(b^2-c^2)*(b*cosh(x)+c*sinh(x)))],
[(A+B*cosh(x)+C*sinh(x))/(b*cosh(x)+c*sinh(x)),x,3,(b*B-c*C)*x/(b^2-c^2)-(B*c-b*C)*log(b*cosh(x)+c*sinh(x))/(b^2-c^2)+A*arctan((c*cosh(x)+b*sinh(x))/sqrt(b^2-c^2))/sqrt(b^2-c^2)],
[(A+B*cosh(x)+C*sinh(x))/(b*cosh(x)+c*sinh(x))^2,x,3,(b*B-c*C)*arctan((c*cosh(x)+b*sinh(x))/sqrt(b^2-c^2))/(b^2-c^2)^(3/2)+(B*c-b*C+A*c*cosh(x)+A*b*sinh(x))/((b^2-c^2)*(b*cosh(x)+c*sinh(x)))],
[(A+B*cosh(x)+C*sinh(x))/(b*cosh(x)+c*sinh(x))^3,x,4,1/2*A*arctan((c*cosh(x)+b*sinh(x))/sqrt(b^2-c^2))/(b^2-c^2)^(3/2)+1/2*(B*c-b*C+A*c*cosh(x)+A*b*sinh(x))/((b^2-c^2)*(b*cosh(x)+c*sinh(x))^2)+(c*(b*B-c*C)*cosh(x)+b*(b*B-c*C)*sinh(x))/((b^2-c^2)^2*(b*cosh(x)+c*sinh(x)))],

# Integrands of the form u (a + b Hyper[d+e x] + c Hyper[d+e x])^p

# Integrands of the form (a + b Cosh[d+e x] + c Sinh[d+e x])^n
[(a+b*cosh(x)+c*sinh(x))^3,x,5,1/2*a*(2*a^2+3*b^2-3*c^2)*x+1/6*c*(11*a^2+4*b^2-4*c^2)*cosh(x)+1/6*b*(11*a^2+4*b^2-4*c^2)*sinh(x)+5/6*(a*c*cosh(x)+a*b*sinh(x))*(a+b*cosh(x)+c*sinh(x))+1/3*(c*cosh(x)+b*sinh(x))*(a+b*cosh(x)+c*sinh(x))^2],
[(a+b*cosh(x)+c*sinh(x))^2,x,4,1/2*(2*a^2+b^2-c^2)*x+3/2*a*c*cosh(x)+3/2*a*b*sinh(x)+1/2*(c*cosh(x)+b*sinh(x))*(a+b*cosh(x)+c*sinh(x))],
[a+b*cosh(x)+c*sinh(x),x,3,a*x+c*cosh(x)+b*sinh(x)],
[1/(a+b*cosh(x)+c*sinh(x)),x,3,-2*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/sqrt(a^2-b^2+c^2)],
[1/(a+b*cosh(x)+c*sinh(x))^2,x,5,-2*a*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/(a^2-b^2+c^2)^(3/2)+(-c*cosh(x)-b*sinh(x))/((a^2-b^2+c^2)*(a+b*cosh(x)+c*sinh(x)))],
[1/(a+b*cosh(x)+c*sinh(x))^3,x,5,-(2*a^2+b^2-c^2)*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/(a^2-b^2+c^2)^(5/2)+1/2*(-c*cosh(x)-b*sinh(x))/((a^2-b^2+c^2)*(a+b*cosh(x)+c*sinh(x))^2)-3/2*(a*c*cosh(x)+a*b*sinh(x))/((a^2-b^2+c^2)^2*(a+b*cosh(x)+c*sinh(x)))],
[1/(a+b*cosh(x)+c*sinh(x))^4,x,6,-a*(2*a^2+3*b^2-3*c^2)*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/(a^2-b^2+c^2)^(7/2)+1/3*(-c*cosh(x)-b*sinh(x))/((a^2-b^2+c^2)*(a+b*cosh(x)+c*sinh(x))^3)-5/6*(a*c*cosh(x)+a*b*sinh(x))/((a^2-b^2+c^2)^2*(a+b*cosh(x)+c*sinh(x))^2)+1/6*(-c*(11*a^2+4*b^2-4*c^2)*cosh(x)-b*(11*a^2+4*b^2-4*c^2)*sinh(x))/((a^2-b^2+c^2)^3*(a+b*cosh(x)+c*sinh(x)))],
[(a+a*cosh(x)+c*sinh(x))^3,x,5,1/2*a*(5*a^2-3*c^2)*x+1/6*c*(15*a^2-4*c^2)*cosh(x)+1/6*a*(15*a^2-4*c^2)*sinh(x)+5/6*(a*c*cosh(x)+a^2*sinh(x))*(a+a*cosh(x)+c*sinh(x))+1/3*(c*cosh(x)+a*sinh(x))*(a+a*cosh(x)+c*sinh(x))^2],
[(a+a*cosh(x)+c*sinh(x))^2,x,4,1/2*(3*a^2-c^2)*x+3/2*a*c*cosh(x)+3/2*a^2*sinh(x)+1/2*(c*cosh(x)+a*sinh(x))*(a+a*cosh(x)+c*sinh(x))],
[a+a*cosh(x)+c*sinh(x),x,3,a*x+c*cosh(x)+a*sinh(x)],
[1/(a+a*cosh(x)+c*sinh(x)),x,2,log(a+c*tanh(1/2*x))/c],
[1/(a+a*cosh(x)+c*sinh(x))^2,x,4,a*log(a+c*tanh(1/2*x))/c^3+(-c*cosh(x)-a*sinh(x))/(c^2*(a+a*cosh(x)+c*sinh(x)))],
[1/(a+a*cosh(x)+c*sinh(x))^3,x,4,1/2*(3*a^2-c^2)*log(a+c*tanh(1/2*x))/c^5+1/2*(-c*cosh(x)-a*sinh(x))/(c^2*(a+a*cosh(x)+c*sinh(x))^2)-3/2*(a*c*cosh(x)+a^2*sinh(x))/(c^4*(a+a*cosh(x)+c*sinh(x)))],
[1/(a+a*cosh(x)+c*sinh(x))^4,x,5,1/2*a*(5*a^2-3*c^2)*log(a+c*tanh(1/2*x))/c^7+1/3*(-c*cosh(x)-a*sinh(x))/(c^2*(a+a*cosh(x)+c*sinh(x))^3)-5/6*(a*c*cosh(x)+a^2*sinh(x))/(c^4*(a+a*cosh(x)+c*sinh(x))^2)+1/6*(-c*(15*a^2-4*c^2)*cosh(x)-a*(15*a^2-4*c^2)*sinh(x))/(c^6*(a+a*cosh(x)+c*sinh(x)))],
[(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^4,x,6,35/8*(b^2-c^2)^2*x+35/8*c*(b^2-c^2)^(3/2)*cosh(x)+35/8*b*(b^2-c^2)^(3/2)*sinh(x)+35/24*(b^2-c^2)*(c*cosh(x)+b*sinh(x))*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))+7/12*(c*cosh(x)+b*sinh(x))*sqrt(b^2-c^2)*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^2+1/4*(c*cosh(x)+b*sinh(x))*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^3],
[(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^3,x,5,5/2*(b^2-c^2)^(3/2)*x+5/2*c*(b^2-c^2)*cosh(x)+5/2*b*(b^2-c^2)*sinh(x)+5/6*(c*cosh(x)+b*sinh(x))*sqrt(b^2-c^2)*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))+1/3*(c*cosh(x)+b*sinh(x))*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^2],
[(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^2,x,4,3/2*(b^2-c^2)*x+3/2*c*cosh(x)*sqrt(b^2-c^2)+3/2*b*sinh(x)*sqrt(b^2-c^2)+1/2*(c*cosh(x)+b*sinh(x))*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))],
[b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2),x,3,c*cosh(x)+b*sinh(x)+x*sqrt(b^2-c^2)],
[1/(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2)),x,1,(-c-sinh(x)*sqrt(b^2-c^2))/(c*(c*cosh(x)+b*sinh(x)))],
[1/(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^2,x,2,1/3*(c*cosh(x)+b*sinh(x))/(sqrt(b^2-c^2)*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^2)+1/3*(-c-sinh(x)*sqrt(b^2-c^2))/(c*(c*cosh(x)+b*sinh(x))*sqrt(b^2-c^2))],
[1/(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^3,x,3,1/5*(c*cosh(x)+b*sinh(x))/(sqrt(b^2-c^2)*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^3)+2/15*(c*cosh(x)+b*sinh(x))/((b^2-c^2)*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^2)-2/15*(c+sinh(x)*sqrt(b^2-c^2))/(c*(b^2-c^2)*(c*cosh(x)+b*sinh(x)))],
[1/(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^4,x,4,1/7*(c*cosh(x)+b*sinh(x))/(sqrt(b^2-c^2)*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^4)+3/35*(c*cosh(x)+b*sinh(x))/((b^2-c^2)*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^3)+2/35*(c*cosh(x)+b*sinh(x))/((b^2-c^2)^(3/2)*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^2)-2/35*(c+sinh(x)*sqrt(b^2-c^2))/(c*(b^2-c^2)^(3/2)*(c*cosh(x)+b*sinh(x)))],
[(a+b*cosh(x)+c*sinh(x))^(5/2),x,7,2/5*(c*cosh(x)+b*sinh(x))*(a+b*cosh(x)+c*sinh(x))^(3/2)+16/15*(a*c*cosh(x)+a*b*sinh(x))*sqrt(a+b*cosh(x)+c*sinh(x))-2/15*I*(23*a^2+9*b^2-9*c^2)*sqrt(cos(1/2*(I*x-arctan(b,-I*c)))^2)/cos(1/2*(I*x-arctan(b,-I*c)))*EllipticE(sin(1/2*(I*x-arctan(b,-I*c))),sqrt(2*sqrt(b^2-c^2)/(a+sqrt(b^2-c^2))))*sqrt(a+b*cosh(x)+c*sinh(x))/sqrt((a+b*cosh(x)+c*sinh(x))/(a+sqrt(b^2-c^2)))+16/15*I*a*(a^2-b^2+c^2)*sqrt(cos(1/2*(I*x-arctan(b,-I*c)))^2)/cos(1/2*(I*x-arctan(b,-I*c)))*EllipticF(sin(1/2*(I*x-arctan(b,-I*c))),sqrt(2*sqrt(b^2-c^2)/(a+sqrt(b^2-c^2))))*sqrt((a+b*cosh(x)+c*sinh(x))/(a+sqrt(b^2-c^2)))/sqrt(a+b*cosh(x)+c*sinh(x))],
[(a+b*cosh(x)+c*sinh(x))^(3/2),x,6,2/3*(c*cosh(x)+b*sinh(x))*sqrt(a+b*cosh(x)+c*sinh(x))-8/3*I*a*sqrt(cos(1/2*(I*x-arctan(b,-I*c)))^2)/cos(1/2*(I*x-arctan(b,-I*c)))*EllipticE(sin(1/2*(I*x-arctan(b,-I*c))),sqrt(2*sqrt(b^2-c^2)/(a+sqrt(b^2-c^2))))*sqrt(a+b*cosh(x)+c*sinh(x))/sqrt((a+b*cosh(x)+c*sinh(x))/(a+sqrt(b^2-c^2)))+2/3*I*(a^2-b^2+c^2)*sqrt(cos(1/2*(I*x-arctan(b,-I*c)))^2)/cos(1/2*(I*x-arctan(b,-I*c)))*EllipticF(sin(1/2*(I*x-arctan(b,-I*c))),sqrt(2*sqrt(b^2-c^2)/(a+sqrt(b^2-c^2))))*sqrt((a+b*cosh(x)+c*sinh(x))/(a+sqrt(b^2-c^2)))/sqrt(a+b*cosh(x)+c*sinh(x))],
[(a+b*cosh(x)+c*sinh(x))^(1/2),x,2,-2*I*sqrt(cos(1/2*(I*x-arctan(b,-I*c)))^2)/cos(1/2*(I*x-arctan(b,-I*c)))*EllipticE(sin(1/2*(I*x-arctan(b,-I*c))),sqrt(2*sqrt(b^2-c^2)/(a+sqrt(b^2-c^2))))*sqrt(a+b*cosh(x)+c*sinh(x))/sqrt((a+b*cosh(x)+c*sinh(x))/(a+sqrt(b^2-c^2)))],
[1/(a+b*cosh(x)+c*sinh(x))^(1/2),x,2,-2*I*sqrt(cos(1/2*(I*x-arctan(b,-I*c)))^2)/cos(1/2*(I*x-arctan(b,-I*c)))*EllipticF(sin(1/2*(I*x-arctan(b,-I*c))),sqrt(2*sqrt(b^2-c^2)/(a+sqrt(b^2-c^2))))*sqrt((a+b*cosh(x)+c*sinh(x))/(a+sqrt(b^2-c^2)))/sqrt(a+b*cosh(x)+c*sinh(x))],
[1/(a+b*cosh(x)+c*sinh(x))^(3/2),x,3,-2*(c*cosh(x)+b*sinh(x))/((a^2-b^2+c^2)*sqrt(a+b*cosh(x)+c*sinh(x)))-2*I*sqrt(cos(1/2*(I*x-arctan(b,-I*c)))^2)/cos(1/2*(I*x-arctan(b,-I*c)))*EllipticE(sin(1/2*(I*x-arctan(b,-I*c))),sqrt(2*sqrt(b^2-c^2)/(a+sqrt(b^2-c^2))))*sqrt(a+b*cosh(x)+c*sinh(x))/((a^2-b^2+c^2)*sqrt((a+b*cosh(x)+c*sinh(x))/(a+sqrt(b^2-c^2))))],
[1/(a+b*cosh(x)+c*sinh(x))^(5/2),x,7,-2/3*(c*cosh(x)+b*sinh(x))/((a^2-b^2+c^2)*(a+b*cosh(x)+c*sinh(x))^(3/2))-8/3*(a*c*cosh(x)+a*b*sinh(x))/((a^2-b^2+c^2)^2*sqrt(a+b*cosh(x)+c*sinh(x)))-8/3*I*a*sqrt(cos(1/2*(I*x-arctan(b,-I*c)))^2)/cos(1/2*(I*x-arctan(b,-I*c)))*EllipticE(sin(1/2*(I*x-arctan(b,-I*c))),sqrt(2*sqrt(b^2-c^2)/(a+sqrt(b^2-c^2))))*sqrt(a+b*cosh(x)+c*sinh(x))/((a^2-b^2+c^2)^2*sqrt((a+b*cosh(x)+c*sinh(x))/(a+sqrt(b^2-c^2))))+2/3*I*sqrt(cos(1/2*(I*x-arctan(b,-I*c)))^2)/cos(1/2*(I*x-arctan(b,-I*c)))*EllipticF(sin(1/2*(I*x-arctan(b,-I*c))),sqrt(2*sqrt(b^2-c^2)/(a+sqrt(b^2-c^2))))*sqrt((a+b*cosh(x)+c*sinh(x))/(a+sqrt(b^2-c^2)))/((a^2-b^2+c^2)*sqrt(a+b*cosh(x)+c*sinh(x)))],
[1/(a+b*cosh(x)+c*sinh(x))^(7/2),x,8,-2/5*(c*cosh(x)+b*sinh(x))/((a^2-b^2+c^2)*(a+b*cosh(x)+c*sinh(x))^(5/2))-16/15*(a*c*cosh(x)+a*b*sinh(x))/((a^2-b^2+c^2)^2*(a+b*cosh(x)+c*sinh(x))^(3/2))-2/15*(c*(23*a^2+9*b^2-9*c^2)*cosh(x)+b*(23*a^2+9*b^2-9*c^2)*sinh(x))/((a^2-b^2+c^2)^3*sqrt(a+b*cosh(x)+c*sinh(x)))-2/15*I*(23*a^2+9*b^2-9*c^2)*sqrt(cos(1/2*(I*x-arctan(b,-I*c)))^2)/cos(1/2*(I*x-arctan(b,-I*c)))*EllipticE(sin(1/2*(I*x-arctan(b,-I*c))),sqrt(2*sqrt(b^2-c^2)/(a+sqrt(b^2-c^2))))*sqrt(a+b*cosh(x)+c*sinh(x))/((a^2-b^2+c^2)^3*sqrt((a+b*cosh(x)+c*sinh(x))/(a+sqrt(b^2-c^2))))+16/15*I*a*sqrt(cos(1/2*(I*x-arctan(b,-I*c)))^2)/cos(1/2*(I*x-arctan(b,-I*c)))*EllipticF(sin(1/2*(I*x-arctan(b,-I*c))),sqrt(2*sqrt(b^2-c^2)/(a+sqrt(b^2-c^2))))*sqrt((a+b*cosh(x)+c*sinh(x))/(a+sqrt(b^2-c^2)))/((a^2-b^2+c^2)^2*sqrt(a+b*cosh(x)+c*sinh(x)))],
[(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^(5/2),x,3,2/5*(c*cosh(x)+b*sinh(x))*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^(3/2)+64/15*(b^2-c^2)*(c*cosh(x)+b*sinh(x))/sqrt(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))+16/15*(c*cosh(x)+b*sinh(x))*sqrt(b^2-c^2)*sqrt(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))],
[(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^(3/2),x,2,8/3*(c*cosh(x)+b*sinh(x))*sqrt(b^2-c^2)/sqrt(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))+2/3*(c*cosh(x)+b*sinh(x))*sqrt(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))],
[(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^(1/2),x,1,2*(c*cosh(x)+b*sinh(x))/sqrt(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))],
[1/(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^(1/2),x,3,arctan((b^2-c^2)^(1/4)*sinh(x+I*arctan(b,-I*c))/(sqrt(2)*sqrt(sqrt(b^2-c^2)+cosh(x+I*arctan(b,-I*c))*sqrt(b^2-c^2))))*sqrt(2)/(b^2-c^2)^(1/4)],
[1/(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^(3/2),x,4,1/2*arctan((b^2-c^2)^(1/4)*sinh(x+I*arctan(b,-I*c))/(sqrt(2)*sqrt(sqrt(b^2-c^2)+cosh(x+I*arctan(b,-I*c))*sqrt(b^2-c^2))))/((b^2-c^2)^(3/4)*sqrt(2))+1/2*(c*cosh(x)+b*sinh(x))/(sqrt(b^2-c^2)*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^(3/2))],
[1/(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^(5/2),x,5,3/16*arctan((b^2-c^2)^(1/4)*sinh(x+I*arctan(b,-I*c))/(sqrt(2)*sqrt(sqrt(b^2-c^2)+cosh(x+I*arctan(b,-I*c))*sqrt(b^2-c^2))))/((b^2-c^2)^(5/4)*sqrt(2))+1/4*(c*cosh(x)+b*sinh(x))/(sqrt(b^2-c^2)*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^(5/2))+3/16*(c*cosh(x)+b*sinh(x))/((b^2-c^2)*(b*cosh(x)+c*sinh(x)+sqrt(b^2-c^2))^(3/2))],
[(b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))^(5/2),x,3,2/5*(c*cosh(x)+b*sinh(x))*(b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))^(3/2)+64/15*(b^2-c^2)*(c*cosh(x)+b*sinh(x))/sqrt(b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))-16/15*(c*cosh(x)+b*sinh(x))*sqrt(b^2-c^2)*sqrt(b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))],
[(b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))^(3/2),x,2,-8/3*(c*cosh(x)+b*sinh(x))*sqrt(b^2-c^2)/sqrt(b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))+2/3*(c*cosh(x)+b*sinh(x))*sqrt(b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))],
[(b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))^(1/2),x,1,2*(c*cosh(x)+b*sinh(x))/sqrt(b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))],
[1/(b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))^(1/2),x,3,-arctanh((b^2-c^2)^(1/4)*sinh(x+I*arctan(b,-I*c))/(sqrt(2)*sqrt(-sqrt(b^2-c^2)+cosh(x+I*arctan(b,-I*c))*sqrt(b^2-c^2))))*sqrt(2)/(b^2-c^2)^(1/4)],
[1/(b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))^(3/2),x,4,1/2*arctanh((b^2-c^2)^(1/4)*sinh(x+I*arctan(b,-I*c))/(sqrt(2)*sqrt(-sqrt(b^2-c^2)+cosh(x+I*arctan(b,-I*c))*sqrt(b^2-c^2))))/((b^2-c^2)^(3/4)*sqrt(2))+1/2*(-c*cosh(x)-b*sinh(x))/((b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))^(3/2)*sqrt(b^2-c^2))],
[1/(b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))^(5/2),x,5,-3/16*arctanh((b^2-c^2)^(1/4)*sinh(x+I*arctan(b,-I*c))/(sqrt(2)*sqrt(-sqrt(b^2-c^2)+cosh(x+I*arctan(b,-I*c))*sqrt(b^2-c^2))))/((b^2-c^2)^(5/4)*sqrt(2))+3/16*(c*cosh(x)+b*sinh(x))/((b^2-c^2)*(b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))^(3/2))+1/4*(-c*cosh(x)-b*sinh(x))/((b*cosh(x)+c*sinh(x)-sqrt(b^2-c^2))^(5/2)*sqrt(b^2-c^2))],

# Integrands of the form (a + b Tanh[d+e x] + c Sech[d+e x])^n
[1/(a+c*sech(x)+b*tanh(x)),x,5,a*x/(a^2-b^2)-b*log(c+a*cosh(x)+b*sinh(x))/(a^2-b^2)-2*a*c*arctan((b+(a-c)*tanh(1/2*x))/sqrt(a^2-b^2-c^2))/((a^2-b^2)*sqrt(a^2-b^2-c^2))],
[1/(a+b*coth(x)+c*csch(x)),x,5,a*x/(a^2-b^2)-b*log(I*c+I*b*cosh(x)+I*a*sinh(x))/(a^2-b^2)+2*a*c*arctanh((a+(b-c)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/((a^2-b^2)*sqrt(a^2-b^2+c^2))],

# Integrands of the form Hyper[x]^m / (a + b Hyper[x] + c Hyper[x])
[sinh(x)/(a+b*cosh(x)+c*sinh(x)),x,4,-c*x/(b^2-c^2)+b*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2)-2*a*c*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/((b^2-c^2)*sqrt(a^2-b^2+c^2))],
[sinh(x)/(1+cosh(x)+sinh(x)),x,1,1/2*x+1/2*cosh(x)-1/2*sinh(x)],
[sech(x)/(a+c*sech(x)+b*tanh(x)),x,4,2*arctan((b+(a-c)*tanh(1/2*x))/sqrt(a^2-b^2-c^2))/sqrt(a^2-b^2-c^2)],
[sech(x)^2/(a+c*sech(x)+b*tanh(x)),x,10,2*c*arctan(tanh(1/2*x))/(b^2+c^2)-b*log(1+tanh(1/2*x)^2)/(b^2+c^2)+b*log(a+c+2*b*tanh(1/2*x)+(a-c)*tanh(1/2*x)^2)/(b^2+c^2)-2*a*c*arctan((b+(a-c)*tanh(1/2*x))/sqrt(a^2-b^2-c^2))/((b^2+c^2)*sqrt(a^2-b^2-c^2))],
[csch(x)/(2+2*coth(x)+3*csch(x)),x,4,-2/3*arctanh(1/3*(2-tanh(1/2*x)))],
[csch(x)/(a+b*coth(x)+c*csch(x)),x,4,-2*arctanh((a+(b-c)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/sqrt(a^2-b^2+c^2)],
[csch(x)^2/(a+b*coth(x)+c*csch(x)),x,9,log(tanh(1/2*x))/(b+c)-b*log(b+c+2*a*tanh(1/2*x)+(b-c)*tanh(1/2*x)^2)/(b^2-c^2)-2*a*c*arctanh((a+(b-c)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/((b^2-c^2)*sqrt(a^2-b^2+c^2))],

# Integrands of the form (A + B Hyper[x]) / (a + b Hyper[x] + c Hyper[x])
[(A+C*sinh(x))/(a+b*cosh(x)+c*sinh(x)),x,4,-c*C*x/(b^2-c^2)+b*C*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2)-2*(A*(b^2-c^2)+a*c*C)*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/((b^2-c^2)*sqrt(a^2-b^2+c^2))],
[(A+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^2,x,4,-2*(a*A+c*C)*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/(a^2-b^2+c^2)^(3/2)+(b*C-(A*c-a*C)*cosh(x)-A*b*sinh(x))/((a^2-b^2+c^2)*(a+b*cosh(x)+c*sinh(x)))],
[(A+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^3,x,5,-(2*a^2*A+A*(b^2-c^2)+3*a*c*C)*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/(a^2-b^2+c^2)^(5/2)+1/2*(b*C-(A*c-a*C)*cosh(x)-A*b*sinh(x))/((a^2-b^2+c^2)*(a+b*cosh(x)+c*sinh(x))^2)+1/2*(a*b*C-(3*a*A*c-a^2*C+2*c^2*C)*cosh(x)-b*(3*a*A+2*c*C)*sinh(x))/((a^2-b^2+c^2)^2*(a+b*cosh(x)+c*sinh(x)))],
[(A+B*cosh(x))/(a+b*cosh(x)+c*sinh(x)),x,4,b*B*x/(b^2-c^2)-B*c*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2)+2*(a*b*B-A*(b^2-c^2))*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/((b^2-c^2)*sqrt(a^2-b^2+c^2))],
[(A+B*cosh(x))/(a+b*cosh(x)+c*sinh(x))^2,x,4,-2*(a*A-b*B)*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/(a^2-b^2+c^2)^(3/2)+(-B*c-A*c*cosh(x)-(A*b-a*B)*sinh(x))/((a^2-b^2+c^2)*(a+b*cosh(x)+c*sinh(x)))],
[(A+B*cosh(x))/(a+b*cosh(x)+c*sinh(x))^3,x,5,-(2*a^2*A-3*a*b*B+A*(b^2-c^2))*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/(a^2-b^2+c^2)^(5/2)+1/2*(-B*c-A*c*cosh(x)-(A*b-a*B)*sinh(x))/((a^2-b^2+c^2)*(a+b*cosh(x)+c*sinh(x))^2)+1/2*(-a*B*c-(3*a*A-2*b*B)*c*cosh(x)-(3*a*A*b-a^2*B-2*b^2*B)*sinh(x))/((a^2-b^2+c^2)^2*(a+b*cosh(x)+c*sinh(x)))],

# Integrands of the form (A + B Hyper[x] + C Hyper[x]) / (a + b Hyper[x] + c Hyper[x])
[(B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x)),x,4,(b*B-c*C)*x/(b^2-c^2)-(B*c-b*C)*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2)+2*a*(b*B-c*C)*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/((b^2-c^2)*sqrt(a^2-b^2+c^2))],
[(B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^2,x,4,2*(b*B-c*C)*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/(a^2-b^2+c^2)^(3/2)+(-B*c+b*C+a*C*cosh(x)+a*B*sinh(x))/((a^2-b^2+c^2)*(a+b*cosh(x)+c*sinh(x)))],
[(B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^3,x,5,3*a*(b*B-c*C)*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/(a^2-b^2+c^2)^(5/2)+1/2*(-B*c+b*C+a*C*cosh(x)+a*B*sinh(x))/((a^2-b^2+c^2)*(a+b*cosh(x)+c*sinh(x))^2)+1/2*(-a*(B*c-b*C)+(2*b*B*c+(a^2-2*c^2)*C)*cosh(x)+(a^2*B+2*b*(b*B-c*C))*sinh(x))/((a^2-b^2+c^2)^2*(a+b*cosh(x)+c*sinh(x)))],
[(A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x)),x,4,(b*B-c*C)*x/(b^2-c^2)-(B*c-b*C)*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2)-2*(A*b^2-a*b*B-A*c^2+a*c*C)*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/((b^2-c^2)*sqrt(a^2-b^2+c^2))],
[(A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^2,x,4,-2*(a*A-b*B+c*C)*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/(a^2-b^2+c^2)^(3/2)+(-B*c+b*C-(A*c-a*C)*cosh(x)-(A*b-a*B)*sinh(x))/((a^2-b^2+c^2)*(a+b*cosh(x)+c*sinh(x)))],
[(A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^3,x,5,-(2*a^2*A+A*b^2-3*a*b*B-A*c^2+3*a*c*C)*arctanh((c-(a-b)*tanh(1/2*x))/sqrt(a^2-b^2+c^2))/(a^2-b^2+c^2)^(5/2)+1/2*(-B*c+b*C-(A*c-a*C)*cosh(x)-(A*b-a*B)*sinh(x))/((a^2-b^2+c^2)*(a+b*cosh(x)+c*sinh(x))^2)+1/2*(-a*(B*c-b*C)-(3*a*A*c-a^2*C-2*c*(b*B-c*C))*cosh(x)-(3*a*A*b-a^2*B-2*b*(b*B-c*C))*sinh(x))/((a^2-b^2+c^2)^2*(a+b*cosh(x)+c*sinh(x)))],
[(b^2-c^2+a*b*cosh(x)+a*c*sinh(x))/(a+b*cosh(x)+c*sinh(x))^2,x,1,(c*cosh(x)+b*sinh(x))/(a+b*cosh(x)+c*sinh(x))],
[(A+C*sinh(x))/(a+b*cosh(x)+b*sinh(x)),x,1,1/2*(2*a*A+b*C)*x/a^2+1/2*C*cosh(x)/a-1/2*(2*a*A*b-a^2*C+b^2*C)*log(a+b*cosh(x)+b*sinh(x))/(a^2*b)-1/2*C*sinh(x)/a],
[(A+B*cosh(x))/(a+b*cosh(x)+b*sinh(x)),x,1,1/2*(2*a*A-b*B)*x/a^2-1/2*B*cosh(x)/a-1/2*(2*a*A*b-a^2*B-b^2*B)*log(a+b*cosh(x)+b*sinh(x))/(a^2*b)+1/2*B*sinh(x)/a],
[(A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+b*sinh(x)),x,1,1/2*(2*a*A-b*(B-C))*x/a^2-1/2*(2*a*A*b-b^2*(B-C)-a^2*(B+C))*log(a+b*cosh(x)+b*sinh(x))/(a^2*b)-1/2*(B-C)*(cosh(x)-sinh(x))/a],
[(A+C*sinh(x))/(a+b*cosh(x)-b*sinh(x)),x,1,1/2*(2*a*A-b*C)*x/a^2+1/2*C*cosh(x)/a+1/2*(2*a*A*b+a^2*C-b^2*C)*log(a+b*cosh(x)-b*sinh(x))/(a^2*b)+1/2*C*sinh(x)/a],
[(A+B*cosh(x))/(a+b*cosh(x)-b*sinh(x)),x,1,1/2*(2*a*A-b*B)*x/a^2+1/2*B*cosh(x)/a+1/2*(2*a*A*b-a^2*B-b^2*B)*log(a+b*cosh(x)-b*sinh(x))/(a^2*b)+1/2*B*sinh(x)/a],
[(A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)-b*sinh(x)),x,1,1/2*(2*a*A-b*(B+C))*x/a^2+1/2*(2*a*A*b-a^2*(B-C)-b^2*(B+C))*log(a+b*cosh(x)-b*sinh(x))/(a^2*b)+1/2*(B+C)*(cosh(x)+sinh(x))/a],

# Integrands of the form u (a Hyper[c+d x]^2 + b Hyper[c+d x]^2)^p
[1/(cosh(x)^2+sinh(x)^2),x,2,arctan(tanh(x))],
[1/(cosh(x)^2+sinh(x)^2)^2,x,2,tanh(x)/(1+tanh(x)^2)],
[1/(cosh(x)^2+sinh(x)^2)^3,x,4,1/2*arctan(tanh(x))+1/2*sech(x)^2*tanh(x)/(1+tanh(x)^2)^2],
[1/(cosh(x)^2-sinh(x)^2),x,2,x],
[1/(cosh(x)^2-sinh(x)^2)^2,x,2,x],
[1/(cosh(x)^2-sinh(x)^2)^3,x,2,x],
[1/(sech(x)^2+tanh(x)^2),x,2,x],
[1/(sech(x)^2+tanh(x)^2)^2,x,2,x],
[1/(sech(x)^2+tanh(x)^2)^3,x,2,x],
[1/(sech(x)^2-tanh(x)^2),x,4,-x+arctanh(sqrt(2)*tanh(x))*sqrt(2)],
[1/(sech(x)^2-tanh(x)^2)^2,x,6,x-arctanh(sqrt(2)*tanh(x))/sqrt(2)+tanh(x)/(1-2*tanh(x)^2)],
[1/(sech(x)^2-tanh(x)^2)^3,x,6,-x+7/4*arctanh(sqrt(2)*tanh(x))/sqrt(2)+1/2*tanh(x)/(1-2*tanh(x)^2)^2-1/4*tanh(x)/(1-2*tanh(x)^2)],
[1/(coth(x)^2+csch(x)^2),x,4,x-arctanh(tanh(x)/sqrt(2))*sqrt(2)],
[1/(coth(x)^2+csch(x)^2)^2,x,6,x-arctanh(tanh(x)/sqrt(2))/sqrt(2)-tanh(x)/(2-tanh(x)^2)],
[1/(coth(x)^2+csch(x)^2)^3,x,6,x-7/4*arctanh(tanh(x)/sqrt(2))/sqrt(2)-1/2*tanh(x)^3/(2-tanh(x)^2)^2-1/4*tanh(x)/(2-tanh(x)^2)],
[1/(coth(x)^2-csch(x)^2),x,2,x],
[1/(coth(x)^2-csch(x)^2)^2,x,2,x],
[1/(coth(x)^2-csch(x)^2)^3,x,2,x],

# Integrands of the form u (a + b Hyper[c+d x]^m + c Hyper[c+d x]^n)^p

# Integrands of the form Hyper[x]^m / (a + b Hyper[x] + c Hyper[x]^2)
[1/(a+b*sinh(x)+c*sinh(x)^2),x,7,2*c*arctan((2*I*c-(I*b+sqrt(-b^2+4*a*c))*tanh(1/2*x))/(sqrt(2)*sqrt(b^2-2*(a-c)*c-I*b*sqrt(-b^2+4*a*c))))*sqrt(2)/(sqrt(-b^2+4*a*c)*sqrt(b^2-2*(a-c)*c-I*b*sqrt(-b^2+4*a*c)))-2*c*arctan((2*I*c-I*b*tanh(1/2*x)+sqrt(-b^2+4*a*c)*tanh(1/2*x))/(sqrt(2)*sqrt(b^2-2*(a-c)*c+I*b*sqrt(-b^2+4*a*c))))*sqrt(2)/(sqrt(-b^2+4*a*c)*sqrt(b^2-2*(a-c)*c+I*b*sqrt(-b^2+4*a*c)))],
[sinh(x)/(a+b*sinh(x)+c*sinh(x)^2),x,8,arctan((2*I*c-(I*b+sqrt(-b^2+4*a*c))*tanh(1/2*x))/(sqrt(2)*sqrt(b^2-2*(a-c)*c-I*b*sqrt(-b^2+4*a*c))))*sqrt(2)*(I-b/sqrt(-b^2+4*a*c))/sqrt(b^2-2*(a-c)*c-I*b*sqrt(-b^2+4*a*c))+arctan((2*I*c-I*b*tanh(1/2*x)+sqrt(-b^2+4*a*c)*tanh(1/2*x))/(sqrt(2)*sqrt(b^2-2*(a-c)*c+I*b*sqrt(-b^2+4*a*c))))*sqrt(2)*(I+b/sqrt(-b^2+4*a*c))/sqrt(b^2-2*(a-c)*c+I*b*sqrt(-b^2+4*a*c))],
[sinh(x)^2/(a+b*sinh(x)+c*sinh(x)^2),x,9,x/c-arctan((2*I*c-(I*b+sqrt(-b^2+4*a*c))*tanh(1/2*x))/(sqrt(2)*sqrt(b^2-2*(a-c)*c-I*b*sqrt(-b^2+4*a*c))))*sqrt(2)*(I*b+(-b^2+2*a*c)/sqrt(-b^2+4*a*c))/(c*sqrt(b^2-2*(a-c)*c-I*b*sqrt(-b^2+4*a*c)))-arctan((2*I*c-(I*b-sqrt(-b^2+4*a*c))*tanh(1/2*x))/(sqrt(2)*sqrt(b^2-2*(a-c)*c+I*b*sqrt(-b^2+4*a*c))))*sqrt(2)*(I*b+(b^2-2*a*c)/sqrt(-b^2+4*a*c))/(c*sqrt(b^2-2*(a-c)*c+I*b*sqrt(-b^2+4*a*c)))],
[sinh(x)^3/(a+b*sinh(x)+c*sinh(x)^2),x,10,-b*x/c^2+cosh(x)/c-arctan((2*I*c-(I*b+sqrt(-b^2+4*a*c))*tanh(1/2*x))/(sqrt(2)*sqrt(b^2-2*(a-c)*c-I*b*sqrt(-b^2+4*a*c))))*sqrt(2)*(-I*(b^2-a*c-3*I*a*b*c/sqrt(-b^2+4*a*c))+b^3/sqrt(-b^2+4*a*c))/(c^2*sqrt(b^2-2*(a-c)*c-I*b*sqrt(-b^2+4*a*c)))+arctan((2*I*c-I*b*tanh(1/2*x)+sqrt(-b^2+4*a*c)*tanh(1/2*x))/(sqrt(2)*sqrt(b^2-2*(a-c)*c+I*b*sqrt(-b^2+4*a*c))))*sqrt(2)*(I*(b^2-a*c+3*I*a*b*c/sqrt(-b^2+4*a*c))+b^3/sqrt(-b^2+4*a*c))/(c^2*sqrt(b^2-2*(a-c)*c+I*b*sqrt(-b^2+4*a*c)))],
[(a+b*sinh(x))/(b^2-2*a*b*sinh(x)+a^2*sinh(x)^2),x,3,cosh(x)/(b-a*sinh(x))],
[(d+e*sinh(x))/(a+b*sinh(x)+c*sinh(x)^2),x,7,arctan((2*I*c-(I*b+sqrt(-b^2+4*a*c))*tanh(1/2*x))/(sqrt(2)*sqrt(b^2-2*(a-c)*c-I*b*sqrt(-b^2+4*a*c))))*sqrt(2)*(I*e+(2*c*d-b*e)/sqrt(-b^2+4*a*c))/sqrt(b^2-2*(a-c)*c-I*b*sqrt(-b^2+4*a*c))+arctan((2*I*c-I*b*tanh(1/2*x)+sqrt(-b^2+4*a*c)*tanh(1/2*x))/(sqrt(2)*sqrt(b^2-2*(a-c)*c+I*b*sqrt(-b^2+4*a*c))))*sqrt(2)*(I*e+(-2*c*d+b*e)/sqrt(-b^2+4*a*c))/sqrt(b^2-2*(a-c)*c+I*b*sqrt(-b^2+4*a*c))],
[1/(a+b*cosh(x)+c*cosh(x)^2),x,5,4*c*arctanh(sqrt(b-2*c-sqrt(b^2-4*a*c))*tanh(1/2*x)/sqrt(b+2*c-sqrt(b^2-4*a*c)))/(sqrt(b^2-4*a*c)*sqrt(b-2*c-sqrt(b^2-4*a*c))*sqrt(b+2*c-sqrt(b^2-4*a*c)))-4*c*arctanh(sqrt(b-2*c+sqrt(b^2-4*a*c))*tanh(1/2*x)/sqrt(b+2*c+sqrt(b^2-4*a*c)))/(sqrt(b^2-4*a*c)*sqrt(b-2*c+sqrt(b^2-4*a*c))*sqrt(b+2*c+sqrt(b^2-4*a*c)))],
[cosh(x)/(a+b*cosh(x)+c*cosh(x)^2),x,6,2*arctanh(sqrt(b-2*c-sqrt(b^2-4*a*c))*tanh(1/2*x)/sqrt(b+2*c-sqrt(b^2-4*a*c)))*(1-b/sqrt(b^2-4*a*c))/(sqrt(b-2*c-sqrt(b^2-4*a*c))*sqrt(b+2*c-sqrt(b^2-4*a*c)))+2*arctanh(sqrt(b-2*c+sqrt(b^2-4*a*c))*tanh(1/2*x)/sqrt(b+2*c+sqrt(b^2-4*a*c)))*(1+b/sqrt(b^2-4*a*c))/(sqrt(b-2*c+sqrt(b^2-4*a*c))*sqrt(b+2*c+sqrt(b^2-4*a*c)))],
[cosh(x)^2/(a+b*cosh(x)+c*cosh(x)^2),x,7,x/c-2*arctanh(sqrt(b-2*c-sqrt(b^2-4*a*c))*tanh(1/2*x)/sqrt(b+2*c-sqrt(b^2-4*a*c)))*(b+(-b^2+2*a*c)/sqrt(b^2-4*a*c))/(c*sqrt(b-2*c-sqrt(b^2-4*a*c))*sqrt(b+2*c-sqrt(b^2-4*a*c)))-2*arctanh(sqrt(b-2*c+sqrt(b^2-4*a*c))*tanh(1/2*x)/sqrt(b+2*c+sqrt(b^2-4*a*c)))*(b+(b^2-2*a*c)/sqrt(b^2-4*a*c))/(c*sqrt(b-2*c+sqrt(b^2-4*a*c))*sqrt(b+2*c+sqrt(b^2-4*a*c)))],
[cosh(x)^3/(a+b*cosh(x)+c*cosh(x)^2),x,8,-b*x/c^2+sinh(x)/c+2*arctanh(sqrt(b-2*c-sqrt(b^2-4*a*c))*tanh(1/2*x)/sqrt(b+2*c-sqrt(b^2-4*a*c)))*(b^2-a*c-b^3/sqrt(b^2-4*a*c)+3*a*b*c/sqrt(b^2-4*a*c))/(c^2*sqrt(b-2*c-sqrt(b^2-4*a*c))*sqrt(b+2*c-sqrt(b^2-4*a*c)))+2*arctanh(sqrt(b-2*c+sqrt(b^2-4*a*c))*tanh(1/2*x)/sqrt(b+2*c+sqrt(b^2-4*a*c)))*(b^2-a*c+b^3/sqrt(b^2-4*a*c)-3*a*b*c/sqrt(b^2-4*a*c))/(c^2*sqrt(b-2*c+sqrt(b^2-4*a*c))*sqrt(b+2*c+sqrt(b^2-4*a*c)))],
[(a+b*cosh(x))/(b^2+2*a*b*cosh(x)+a^2*cosh(x)^2),x,3,sinh(x)/(b+a*cosh(x))],
[(d+e*cosh(x))/(a+b*cosh(x)+c*cosh(x)^2),x,5,2*arctanh(sqrt(b-2*c-sqrt(b^2-4*a*c))*tanh(1/2*x)/sqrt(b+2*c-sqrt(b^2-4*a*c)))*(e+(2*c*d-b*e)/sqrt(b^2-4*a*c))/(sqrt(b-2*c-sqrt(b^2-4*a*c))*sqrt(b+2*c-sqrt(b^2-4*a*c)))+2*arctanh(sqrt(b-2*c+sqrt(b^2-4*a*c))*tanh(1/2*x)/sqrt(b+2*c+sqrt(b^2-4*a*c)))*(e+(-2*c*d+b*e)/sqrt(b^2-4*a*c))/(sqrt(b-2*c+sqrt(b^2-4*a*c))*sqrt(b+2*c+sqrt(b^2-4*a*c)))],

# Integrands of the form Hyper[x]^m (a Hyper[x]^n + b Hyper[x]^n)^p
[sinh(x)^2/(a*cosh(x)^2+b*sinh(x)^2),x,4,x/(a+b)-arctan(sqrt(b)*tanh(x)/sqrt(a))*sqrt(a)/((a+b)*sqrt(b))],
[cosh(x)^2/(a*cosh(x)^2+b*sinh(x)^2),x,4,x/(a+b)+arctan(sqrt(b)*tanh(x)/sqrt(a))*sqrt(b)/((a+b)*sqrt(a))],
[sinh(x)^3/(cosh(x)^3+sinh(x)^3),x,6,1/2*x+2/3*arctan((1-2*tanh(x))/sqrt(3))/sqrt(3)+1/6/(1+tanh(x))],
[cosh(x)^3/(cosh(x)^3+sinh(x)^3),x,6,1/2*x-2/3*arctan((1-2*tanh(x))/sqrt(3))/sqrt(3)+(-1/6)/(1+tanh(x))],

# Integrands of the form x^m Csch[x] Sech[x] (a Sech[x]^n)^p
[x*csch(x)*sech(x)/sqrt(a*sech(x)^2),x,6,-2*x*arctanh(exp(x))*sech(x)/sqrt(a*sech(x)^2)-polylog(2,-exp(x))*sech(x)/sqrt(a*sech(x)^2)+polylog(2,exp(x))*sech(x)/sqrt(a*sech(x)^2)],
[x^2*csch(x)*sech(x)/sqrt(a*sech(x)^2),x,8,-2*x^2*arctanh(exp(x))*sech(x)/sqrt(a*sech(x)^2)-2*x*polylog(2,-exp(x))*sech(x)/sqrt(a*sech(x)^2)+2*x*polylog(2,exp(x))*sech(x)/sqrt(a*sech(x)^2)+2*polylog(3,-exp(x))*sech(x)/sqrt(a*sech(x)^2)-2*polylog(3,exp(x))*sech(x)/sqrt(a*sech(x)^2)],
[x^3*csch(x)*sech(x)/sqrt(a*sech(x)^2),x,10,-2*x^3*arctanh(exp(x))*sech(x)/sqrt(a*sech(x)^2)-3*x^2*polylog(2,-exp(x))*sech(x)/sqrt(a*sech(x)^2)+3*x^2*polylog(2,exp(x))*sech(x)/sqrt(a*sech(x)^2)+6*x*polylog(3,-exp(x))*sech(x)/sqrt(a*sech(x)^2)-6*x*polylog(3,exp(x))*sech(x)/sqrt(a*sech(x)^2)-6*polylog(4,-exp(x))*sech(x)/sqrt(a*sech(x)^2)+6*polylog(4,exp(x))*sech(x)/sqrt(a*sech(x)^2)],
[x*csch(x)*sech(x)/sqrt(a*sech(x)^4),x,5,-1/2*x^2*sech(x)^2/sqrt(a*sech(x)^4)+x*log(1-exp(2*x))*sech(x)^2/sqrt(a*sech(x)^4)+1/2*polylog(2,exp(2*x))*sech(x)^2/sqrt(a*sech(x)^4)],
[x^2*csch(x)*sech(x)/sqrt(a*sech(x)^4),x,6,-1/3*x^3*sech(x)^2/sqrt(a*sech(x)^4)+x^2*log(1-exp(2*x))*sech(x)^2/sqrt(a*sech(x)^4)+x*polylog(2,exp(2*x))*sech(x)^2/sqrt(a*sech(x)^4)-1/2*polylog(3,exp(2*x))*sech(x)^2/sqrt(a*sech(x)^4)],
[x^3*csch(x)*sech(x)/sqrt(a*sech(x)^4),x,7,-1/4*x^4*sech(x)^2/sqrt(a*sech(x)^4)+x^3*log(1-exp(2*x))*sech(x)^2/sqrt(a*sech(x)^4)+3/2*x^2*polylog(2,exp(2*x))*sech(x)^2/sqrt(a*sech(x)^4)-3/2*x*polylog(3,exp(2*x))*sech(x)^2/sqrt(a*sech(x)^4)+3/4*polylog(4,exp(2*x))*sech(x)^2/sqrt(a*sech(x)^4)],
[x*csch(x)*sech(x)*sqrt(a*sech(x)^2),x,10,x*sqrt(a*sech(x)^2)-arctan(sinh(x))*cosh(x)*sqrt(a*sech(x)^2)-2*x*arctanh(exp(x))*cosh(x)*sqrt(a*sech(x)^2)-cosh(x)*polylog(2,-exp(x))*sqrt(a*sech(x)^2)+cosh(x)*polylog(2,exp(x))*sqrt(a*sech(x)^2)],
[x^2*csch(x)*sech(x)*sqrt(a*sech(x)^2),x,17,x^2*sqrt(a*sech(x)^2)-4*x*arctan(exp(x))*cosh(x)*sqrt(a*sech(x)^2)-2*x^2*arctanh(exp(x))*cosh(x)*sqrt(a*sech(x)^2)-2*x*cosh(x)*polylog(2,-exp(x))*sqrt(a*sech(x)^2)+2*I*cosh(x)*polylog(2,-I*exp(x))*sqrt(a*sech(x)^2)-2*I*cosh(x)*polylog(2,I*exp(x))*sqrt(a*sech(x)^2)+2*x*cosh(x)*polylog(2,exp(x))*sqrt(a*sech(x)^2)+2*cosh(x)*polylog(3,-exp(x))*sqrt(a*sech(x)^2)-2*cosh(x)*polylog(3,exp(x))*sqrt(a*sech(x)^2)],
[x^3*csch(x)*sech(x)*sqrt(a*sech(x)^2),x,21,x^3*sqrt(a*sech(x)^2)-6*x^2*arctan(exp(x))*cosh(x)*sqrt(a*sech(x)^2)-2*x^3*arctanh(exp(x))*cosh(x)*sqrt(a*sech(x)^2)-3*x^2*cosh(x)*polylog(2,-exp(x))*sqrt(a*sech(x)^2)+6*I*x*cosh(x)*polylog(2,-I*exp(x))*sqrt(a*sech(x)^2)-6*I*x*cosh(x)*polylog(2,I*exp(x))*sqrt(a*sech(x)^2)+3*x^2*cosh(x)*polylog(2,exp(x))*sqrt(a*sech(x)^2)+6*x*cosh(x)*polylog(3,-exp(x))*sqrt(a*sech(x)^2)-6*I*cosh(x)*polylog(3,-I*exp(x))*sqrt(a*sech(x)^2)+6*I*cosh(x)*polylog(3,I*exp(x))*sqrt(a*sech(x)^2)-6*x*cosh(x)*polylog(3,exp(x))*sqrt(a*sech(x)^2)-6*cosh(x)*polylog(4,-exp(x))*sqrt(a*sech(x)^2)+6*cosh(x)*polylog(4,exp(x))*sqrt(a*sech(x)^2)],
[x*csch(x)*sech(x)*sqrt(a*sech(x)^4),x,12,1/2*x*cosh(x)^2*sqrt(a*sech(x)^4)-2*x*arctanh(exp(2*x))*cosh(x)^2*sqrt(a*sech(x)^4)-1/2*cosh(x)^2*polylog(2,-exp(2*x))*sqrt(a*sech(x)^4)+1/2*cosh(x)^2*polylog(2,exp(2*x))*sqrt(a*sech(x)^4)-1/2*cosh(x)*sinh(x)*sqrt(a*sech(x)^4)-1/2*x*sinh(x)^2*sqrt(a*sech(x)^4)],
[x^2*csch(x)*sech(x)*sqrt(a*sech(x)^4),x,16,1/2*x^2*cosh(x)^2*sqrt(a*sech(x)^4)-2*x^2*arctanh(exp(2*x))*cosh(x)^2*sqrt(a*sech(x)^4)+cosh(x)^2*log(cosh(x))*sqrt(a*sech(x)^4)-x*cosh(x)^2*polylog(2,-exp(2*x))*sqrt(a*sech(x)^4)+x*cosh(x)^2*polylog(2,exp(2*x))*sqrt(a*sech(x)^4)+1/2*cosh(x)^2*polylog(3,-exp(2*x))*sqrt(a*sech(x)^4)-1/2*cosh(x)^2*polylog(3,exp(2*x))*sqrt(a*sech(x)^4)-x*cosh(x)*sinh(x)*sqrt(a*sech(x)^4)-1/2*x^2*sinh(x)^2*sqrt(a*sech(x)^4)],
[x^3*csch(x)*sech(x)*sqrt(a*sech(x)^4),x,21,-3/2*x^2*cosh(x)^2*sqrt(a*sech(x)^4)+1/2*x^3*cosh(x)^2*sqrt(a*sech(x)^4)-2*x^3*arctanh(exp(2*x))*cosh(x)^2*sqrt(a*sech(x)^4)+3*x*cosh(x)^2*log(1+exp(2*x))*sqrt(a*sech(x)^4)+3/2*cosh(x)^2*polylog(2,-exp(2*x))*sqrt(a*sech(x)^4)-3/2*x^2*cosh(x)^2*polylog(2,-exp(2*x))*sqrt(a*sech(x)^4)+3/2*x^2*cosh(x)^2*polylog(2,exp(2*x))*sqrt(a*sech(x)^4)+3/2*x*cosh(x)^2*polylog(3,-exp(2*x))*sqrt(a*sech(x)^4)-3/2*x*cosh(x)^2*polylog(3,exp(2*x))*sqrt(a*sech(x)^4)-3/4*cosh(x)^2*polylog(4,-exp(2*x))*sqrt(a*sech(x)^4)+3/4*cosh(x)^2*polylog(4,exp(2*x))*sqrt(a*sech(x)^4)-3/2*x^2*cosh(x)*sinh(x)*sqrt(a*sech(x)^4)-1/2*x^3*sinh(x)^2*sqrt(a*sech(x)^4)],

# Integrands of the form u (a + b Hyper[c+d x] Hyper[c+d x])^p

# Integrands of the form (a + b Hyper[c+d x] Hyper[c+d x])^n
[(a+b*cosh(c+d*x)*sinh(c+d*x))^m,x,4,I*AppellF1(1/2,1/2,-m,3/2,1/2*(1-I*sinh(2*c+2*d*x)),b*(1-I*sinh(2*c+2*d*x))/(2*I*a+b))*cosh(2*c+2*d*x)*(a+1/2*b*sinh(2*c+2*d*x))^m/(d*((2*a+b*sinh(2*c+2*d*x))/(2*a-I*b))^m*sqrt(2)*sqrt(1+I*sinh(2*c+2*d*x)))],
[(a+b*cosh(c+d*x)*sinh(c+d*x))^3,x,3,1/8*a*(8*a^2-3*b^2)*x+1/24*b*(16*a^2-b^2)*cosh(2*c+2*d*x)/d+5/48*a*b^2*cosh(2*c+2*d*x)*sinh(2*c+2*d*x)/d+1/48*b*cosh(2*c+2*d*x)*(2*a+b*sinh(2*c+2*d*x))^2/d],
[(a+b*cosh(c+d*x)*sinh(c+d*x))^2,x,2,1/8*(8*a^2-b^2)*x+1/2*a*b*cosh(2*c+2*d*x)/d+1/16*b^2*cosh(2*c+2*d*x)*sinh(2*c+2*d*x)/d],
[a+b*cosh(c+d*x)*sinh(c+d*x),x,3,a*x+1/2*b*sinh(c+d*x)^2/d],
[1/(a+b*cosh(c+d*x)*sinh(c+d*x)),x,4,-2*arctanh((b-2*a*tanh(c+d*x))/sqrt(4*a^2+b^2))/(d*sqrt(4*a^2+b^2))],
[1/(a+b*cosh(c+d*x)*sinh(c+d*x))^2,x,6,-8*a*arctanh((b-2*a*tanh(c+d*x))/sqrt(4*a^2+b^2))/((4*a^2+b^2)^(3/2)*d)-2*b*cosh(2*c+2*d*x)/((4*a^2+b^2)*d*(2*a+b*sinh(2*c+2*d*x)))],
[1/(a+b*cosh(c+d*x)*sinh(c+d*x))^3,x,7,-4*(8*a^2-b^2)*arctanh((b-2*a*tanh(c+d*x))/sqrt(4*a^2+b^2))/((4*a^2+b^2)^(5/2)*d)-2*b*cosh(2*c+2*d*x)/((4*a^2+b^2)*d*(2*a+b*sinh(2*c+2*d*x))^2)-12*a*b*cosh(2*c+2*d*x)/((4*a^2+b^2)^2*d*(2*a+b*sinh(2*c+2*d*x)))],
[(a+b*cosh(c+d*x)*sinh(c+d*x))^(5/2),x,8,1/20*b*cosh(2*c+2*d*x)*(2*a+b*sinh(2*c+2*d*x))^(3/2)/(d*sqrt(2))+2/15*a*b*cosh(2*c+2*d*x)*sqrt(2)*sqrt(2*a+b*sinh(2*c+2*d*x))/d-1/60*I*(92*a^2-9*b^2)*sqrt(cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))^2)/cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))*EllipticE(sin(1/2*(2*I*c-1/2*Pi+2*I*d*x)),sqrt(2*b/(2*I*a+b)))*sqrt(2*a+b*sinh(2*c+2*d*x))/(d*sqrt(2)*sqrt((2*a+b*sinh(2*c+2*d*x))/(2*a-I*b)))+2/15*I*a*(4*a^2+b^2)*sqrt(cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))^2)/cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))*EllipticF(sin(1/2*(2*I*c-1/2*Pi+2*I*d*x)),sqrt(2*b/(2*I*a+b)))*sqrt(2)*sqrt((2*a+b*sinh(2*c+2*d*x))/(2*a-I*b))/(d*sqrt(2*a+b*sinh(2*c+2*d*x)))],
[(a+b*cosh(c+d*x)*sinh(c+d*x))^(3/2),x,7,1/6*b*cosh(2*c+2*d*x)*sqrt(2*a+b*sinh(2*c+2*d*x))/(d*sqrt(2))-2/3*I*a*sqrt(cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))^2)/cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))*EllipticE(sin(1/2*(2*I*c-1/2*Pi+2*I*d*x)),sqrt(2*b/(2*I*a+b)))*sqrt(2)*sqrt(2*a+b*sinh(2*c+2*d*x))/(d*sqrt((2*a+b*sinh(2*c+2*d*x))/(2*a-I*b)))+1/6*I*(4*a^2+b^2)*sqrt(cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))^2)/cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))*EllipticF(sin(1/2*(2*I*c-1/2*Pi+2*I*d*x)),sqrt(2*b/(2*I*a+b)))*sqrt((2*a+b*sinh(2*c+2*d*x))/(2*a-I*b))/(d*sqrt(2)*sqrt(2*a+b*sinh(2*c+2*d*x)))],
[(a+b*cosh(c+d*x)*sinh(c+d*x))^(1/2),x,3,-I*sqrt(cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))^2)/cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))*EllipticE(sin(1/2*(2*I*c-1/2*Pi+2*I*d*x)),sqrt(2*b/(2*I*a+b)))*sqrt(2*a+b*sinh(2*c+2*d*x))/(d*sqrt(2)*sqrt((2*a+b*sinh(2*c+2*d*x))/(2*a-I*b)))],
[1/(a+b*cosh(c+d*x)*sinh(c+d*x))^(1/2),x,3,-I*sqrt(cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))^2)/cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))*EllipticF(sin(1/2*(2*I*c-1/2*Pi+2*I*d*x)),sqrt(2*b/(2*I*a+b)))*sqrt(2)*sqrt((2*a+b*sinh(2*c+2*d*x))/(2*a-I*b))/(d*sqrt(2*a+b*sinh(2*c+2*d*x)))],
[1/(a+b*cosh(c+d*x)*sinh(c+d*x))^(3/2),x,5,-2*b*cosh(2*c+2*d*x)*sqrt(2)/((4*a^2+b^2)*d*sqrt(2*a+b*sinh(2*c+2*d*x)))-2*I*sqrt(cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))^2)/cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))*EllipticE(sin(1/2*(2*I*c-1/2*Pi+2*I*d*x)),sqrt(2*b/(2*I*a+b)))*sqrt(2)*sqrt(2*a+b*sinh(2*c+2*d*x))/((4*a^2+b^2)*d*sqrt((2*a+b*sinh(2*c+2*d*x))/(2*a-I*b)))],
[1/(a+b*cosh(c+d*x)*sinh(c+d*x))^(5/2),x,8,-4/3*b*cosh(2*c+2*d*x)*sqrt(2)/((4*a^2+b^2)*d*(2*a+b*sinh(2*c+2*d*x))^(3/2))-32/3*a*b*cosh(2*c+2*d*x)*sqrt(2)/((4*a^2+b^2)^2*d*sqrt(2*a+b*sinh(2*c+2*d*x)))-32/3*I*a*sqrt(cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))^2)/cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))*EllipticE(sin(1/2*(2*I*c-1/2*Pi+2*I*d*x)),sqrt(2*b/(2*I*a+b)))*sqrt(2)*sqrt(2*a+b*sinh(2*c+2*d*x))/((4*a^2+b^2)^2*d*sqrt((2*a+b*sinh(2*c+2*d*x))/(2*a-I*b)))+4/3*I*sqrt(cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))^2)/cos(1/2*(2*I*c-1/2*Pi+2*I*d*x))*EllipticF(sin(1/2*(2*I*c-1/2*Pi+2*I*d*x)),sqrt(2*b/(2*I*a+b)))*sqrt(2)*sqrt((2*a+b*sinh(2*c+2*d*x))/(2*a-I*b))/((4*a^2+b^2)*d*sqrt(2*a+b*sinh(2*c+2*d*x)))],

# Integrands of the form x^m (a + b Hyper[c+d x] Hyper[c+d x])^n
[x^3/(a+b*cosh(x)*sinh(x)),x,13,x^3*log(1+b*exp(2*x)/(2*a-sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)-x^3*log(1+b*exp(2*x)/(2*a+sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)+3/2*x^2*polylog(2,-b*exp(2*x)/(2*a-sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)-3/2*x^2*polylog(2,-b*exp(2*x)/(2*a+sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)-3/2*x*polylog(3,-b*exp(2*x)/(2*a-sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)+3/2*x*polylog(3,-b*exp(2*x)/(2*a+sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)+3/4*polylog(4,-b*exp(2*x)/(2*a-sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)-3/4*polylog(4,-b*exp(2*x)/(2*a+sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)],
[x^2/(a+b*cosh(x)*sinh(x)),x,11,x^2*log(1+b*exp(2*x)/(2*a-sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)-x^2*log(1+b*exp(2*x)/(2*a+sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)+x*polylog(2,-b*exp(2*x)/(2*a-sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)-x*polylog(2,-b*exp(2*x)/(2*a+sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)-1/2*polylog(3,-b*exp(2*x)/(2*a-sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)+1/2*polylog(3,-b*exp(2*x)/(2*a+sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)],
[x/(a+b*cosh(x)*sinh(x)),x,9,x*log(1+b*exp(2*x)/(2*a-sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)-x*log(1+b*exp(2*x)/(2*a+sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)+1/2*polylog(2,-b*exp(2*x)/(2*a-sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)-1/2*polylog(2,-b*exp(2*x)/(2*a+sqrt(4*a^2+b^2)))/sqrt(4*a^2+b^2)],
[1/(x*(a+b*cosh(x)*sinh(x))),x,1,Unintegrable(1/(x*(a+1/2*b*sinh(2*x))),x)],

# Integrands of the form F^(c (a+b x)) Hyper[d+e x]^n

# Integrands of the form E^(c (a+b x)) Sinh[d+e x]^n
[F^(c*(a+b*x))*sinh(d+e*x)^n,x,2,-F^(c*(a+b*x))*hypergeom([-n,1/2*(-e*n+b*c*log(F))/e],[1/2*(2-n+b*c*log(F)/e)],exp(2*(d+e*x)))*sinh(d+e*x)^n/((1-exp(2*(d+e*x)))^n*(e*n-b*c*log(F)))],
[exp(2*(a+b*x))*sinh(a+b*x)^3,x,4,1/8*exp(-a-b*x)/b+3/8*exp(a+b*x)/b-1/8*exp(3*a+3*b*x)/b+1/40*exp(5*a+5*b*x)/b],
[exp(2*(a+b*x))*sinh(a+b*x)^2,x,5,-1/4*exp(2*a+2*b*x)/b+1/16*exp(4*a+4*b*x)/b+1/4*x],
[exp(2*(a+b*x))*sinh(a+b*x),x,3,-1/2*exp(a+b*x)/b+1/6*exp(3*a+3*b*x)/b],
[exp(2*(a+b*x))*csch(a+b*x),x,4,2*exp(a+b*x)/b-2*arctanh(exp(a+b*x))/b],
[exp(2*(a+b*x))*csch(a+b*x)^2,x,5,2/(b*(1-exp(2*a+2*b*x)))+2*log(1-exp(2*a+2*b*x))/b],
[exp(2*(a+b*x))*csch(a+b*x)^3,x,5,-2*exp(3*a+3*b*x)/(b*(1-exp(2*a+2*b*x))^2)+3*exp(a+b*x)/(b*(1-exp(2*a+2*b*x)))-3*arctanh(exp(a+b*x))/b],
[exp(a+b*x)*sinh(c+d*x)^3,x,2,-6*d^3*exp(a+b*x)*cosh(c+d*x)/(b^4-10*b^2*d^2+9*d^4)+6*b*d^2*exp(a+b*x)*sinh(c+d*x)/(b^4-10*b^2*d^2+9*d^4)-3*d*exp(a+b*x)*cosh(c+d*x)*sinh(c+d*x)^2/(b^2-9*d^2)+b*exp(a+b*x)*sinh(c+d*x)^3/(b^2-9*d^2)],
[exp(a+b*x)*sinh(c+d*x)^2,x,2,2*d^2*exp(a+b*x)/(b*(b^2-4*d^2))-2*d*exp(a+b*x)*cosh(c+d*x)*sinh(c+d*x)/(b^2-4*d^2)+b*exp(a+b*x)*sinh(c+d*x)^2/(b^2-4*d^2)],
[exp(a+b*x)*sinh(c+d*x),x,1,-d*exp(a+b*x)*cosh(c+d*x)/(b^2-d^2)+b*exp(a+b*x)*sinh(c+d*x)/(b^2-d^2)],
[exp(a+b*x)*csch(c+d*x),x,1,-2*exp(a+c+b*x+d*x)*hypergeom([1,1/2*(b+d)/d],[1/2*(3+b/d)],exp(2*(c+d*x)))/(b+d)],
[exp(c+d*x)*csch(a+b*x)^2,x,1,4*exp(c+d*x+2*(a+b*x))*hypergeom([2,1+1/2*d/b],[2+1/2*d/b],exp(2*(a+b*x)))/(2*b+d)],
[exp(c+d*x)*csch(a+b*x)^3,x,2,-1/2*d*exp(c+d*x)*csch(a+b*x)/b^2-1/2*exp(c+d*x)*coth(a+b*x)*csch(a+b*x)/b+(b-d)*exp(a+c+b*x+d*x)*hypergeom([1,1/2*(b+d)/b],[1/2*(3+d/b)],exp(2*(a+b*x)))/b^2],

# Integrands of the form E^(c (a+b x)) Cosh[d+e x]^n
[F^(c*(a+b*x))*cosh(d+e*x)^n,x,2,-F^(c*(a+b*x))*cosh(d+e*x)^n*hypergeom([-n,1/2*(-e*n+b*c*log(F))/e],[1/2*(2-n+b*c*log(F)/e)],-exp(2*(d+e*x)))/((1+exp(2*(d+e*x)))^n*(e*n-b*c*log(F)))],
[exp(a+b*x)*cosh(c+d*x)^3,x,2,-6*b*d^2*exp(a+b*x)*cosh(c+d*x)/(b^4-10*b^2*d^2+9*d^4)+b*exp(a+b*x)*cosh(c+d*x)^3/(b^2-9*d^2)+6*d^3*exp(a+b*x)*sinh(c+d*x)/(b^4-10*b^2*d^2+9*d^4)-3*d*exp(a+b*x)*cosh(c+d*x)^2*sinh(c+d*x)/(b^2-9*d^2)],
[exp(a+b*x)*cosh(c+d*x)^2,x,2,-2*d^2*exp(a+b*x)/(b*(b^2-4*d^2))+b*exp(a+b*x)*cosh(c+d*x)^2/(b^2-4*d^2)-2*d*exp(a+b*x)*cosh(c+d*x)*sinh(c+d*x)/(b^2-4*d^2)],
[exp(a+b*x)*cosh(c+d*x),x,1,b*exp(a+b*x)*cosh(c+d*x)/(b^2-d^2)-d*exp(a+b*x)*sinh(c+d*x)/(b^2-d^2)],
[exp(a+b*x)*sech(c+d*x),x,1,2*exp(a+c+b*x+d*x)*hypergeom([1,1/2*(b+d)/d],[1/2*(3+b/d)],-exp(2*(c+d*x)))/(b+d)],
[exp(a+b*x)*sech(c+d*x)^2,x,1,4*exp(a+b*x+2*(c+d*x))*hypergeom([2,1+1/2*b/d],[2+1/2*b/d],-exp(2*(c+d*x)))/(b+2*d)],
[exp(a+b*x)*sech(c+d*x)^3,x,2,-(b-d)*exp(a+c+b*x+d*x)*hypergeom([1,1/2*(b+d)/d],[1/2*(3+b/d)],-exp(2*(c+d*x)))/d^2+1/2*b*exp(a+b*x)*sech(c+d*x)/d^2+1/2*exp(a+b*x)*sech(c+d*x)*tanh(c+d*x)/d],

# Integrands of the form E^(c (a+b x)) Sech[d+e x]^n
[F^(c*(a+b*x))*sech(d+e*x)^n,x,2,(1+exp(2*(d+e*x)))^n*F^(a*c+b*c*x)*hypergeom([n,1/2*(e*n+b*c*log(F))/e],[1+1/2*(e*n+b*c*log(F))/e],-exp(2*(d+e*x)))*sech(d+e*x)^n/(e*n+b*c*log(F))],

# Integrands of the form E^(c (a+b x)) Csch[d+e x]^n
[F^(c*(a+b*x))*csch(d+e*x)^n,x,2,-(1+(-1)/exp(2*(d+e*x)))^n*F^(a*c+b*c*x)*csch(d+e*x)^n*hypergeom([n,1/2*(e*n-b*c*log(F))/e],[1/2*(2+n-b*c*log(F)/e)],exp(-2*(d+e*x)))/(e*n-b*c*log(F))],

# Integrands of the form F^(c (a+b x)) (f + g Hyper[d+e x])^n
[F^(c*(a+b*x))*(f+I*f*sinh(d+e*x))^2,x,8,f^2*F^(a*c+b*c*x)/(b*c*log(F))+2*I*e*f^2*F^(a*c+b*c*x)*cosh(d+e*x)/(e^2-b^2*c^2*log(F)^2)+2*e^2*f^2*F^(a*c+b*c*x)/(b*c*log(F)*(4*e^2-b^2*c^2*log(F)^2))-2*I*b*c*f^2*F^(a*c+b*c*x)*log(F)*sinh(d+e*x)/(e^2-b^2*c^2*log(F)^2)-2*e*f^2*F^(a*c+b*c*x)*cosh(d+e*x)*sinh(d+e*x)/(4*e^2-b^2*c^2*log(F)^2)+b*c*f^2*F^(a*c+b*c*x)*log(F)*sinh(d+e*x)^2/(4*e^2-b^2*c^2*log(F)^2)],
[F^(c*(a+b*x))*(f+I*f*sinh(d+e*x)),x,6,f*F^(a*c+b*c*x)/(b*c*log(F))+I*e*f*F^(a*c+b*c*x)*cosh(d+e*x)/(e^2-b^2*c^2*log(F)^2)-I*b*c*f*F^(a*c+b*c*x)*log(F)*sinh(d+e*x)/(e^2-b^2*c^2*log(F)^2)],
[F^(c*(a+b*x))/(f+I*f*sinh(d+e*x)),x,2,2*exp(1/2*(2*d+I*Pi+2*e*x))*F^(c*(a+b*x))*hypergeom([2,1+b*c*log(F)/e],[2+b*c*log(F)/e],-exp(1/2*(2*d+I*Pi+2*e*x)))/(f*(e+b*c*log(F)))],
[F^(c*(a+b*x))/(f+I*f*sinh(d+e*x))^2,x,3,2/3*exp(1/2*(2*d+I*Pi+2*e*x))*F^(c*(a+b*x))*hypergeom([2,1+b*c*log(F)/e],[2+b*c*log(F)/e],-exp(1/2*(2*d+I*Pi+2*e*x)))*(e-b*c*log(F))/(e^2*f^2)+1/6*b*c*F^(c*(a+b*x))*log(F)*sech(1/2*d+1/4*I*Pi+1/2*e*x)^2/(e^2*f^2)+1/6*F^(c*(a+b*x))*sech(1/2*d+1/4*I*Pi+1/2*e*x)^2*tanh(1/2*d+1/4*I*Pi+1/2*e*x)/(e*f^2)],
[F^(c*(a+b*x))*(f+f*cosh(d+e*x))^2,x,8,f^2*F^(a*c+b*c*x)/(b*c*log(F))-2*b*c*f^2*F^(a*c+b*c*x)*cosh(d+e*x)*log(F)/(e^2-b^2*c^2*log(F)^2)+2*e^2*f^2*F^(a*c+b*c*x)/(b*c*log(F)*(4*e^2-b^2*c^2*log(F)^2))-b*c*f^2*F^(a*c+b*c*x)*cosh(d+e*x)^2*log(F)/(4*e^2-b^2*c^2*log(F)^2)+2*e*f^2*F^(a*c+b*c*x)*sinh(d+e*x)/(e^2-b^2*c^2*log(F)^2)+2*e*f^2*F^(a*c+b*c*x)*cosh(d+e*x)*sinh(d+e*x)/(4*e^2-b^2*c^2*log(F)^2)],
[F^(c*(a+b*x))*(f+f*cosh(d+e*x)),x,6,f*F^(a*c+b*c*x)/(b*c*log(F))-b*c*f*F^(a*c+b*c*x)*cosh(d+e*x)*log(F)/(e^2-b^2*c^2*log(F)^2)+e*f*F^(a*c+b*c*x)*sinh(d+e*x)/(e^2-b^2*c^2*log(F)^2)],
[F^(c*(a+b*x))/(f+f*cosh(d+e*x)),x,2,2*exp(d+e*x)*F^(c*(a+b*x))*hypergeom([2,1+b*c*log(F)/e],[2+b*c*log(F)/e],-exp(d+e*x))/(f*(e+b*c*log(F)))],
[F^(c*(a+b*x))/(f+f*cosh(d+e*x))^2,x,3,2/3*exp(d+e*x)*F^(c*(a+b*x))*hypergeom([2,1+b*c*log(F)/e],[2+b*c*log(F)/e],-exp(d+e*x))*(e-b*c*log(F))/(e^2*f^2)+1/6*b*c*F^(c*(a+b*x))*log(F)*sech(1/2*d+1/2*e*x)^2/(e^2*f^2)+1/6*F^(c*(a+b*x))*sech(1/2*d+1/2*e*x)^2*tanh(1/2*d+1/2*e*x)/(e*f^2)],

# Integrands of the form E^(a+b x) Cosh[c+d x]^m Sinh[c+d x]^n

# Integrands of the form E^(a+b x) Cosh[a+b x]^m Sinh[a+b x]^n

# m>0
[exp(a+b*x)*cosh(a+b*x)*sinh(a+b*x)^3,x,4,1/48*exp(-3*a-3*b*x)/b-1/8*exp(-a-b*x)/b-1/24*exp(3*a+3*b*x)/b+1/80*exp(5*a+5*b*x)/b],
[exp(a+b*x)*cosh(a+b*x)*sinh(a+b*x)^2,x,5,-1/16*exp(-2*a-2*b*x)/b-1/16*exp(2*a+2*b*x)/b+1/32*exp(4*a+4*b*x)/b-1/8*x],
[exp(a+b*x)*cosh(a+b*x)*sinh(a+b*x),x,4,1/4*exp(-a-b*x)/b+1/12*exp(3*a+3*b*x)/b],
[exp(a+b*x)*cosh(a+b*x)*csch(a+b*x),x,3,exp(a+b*x)/b-2*arctanh(exp(a+b*x))/b],
[exp(a+b*x)*cosh(a+b*x)*csch(a+b*x)^2,x,5,2/(b*(1-exp(2*a+2*b*x)))+log(1-exp(2*a+2*b*x))/b],
[exp(a+b*x)*cosh(a+b*x)*csch(a+b*x)^3,x,5,-2*exp(a+b*x)/(b*(1-exp(2*a+2*b*x))^2)+3*exp(a+b*x)/(b*(1-exp(2*a+2*b*x)))-arctanh(exp(a+b*x))/b],
[exp(a+b*x)*cosh(a+b*x)^2*sinh(a+b*x)^3,x,5,1/128*exp(-4*a-4*b*x)/b-1/64*exp(-2*a-2*b*x)/b-1/32*exp(2*a+2*b*x)/b-1/128*exp(4*a+4*b*x)/b+1/192*exp(6*a+6*b*x)/b+1/16*x],
[exp(a+b*x)*cosh(a+b*x)^2*sinh(a+b*x)^2,x,4,-1/48*exp(-3*a-3*b*x)/b-1/8*exp(a+b*x)/b+1/80*exp(5*a+5*b*x)/b],
[exp(a+b*x)*cosh(a+b*x)^2*sinh(a+b*x),x,5,1/16*exp(-2*a-2*b*x)/b+1/16*exp(2*a+2*b*x)/b+1/32*exp(4*a+4*b*x)/b-1/8*x],
[exp(a+b*x)*cosh(a+b*x)^2*csch(a+b*x),x,5,1/4*exp(2*a+2*b*x)/b-1/2*x+log(1-exp(2*a+2*b*x))/b],
[exp(a+b*x)*cosh(a+b*x)^2*csch(a+b*x)^2,x,5,exp(a+b*x)/b+2*exp(a+b*x)/(b*(1-exp(2*a+2*b*x)))-2*arctanh(exp(a+b*x))/b],
[exp(a+b*x)*cosh(a+b*x)^2*csch(a+b*x)^3,x,5,(-2)/(b*(1-exp(2*a+2*b*x))^2)+4/(b*(1-exp(2*a+2*b*x)))+log(1-exp(2*a+2*b*x))/b],
[exp(a+b*x)*cosh(a+b*x)^3*sinh(a+b*x)^3,x,4,1/320*exp(-5*a-5*b*x)/b-3/64*exp(-a-b*x)/b-1/64*exp(3*a+3*b*x)/b+1/448*exp(7*a+7*b*x)/b],
[exp(a+b*x)*cosh(a+b*x)^3*sinh(a+b*x)^2,x,5,-1/128*exp(-4*a-4*b*x)/b-1/64*exp(-2*a-2*b*x)/b-1/32*exp(2*a+2*b*x)/b+1/128*exp(4*a+4*b*x)/b+1/192*exp(6*a+6*b*x)/b-1/16*x],
[exp(a+b*x)*cosh(a+b*x)^3*sinh(a+b*x),x,4,1/48*exp(-3*a-3*b*x)/b+1/8*exp(-a-b*x)/b+1/24*exp(3*a+3*b*x)/b+1/80*exp(5*a+5*b*x)/b],
[exp(a+b*x)*cosh(a+b*x)^3*csch(a+b*x),x,5,1/4*exp(-a-b*x)/b+exp(a+b*x)/b+1/12*exp(3*a+3*b*x)/b-2*arctanh(exp(a+b*x))/b],
[exp(a+b*x)*cosh(a+b*x)^3*csch(a+b*x)^2,x,5,1/4*exp(2*a+2*b*x)/b+2/(b*(1-exp(2*a+2*b*x)))+1/2*x+log(1-exp(2*a+2*b*x))/b],
[exp(a+b*x)*cosh(a+b*x)^3*csch(a+b*x)^3,x,7,exp(a+b*x)/b-2*exp(a+b*x)/(b*(1-exp(2*a+2*b*x))^2)+3*exp(a+b*x)/(b*(1-exp(2*a+2*b*x)))-3*arctanh(exp(a+b*x))/b],

# m<0

# Integrands of the form E^(a+b x) Cosh[n (a+b x)]^m Sinh[n (a+b x)]^p

# m>0
[exp(2*(a+b*x))*cosh(a+b*x)*sinh(a+b*x)^3,x,5,1/32*exp(-2*a-2*b*x)/b-1/32*exp(4*a+4*b*x)/b+1/96*exp(6*a+6*b*x)/b+1/8*x],
[exp(2*(a+b*x))*cosh(a+b*x)*sinh(a+b*x)^2,x,4,-1/8*exp(-a-b*x)/b-1/8*exp(a+b*x)/b-1/24*exp(3*a+3*b*x)/b+1/40*exp(5*a+5*b*x)/b],
[exp(2*(a+b*x))*cosh(a+b*x)*sinh(a+b*x),x,4,1/16*exp(4*a+4*b*x)/b-1/4*x],
[exp(2*(a+b*x))*cosh(a+b*x)*csch(a+b*x),x,4,1/2*exp(2*a+2*b*x)/b+log(1-exp(2*a+2*b*x))/b],
[exp(2*(a+b*x))*cosh(a+b*x)*csch(a+b*x)^2,x,5,2*exp(a+b*x)/b+2*exp(a+b*x)/(b*(1-exp(2*a+2*b*x)))-4*arctanh(exp(a+b*x))/b],
[exp(2*(a+b*x))*cosh(a+b*x)*csch(a+b*x)^3,x,5,(-2)/(b*(1-exp(2*a+2*b*x))^2)+6/(b*(1-exp(2*a+2*b*x)))+2*log(1-exp(2*a+2*b*x))/b],
[exp(2*(a+b*x))*cosh(a+b*x)^2*sinh(a+b*x)^3,x,4,1/96*exp(-3*a-3*b*x)/b-1/32*exp(-a-b*x)/b+1/16*exp(a+b*x)/b-1/48*exp(3*a+3*b*x)/b-1/160*exp(5*a+5*b*x)/b+1/224*exp(7*a+7*b*x)/b],
[exp(2*(a+b*x))*cosh(a+b*x)^2*sinh(a+b*x)^2,x,4,-1/32*exp(-2*a-2*b*x)/b-1/16*exp(2*a+2*b*x)/b+1/96*exp(6*a+6*b*x)/b],
[exp(2*(a+b*x))*cosh(a+b*x)^2*sinh(a+b*x),x,4,1/8*exp(-a-b*x)/b-1/8*exp(a+b*x)/b+1/24*exp(3*a+3*b*x)/b+1/40*exp(5*a+5*b*x)/b],
[exp(2*(a+b*x))*cosh(a+b*x)^2*csch(a+b*x),x,5,3/2*exp(a+b*x)/b+1/6*exp(3*a+3*b*x)/b-2*arctanh(exp(a+b*x))/b],
[exp(2*(a+b*x))*cosh(a+b*x)^2*csch(a+b*x)^2,x,4,1/2*exp(2*a+2*b*x)/b+2/(b*(1-exp(2*a+2*b*x)))+2*log(1-exp(2*a+2*b*x))/b],
[exp(2*(a+b*x))*cosh(a+b*x)^2*csch(a+b*x)^3,x,6,2*exp(a+b*x)/b-2*exp(3*a+3*b*x)/(b*(1-exp(2*a+2*b*x))^2)+3*exp(a+b*x)/(b*(1-exp(2*a+2*b*x)))-5*arctanh(exp(a+b*x))/b],
[exp(2*(a+b*x))*cosh(a+b*x)^3*sinh(a+b*x)^3,x,5,1/256*exp(-4*a-4*b*x)/b-3/256*exp(4*a+4*b*x)/b+1/512*exp(8*a+8*b*x)/b+3/64*x],
[exp(2*(a+b*x))*cosh(a+b*x)^3*sinh(a+b*x)^2,x,4,-1/96*exp(-3*a-3*b*x)/b-1/32*exp(-a-b*x)/b-1/16*exp(a+b*x)/b-1/48*exp(3*a+3*b*x)/b+1/160*exp(5*a+5*b*x)/b+1/224*exp(7*a+7*b*x)/b],
[exp(2*(a+b*x))*cosh(a+b*x)^3*sinh(a+b*x),x,5,1/32*exp(-2*a-2*b*x)/b+1/32*exp(4*a+4*b*x)/b+1/96*exp(6*a+6*b*x)/b-1/8*x],
[exp(2*(a+b*x))*cosh(a+b*x)^3*csch(a+b*x),x,5,1/2*exp(2*a+2*b*x)/b+1/16*exp(4*a+4*b*x)/b-1/4*x+log(1-exp(2*a+2*b*x))/b],
[exp(2*(a+b*x))*cosh(a+b*x)^3*csch(a+b*x)^2,x,6,5/2*exp(a+b*x)/b+1/6*exp(3*a+3*b*x)/b+2*exp(a+b*x)/(b*(1-exp(2*a+2*b*x)))-4*arctanh(exp(a+b*x))/b],
[exp(2*(a+b*x))*cosh(a+b*x)^3*csch(a+b*x)^3,x,4,1/2*exp(2*a+2*b*x)/b+(-2)/(b*(1-exp(2*a+2*b*x))^2)+6/(b*(1-exp(2*a+2*b*x)))+3*log(1-exp(2*a+2*b*x))/b],

# m<0
[exp(x)*sech(2*x)*tanh(2*x),x,12,-exp(3*x)/(1+exp(4*x))-1/2*arctan(1-exp(x)*sqrt(2))/sqrt(2)+1/2*arctan(1+exp(x)*sqrt(2))/sqrt(2)+1/4*log(1+exp(2*x)-exp(x)*sqrt(2))/sqrt(2)-1/4*log(1+exp(2*x)+exp(x)*sqrt(2))/sqrt(2)],
[exp(x)*sech(2*x)^2*tanh(2*x),x,13,-exp(5*x)/(1+exp(4*x))^2-1/4*exp(x)/(1+exp(4*x))-1/8*arctan(1-exp(x)*sqrt(2))/sqrt(2)+1/8*arctan(1+exp(x)*sqrt(2))/sqrt(2)-1/16*log(1+exp(2*x)-exp(x)*sqrt(2))/sqrt(2)+1/16*log(1+exp(2*x)+exp(x)*sqrt(2))/sqrt(2)],
[exp(x)*sech(2*x)*tanh(2*x)^2,x,13,exp(3*x)/(1+exp(4*x))^2-3/4*exp(3*x)/(1+exp(4*x))-5/8*arctan(1-exp(x)*sqrt(2))/sqrt(2)+5/8*arctan(1+exp(x)*sqrt(2))/sqrt(2)+5/16*log(1+exp(2*x)-exp(x)*sqrt(2))/sqrt(2)-5/16*log(1+exp(2*x)+exp(x)*sqrt(2))/sqrt(2)],
[exp(x)*sech(2*x)^2*tanh(2*x)^2,x,14,4/3*exp(5*x)/(1+exp(4*x))^3-5/6*exp(5*x)/(1+exp(4*x))^2-3/8*exp(x)/(1+exp(4*x))-3/16*arctan(1-exp(x)*sqrt(2))/sqrt(2)+3/16*arctan(1+exp(x)*sqrt(2))/sqrt(2)-3/32*log(1+exp(2*x)-exp(x)*sqrt(2))/sqrt(2)+3/32*log(1+exp(2*x)+exp(x)*sqrt(2))/sqrt(2)],
[exp(x)*coth(2*x)*csch(2*x),x,6,exp(3*x)/(1-exp(4*x))+1/2*arctan(exp(x))-1/2*arctanh(exp(x))],
[exp(x)*coth(2*x)*csch(2*x)^2,x,7,-exp(5*x)/(1-exp(4*x))^2+1/4*exp(x)/(1-exp(4*x))-1/8*arctan(exp(x))-1/8*arctanh(exp(x))],
[exp(x)*coth(2*x)^2*csch(2*x),x,7,-exp(3*x)/(1-exp(4*x))^2+3/4*exp(3*x)/(1-exp(4*x))+5/8*arctan(exp(x))-5/8*arctanh(exp(x))],
[exp(x)*coth(2*x)^2*csch(2*x)^2,x,8,4/3*exp(5*x)/(1-exp(4*x))^3-5/6*exp(5*x)/(1-exp(4*x))^2+3/8*exp(x)/(1-exp(4*x))-3/16*arctan(exp(x))-3/16*arctanh(exp(x))],

# Integrands of the form E^(a+b x) Cosh[c+d x]^m Sinh[c+d x]^n

# m>=0
[exp(c+d*x)*cosh(a+b*x)*sinh(a+b*x)^3,x,4,-1/2*b*exp(c+d*x)*cosh(2*a+2*b*x)/(4*b^2-d^2)+1/2*b*exp(c+d*x)*cosh(4*a+4*b*x)/(16*b^2-d^2)+1/4*d*exp(c+d*x)*sinh(2*a+2*b*x)/(4*b^2-d^2)-1/8*d*exp(c+d*x)*sinh(4*a+4*b*x)/(16*b^2-d^2)],
[exp(c+d*x)*cosh(a+b*x)*sinh(a+b*x)^2,x,4,1/4*d*exp(c+d*x)*cosh(a+b*x)/(b^2-d^2)-1/4*d*exp(c+d*x)*cosh(3*a+3*b*x)/(9*b^2-d^2)-1/4*b*exp(c+d*x)*sinh(a+b*x)/(b^2-d^2)+3/4*b*exp(c+d*x)*sinh(3*a+3*b*x)/(9*b^2-d^2)],
[exp(c+d*x)*cosh(a+b*x)*sinh(a+b*x),x,3,b*exp(c+d*x)*cosh(2*a+2*b*x)/(4*b^2-d^2)-1/2*d*exp(c+d*x)*sinh(2*a+2*b*x)/(4*b^2-d^2)],
[exp(c+d*x)*cosh(a+b*x),x,1,-d*exp(c+d*x)*cosh(a+b*x)/(b^2-d^2)+b*exp(c+d*x)*sinh(a+b*x)/(b^2-d^2)],
[exp(c+d*x)*cosh(a+b*x)*csch(a+b*x),x,4,exp(c+d*x)/d-2*exp(c+d*x)*hypergeom([1,1/2*d/b],[1+1/2*d/b],exp(2*(a+b*x)))/d],
[exp(c+d*x)*cosh(a+b*x)*csch(a+b*x)^2,x,4,-2*exp(a+c+(b+d)*x)*hypergeom([1,1/2*(b+d)/b],[1/2*(3*b+d)/b],exp(2*(a+b*x)))/(b+d)+4*exp(a+c+(b+d)*x)*hypergeom([2,1/2*(b+d)/b],[1/2*(3*b+d)/b],exp(2*(a+b*x)))/(b+d)],
[exp(c+d*x)*cosh(a+b*x)*csch(a+b*x)^3,x,4,4*exp(2*a+c+(2*b+d)*x)*hypergeom([2,1/2*(2+d/b)],[1/2*(4+d/b)],exp(2*(a+b*x)))/(2*b+d)-8*exp(2*a+c+(2*b+d)*x)*hypergeom([3,1/2*(2+d/b)],[1/2*(4+d/b)],exp(2*(a+b*x)))/(2*b+d)],
[exp(c+d*x)*cosh(a+b*x)^2*sinh(a+b*x)^3,x,5,-1/8*b*exp(c+d*x)*cosh(a+b*x)/(b^2-d^2)-3/16*b*exp(c+d*x)*cosh(3*a+3*b*x)/(9*b^2-d^2)+5/16*b*exp(c+d*x)*cosh(5*a+5*b*x)/(25*b^2-d^2)+1/8*d*exp(c+d*x)*sinh(a+b*x)/(b^2-d^2)+1/16*d*exp(c+d*x)*sinh(3*a+3*b*x)/(9*b^2-d^2)-1/16*d*exp(c+d*x)*sinh(5*a+5*b*x)/(25*b^2-d^2)],
[exp(c+d*x)*cosh(a+b*x)^2*sinh(a+b*x)^2,x,4,-1/8*exp(c+d*x)/d-1/8*d*exp(c+d*x)*cosh(4*a+4*b*x)/(16*b^2-d^2)+1/2*b*exp(c+d*x)*sinh(4*a+4*b*x)/(16*b^2-d^2)],
[exp(c+d*x)*cosh(a+b*x)^2*sinh(a+b*x),x,4,1/4*b*exp(c+d*x)*cosh(a+b*x)/(b^2-d^2)+3/4*b*exp(c+d*x)*cosh(3*a+3*b*x)/(9*b^2-d^2)-1/4*d*exp(c+d*x)*sinh(a+b*x)/(b^2-d^2)-1/4*d*exp(c+d*x)*sinh(3*a+3*b*x)/(9*b^2-d^2)],
[exp(c+d*x)*cosh(a+b*x)^2,x,2,2*b^2*exp(c+d*x)/(d*(4*b^2-d^2))-d*exp(c+d*x)*cosh(a+b*x)^2/(4*b^2-d^2)+2*b*exp(c+d*x)*cosh(a+b*x)*sinh(a+b*x)/(4*b^2-d^2)],
[exp(c+d*x)*cosh(a+b*x)^2*csch(a+b*x),x,6,-3/2*exp(-a+c-(b-d)*x)/(b-d)+1/2*exp(a+c+(b+d)*x)/(b+d)+2*exp(-a+c-(b-d)*x)*hypergeom([1,1/2*(-b+d)/b],[1/2*(b+d)/b],exp(2*(a+b*x)))/(b-d)],
[exp(c+d*x)*cosh(a+b*x)^2*csch(a+b*x)^2,x,5,exp(c+d*x)/d-4*exp(c+d*x)*hypergeom([1,1/2*d/b],[1+1/2*d/b],exp(2*(a+b*x)))/d+4*exp(c+d*x)*hypergeom([2,1/2*d/b],[1+1/2*d/b],exp(2*(a+b*x)))/d],
[exp(c+d*x)*cosh(a+b*x)^2*csch(a+b*x)^3,x,5,-2*exp(a+c+(b+d)*x)*hypergeom([1,1/2*(b+d)/b],[1/2*(3*b+d)/b],exp(2*(a+b*x)))/(b+d)+8*exp(a+c+(b+d)*x)*hypergeom([2,1/2*(b+d)/b],[1/2*(3*b+d)/b],exp(2*(a+b*x)))/(b+d)-8*exp(a+c+(b+d)*x)*hypergeom([3,1/2*(b+d)/b],[1/2*(3*b+d)/b],exp(2*(a+b*x)))/(b+d)],
[exp(c+d*x)*cosh(a+b*x)^3*sinh(a+b*x)^3,x,4,-3/16*b*exp(c+d*x)*cosh(2*a+2*b*x)/(4*b^2-d^2)+3/16*b*exp(c+d*x)*cosh(6*a+6*b*x)/(36*b^2-d^2)+3/32*d*exp(c+d*x)*sinh(2*a+2*b*x)/(4*b^2-d^2)-1/32*d*exp(c+d*x)*sinh(6*a+6*b*x)/(36*b^2-d^2)],
[exp(c+d*x)*cosh(a+b*x)^3*sinh(a+b*x)^2,x,5,1/8*d*exp(c+d*x)*cosh(a+b*x)/(b^2-d^2)-1/16*d*exp(c+d*x)*cosh(3*a+3*b*x)/(9*b^2-d^2)-1/16*d*exp(c+d*x)*cosh(5*a+5*b*x)/(25*b^2-d^2)-1/8*b*exp(c+d*x)*sinh(a+b*x)/(b^2-d^2)+3/16*b*exp(c+d*x)*sinh(3*a+3*b*x)/(9*b^2-d^2)+5/16*b*exp(c+d*x)*sinh(5*a+5*b*x)/(25*b^2-d^2)],
[exp(c+d*x)*cosh(a+b*x)^3*sinh(a+b*x),x,4,1/2*b*exp(c+d*x)*cosh(2*a+2*b*x)/(4*b^2-d^2)+1/2*b*exp(c+d*x)*cosh(4*a+4*b*x)/(16*b^2-d^2)-1/4*d*exp(c+d*x)*sinh(2*a+2*b*x)/(4*b^2-d^2)-1/8*d*exp(c+d*x)*sinh(4*a+4*b*x)/(16*b^2-d^2)],
[exp(c+d*x)*cosh(a+b*x)^3,x,2,-6*b^2*d*exp(c+d*x)*cosh(a+b*x)/(9*b^4-10*b^2*d^2+d^4)-d*exp(c+d*x)*cosh(a+b*x)^3/(9*b^2-d^2)+6*b^3*exp(c+d*x)*sinh(a+b*x)/(9*b^4-10*b^2*d^2+d^4)+3*b*exp(c+d*x)*cosh(a+b*x)^2*sinh(a+b*x)/(9*b^2-d^2)],
[exp(c+d*x)*cosh(a+b*x)^3*csch(a+b*x),x,8,-7/4*exp(-2*a+c-(2*b-d)*x)/(2*b-d)+exp(c+d*x)/d+1/4*exp(2*a+c+(2*b+d)*x)/(2*b+d)+2*exp(-2*a+c-(2*b-d)*x)*hypergeom([1,1/2*(-2+d/b)],[1/2*d/b],exp(2*(a+b*x)))/(2*b-d)],
[exp(c+d*x)*cosh(a+b*x)^3*csch(a+b*x)^2,x,7,-5/2*exp(-a+c-(b-d)*x)/(b-d)+1/2*exp(a+c+(b+d)*x)/(b+d)+6*exp(-a+c-(b-d)*x)*hypergeom([1,1/2*(-b+d)/b],[1/2*(b+d)/b],exp(2*(a+b*x)))/(b-d)-4*exp(-a+c-(b-d)*x)*hypergeom([2,1/2*(-b+d)/b],[1/2*(b+d)/b],exp(2*(a+b*x)))/(b-d)],
[exp(c+d*x)*cosh(a+b*x)^3*csch(a+b*x)^3,x,6,exp(c+d*x)/d-6*exp(c+d*x)*hypergeom([1,1/2*d/b],[1+1/2*d/b],exp(2*(a+b*x)))/d+12*exp(c+d*x)*hypergeom([2,1/2*d/b],[1+1/2*d/b],exp(2*(a+b*x)))/d-8*exp(c+d*x)*hypergeom([3,1/2*d/b],[1+1/2*d/b],exp(2*(a+b*x)))/d],
[exp(a+b*x)*sinh(c+d*x)^(3/2)-3/4*d^2*exp(a+b*x)/((b^2-9/4*d^2)*sqrt(sinh(c+d*x))),x,10,4*b*exp(a+b*x)*sinh(c+d*x)^(3/2)/(4*b^2-9*d^2)-6*d*exp(a+b*x)*cosh(c+d*x)*sqrt(sinh(c+d*x))/(4*b^2-9*d^2)],

# m<0

# Products of functions of a hyperbolic function and its derivative

# Integrands of the form F[Cosh[a+b x]] Sinh[a+b x]^n when n odd
[exp(n*cosh(a+b*x))*sinh(a+b*x),x,2,exp(n*cosh(a+b*x))/(b*n)],
[exp(n*cosh(a*c+b*c*x))*sinh(c*(a+b*x)),x,2,exp(n*cosh(c*(a+b*x)))/(b*c*n)],
[exp(n*cosh(c*(a+b*x)))*sinh(a*c+b*c*x),x,2,exp(n*cosh(a*c+b*c*x))/(b*c*n)],
[exp(n*cosh(a+b*x))*tanh(a+b*x),x,2,Ei(n*cosh(a+b*x))/b],
[exp(n*cosh(a*c+b*c*x))*tanh(c*(a+b*x)),x,2,Ei(n*cosh(c*(a+b*x)))/(b*c)],
[exp(n*cosh(c*(a+b*x)))*tanh(a*c+b*c*x),x,2,Ei(n*cosh(a*c+b*c*x))/(b*c)],

# Integrands of the form F[Sinh[a+b x]] Cosh[a+b x]^n when n odd
[exp(n*sinh(a+b*x))*cosh(a+b*x),x,2,exp(n*sinh(a+b*x))/(b*n)],
[exp(n*sinh(a*c+b*c*x))*cosh(c*(a+b*x)),x,2,exp(n*sinh(c*(a+b*x)))/(b*c*n)],
[exp(n*sinh(c*(a+b*x)))*cosh(a*c+b*c*x),x,2,exp(n*sinh(a*c+b*c*x))/(b*c*n)],
[exp(n*sinh(a+b*x))*coth(a+b*x),x,2,Ei(n*sinh(a+b*x))/b],
[exp(n*sinh(a*c+b*c*x))*coth(c*(a+b*x)),x,2,Ei(n*sinh(c*(a+b*x)))/(b*c)],
[exp(n*sinh(c*(a+b*x)))*coth(a*c+b*c*x),x,2,Ei(n*sinh(a*c+b*c*x))/(b*c)],

# Integrands of the form F[Tanh[a+b x]] Sech[a+b x]^n when n even
[sech(x)^2/(a+b*tanh(x)),x,2,log(a+b*tanh(x))/b],
[sech(x)^2/(1+tanh(x)^2),x,2,arctan(tanh(x))],
[sech(x)^2/(9+tanh(x)^2),x,2,1/3*arctan(1/3*tanh(x))],
[sech(x)^2*(a+b*tanh(x))^n,x,2,(a+b*tanh(x))^(1+n)/(b*(1+n))],
[sech(x)^2*(1+1/(1-tanh(x)^2)),x,3,x+tanh(x)],
[sech(x)^2*(2-tanh(x)^2)/(1-tanh(x)^2),x,4,x+tanh(x)],
[sech(x)^2/(2+2*tanh(x)+tanh(x)^2),x,3,arctan(1+tanh(x))],
[sech(x)^2/(tanh(x)^2+tanh(x)^3),x,3,-coth(x)-log(tanh(x))+log(1+tanh(x))],
[sech(x)^2/(-tanh(x)^2+tanh(x)^3),x,3,coth(x)+log(1-tanh(x))-log(tanh(x))],
[sech(x)^2/(3-4*tanh(x)^3),x,7,1/3*arctan((3^(1/3)+2*2^(2/3)*tanh(x))/3^(5/6))/(2^(2/3)*3^(1/6))-1/3*log(3^(1/3)-2^(2/3)*tanh(x))/6^(2/3)+1/6*log(3^(2/3)+2^(2/3)*3^(1/3)*tanh(x)+2*2^(1/3)*tanh(x)^2)/6^(2/3)],
[sech(x)^2/(11-5*tanh(x)+5*tanh(x)^2),x,3,-2*arctan(sqrt(5/39)*(1-2*tanh(x)))/sqrt(195)],
[sech(x)^2*(a+b*tanh(x))/(c+d*tanh(x)),x,3,-(b*c-a*d)*log(c+d*tanh(x))/d^2+b*tanh(x)/d],
[sech(x)^2*(a+b*tanh(x))^2/(c+d*tanh(x)),x,3,(b*c-a*d)^2*log(c+d*tanh(x))/d^3-b*(b*c-a*d)*tanh(x)/d^2+1/2*(a+b*tanh(x))^2/d],
[sech(x)^2*(a+b*tanh(x))^3/(c+d*tanh(x)),x,3,-(b*c-a*d)^3*log(c+d*tanh(x))/d^4+b*(b*c-a*d)^2*tanh(x)/d^3-1/2*(b*c-a*d)*(a+b*tanh(x))^2/d^2+1/3*(a+b*tanh(x))^3/d],
[sech(x)^2*tanh(x)^2/(2+tanh(x)^3)^2,x,2,(-1/3)/(2+tanh(x)^3)],
[sech(x)^2*tanh(x)^6*(1-tanh(x)^2)^3,x,4,1/7*tanh(x)^7-1/3*tanh(x)^9+3/11*tanh(x)^11-1/13*tanh(x)^13],
[sech(x)^2*(2+tanh(x)^2)/(1+tanh(x)^3),x,5,log(1+tanh(x))-2*arctan((1-2*tanh(x))/sqrt(3))/sqrt(3)],
[(1+cosh(x)^2)*sech(x)^2,x,2,x+tanh(x)],
[sech(x)^2/(1+sech(x)^2-3*tanh(x)),x,3,2*arctanh((3+2*tanh(x))/sqrt(17))/sqrt(17)],
[sech(x)^2/sqrt(4-sech(x)^2),x,2,arcsinh(tanh(x)/sqrt(3))],
[sech(x)^2/sqrt(1-4*tanh(x)^2),x,2,1/2*arcsin(2*tanh(x))],
[sech(x)^2/sqrt(-4+tanh(x)^2),x,3,arctanh(tanh(x)/sqrt(-4+tanh(x)^2))],
[sech(x)^2*sqrt(1+coth(x)^2),x,3,-arcsinh(coth(x))+sqrt(1+coth(x)^2)*tanh(x)],
[sech(x)^2*sqrt(1+tanh(x)^2),x,3,1/2*arcsinh(tanh(x))+1/2*sqrt(1+tanh(x)^2)*tanh(x)],
[sech(x)^4*(-1+sech(x)^2)^2*tanh(x),x,4,1/6*tanh(x)^6-1/8*tanh(x)^8],

# Integrands of the form F[Coth[a+b x]] Csch[a+b x]^n when n even

# Integrands of the form F[Sech[a+b x]] Sech[a+b x] Tanh[a+b x]

# Integrands of the form F[Csch[a+b x]] Csch[a+b x] Coth[a+b x]

# Integrands of the form F[Sinh[(a+b x)/2]] Sinh[a+b x]
[exp(n*sinh(a+b*x))*sinh(2*a+2*b*x),x,4,-2*exp(n*sinh(a+b*x))/(b*n^2)+2*exp(n*sinh(a+b*x))*sinh(a+b*x)/(b*n)],
[exp(n*sinh(a+b*x))*sinh(2*(a+b*x)),x,4,-2*exp(n*sinh(a+b*x))/(b*n^2)+2*exp(n*sinh(a+b*x))*sinh(a+b*x)/(b*n)],
[exp(n*sinh(1/2*a+1/2*b*x))*sinh(a+b*x),x,4,-4*exp(n*sinh(1/2*a+1/2*b*x))/(b*n^2)+4*exp(n*sinh(1/2*a+1/2*b*x))*sinh(1/2*a+1/2*b*x)/(b*n)],
[exp(n*sinh(1/2*(a+b*x)))*sinh(a+b*x),x,4,-4*exp(n*sinh(1/2*a+1/2*b*x))/(b*n^2)+4*exp(n*sinh(1/2*a+1/2*b*x))*sinh(1/2*a+1/2*b*x)/(b*n)],

# Integrands of the form F[Cosh[(a+b x)/2]] Sinh[a+b x]
[exp(n*cosh(a+b*x))*sinh(2*a+2*b*x),x,4,-2*exp(n*cosh(a+b*x))/(b*n^2)+2*exp(n*cosh(a+b*x))*cosh(a+b*x)/(b*n)],
[exp(n*cosh(a+b*x))*sinh(2*(a+b*x)),x,4,-2*exp(n*cosh(a+b*x))/(b*n^2)+2*exp(n*cosh(a+b*x))*cosh(a+b*x)/(b*n)],
[exp(n*cosh(1/2*a+1/2*b*x))*sinh(a+b*x),x,4,-4*exp(n*cosh(1/2*a+1/2*b*x))/(b*n^2)+4*exp(n*cosh(1/2*a+1/2*b*x))*cosh(1/2*a+1/2*b*x)/(b*n)],
[exp(n*cosh(1/2*(a+b*x)))*sinh(a+b*x),x,4,-4*exp(n*cosh(1/2*a+1/2*b*x))/(b*n^2)+4*exp(n*cosh(1/2*a+1/2*b*x))*cosh(1/2*a+1/2*b*x)/(b*n)],

# Integrands of the form F[Tanh[a+b x]] when n even
[csch(x)*log(tanh(x))*sech(x),x,1,1/2*log(tanh(x))^2],
[csch(2*x)*log(tanh(x)),x,1,1/4*log(tanh(x))^2],

# Products of functions of a hyperbolic function and its derivative
[cosh(a+b*x)*F(c,d,sinh(a+b*x),r,s),x,1,CannotIntegrate(cosh(a+b*x)*F(c,d,sinh(a+b*x),r,s),x)],
[F(c,d,cosh(a+b*x),r,s)*sinh(a+b*x),x,1,CannotIntegrate(F(c,d,cosh(a+b*x),r,s)*sinh(a+b*x),x)],
[F(c,d,tanh(a+b*x),r,s)*sech(a+b*x)^2,x,1,CannotIntegrate(F(c,d,tanh(a+b*x),r,s)*sech(a+b*x)^2,x)],
[csch(a+b*x)^2*F(c,d,coth(a+b*x),r,s),x,1,CannotIntegrate(csch(a+b*x)^2*F(c,d,coth(a+b*x),r,s),x)],
[sech(x)*(5-11*sech(x)^2)*tanh(x),x,3,-5*sech(x)+11/3*sech(x)^3],
[csch(x)^2/(a+b*coth(x)),x,2,-log(a+b*coth(x))/b],
[(a+b*coth(x))^n*csch(x)^2,x,2,-(a+b*coth(x))^(1+n)/(b*(1+n))],
[csch(x)^2*(-1+sinh(x)^2),x,2,x+coth(x)],
[(-1+(-1)/(1-coth(x)^2))*csch(x)^2,x,3,x+coth(x)],
[(a+b*coth(x))*csch(x)^2/(c+d*coth(x)),x,3,-b*coth(x)/d+(b*c-a*d)*log(c+d*coth(x))/d^2],
[(a+b*coth(x))^2*csch(x)^2/(c+d*coth(x)),x,3,b*(b*c-a*d)*coth(x)/d^2-1/2*(a+b*coth(x))^2/d-(b*c-a*d)^2*log(c+d*coth(x))/d^3],
[(a+b*coth(x))^3*csch(x)^2/(c+d*coth(x)),x,3,-b*(b*c-a*d)^2*coth(x)/d^3+1/2*(b*c-a*d)*(a+b*coth(x))^2/d^2-1/3*(a+b*coth(x))^3/d+(b*c-a*d)^3*log(c+d*coth(x))/d^4],
[cosh(x)^3*(a+b*cosh(x)^2)^3*sinh(x),x,4,-1/8*a*(a+b*cosh(x)^2)^4/b^2+1/10*(a+b*cosh(x)^2)^5/b^2],
[cosh(x)*sinh(x)^3*(a+b*sinh(x)^2)^3,x,4,-1/8*a*(a+b*sinh(x)^2)^4/b^2+1/10*(a+b*sinh(x)^2)^5/b^2],
[cosh(x)*sinh(x)*sqrt(a+b*sinh(x)^2),x,2,1/3*(a+b*sinh(x)^2)^(3/2)/b],
[csch(x)*sech(x)*sqrt(1+log(coth(x))^2),x,3,-1/2*arcsinh(log(coth(x)))-1/2*log(coth(x))*sqrt(1+log(coth(x))^2)],

# Miscellaneous integrands involving hyperbolic functions
[coth(sqrt(x))*csch(sqrt(x))/sqrt(x),x,3,-2*csch(sqrt(x))],
[cosh(sqrt(x))*sinh(sqrt(x))/sqrt(x),x,1,sinh(sqrt(x))^2],
[sech(sqrt(x))*tanh(sqrt(x))/sqrt(x),x,3,-2*sech(sqrt(x))],
[sinh(x)^2/(a+b*sinh(2*x)),x,9,1/4*log(a+b*sinh(2*x))/b+1/2*arctanh((b-a*tanh(x))/sqrt(a^2+b^2))/sqrt(a^2+b^2),1/2*log(cosh(x))/b+1/4*log(a+2*b*tanh(x)-a*tanh(x)^2)/b+1/2*arctanh((b-a*tanh(x))/sqrt(a^2+b^2))/sqrt(a^2+b^2)],
[cosh(x)^2/(a+b*sinh(2*x)),x,8,1/4*log(a+b*sinh(2*x))/b-1/2*arctanh((b-a*tanh(x))/sqrt(a^2+b^2))/sqrt(a^2+b^2),1/2*log(cosh(x))/b+1/4*log(a+2*b*tanh(x)-a*tanh(x)^2)/b-1/2*arctanh((b-a*tanh(x))/sqrt(a^2+b^2))/sqrt(a^2+b^2)],
[sinh(x)^2/(a+b*cosh(2*x)),x,4,1/2*x/b-1/2*arctanh(sqrt(a-b)*tanh(x)/sqrt(a+b))*sqrt(a+b)/(b*sqrt(a-b))],
[cosh(x)^2/(a+b*cosh(2*x)),x,4,1/2*x/b-1/2*arctanh(sqrt(a-b)*tanh(x)/sqrt(a+b))*sqrt(a-b)/(b*sqrt(a+b))],
[tanh(c+d*x)/sqrt(a*sinh(c+d*x)^2),x,3,arctan(sqrt(a*sinh(c+d*x)^2)/sqrt(a))/(d*sqrt(a))],
[coth(c+d*x)/sqrt(a*cosh(c+d*x)^2),x,3,-arctanh(sqrt(a*cosh(c+d*x)^2)/sqrt(a))/(d*sqrt(a))],
[x*cosh(2*x)*sech(x),x,12,-2*x*arctan(exp(x))-2*cosh(x)+I*polylog(2,-I*exp(x))-I*polylog(2,I*exp(x))+2*x*sinh(x)],
[x*cosh(2*x)*sech(x)^2,x,5,x^2+log(cosh(x))-x*tanh(x)],
[x*cosh(2*x)*sech(x)^3,x,19,3*x*arctan(exp(x))-3/2*I*polylog(2,-I*exp(x))+3/2*I*polylog(2,I*exp(x))-1/2*sech(x)-1/2*x*sech(x)*tanh(x)],
[sqrt(csch(x))*(x*cosh(x)-4*sech(x)*tanh(x)),x,8,-4*sech(x)/csch(x)^(3/2)+2*x/sqrt(csch(x))],
[sinh(x)*(cosh(x)+sinh(x)),x,6,-1/2*x+1/2*cosh(x)*sinh(x)+1/2*sinh(x)^2],
[(1+sinh(x)^2)/(1+cosh(x)+sinh(x)),x,5,1/4*log(1-tanh(1/2*x))+3/4*log(1+tanh(1/2*x))+1/2/(1-tanh(1/2*x))+(-1/2)/(1+tanh(1/2*x))^2+1/(1+tanh(1/2*x))],
[x^5*cosh(a+b*x^3)^7*sinh(a+b*x^3),x,7,-35/3072*x^3/b+1/24*x^3*cosh(a+b*x^3)^8/b-35/3072*cosh(a+b*x^3)*sinh(a+b*x^3)/b^2-35/4608*cosh(a+b*x^3)^3*sinh(a+b*x^3)/b^2-7/1152*cosh(a+b*x^3)^5*sinh(a+b*x^3)/b^2-1/192*cosh(a+b*x^3)^7*sinh(a+b*x^3)/b^2],

#  {Csch[x^5]/x, x, Unintegrable[Csch[x^5]/x, x]} 
[cosh(x)^2/(1+exp(x)),x,4,(-1/8)/exp(2*x)+1/4/exp(x)+1/4*exp(x)+3/4*x-log(1+exp(x))],
[sech(x)*sqrt(1+sech(x))*tanh(x)^3,x,6,-4/5*(1+sech(x))^(5/2)+2/7*(1+sech(x))^(7/2)],
[coth(x)^3*csch(x)*sqrt(1+csch(x)),x,5,-4/3*(1+csch(x))^(3/2)+4/5*(1+csch(x))^(5/2)-2/7*(1+csch(x))^(7/2)],
[cosh(x)^x*(log(cosh(x))+x*tanh(x)),x,3,cosh(x)^x],

#  Nonidempotent expansion results in infinite recursion: 

#  {(x*Cosh[x] - Sinh[x])/(x - Sinh[x])^2, x, -7, x/(x - Sinh[x])} 

#  {(-Cosh[x] + x*Sinh[x])/(x - Cosh[x])^2, x, 0, x/(x - Cosh[x])} 
[F^(a+b*x)*(cosh(c+d*x)+sinh(c+d*x))^n,x,4,(exp(c+d*x))^n*F^(a+b*x)/(d*n+b*log(F))],
[F^(a+b*x)*(cosh(c+d*x)-sinh(c+d*x))^n,x,4,-(exp(-c-d*x))^n*F^(a+b*x)/(d*n-b*log(F))],

#  {(Cosh[a + b*x]^5 - Sinh[a + b*x]^5)/(Cosh[a + b*x]^5 + Sinh[a + b*x]^5), x, 5, 0} 
[(cosh(a+b*x)^4-sinh(a+b*x)^4)/(cosh(a+b*x)^4+sinh(a+b*x)^4),x,6,-arctan(1-sqrt(2)*tanh(a+b*x))/(b*sqrt(2))+arctan(1+sqrt(2)*tanh(a+b*x))/(b*sqrt(2))],
[(cosh(a+b*x)^3-sinh(a+b*x)^3)/(cosh(a+b*x)^3+sinh(a+b*x)^3),x,5,-4/3*arctan((1-2*tanh(a+b*x))/sqrt(3))/(b*sqrt(3))+(-1/3)/(b*(1+tanh(a+b*x)))],
[(cosh(a+b*x)^2-sinh(a+b*x)^2)/(cosh(a+b*x)^2+sinh(a+b*x)^2),x,3,arctan(tanh(a+b*x))/b],
[(cosh(a+b*x)-sinh(a+b*x))/(cosh(a+b*x)+sinh(a+b*x)),x,1,(-1/2)/(b*(cosh(a+b*x)+sinh(a+b*x))^2)],
[(-csch(a+b*x)+sech(a+b*x))/(csch(a+b*x)+sech(a+b*x)),x,2,1/(b*(1+tanh(a+b*x)))],
[(-csch(a+b*x)^2+sech(a+b*x)^2)/(csch(a+b*x)^2+sech(a+b*x)^2),x,2,-arctan(tanh(a+b*x))/b],
[(-csch(a+b*x)^3+sech(a+b*x)^3)/(csch(a+b*x)^3+sech(a+b*x)^3),x,5,4/3*arctan((1-2*tanh(a+b*x))/sqrt(3))/(b*sqrt(3))+1/3/(b*(1+tanh(a+b*x)))],
[(-csch(a+b*x)^4+sech(a+b*x)^4)/(csch(a+b*x)^4+sech(a+b*x)^4),x,6,arctan(1-sqrt(2)*tanh(a+b*x))/(b*sqrt(2))-arctan(1+sqrt(2)*tanh(a+b*x))/(b*sqrt(2))]]:
