# Maple integration test file: "6 Hyperbolic functions\6.4 Hyperbolic cotangent\6.4.1 (c+d x)^m (a+b coth)^n.txt"

lst:=[

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

# Integrands of the form (c+d x)^m (b Coth[e+f x])^n

# Integrands of the form x^m Coth[e+f x]^n
[x^3*coth(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*coth(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*coth(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],
[coth(a+b*x)/x,x,0,Unintegrable(coth(a+b*x)/x,x)],
[coth(a+b*x)/x^2,x,0,Unintegrable(coth(a+b*x)/x^2,x)],
[x^3*coth(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*coth(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*coth(a+b*x)^2,x,3,1/2*x^2-x*coth(a+b*x)/b+log(sinh(a+b*x))/b^2],
[coth(a+b*x)^2/x,x,0,Unintegrable(coth(a+b*x)^2/x,x)],
[coth(a+b*x)^2/x^2,x,0,Unintegrable(coth(a+b*x)^2/x^2,x)],
[x^3*coth(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*coth(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*coth(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],
[coth(a+b*x)^3/x,x,0,Unintegrable(coth(a+b*x)^3/x,x)],
[coth(a+b*x)^3/x^2,x,0,Unintegrable(coth(a+b*x)^3/x^2,x)],

# Integrands of the form x^m Coth[e+f x]^(n/2)

# Integrands of the form (c+d x)^m (a+b Coth[e+f x])^n with a^2-b^2=0

# Integrands of the form (c+d x)^m (a+a Coth[e+f x])^n

# n>0

# n<0
[(c+d*x)^3/(a+a*coth(e+f*x)),x,5,3/8*d^3*x/(a*f^3)+3/8*d*(c+d*x)^2/(a*f^2)+1/4*(c+d*x)^3/(a*f)+1/8*(c+d*x)^4/(a*d)-3/8*d^3/(f^4*(a+a*coth(e+f*x)))-3/4*d^2*(c+d*x)/(f^3*(a+a*coth(e+f*x)))-3/4*d*(c+d*x)^2/(f^2*(a+a*coth(e+f*x)))-1/2*(c+d*x)^3/(f*(a+a*coth(e+f*x)))],
[(c+d*x)^2/(a+a*coth(e+f*x)),x,4,1/4*d^2*x/(a*f^2)+1/4*(c+d*x)^2/(a*f)+1/6*(c+d*x)^3/(a*d)-1/4*d^2/(f^3*(a+a*coth(e+f*x)))-1/2*d*(c+d*x)/(f^2*(a+a*coth(e+f*x)))-1/2*(c+d*x)^2/(f*(a+a*coth(e+f*x)))],
[(c+d*x)/(a+a*coth(e+f*x)),x,3,1/4*d*x/(a*f)+1/4*(c+d*x)^2/(a*d)-1/4*d/(f^2*(a+a*coth(e+f*x)))+1/2*(-c-d*x)/(f*(a+a*coth(e+f*x)))],
[1/((c+d*x)*(a+a*coth(e+f*x))),x,7,-1/2*Chi(2*c*f/d+2*f*x)*cosh(2*e-2*c*f/d)/(a*d)+1/2*log(c+d*x)/(a*d)+1/2*cosh(2*e-2*c*f/d)*Shi(2*c*f/d+2*f*x)/(a*d)+1/2*Chi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a*d)-1/2*Shi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a*d)],
[1/((c+d*x)^2*(a+a*coth(e+f*x))),x,7,f*Chi(2*c*f/d+2*f*x)*cosh(2*e-2*c*f/d)/(a*d^2)+(-1)/(d*(c+d*x)*(a+a*coth(e+f*x)))-f*cosh(2*e-2*c*f/d)*Shi(2*c*f/d+2*f*x)/(a*d^2)-f*Chi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a*d^2)+f*Shi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a*d^2)],
[1/((c+d*x)^3*(a+a*coth(e+f*x))),x,8,-1/2*f/(a*d^2*(c+d*x))-f^2*Chi(2*c*f/d+2*f*x)*cosh(2*e-2*c*f/d)/(a*d^3)+(-1/2)/(d*(c+d*x)^2*(a+a*coth(e+f*x)))+f/(d^2*(c+d*x)*(a+a*coth(e+f*x)))+f^2*cosh(2*e-2*c*f/d)*Shi(2*c*f/d+2*f*x)/(a*d^3)+f^2*Chi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a*d^3)-f^2*Shi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a*d^3)],
[(c+d*x)^3/(a+a*coth(e+f*x))^2,x,10,-3/512*d^3*exp(-4*e-4*f*x)/(a^2*f^4)+3/16*d^3*exp(-2*e-2*f*x)/(a^2*f^4)-3/128*d^2*exp(-4*e-4*f*x)*(c+d*x)/(a^2*f^3)+3/8*d^2*exp(-2*e-2*f*x)*(c+d*x)/(a^2*f^3)-3/64*d*exp(-4*e-4*f*x)*(c+d*x)^2/(a^2*f^2)+3/8*d*exp(-2*e-2*f*x)*(c+d*x)^2/(a^2*f^2)-1/16*exp(-4*e-4*f*x)*(c+d*x)^3/(a^2*f)+1/4*exp(-2*e-2*f*x)*(c+d*x)^3/(a^2*f)+1/16*(c+d*x)^4/(a^2*d)],
[(c+d*x)^2/(a+a*coth(e+f*x))^2,x,8,-1/128*d^2*exp(-4*e-4*f*x)/(a^2*f^3)+1/8*d^2*exp(-2*e-2*f*x)/(a^2*f^3)-1/32*d*exp(-4*e-4*f*x)*(c+d*x)/(a^2*f^2)+1/4*d*exp(-2*e-2*f*x)*(c+d*x)/(a^2*f^2)-1/16*exp(-4*e-4*f*x)*(c+d*x)^2/(a^2*f)+1/4*exp(-2*e-2*f*x)*(c+d*x)^2/(a^2*f)+1/12*(c+d*x)^3/(a^2*d)],
[(c+d*x)/(a+a*coth(e+f*x))^2,x,7,3/16*d*x/(a^2*f)-1/8*d*x^2/a^2+1/4*x*(c+d*x)/a^2-1/16*d/(f^2*(a+a*coth(e+f*x))^2)+1/4*(-c-d*x)/(f*(a+a*coth(e+f*x))^2)-3/16*d/(f^2*(a^2+a^2*coth(e+f*x)))+1/4*(-c-d*x)/(f*(a^2+a^2*coth(e+f*x)))],
[1/((c+d*x)*(a+a*coth(e+f*x))^2),x,21,1/4*Chi(4*c*f/d+4*f*x)*cosh(4*e-4*c*f/d)/(a^2*d)-1/2*Chi(2*c*f/d+2*f*x)*cosh(2*e-2*c*f/d)/(a^2*d)+1/4*log(c+d*x)/(a^2*d)+1/2*cosh(2*e-2*c*f/d)*Shi(2*c*f/d+2*f*x)/(a^2*d)-1/4*cosh(4*e-4*c*f/d)*Shi(4*c*f/d+4*f*x)/(a^2*d)-1/4*Chi(4*c*f/d+4*f*x)*sinh(4*e-4*c*f/d)/(a^2*d)+1/4*Shi(4*c*f/d+4*f*x)*sinh(4*e-4*c*f/d)/(a^2*d)+1/2*Chi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a^2*d)-1/2*Shi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a^2*d)],
[1/((c+d*x)^2*(a+a*coth(e+f*x))^2),x,24,(-1/4)/(a^2*d*(c+d*x))-f*Chi(4*c*f/d+4*f*x)*cosh(4*e-4*c*f/d)/(a^2*d^2)+f*Chi(2*c*f/d+2*f*x)*cosh(2*e-2*c*f/d)/(a^2*d^2)+1/2*cosh(2*e+2*f*x)/(a^2*d*(c+d*x))-1/4*cosh(2*e+2*f*x)^2/(a^2*d*(c+d*x))-f*cosh(2*e-2*c*f/d)*Shi(2*c*f/d+2*f*x)/(a^2*d^2)+f*cosh(4*e-4*c*f/d)*Shi(4*c*f/d+4*f*x)/(a^2*d^2)+f*Chi(4*c*f/d+4*f*x)*sinh(4*e-4*c*f/d)/(a^2*d^2)-f*Shi(4*c*f/d+4*f*x)*sinh(4*e-4*c*f/d)/(a^2*d^2)-f*Chi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a^2*d^2)+f*Shi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a^2*d^2)-1/2*sinh(2*e+2*f*x)/(a^2*d*(c+d*x))-1/4*sinh(2*e+2*f*x)^2/(a^2*d*(c+d*x))+1/4*sinh(4*e+4*f*x)/(a^2*d*(c+d*x))],
[(c+d*x)^3/(a+a*coth(e+f*x))^3,x,14,1/1728*d^3*exp(-6*e-6*f*x)/(a^3*f^4)-9/1024*d^3*exp(-4*e-4*f*x)/(a^3*f^4)+9/64*d^3*exp(-2*e-2*f*x)/(a^3*f^4)+1/288*d^2*exp(-6*e-6*f*x)*(c+d*x)/(a^3*f^3)-9/256*d^2*exp(-4*e-4*f*x)*(c+d*x)/(a^3*f^3)+9/32*d^2*exp(-2*e-2*f*x)*(c+d*x)/(a^3*f^3)+1/96*d*exp(-6*e-6*f*x)*(c+d*x)^2/(a^3*f^2)-9/128*d*exp(-4*e-4*f*x)*(c+d*x)^2/(a^3*f^2)+9/32*d*exp(-2*e-2*f*x)*(c+d*x)^2/(a^3*f^2)+1/48*exp(-6*e-6*f*x)*(c+d*x)^3/(a^3*f)-3/32*exp(-4*e-4*f*x)*(c+d*x)^3/(a^3*f)+3/16*exp(-2*e-2*f*x)*(c+d*x)^3/(a^3*f)+1/32*(c+d*x)^4/(a^3*d)],
[(c+d*x)^2/(a+a*coth(e+f*x))^3,x,11,1/864*d^2*exp(-6*e-6*f*x)/(a^3*f^3)-3/256*d^2*exp(-4*e-4*f*x)/(a^3*f^3)+3/32*d^2*exp(-2*e-2*f*x)/(a^3*f^3)+1/144*d*exp(-6*e-6*f*x)*(c+d*x)/(a^3*f^2)-3/64*d*exp(-4*e-4*f*x)*(c+d*x)/(a^3*f^2)+3/16*d*exp(-2*e-2*f*x)*(c+d*x)/(a^3*f^2)+1/48*exp(-6*e-6*f*x)*(c+d*x)^2/(a^3*f)-3/32*exp(-4*e-4*f*x)*(c+d*x)^2/(a^3*f)+3/16*exp(-2*e-2*f*x)*(c+d*x)^2/(a^3*f)+1/24*(c+d*x)^3/(a^3*d)],
[(c+d*x)/(a+a*coth(e+f*x))^3,x,11,11/96*d*x/(a^3*f)-1/16*d*x^2/a^3+1/8*x*(c+d*x)/a^3-1/36*d/(f^2*(a+a*coth(e+f*x))^3)+1/6*(-c-d*x)/(f*(a+a*coth(e+f*x))^3)-5/96*d/(a*f^2*(a+a*coth(e+f*x))^2)+1/8*(-c-d*x)/(a*f*(a+a*coth(e+f*x))^2)-11/96*d/(f^2*(a^3+a^3*coth(e+f*x)))+1/8*(-c-d*x)/(f*(a^3+a^3*coth(e+f*x)))],
[1/((c+d*x)*(a+a*coth(e+f*x))^3),x,53,-1/8*Chi(6*c*f/d+6*f*x)*cosh(6*e-6*c*f/d)/(a^3*d)+3/8*Chi(4*c*f/d+4*f*x)*cosh(4*e-4*c*f/d)/(a^3*d)-3/8*Chi(2*c*f/d+2*f*x)*cosh(2*e-2*c*f/d)/(a^3*d)+1/8*log(c+d*x)/(a^3*d)+3/8*cosh(2*e-2*c*f/d)*Shi(2*c*f/d+2*f*x)/(a^3*d)-3/8*cosh(4*e-4*c*f/d)*Shi(4*c*f/d+4*f*x)/(a^3*d)+1/8*cosh(6*e-6*c*f/d)*Shi(6*c*f/d+6*f*x)/(a^3*d)+1/8*Chi(6*c*f/d+6*f*x)*sinh(6*e-6*c*f/d)/(a^3*d)-1/8*Shi(6*c*f/d+6*f*x)*sinh(6*e-6*c*f/d)/(a^3*d)-3/8*Chi(4*c*f/d+4*f*x)*sinh(4*e-4*c*f/d)/(a^3*d)+3/8*Shi(4*c*f/d+4*f*x)*sinh(4*e-4*c*f/d)/(a^3*d)+3/8*Chi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a^3*d)-3/8*Shi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a^3*d)],
[1/((c+d*x)^2*(a+a*coth(e+f*x))^3),x,60,(-1/8)/(a^3*d*(c+d*x))+3/4*f*Chi(6*c*f/d+6*f*x)*cosh(6*e-6*c*f/d)/(a^3*d^2)-3/2*f*Chi(4*c*f/d+4*f*x)*cosh(4*e-4*c*f/d)/(a^3*d^2)+3/4*f*Chi(2*c*f/d+2*f*x)*cosh(2*e-2*c*f/d)/(a^3*d^2)+9/32*cosh(2*e+2*f*x)/(a^3*d*(c+d*x))-3/8*cosh(2*e+2*f*x)^2/(a^3*d*(c+d*x))+1/8*cosh(2*e+2*f*x)^3/(a^3*d*(c+d*x))+3/32*cosh(6*e+6*f*x)/(a^3*d*(c+d*x))-3/4*f*cosh(2*e-2*c*f/d)*Shi(2*c*f/d+2*f*x)/(a^3*d^2)+3/2*f*cosh(4*e-4*c*f/d)*Shi(4*c*f/d+4*f*x)/(a^3*d^2)-3/4*f*cosh(6*e-6*c*f/d)*Shi(6*c*f/d+6*f*x)/(a^3*d^2)-3/4*f*Chi(6*c*f/d+6*f*x)*sinh(6*e-6*c*f/d)/(a^3*d^2)+3/4*f*Shi(6*c*f/d+6*f*x)*sinh(6*e-6*c*f/d)/(a^3*d^2)+3/2*f*Chi(4*c*f/d+4*f*x)*sinh(4*e-4*c*f/d)/(a^3*d^2)-3/2*f*Shi(4*c*f/d+4*f*x)*sinh(4*e-4*c*f/d)/(a^3*d^2)-3/4*f*Chi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a^3*d^2)+3/4*f*Shi(2*c*f/d+2*f*x)*sinh(2*e-2*c*f/d)/(a^3*d^2)-15/32*sinh(2*e+2*f*x)/(a^3*d*(c+d*x))-3/8*sinh(2*e+2*f*x)^2/(a^3*d*(c+d*x))-1/8*sinh(2*e+2*f*x)^3/(a^3*d*(c+d*x))+3/8*sinh(4*e+4*f*x)/(a^3*d*(c+d*x))-3/32*sinh(6*e+6*f*x)/(a^3*d*(c+d*x))],

# Integrands of the form (c+d x)^m (a+a Coth[e+f x])^n with m symbolic
[(c+d*x)^m*(a+a*coth(e+f*x))^2,x,0,Unintegrable((c+d*x)^m*(a+a*coth(e+f*x))^2,x)],
[(c+d*x)^m*(a+a*coth(e+f*x)),x,0,Unintegrable((c+d*x)^m*(a+a*coth(e+f*x)),x)],
[(c+d*x)^m/(a+a*coth(e+f*x)),x,2,1/2*(c+d*x)^(1+m)/(a*d*(1+m))+2^(-2-m)*exp(-2*e+2*c*f/d)*(c+d*x)^m*GAMMA(1+m,2*f*(c+d*x)/d)/(a*f*(f*(c+d*x)/d)^m)],
[(c+d*x)^m/(a+a*coth(e+f*x))^2,x,4,1/4*(c+d*x)^(1+m)/(a^2*d*(1+m))+2^(-2-m)*exp(-2*e+2*c*f/d)*(c+d*x)^m*GAMMA(1+m,2*f*(c+d*x)/d)/(a^2*f*(f*(c+d*x)/d)^m)-4^(-2-m)*exp(-4*e+4*c*f/d)*(c+d*x)^m*GAMMA(1+m,4*f*(c+d*x)/d)/(a^2*f*(f*(c+d*x)/d)^m)],
[(c+d*x)^m/(a+a*coth(e+f*x))^3,x,5,1/8*(c+d*x)^(1+m)/(a^3*d*(1+m))+3*2^(-4-m)*exp(-2*e+2*c*f/d)*(c+d*x)^m*GAMMA(1+m,2*f*(c+d*x)/d)/(a^3*f*(f*(c+d*x)/d)^m)-3*2^(-5-2*m)*exp(-4*e+4*c*f/d)*(c+d*x)^m*GAMMA(1+m,4*f*(c+d*x)/d)/(a^3*f*(f*(c+d*x)/d)^m)+2^(-4-m)*3^(-1-m)*exp(-6*e+6*c*f/d)*(c+d*x)^m*GAMMA(1+m,6*f*(c+d*x)/d)/(a^3*f*(f*(c+d*x)/d)^m)],

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

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

# n>0
[(c+d*x)^3*(a+b*coth(e+f*x)),x,8,1/4*a*(c+d*x)^4/d-1/4*b*(c+d*x)^4/d+b*(c+d*x)^3*log(1-exp(2*(e+f*x)))/f+3/2*b*d*(c+d*x)^2*polylog(2,exp(2*(e+f*x)))/f^2-3/2*b*d^2*(c+d*x)*polylog(3,exp(2*(e+f*x)))/f^3+3/4*b*d^3*polylog(4,exp(2*(e+f*x)))/f^4],
[(c+d*x)^2*(a+b*coth(e+f*x)),x,7,1/3*a*(c+d*x)^3/d-1/3*b*(c+d*x)^3/d+b*(c+d*x)^2*log(1-exp(2*(e+f*x)))/f+b*d*(c+d*x)*polylog(2,exp(2*(e+f*x)))/f^2-1/2*b*d^2*polylog(3,exp(2*(e+f*x)))/f^3],
[(c+d*x)*(a+b*coth(e+f*x)),x,6,1/2*a*(c+d*x)^2/d-1/2*b*(c+d*x)^2/d+b*(c+d*x)*log(1-exp(2*(e+f*x)))/f+1/2*b*d*polylog(2,exp(2*(e+f*x)))/f^2],
[(a+b*coth(e+f*x))/(c+d*x),x,0,Unintegrable((a+b*coth(e+f*x))/(c+d*x),x)],
[(a+b*coth(e+f*x))/(c+d*x)^2,x,0,Unintegrable((a+b*coth(e+f*x))/(c+d*x)^2,x)],
[(c+d*x)^3*(a+b*coth(e+f*x))^2,x,15,-b^2*(c+d*x)^3/f+1/4*a^2*(c+d*x)^4/d-1/2*a*b*(c+d*x)^4/d+1/4*b^2*(c+d*x)^4/d-b^2*(c+d*x)^3*coth(e+f*x)/f+3*b^2*d*(c+d*x)^2*log(1-exp(2*(e+f*x)))/f^2+2*a*b*(c+d*x)^3*log(1-exp(2*(e+f*x)))/f+3*b^2*d^2*(c+d*x)*polylog(2,exp(2*(e+f*x)))/f^3+3*a*b*d*(c+d*x)^2*polylog(2,exp(2*(e+f*x)))/f^2-3/2*b^2*d^3*polylog(3,exp(2*(e+f*x)))/f^4-3*a*b*d^2*(c+d*x)*polylog(3,exp(2*(e+f*x)))/f^3+3/2*a*b*d^3*polylog(4,exp(2*(e+f*x)))/f^4],
[(c+d*x)^2*(a+b*coth(e+f*x))^2,x,13,-b^2*(c+d*x)^2/f+1/3*a^2*(c+d*x)^3/d-2/3*a*b*(c+d*x)^3/d+1/3*b^2*(c+d*x)^3/d-b^2*(c+d*x)^2*coth(e+f*x)/f+2*b^2*d*(c+d*x)*log(1-exp(2*(e+f*x)))/f^2+2*a*b*(c+d*x)^2*log(1-exp(2*(e+f*x)))/f+b^2*d^2*polylog(2,exp(2*(e+f*x)))/f^3+2*a*b*d*(c+d*x)*polylog(2,exp(2*(e+f*x)))/f^2-a*b*d^2*polylog(3,exp(2*(e+f*x)))/f^3],
[(c+d*x)*(a+b*coth(e+f*x))^2,x,9,b^2*c*x+1/2*b^2*d*x^2+1/2*a^2*(c+d*x)^2/d-a*b*(c+d*x)^2/d-b^2*(c+d*x)*coth(e+f*x)/f+2*a*b*(c+d*x)*log(1-exp(2*(e+f*x)))/f+b^2*d*log(sinh(e+f*x))/f^2+a*b*d*polylog(2,exp(2*(e+f*x)))/f^2],
[(a+b*coth(e+f*x))^2/(c+d*x),x,0,Unintegrable((a+b*coth(e+f*x))^2/(c+d*x),x)],
[(a+b*coth(e+f*x))^2/(c+d*x)^2,x,0,Unintegrable((a+b*coth(e+f*x))^2/(c+d*x)^2,x)],
[(c+d*x)^3*(a+b*coth(e+f*x))^3,x,28,-3/2*b^3*d*(c+d*x)^2/f^2-3*a*b^2*(c+d*x)^3/f+1/2*b^3*(c+d*x)^3/f+1/4*a^3*(c+d*x)^4/d-3/4*a^2*b*(c+d*x)^4/d+3/4*a*b^2*(c+d*x)^4/d-1/4*b^3*(c+d*x)^4/d-3/2*b^3*d*(c+d*x)^2*coth(e+f*x)/f^2-3*a*b^2*(c+d*x)^3*coth(e+f*x)/f-1/2*b^3*(c+d*x)^3*coth(e+f*x)^2/f+3*b^3*d^2*(c+d*x)*log(1-exp(2*(e+f*x)))/f^3+9*a*b^2*d*(c+d*x)^2*log(1-exp(2*(e+f*x)))/f^2+3*a^2*b*(c+d*x)^3*log(1-exp(2*(e+f*x)))/f+b^3*(c+d*x)^3*log(1-exp(2*(e+f*x)))/f+3/2*b^3*d^3*polylog(2,exp(2*(e+f*x)))/f^4+9*a*b^2*d^2*(c+d*x)*polylog(2,exp(2*(e+f*x)))/f^3+9/2*a^2*b*d*(c+d*x)^2*polylog(2,exp(2*(e+f*x)))/f^2+3/2*b^3*d*(c+d*x)^2*polylog(2,exp(2*(e+f*x)))/f^2-9/2*a*b^2*d^3*polylog(3,exp(2*(e+f*x)))/f^4-9/2*a^2*b*d^2*(c+d*x)*polylog(3,exp(2*(e+f*x)))/f^3-3/2*b^3*d^2*(c+d*x)*polylog(3,exp(2*(e+f*x)))/f^3+9/4*a^2*b*d^3*polylog(4,exp(2*(e+f*x)))/f^4+3/4*b^3*d^3*polylog(4,exp(2*(e+f*x)))/f^4],
[(c+d*x)^2*(a+b*coth(e+f*x))^3,x,22,b^3*c*d*x/f+1/2*b^3*d^2*x^2/f-3*a*b^2*(c+d*x)^2/f+1/3*a^3*(c+d*x)^3/d-a^2*b*(c+d*x)^3/d+a*b^2*(c+d*x)^3/d-1/3*b^3*(c+d*x)^3/d-b^3*d*(c+d*x)*coth(e+f*x)/f^2-3*a*b^2*(c+d*x)^2*coth(e+f*x)/f-1/2*b^3*(c+d*x)^2*coth(e+f*x)^2/f+6*a*b^2*d*(c+d*x)*log(1-exp(2*(e+f*x)))/f^2+3*a^2*b*(c+d*x)^2*log(1-exp(2*(e+f*x)))/f+b^3*(c+d*x)^2*log(1-exp(2*(e+f*x)))/f+b^3*d^2*log(sinh(e+f*x))/f^3+3*a*b^2*d^2*polylog(2,exp(2*(e+f*x)))/f^3+3*a^2*b*d*(c+d*x)*polylog(2,exp(2*(e+f*x)))/f^2+b^3*d*(c+d*x)*polylog(2,exp(2*(e+f*x)))/f^2-3/2*a^2*b*d^2*polylog(3,exp(2*(e+f*x)))/f^3-1/2*b^3*d^2*polylog(3,exp(2*(e+f*x)))/f^3],
[(c+d*x)*(a+b*coth(e+f*x))^3,x,16,3*a*b^2*c*x+1/2*b^3*d*x/f+3/2*a*b^2*d*x^2+1/2*a^3*(c+d*x)^2/d-3/2*a^2*b*(c+d*x)^2/d-1/2*b^3*(c+d*x)^2/d-1/2*b^3*d*coth(e+f*x)/f^2-3*a*b^2*(c+d*x)*coth(e+f*x)/f-1/2*b^3*(c+d*x)*coth(e+f*x)^2/f+3*a^2*b*(c+d*x)*log(1-exp(2*(e+f*x)))/f+b^3*(c+d*x)*log(1-exp(2*(e+f*x)))/f+3*a*b^2*d*log(sinh(e+f*x))/f^2+3/2*a^2*b*d*polylog(2,exp(2*(e+f*x)))/f^2+1/2*b^3*d*polylog(2,exp(2*(e+f*x)))/f^2],
[(a+b*coth(e+f*x))^3/(c+d*x),x,0,Unintegrable((a+b*coth(e+f*x))^3/(c+d*x),x)],
[(a+b*coth(e+f*x))^3/(c+d*x)^2,x,0,Unintegrable((a+b*coth(e+f*x))^3/(c+d*x)^2,x)],

# n<0
[(c+d*x)^3/(a+b*coth(e+f*x)),x,6,1/4*(c+d*x)^4/((a+b)*d)-b*(c+d*x)^3*log(1+(-a+b)/((a+b)*exp(2*(e+f*x))))/((a^2-b^2)*f)+3/2*b*d*(c+d*x)^2*polylog(2,(a-b)/((a+b)*exp(2*(e+f*x))))/((a^2-b^2)*f^2)+3/2*b*d^2*(c+d*x)*polylog(3,(a-b)/((a+b)*exp(2*(e+f*x))))/((a^2-b^2)*f^3)+3/4*b*d^3*polylog(4,(a-b)/((a+b)*exp(2*(e+f*x))))/((a^2-b^2)*f^4)],
[(c+d*x)^2/(a+b*coth(e+f*x)),x,5,1/3*(c+d*x)^3/((a+b)*d)-b*(c+d*x)^2*log(1+(-a+b)/((a+b)*exp(2*(e+f*x))))/((a^2-b^2)*f)+b*d*(c+d*x)*polylog(2,(a-b)/((a+b)*exp(2*(e+f*x))))/((a^2-b^2)*f^2)+1/2*b*d^2*polylog(3,(a-b)/((a+b)*exp(2*(e+f*x))))/((a^2-b^2)*f^3)],
[(c+d*x)/(a+b*coth(e+f*x)),x,4,1/2*(c+d*x)^2/((a+b)*d)-b*(c+d*x)*log(1+(-a+b)/((a+b)*exp(2*(e+f*x))))/((a^2-b^2)*f)+1/2*b*d*polylog(2,(a-b)/((a+b)*exp(2*(e+f*x))))/((a^2-b^2)*f^2)],
[1/((c+d*x)*(a+b*coth(e+f*x))),x,0,Unintegrable(1/((c+d*x)*(a+b*coth(e+f*x))),x)],
[1/((c+d*x)^2*(a+b*coth(e+f*x))),x,0,Unintegrable(1/((c+d*x)^2*(a+b*coth(e+f*x))),x)],
[(c+d*x)^3/(a+b*coth(e+f*x))^2,x,28,-2*b^2*(c+d*x)^3/((a^2-b^2)^2*f)+2*b^2*(c+d*x)^3/((a-b)*(a+b)^2*(a-b-(a+b)*exp(2*e+2*f*x))*f)+1/4*(c+d*x)^4/((a-b)^2*d)+3*b^2*d*(c+d*x)^2*log(1-(a+b)*exp(2*e+2*f*x)/(a-b))/((a^2-b^2)^2*f^2)-2*b*(c+d*x)^3*log(1-(a+b)*exp(2*e+2*f*x)/(a-b))/((a-b)^2*(a+b)*f)+2*b^2*(c+d*x)^3*log(1-(a+b)*exp(2*e+2*f*x)/(a-b))/((a^2-b^2)^2*f)+3*b^2*d^2*(c+d*x)*polylog(2,(a+b)*exp(2*e+2*f*x)/(a-b))/((a^2-b^2)^2*f^3)-3*b*d*(c+d*x)^2*polylog(2,(a+b)*exp(2*e+2*f*x)/(a-b))/((a-b)^2*(a+b)*f^2)+3*b^2*d*(c+d*x)^2*polylog(2,(a+b)*exp(2*e+2*f*x)/(a-b))/((a^2-b^2)^2*f^2)-3/2*b^2*d^3*polylog(3,(a+b)*exp(2*e+2*f*x)/(a-b))/((a^2-b^2)^2*f^4)+3*b*d^2*(c+d*x)*polylog(3,(a+b)*exp(2*e+2*f*x)/(a-b))/((a-b)^2*(a+b)*f^3)-3*b^2*d^2*(c+d*x)*polylog(3,(a+b)*exp(2*e+2*f*x)/(a-b))/((a^2-b^2)^2*f^3)-3/2*b*d^3*polylog(4,(a+b)*exp(2*e+2*f*x)/(a-b))/((a-b)^2*(a+b)*f^4)+3/2*b^2*d^3*polylog(4,(a+b)*exp(2*e+2*f*x)/(a-b))/((a^2-b^2)^2*f^4)],
[(c+d*x)^2/(a+b*coth(e+f*x))^2,x,24,-2*b^2*(c+d*x)^2/((a^2-b^2)^2*f)+2*b^2*(c+d*x)^2/((a-b)*(a+b)^2*(a-b-(a+b)*exp(2*e+2*f*x))*f)+1/3*(c+d*x)^3/((a-b)^2*d)+2*b^2*d*(c+d*x)*log(1-(a+b)*exp(2*e+2*f*x)/(a-b))/((a^2-b^2)^2*f^2)-2*b*(c+d*x)^2*log(1-(a+b)*exp(2*e+2*f*x)/(a-b))/((a-b)^2*(a+b)*f)+2*b^2*(c+d*x)^2*log(1-(a+b)*exp(2*e+2*f*x)/(a-b))/((a^2-b^2)^2*f)+b^2*d^2*polylog(2,(a+b)*exp(2*e+2*f*x)/(a-b))/((a^2-b^2)^2*f^3)-2*b*d*(c+d*x)*polylog(2,(a+b)*exp(2*e+2*f*x)/(a-b))/((a-b)^2*(a+b)*f^2)+2*b^2*d*(c+d*x)*polylog(2,(a+b)*exp(2*e+2*f*x)/(a-b))/((a^2-b^2)^2*f^2)+b*d^2*polylog(3,(a+b)*exp(2*e+2*f*x)/(a-b))/((a-b)^2*(a+b)*f^3)-b^2*d^2*polylog(3,(a+b)*exp(2*e+2*f*x)/(a-b))/((a^2-b^2)^2*f^3)],
[(c+d*x)/(a+b*coth(e+f*x))^2,x,5,-1/2*(c+d*x)^2/((a^2-b^2)*d)+1/4*(b*d-2*a*c*f-2*a*d*f*x)^2/(a*(a-b)*(a+b)^2*d*f^2)+b*(c+d*x)/((a^2-b^2)*f*(a+b*coth(e+f*x)))+b*(b*d-2*a*c*f-2*a*d*f*x)*log(1+(-a+b)/((a+b)*exp(2*(e+f*x))))/((a^2-b^2)^2*f^2)+a*b*d*polylog(2,(a-b)/((a+b)*exp(2*(e+f*x))))/((a^2-b^2)^2*f^2)],
[1/((c+d*x)*(a+b*coth(e+f*x))^2),x,0,Unintegrable(1/((c+d*x)*(a+b*coth(e+f*x))^2),x)],
[1/((c+d*x)^2*(a+b*coth(e+f*x))^2),x,0,Unintegrable(1/((c+d*x)^2*(a+b*coth(e+f*x))^2),x)]]:
