# Maple integration test file: "7 Inverse hyperbolic functions\7.4 Inverse hyperbolic cotangent\7.4.1 Inverse hyperbolic cotangent functions.txt"

lst:=[

# Integrands involving inverse hyperbolic cotangents

# Integrands of the form u ArcCoth[a x]^n

# Integrands of the form x^m ArcCoth[a x]^n

# n>0
[x^5*arccoth(a*x),x,4,1/6*x/a^5+1/18*x^3/a^3+1/30*x^5/a+1/6*x^6*arccoth(a*x)-1/6*arctanh(a*x)/a^6],
[x^4*arccoth(a*x),x,4,1/10*x^2/a^3+1/20*x^4/a+1/5*x^5*arccoth(a*x)+1/10*log(1-a^2*x^2)/a^5],
[x^3*arccoth(a*x),x,4,1/4*x/a^3+1/12*x^3/a+1/4*x^4*arccoth(a*x)-1/4*arctanh(a*x)/a^4],
[x^2*arccoth(a*x),x,4,1/6*x^2/a+1/3*x^3*arccoth(a*x)+1/6*log(1-a^2*x^2)/a^3],
[x*arccoth(a*x),x,3,1/2*x/a+1/2*x^2*arccoth(a*x)-1/2*arctanh(a*x)/a^2],
[arccoth(a*x),x,2,x*arccoth(a*x)+1/2*log(1-a^2*x^2)/a],
[arccoth(a*x)/x,x,1,1/2*polylog(2,(-1)/(a*x))-1/2*polylog(2,1/(a*x))],
[arccoth(a*x)/x^2,x,5,-arccoth(a*x)/x+a*log(x)-1/2*a*log(1-a^2*x^2)],
[arccoth(a*x)/x^3,x,3,-1/2*a/x-1/2*arccoth(a*x)/x^2+1/2*a^2*arctanh(a*x)],
[arccoth(a*x)/x^4,x,4,-1/6*a/x^2-1/3*arccoth(a*x)/x^3+1/3*a^3*log(x)-1/6*a^3*log(1-a^2*x^2)],
[arccoth(a*x)/x^5,x,4,-1/12*a/x^3-1/4*a^3/x-1/4*arccoth(a*x)/x^4+1/4*a^4*arctanh(a*x)],
[x^5*arccoth(a*x)^2,x,15,4/45*x^2/a^4+1/60*x^4/a^2+1/3*x*arccoth(a*x)/a^5+1/9*x^3*arccoth(a*x)/a^3+1/15*x^5*arccoth(a*x)/a-1/6*arccoth(a*x)^2/a^6+1/6*x^6*arccoth(a*x)^2+23/90*log(1-a^2*x^2)/a^6],
[x^4*arccoth(a*x)^2,x,14,3/10*x/a^4+1/30*x^3/a^2+1/5*x^2*arccoth(a*x)/a^3+1/10*x^4*arccoth(a*x)/a+1/5*arccoth(a*x)^2/a^5+1/5*x^5*arccoth(a*x)^2-3/10*arctanh(a*x)/a^5-2/5*arccoth(a*x)*log(2/(1-a*x))/a^5-1/5*polylog(2,1+(-2)/(1-a*x))/a^5],
[x^3*arccoth(a*x)^2,x,10,1/12*x^2/a^2+1/2*x*arccoth(a*x)/a^3+1/6*x^3*arccoth(a*x)/a-1/4*arccoth(a*x)^2/a^4+1/4*x^4*arccoth(a*x)^2+1/3*log(1-a^2*x^2)/a^4],
[x^2*arccoth(a*x)^2,x,9,1/3*x/a^2+1/3*x^2*arccoth(a*x)/a+1/3*arccoth(a*x)^2/a^3+1/3*x^3*arccoth(a*x)^2-1/3*arctanh(a*x)/a^3-2/3*arccoth(a*x)*log(2/(1-a*x))/a^3-1/3*polylog(2,1+(-2)/(1-a*x))/a^3],
[x*arccoth(a*x)^2,x,5,x*arccoth(a*x)/a-1/2*arccoth(a*x)^2/a^2+1/2*x^2*arccoth(a*x)^2+1/2*log(1-a^2*x^2)/a^2],
[arccoth(a*x)^2,x,5,arccoth(a*x)^2/a+x*arccoth(a*x)^2-2*arccoth(a*x)*log(2/(1-a*x))/a-polylog(2,1+(-2)/(1-a*x))/a],
[arccoth(a*x)^2/x,x,6,2*arccoth(a*x)^2*arccoth(1+(-2)/(1-a*x))+arccoth(a*x)*polylog(2,1+(-2)/(1+a*x))-arccoth(a*x)*polylog(2,1-2*a*x/(1+a*x))+1/2*polylog(3,1+(-2)/(1+a*x))-1/2*polylog(3,1-2*a*x/(1+a*x))],
[arccoth(a*x)^2/x^2,x,4,a*arccoth(a*x)^2-arccoth(a*x)^2/x+2*a*arccoth(a*x)*log(2+(-2)/(1+a*x))-a*polylog(2,-1+2/(1+a*x))],
[arccoth(a*x)^2/x^3,x,8,-a*arccoth(a*x)/x+1/2*a^2*arccoth(a*x)^2-1/2*arccoth(a*x)^2/x^2+a^2*log(x)-1/2*a^2*log(1-a^2*x^2)],
[arccoth(a*x)^2/x^4,x,8,-1/3*a^2/x-1/3*a*arccoth(a*x)/x^2+1/3*a^3*arccoth(a*x)^2-1/3*arccoth(a*x)^2/x^3+1/3*a^3*arctanh(a*x)+2/3*a^3*arccoth(a*x)*log(2+(-2)/(1+a*x))-1/3*a^3*polylog(2,-1+2/(1+a*x))],
[arccoth(a*x)^2/x^5,x,13,-1/12*a^2/x^2-1/6*a*arccoth(a*x)/x^3-1/2*a^3*arccoth(a*x)/x+1/4*a^4*arccoth(a*x)^2-1/4*arccoth(a*x)^2/x^4+2/3*a^4*log(x)-1/3*a^4*log(1-a^2*x^2)],
[x^5*arccoth(a*x)^3,x,33,19/60*x/a^5+1/60*x^3/a^3+4/15*x^2*arccoth(a*x)/a^4+1/20*x^4*arccoth(a*x)/a^2+23/30*arccoth(a*x)^2/a^6+1/2*x*arccoth(a*x)^2/a^5+1/6*x^3*arccoth(a*x)^2/a^3+1/10*x^5*arccoth(a*x)^2/a-1/6*arccoth(a*x)^3/a^6+1/6*x^6*arccoth(a*x)^3-19/60*arctanh(a*x)/a^6-23/15*arccoth(a*x)*log(2/(1-a*x))/a^6-23/30*polylog(2,1+(-2)/(1-a*x))/a^6],
[x^4*arccoth(a*x)^3,x,22,1/20*x^2/a^3+9/10*x*arccoth(a*x)/a^4+1/10*x^3*arccoth(a*x)/a^2-9/20*arccoth(a*x)^2/a^5+3/10*x^2*arccoth(a*x)^2/a^3+3/20*x^4*arccoth(a*x)^2/a+1/5*arccoth(a*x)^3/a^5+1/5*x^5*arccoth(a*x)^3-3/5*arccoth(a*x)^2*log(2/(1-a*x))/a^5+1/2*log(1-a^2*x^2)/a^5-3/5*arccoth(a*x)*polylog(2,1+(-2)/(1-a*x))/a^5+3/10*polylog(3,1+(-2)/(1-a*x))/a^5],
[x^3*arccoth(a*x)^3,x,18,1/4*x/a^3+1/4*x^2*arccoth(a*x)/a^2+arccoth(a*x)^2/a^4+3/4*x*arccoth(a*x)^2/a^3+1/4*x^3*arccoth(a*x)^2/a-1/4*arccoth(a*x)^3/a^4+1/4*x^4*arccoth(a*x)^3-1/4*arctanh(a*x)/a^4-2*arccoth(a*x)*log(2/(1-a*x))/a^4-polylog(2,1+(-2)/(1-a*x))/a^4],
[x^2*arccoth(a*x)^3,x,11,x*arccoth(a*x)/a^2-1/2*arccoth(a*x)^2/a^3+1/2*x^2*arccoth(a*x)^2/a+1/3*arccoth(a*x)^3/a^3+1/3*x^3*arccoth(a*x)^3-arccoth(a*x)^2*log(2/(1-a*x))/a^3+1/2*log(1-a^2*x^2)/a^3-arccoth(a*x)*polylog(2,1+(-2)/(1-a*x))/a^3+1/2*polylog(3,1+(-2)/(1-a*x))/a^3],
[x*arccoth(a*x)^3,x,8,3/2*arccoth(a*x)^2/a^2+3/2*x*arccoth(a*x)^2/a-1/2*arccoth(a*x)^3/a^2+1/2*x^2*arccoth(a*x)^3-3*arccoth(a*x)*log(2/(1-a*x))/a^2-3/2*polylog(2,1+(-2)/(1-a*x))/a^2],
[arccoth(a*x)^3,x,5,arccoth(a*x)^3/a+x*arccoth(a*x)^3-3*arccoth(a*x)^2*log(2/(1-a*x))/a-3*arccoth(a*x)*polylog(2,1+(-2)/(1-a*x))/a+3/2*polylog(3,1+(-2)/(1-a*x))/a],
[arccoth(a*x)^3/x,x,8,2*arccoth(a*x)^3*arccoth(1+(-2)/(1-a*x))+3/2*arccoth(a*x)^2*polylog(2,1+(-2)/(1+a*x))-3/2*arccoth(a*x)^2*polylog(2,1-2*a*x/(1+a*x))+3/2*arccoth(a*x)*polylog(3,1+(-2)/(1+a*x))-3/2*arccoth(a*x)*polylog(3,1-2*a*x/(1+a*x))+3/4*polylog(4,1+(-2)/(1+a*x))-3/4*polylog(4,1-2*a*x/(1+a*x))],
[arccoth(a*x)^3/x^2,x,5,a*arccoth(a*x)^3-arccoth(a*x)^3/x+3*a*arccoth(a*x)^2*log(2+(-2)/(1+a*x))-3*a*arccoth(a*x)*polylog(2,-1+2/(1+a*x))-3/2*a*polylog(3,-1+2/(1+a*x))],
[arccoth(a*x)^3/x^3,x,7,3/2*a^2*arccoth(a*x)^2-3/2*a*arccoth(a*x)^2/x+1/2*a^2*arccoth(a*x)^3-1/2*arccoth(a*x)^3/x^2+3*a^2*arccoth(a*x)*log(2+(-2)/(1+a*x))-3/2*a^2*polylog(2,-1+2/(1+a*x))],
[arccoth(a*x)^3/x^4,x,14,-a^2*arccoth(a*x)/x+1/2*a^3*arccoth(a*x)^2-1/2*a*arccoth(a*x)^2/x^2+1/3*a^3*arccoth(a*x)^3-1/3*arccoth(a*x)^3/x^3+a^3*log(x)-1/2*a^3*log(1-a^2*x^2)+a^3*arccoth(a*x)^2*log(2+(-2)/(1+a*x))-a^3*arccoth(a*x)*polylog(2,-1+2/(1+a*x))-1/2*a^3*polylog(3,-1+2/(1+a*x))],
[arccoth(a*x)^3/x^5,x,16,-1/4*a^3/x-1/4*a^2*arccoth(a*x)/x^2+a^4*arccoth(a*x)^2-1/4*a*arccoth(a*x)^2/x^3-3/4*a^3*arccoth(a*x)^2/x+1/4*a^4*arccoth(a*x)^3-1/4*arccoth(a*x)^3/x^4+1/4*a^4*arctanh(a*x)+2*a^4*arccoth(a*x)*log(2+(-2)/(1+a*x))-a^4*polylog(2,-1+2/(1+a*x))],

# n<0

# Integrands of the form (d+e x)^m (a+b ArcCoth[c x])^n
[arccoth(c*x)^2/(d+e*x),x,1,-arccoth(c*x)^2*log(2/(1+c*x))/e+arccoth(c*x)^2*log(2*c*(d+e*x)/((c*d+e)*(1+c*x)))/e+arccoth(c*x)*polylog(2,1+(-2)/(1+c*x))/e-arccoth(c*x)*polylog(2,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/e+1/2*polylog(3,1+(-2)/(1+c*x))/e-1/2*polylog(3,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/e],

# Integrands of the form ArcCoth[a x] (c+d x^2)^p
[(c+d*x^2)^4*arccoth(a*x),x,4,1/630*d*(420*a^6*c^3+378*a^4*c^2*d+180*a^2*c*d^2+35*d^3)*x^2/a^7+1/1260*d^2*(378*a^4*c^2+180*a^2*c*d+35*d^2)*x^4/a^5+1/378*d^3*(36*a^2*c+7*d)*x^6/a^3+1/72*d^4*x^8/a+c^4*x*arccoth(a*x)+4/3*c^3*d*x^3*arccoth(a*x)+6/5*c^2*d^2*x^5*arccoth(a*x)+4/7*c*d^3*x^7*arccoth(a*x)+1/9*d^4*x^9*arccoth(a*x)+1/630*(315*a^8*c^4+420*a^6*c^3*d+378*a^4*c^2*d^2+180*a^2*c*d^3+35*d^4)*log(1-a^2*x^2)/a^9],
[(c+d*x^2)^3*arccoth(a*x),x,4,1/70*d*(35*a^4*c^2+21*a^2*c*d+5*d^2)*x^2/a^5+1/140*d^2*(21*a^2*c+5*d)*x^4/a^3+1/42*d^3*x^6/a+c^3*x*arccoth(a*x)+c^2*d*x^3*arccoth(a*x)+3/5*c*d^2*x^5*arccoth(a*x)+1/7*d^3*x^7*arccoth(a*x)+1/70*(35*a^6*c^3+35*a^4*c^2*d+21*a^2*c*d^2+5*d^3)*log(1-a^2*x^2)/a^7],
[(c+d*x^2)^2*arccoth(a*x),x,5,1/30*d*(10*a^2*c+3*d)*x^2/a^3+1/20*d^2*x^4/a+c^2*x*arccoth(a*x)+2/3*c*d*x^3*arccoth(a*x)+1/5*d^2*x^5*arccoth(a*x)+1/30*(15*a^4*c^2+10*a^2*c*d+3*d^2)*log(1-a^2*x^2)/a^5],
[(c+d*x^2)*arccoth(a*x),x,5,1/6*d*x^2/a+c*x*arccoth(a*x)+1/3*d*x^3*arccoth(a*x)+1/6*(3*a^2*c+d)*log(1-a^2*x^2)/a^3],
[arccoth(a*x)/(c+d*x^2),x,27,-1/2*arctan(x*sqrt(d)/sqrt(c))*log(1+(-1)/(a*x))/(sqrt(c)*sqrt(d))+1/2*arctan(x*sqrt(d)/sqrt(c))*log(1+1/(a*x))/(sqrt(c)*sqrt(d))+1/2*arctan(x*sqrt(d)/sqrt(c))*log(-2*(1-a*x)*sqrt(c)*sqrt(d)/((I*a*sqrt(c)-sqrt(d))*(sqrt(c)-I*x*sqrt(d))))/(sqrt(c)*sqrt(d))-1/2*arctan(x*sqrt(d)/sqrt(c))*log(2*(1+a*x)*sqrt(c)*sqrt(d)/((I*a*sqrt(c)+sqrt(d))*(sqrt(c)-I*x*sqrt(d))))/(sqrt(c)*sqrt(d))-1/4*I*polylog(2,1+2*(1-a*x)*sqrt(c)*sqrt(d)/((I*a*sqrt(c)-sqrt(d))*(sqrt(c)-I*x*sqrt(d))))/(sqrt(c)*sqrt(d))+1/4*I*polylog(2,1-2*(1+a*x)*sqrt(c)*sqrt(d)/((I*a*sqrt(c)+sqrt(d))*(sqrt(c)-I*x*sqrt(d))))/(sqrt(c)*sqrt(d))],
[arccoth(a*x)/(c+d*x^2)^2,x,24,1/2*x*arccoth(a*x)/(c*(c+d*x^2))+1/4*a*log(1-a^2*x^2)/(c*(a^2*c+d))-1/4*a*log(c+d*x^2)/(c*(a^2*c+d))+1/2*arccoth(a*x)*arctan(x*sqrt(d)/sqrt(c))/(c^(3/2)*sqrt(d))-1/8*I*log(-(1+a*x)*sqrt(d)/(I*a*sqrt(c)-sqrt(d)))*log(1-I*x*sqrt(d)/sqrt(c))/(c^(3/2)*sqrt(d))+1/8*I*log((1-a*x)*sqrt(d)/(I*a*sqrt(c)+sqrt(d)))*log(1-I*x*sqrt(d)/sqrt(c))/(c^(3/2)*sqrt(d))-1/8*I*log(-(1-a*x)*sqrt(d)/(I*a*sqrt(c)-sqrt(d)))*log(1+I*x*sqrt(d)/sqrt(c))/(c^(3/2)*sqrt(d))+1/8*I*log((1+a*x)*sqrt(d)/(I*a*sqrt(c)+sqrt(d)))*log(1+I*x*sqrt(d)/sqrt(c))/(c^(3/2)*sqrt(d))+1/8*I*polylog(2,a*(sqrt(c)-I*x*sqrt(d))/(a*sqrt(c)-I*sqrt(d)))/(c^(3/2)*sqrt(d))-1/8*I*polylog(2,a*(sqrt(c)-I*x*sqrt(d))/(a*sqrt(c)+I*sqrt(d)))/(c^(3/2)*sqrt(d))+1/8*I*polylog(2,a*(sqrt(c)+I*x*sqrt(d))/(a*sqrt(c)-I*sqrt(d)))/(c^(3/2)*sqrt(d))-1/8*I*polylog(2,a*(sqrt(c)+I*x*sqrt(d))/(a*sqrt(c)+I*sqrt(d)))/(c^(3/2)*sqrt(d))],
[arccoth(a*x)/(c+d*x^2)^3,x,23,1/8*a/(c*(a^2*c+d)*(c+d*x^2))+1/4*x*arccoth(a*x)/(c*(c+d*x^2)^2)+3/8*x*arccoth(a*x)/(c^2*(c+d*x^2))+1/16*a*(5*a^2*c+3*d)*log(1-a^2*x^2)/(c^2*(a^2*c+d)^2)-1/16*a*(5*a^2*c+3*d)*log(c+d*x^2)/(c^2*(a^2*c+d)^2)+3/8*arccoth(a*x)*arctan(x*sqrt(d)/sqrt(c))/(c^(5/2)*sqrt(d))-3/32*I*log(-(1+a*x)*sqrt(d)/(I*a*sqrt(c)-sqrt(d)))*log(1-I*x*sqrt(d)/sqrt(c))/(c^(5/2)*sqrt(d))+3/32*I*log((1-a*x)*sqrt(d)/(I*a*sqrt(c)+sqrt(d)))*log(1-I*x*sqrt(d)/sqrt(c))/(c^(5/2)*sqrt(d))-3/32*I*log(-(1-a*x)*sqrt(d)/(I*a*sqrt(c)-sqrt(d)))*log(1+I*x*sqrt(d)/sqrt(c))/(c^(5/2)*sqrt(d))+3/32*I*log((1+a*x)*sqrt(d)/(I*a*sqrt(c)+sqrt(d)))*log(1+I*x*sqrt(d)/sqrt(c))/(c^(5/2)*sqrt(d))+3/32*I*polylog(2,a*(sqrt(c)-I*x*sqrt(d))/(a*sqrt(c)-I*sqrt(d)))/(c^(5/2)*sqrt(d))-3/32*I*polylog(2,a*(sqrt(c)-I*x*sqrt(d))/(a*sqrt(c)+I*sqrt(d)))/(c^(5/2)*sqrt(d))+3/32*I*polylog(2,a*(sqrt(c)+I*x*sqrt(d))/(a*sqrt(c)-I*sqrt(d)))/(c^(5/2)*sqrt(d))-3/32*I*polylog(2,a*(sqrt(c)+I*x*sqrt(d))/(a*sqrt(c)+I*sqrt(d)))/(c^(5/2)*sqrt(d))],
[(c+d*x^2)^(1/2)*arccoth(a*x),x,0,Unintegrable(arccoth(a*x)*sqrt(c+d*x^2),x)],
[arccoth(a*x)/(c+d*x^2)^(1/2),x,0,Unintegrable(arccoth(a*x)/sqrt(c+d*x^2),x)],
[arccoth(a*x)/(c+d*x^2)^(3/2),x,5,-arctanh(a*sqrt(c+d*x^2)/sqrt(a^2*c+d))/(c*sqrt(a^2*c+d))+x*arccoth(a*x)/(c*sqrt(c+d*x^2))],
[arccoth(a*x)/(c+d*x^2)^(5/2),x,7,1/3*x*arccoth(a*x)/(c*(c+d*x^2)^(3/2))-1/3*(3*a^2*c+2*d)*arctanh(a*sqrt(c+d*x^2)/sqrt(a^2*c+d))/(c^2*(a^2*c+d)^(3/2))+1/3*a/(c*(a^2*c+d)*sqrt(c+d*x^2))+2/3*x*arccoth(a*x)/(c^2*sqrt(c+d*x^2))],
[arccoth(a*x)/(c+d*x^2)^(7/2),x,8,1/15*a/(c*(a^2*c+d)*(c+d*x^2)^(3/2))+1/5*x*arccoth(a*x)/(c*(c+d*x^2)^(5/2))+4/15*x*arccoth(a*x)/(c^2*(c+d*x^2)^(3/2))-1/15*(15*a^4*c^2+20*a^2*c*d+8*d^2)*arctanh(a*sqrt(c+d*x^2)/sqrt(a^2*c+d))/(c^3*(a^2*c+d)^(5/2))+1/15*a*(7*a^2*c+4*d)/(c^2*(a^2*c+d)^2*sqrt(c+d*x^2))+8/15*x*arccoth(a*x)/(c^3*sqrt(c+d*x^2))],
[arccoth(a*x)/(c+d*x^2)^(9/2),x,8,1/35*a/(c*(a^2*c+d)*(c+d*x^2)^(5/2))+1/105*a*(11*a^2*c+6*d)/(c^2*(a^2*c+d)^2*(c+d*x^2)^(3/2))+1/7*x*arccoth(a*x)/(c*(c+d*x^2)^(7/2))+6/35*x*arccoth(a*x)/(c^2*(c+d*x^2)^(5/2))+8/35*x*arccoth(a*x)/(c^3*(c+d*x^2)^(3/2))-1/35*(35*a^6*c^3+70*a^4*c^2*d+56*a^2*c*d^2+16*d^3)*arctanh(a*sqrt(c+d*x^2)/sqrt(a^2*c+d))/(c^4*(a^2*c+d)^(7/2))+1/35*a*(19*a^4*c^2+22*a^2*c*d+8*d^2)/(c^3*(a^2*c+d)^3*sqrt(c+d*x^2))+16/35*x*arccoth(a*x)/(c^4*sqrt(c+d*x^2))],
[(a-a*x^2)^(1/2)*arccoth(x),x,3,-a*arccoth(x)*arctan(sqrt(1-x)/sqrt(1+x))*sqrt(1-x^2)/sqrt(a-a*x^2)-1/2*I*a*polylog(2,-I*sqrt(1-x)/sqrt(1+x))*sqrt(1-x^2)/sqrt(a-a*x^2)+1/2*I*a*polylog(2,I*sqrt(1-x)/sqrt(1+x))*sqrt(1-x^2)/sqrt(a-a*x^2)+1/2*sqrt(a-a*x^2)+1/2*x*arccoth(x)*sqrt(a-a*x^2)],
[arccoth(x)/(a-a*x^2)^(1/2),x,2,-2*arccoth(x)*arctan(sqrt(1-x)/sqrt(1+x))*sqrt(1-x^2)/sqrt(a-a*x^2)-I*polylog(2,-I*sqrt(1-x)/sqrt(1+x))*sqrt(1-x^2)/sqrt(a-a*x^2)+I*polylog(2,I*sqrt(1-x)/sqrt(1+x))*sqrt(1-x^2)/sqrt(a-a*x^2)],
[arccoth(x)/(a-a*x^2)^(3/2),x,1,(-1)/(a*sqrt(a-a*x^2))+x*arccoth(x)/(a*sqrt(a-a*x^2))],
[arccoth(x)/(a-a*x^2)^(5/2),x,2,(-1/9)/(a*(a-a*x^2)^(3/2))+1/3*x*arccoth(x)/(a*(a-a*x^2)^(3/2))+(-2/3)/(a^2*sqrt(a-a*x^2))+2/3*x*arccoth(x)/(a^2*sqrt(a-a*x^2))],
[arccoth(x)/(a-a*x^2)^(7/2),x,3,(-1/25)/(a*(a-a*x^2)^(5/2))+(-4/45)/(a^2*(a-a*x^2)^(3/2))+1/5*x*arccoth(x)/(a*(a-a*x^2)^(5/2))+4/15*x*arccoth(x)/(a^2*(a-a*x^2)^(3/2))+(-8/15)/(a^3*sqrt(a-a*x^2))+8/15*x*arccoth(x)/(a^3*sqrt(a-a*x^2))],

# Integrands of the form ArcCoth[a x]^m (c+d x^2)^n
[1/((1-x^2)*arccoth(x)),x,1,log(arccoth(x))],
[arccoth(x)^n/(1-x^2),x,1,arccoth(x)^(1+n)/(1+n)],
[arccoth(x)^2/(1-x^2)^2,x,4,1/4*x/(1-x^2)-1/2*arccoth(x)/(1-x^2)+1/2*x*arccoth(x)^2/(1-x^2)+1/6*arccoth(x)^3+1/4*arctanh(x)],

# Integrands of the form x^m ArcCoth[a x] (c+d x^2)^n
[x*arccoth(x)/(1-x^2),x,4,-1/2*arccoth(x)^2+arccoth(x)*log(2/(1-x))+1/2*polylog(2,(1+x)/(-1+x))],
[arccoth(x)/(1-x^2),x,1,1/2*arccoth(x)^2],
[x*arccoth(x)/(1-x^2)^2,x,3,-1/4*x/(1-x^2)+1/2*arccoth(x)/(1-x^2)-1/4*arctanh(x)],
[arccoth(x)/(1-x^2)^2,x,2,(-1/4)/(1-x^2)+1/2*x*arccoth(x)/(1-x^2)+1/4*arccoth(x)^2],
[x*arccoth(x)/(1-x^2)^3,x,4,-1/16*x/(1-x^2)^2-3/32*x/(1-x^2)+1/4*arccoth(x)/(1-x^2)^2-3/32*arctanh(x)],
[arccoth(x)/(1-x^2)^3,x,3,(-1/16)/(1-x^2)^2+(-3/16)/(1-x^2)+1/4*x*arccoth(x)/(1-x^2)^2+3/8*x*arccoth(x)/(1-x^2)+3/16*arccoth(x)^2],

# Integrands of the form u ArcCoth[a+b x]^n

# Integrands of the form x^m ArcCoth[a+b x]^n
[x^3*arccoth(a+b*x),x,7,1/4*(1+6*a^2)*x/b^3-1/2*a*(a+b*x)^2/b^4+1/12*(a+b*x)^3/b^4+1/4*x^4*arccoth(a+b*x)+1/8*(1-a)^4*log(1-a-b*x)/b^4-1/8*(1+a)^4*log(1+a+b*x)/b^4],
[x^2*arccoth(a+b*x),x,7,-a*x/b^2+1/6*(a+b*x)^2/b^3+1/3*x^3*arccoth(a+b*x)+1/6*(1-a)^3*log(1-a-b*x)/b^3+1/6*(1+a)^3*log(1+a+b*x)/b^3],
[x*arccoth(a+b*x),x,7,1/2*x/b+1/2*x^2*arccoth(a+b*x)+1/4*(1-a)^2*log(1-a-b*x)/b^2-1/4*(1+a)^2*log(1+a+b*x)/b^2],
[arccoth(a+b*x),x,3,(a+b*x)*arccoth(a+b*x)/b+1/2*log(1-(a+b*x)^2)/b],
[arccoth(a+b*x)/x,x,5,-arccoth(a+b*x)*log(2/(1+a+b*x))+arccoth(a+b*x)*log(2*b*x/((1-a)*(1+a+b*x)))+1/2*polylog(2,1+(-2)/(1+a+b*x))-1/2*polylog(2,1-2*b*x/((1-a)*(1+a+b*x)))],
[arccoth(a+b*x)/x^2,x,7,-arccoth(a+b*x)/x+b*log(x)/(1-a^2)-1/2*b*log(1-a-b*x)/(1-a)-1/2*b*log(1+a+b*x)/(1+a)],
[arccoth(a+b*x)/x^3,x,5,-1/2*b/((1-a^2)*x)-1/2*arccoth(a+b*x)/x^2+a*b^2*log(x)/(1-a^2)^2-1/4*b^2*log(1-a-b*x)/(1-a)^2+1/4*b^2*log(1+a+b*x)/(1+a)^2],
[x^3*arccoth(a+b*x)^2,x,19,-a*x/b^3+1/12*(a+b*x)^2/b^4+1/2*(1+6*a^2)*(a+b*x)*arccoth(a+b*x)/b^4-a*(a+b*x)^2*arccoth(a+b*x)/b^4+1/6*(a+b*x)^3*arccoth(a+b*x)/b^4-a*(1+a^2)*arccoth(a+b*x)^2/b^4-1/4*(1+6*a^2+a^4)*arccoth(a+b*x)^2/b^4+1/4*x^4*arccoth(a+b*x)^2+a*arctanh(a+b*x)/b^4+2*a*(1+a^2)*arccoth(a+b*x)*log(2/(1-a-b*x))/b^4+1/12*log(1-(a+b*x)^2)/b^4+1/4*(1+6*a^2)*log(1-(a+b*x)^2)/b^4+a*(1+a^2)*polylog(2,(-1-a-b*x)/(1-a-b*x))/b^4],
[x^2*arccoth(a+b*x)^2,x,15,1/3*x/b^2-2*a*(a+b*x)*arccoth(a+b*x)/b^3+1/3*(a+b*x)^2*arccoth(a+b*x)/b^3+1/3*a*(3+a^2)*arccoth(a+b*x)^2/b^3+1/3*(1+3*a^2)*arccoth(a+b*x)^2/b^3+1/3*x^3*arccoth(a+b*x)^2-1/3*arctanh(a+b*x)/b^3-2/3*(1+3*a^2)*arccoth(a+b*x)*log(2/(1-a-b*x))/b^3-a*log(1-(a+b*x)^2)/b^3-1/3*(1+3*a^2)*polylog(2,(-1-a-b*x)/(1-a-b*x))/b^3],
[x*arccoth(a+b*x)^2,x,12,(a+b*x)*arccoth(a+b*x)/b^2-a*arccoth(a+b*x)^2/b^2-1/2*(1+a^2)*arccoth(a+b*x)^2/b^2+1/2*x^2*arccoth(a+b*x)^2+2*a*arccoth(a+b*x)*log(2/(1-a-b*x))/b^2+1/2*log(1-(a+b*x)^2)/b^2+a*polylog(2,(-1-a-b*x)/(1-a-b*x))/b^2],
[arccoth(a+b*x)^2,x,6,arccoth(a+b*x)^2/b+(a+b*x)*arccoth(a+b*x)^2/b-2*arccoth(a+b*x)*log(2/(1-a-b*x))/b-polylog(2,(-1-a-b*x)/(1-a-b*x))/b],
[arccoth(a+b*x)^2/x,x,2,-arccoth(a+b*x)^2*log(2/(1+a+b*x))+arccoth(a+b*x)^2*log(2*b*x/((1-a)*(1+a+b*x)))+arccoth(a+b*x)*polylog(2,1+(-2)/(1+a+b*x))-arccoth(a+b*x)*polylog(2,1-2*b*x/((1-a)*(1+a+b*x)))+1/2*polylog(3,1+(-2)/(1+a+b*x))-1/2*polylog(3,1-2*b*x/((1-a)*(1+a+b*x)))],
[arccoth(a+b*x)^2/x^2,x,17,-arccoth(a+b*x)^2/x+b*arccoth(a+b*x)*log(2/(1-a-b*x))/(1-a)+b*arccoth(a+b*x)*log(2/(1+a+b*x))/(1+a)-2*b*arccoth(a+b*x)*log(2/(1+a+b*x))/(1-a^2)+2*b*arccoth(a+b*x)*log(2*b*x/((1-a)*(1+a+b*x)))/(1-a^2)+1/2*b*polylog(2,(-1-a-b*x)/(1-a-b*x))/(1-a)-1/2*b*polylog(2,1+(-2)/(1+a+b*x))/(1+a)+b*polylog(2,1+(-2)/(1+a+b*x))/(1-a^2)-b*polylog(2,1-2*b*x/((1-a)*(1+a+b*x)))/(1-a^2)],
[arccoth(a+b*x)^2/x^3,x,21,-b*arccoth(a+b*x)/((1-a^2)*x)-1/2*arccoth(a+b*x)^2/x^2+b^2*log(x)/(1-a^2)^2+1/2*b^2*arccoth(a+b*x)*log(2/(1-a-b*x))/(1-a)^2-1/2*b^2*log(1-a-b*x)/((1-a)^2*(1+a))-1/2*b^2*arccoth(a+b*x)*log(2/(1+a+b*x))/(1+a)^2-2*a*b^2*arccoth(a+b*x)*log(2/(1+a+b*x))/(1-a^2)^2+2*a*b^2*arccoth(a+b*x)*log(2*b*x/((1-a)*(1+a+b*x)))/(1-a^2)^2-1/2*b^2*log(1+a+b*x)/((1-a)*(1+a)^2)+1/4*b^2*polylog(2,(-1-a-b*x)/(1-a-b*x))/(1-a)^2+1/4*b^2*polylog(2,1+(-2)/(1+a+b*x))/(1+a)^2+a*b^2*polylog(2,1+(-2)/(1+a+b*x))/(1-a^2)^2-a*b^2*polylog(2,1-2*b*x/((1-a)*(1+a+b*x)))/(1-a^2)^2],

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

#  {ArcCoth[a + b*x]/(c + d*x^3), x, 51, (Log[(d^(1/3)*(1 - a - b*x))/(b*c^(1/3) + (1 - a)*d^(1/3))]*Log[-c^(1/3) - d^(1/3)*x])/(6*c^(2/3)*d^(1/3)) - (Log[-((d^(1/3)*(1 + a + b*x))/(b*c^(1/3) - (1 + a)*d^(1/3)))]*Log[-c^(1/3) - d^(1/3)*x])/(6*c^(2/3)*d^(1/3)) - ((-1)^(1/3)*Log[-((d^(1/3)*(1 - a - b*x))/((-1)^(1/3)*b*c^(1/3) - (1 - a)*d^(1/3)))]*Log[(-1)^(1/3)*c^(1/3) - d^(1/3)*x])/(6*c^(2/3)*d^(1/3)) + ((-1)^(1/3)*Log[(d^(1/3)*(1 + a + b*x))/((-1)^(1/3)*b*c^(1/3) + (1 + a)*d^(1/3))]*Log[(-1)^(1/3)*c^(1/3) - d^(1/3)*x])/(6*c^(2/3)*d^(1/3)) + ((-1)^(2/3)*Log[(d^(1/3)*(1 - a - b*x))/((-1)^(2/3)*b*c^(1/3) + (1 - a)*d^(1/3))]*Log[(-(-1)^(2/3))*c^(1/3) - d^(1/3)*x])/(6*c^(2/3)*d^(1/3)) - ((-1)^(2/3)*Log[-((d^(1/3)*(1 + a + b*x))/((-1)^(2/3)*b*c^(1/3) - (1 + a)*d^(1/3)))]*Log[(-(-1)^(2/3))*c^(1/3) - d^(1/3)*x])/(6*c^(2/3)*d^(1/3)) - (Log[-c^(1/3) - d^(1/3)*x]*Log[1 - 1/(a + b*x)])/(6*c^(2/3)*d^(1/3)) + ((-1)^(1/3)*Log[(-1)^(1/3)*c^(1/3) - d^(1/3)*x]*Log[1 - 1/(a + b*x)])/(6*c^(2/3)*d^(1/3)) - ((-1)^(2/3)*Log[(-(-1)^(2/3))*c^(1/3) - d^(1/3)*x]*Log[1 - 1/(a + b*x)])/(6*c^(2/3)*d^(1/3)) + (Log[-c^(1/3) - d^(1/3)*x]*Log[1 + 1/(a + b*x)])/(6*c^(2/3)*d^(1/3)) - ((-1)^(1/3)*Log[(-1)^(1/3)*c^(1/3) - d^(1/3)*x]*Log[1 + 1/(a + b*x)])/(6*c^(2/3)*d^(1/3)) + ((-1)^(2/3)*Log[(-(-1)^(2/3))*c^(1/3) - d^(1/3)*x]*Log[1 + 1/(a + b*x)])/(6*c^(2/3)*d^(1/3)) + PolyLog[2, (b*(c^(1/3) + d^(1/3)*x))/(b*c^(1/3) + (1 - a)*d^(1/3))]/(6*c^(2/3)*d^(1/3)) - PolyLog[2, (b*(c^(1/3) + d^(1/3)*x))/(b*c^(1/3) - (1 + a)*d^(1/3))]/(6*c^(2/3)*d^(1/3)) + ((-1)^(2/3)*PolyLog[2, (b*((-1)^(2/3)*c^(1/3) + d^(1/3)*x))/((-1)^(2/3)*b*c^(1/3) + (1 - a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) - ((-1)^(2/3)*PolyLog[2, (b*((-1)^(2/3)*c^(1/3) + d^(1/3)*x))/((-1)^(2/3)*b*c^(1/3) - (1 + a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) - ((-1)^(1/3)*PolyLog[2, ((-1)^(1/3)*b*(c^(1/3) + (-1)^(2/3)*d^(1/3)*x))/((-1)^(1/3)*b*c^(1/3) - (1 - a)*d^(1/3))])/(6*c^(2/3)*d^(1/3)) + ((-1)^(1/3)*PolyLog[2, ((-1)^(1/3)*b*(c^(1/3) + (-1)^(2/3)*d^(1/3)*x))/((-1)^(1/3)*b*c^(1/3) + (1 + a)*d^(1/3))])/(6*c^(2/3)*d^(1/3))} 
[arccoth(a+b*x)/(c+d*x^2),x,15,1/4*log((-1+a+b*x)/(a+b*x))*log(1+(b^2*c+a^2*d)*(1-a-b*x)/((a+b*x)*(b^2*c-(1-a)*a*d-b*sqrt(-c)*sqrt(d))))/(sqrt(-c)*sqrt(d))+1/4*log((1+a+b*x)/(a+b*x))*log(1-(b^2*c+a^2*d)*(1+a+b*x)/((a+b*x)*(b^2*c+a*(1+a)*d-b*sqrt(-c)*sqrt(d))))/(sqrt(-c)*sqrt(d))-1/4*log((-1+a+b*x)/(a+b*x))*log(1+(b^2*c+a^2*d)*(1-a-b*x)/((a+b*x)*(b^2*c-(1-a)*a*d+b*sqrt(-c)*sqrt(d))))/(sqrt(-c)*sqrt(d))-1/4*log((1+a+b*x)/(a+b*x))*log(1-(b^2*c+a^2*d)*(1+a+b*x)/((a+b*x)*(b^2*c+a*(1+a)*d+b*sqrt(-c)*sqrt(d))))/(sqrt(-c)*sqrt(d))+1/4*polylog(2,-(b^2*c+a^2*d)*(1-a-b*x)/((a+b*x)*(b^2*c-(1-a)*a*d-b*sqrt(-c)*sqrt(d))))/(sqrt(-c)*sqrt(d))+1/4*polylog(2,(b^2*c+a^2*d)*(1+a+b*x)/((a+b*x)*(b^2*c+a*(1+a)*d-b*sqrt(-c)*sqrt(d))))/(sqrt(-c)*sqrt(d))-1/4*polylog(2,-(b^2*c+a^2*d)*(1-a-b*x)/((a+b*x)*(b^2*c-(1-a)*a*d+b*sqrt(-c)*sqrt(d))))/(sqrt(-c)*sqrt(d))-1/4*polylog(2,(b^2*c+a^2*d)*(1+a+b*x)/((a+b*x)*(b^2*c+a*(1+a)*d+b*sqrt(-c)*sqrt(d))))/(sqrt(-c)*sqrt(d))],
[arccoth(a+b*x)/(c+d*x),x,5,-arccoth(a+b*x)*log(2/(1+a+b*x))/d+arccoth(a+b*x)*log(2*b*(c+d*x)/((b*c+d-a*d)*(1+a+b*x)))/d+1/2*polylog(2,1+(-2)/(1+a+b*x))/d-1/2*polylog(2,1-2*b*(c+d*x)/((b*c+d-a*d)*(1+a+b*x)))/d],
[arccoth(a+b*x)/(c+d/x),x,37,1/2*(1-a-b*x)*log((-1+a+b*x)/(a+b*x))/(b*c)+1/2*log(a+b*x)/(b*c)+1/2*log(1+a+b*x)/(b*c)+1/2*(a+b*x)*log((1+a+b*x)/(a+b*x))/(b*c)-1/2*d*log(c*(1-a-b*x)/(c-a*c+b*d))*log(d+c*x)/c^2+1/2*d*log((-1+a+b*x)/(a+b*x))*log(d+c*x)/c^2+1/2*d*log(c*(1+a+b*x)/(c+a*c-b*d))*log(d+c*x)/c^2-1/2*d*log((1+a+b*x)/(a+b*x))*log(d+c*x)/c^2+1/2*d*polylog(2,-b*(d+c*x)/(c+a*c-b*d))/c^2-1/2*d*polylog(2,b*(d+c*x)/(c-a*c+b*d))/c^2,1/2*(1-a-b*x)*log(-1+a+b*x)/(b*c)+1/2*x*(log(-1+a+b*x)-log((-1+a+b*x)/(a+b*x))-log(a+b*x))/c+1/2*(1+a+b*x)*log(1+a+b*x)/(b*c)+1/2*x*(log(a+b*x)-log(1+a+b*x)+log((1+a+b*x)/(a+b*x)))/c-1/2*d*(log(-1+a+b*x)-log((-1+a+b*x)/(a+b*x))-log(a+b*x))*log(d+c*x)/c^2-1/2*d*(log(a+b*x)-log(1+a+b*x)+log((1+a+b*x)/(a+b*x)))*log(d+c*x)/c^2-1/2*d*log(1+a+b*x)*log(-b*(d+c*x)/(c+a*c-b*d))/c^2+1/2*d*log(-1+a+b*x)*log(b*(d+c*x)/(c-a*c+b*d))/c^2+1/2*d*polylog(2,c*(1-a-b*x)/(c-a*c+b*d))/c^2-1/2*d*polylog(2,c*(1+a+b*x)/(c+a*c-b*d))/c^2],
[arccoth(a+b*x)/(c+d/x^2),x,57,1/2*(1-a-b*x)*log(-1+a+b*x)/(b*c)+1/2*x*(log(-1+a+b*x)-log((-1+a+b*x)/(a+b*x))-log(a+b*x))/c+1/2*(1+a+b*x)*log(1+a+b*x)/(b*c)+1/2*x*(log(a+b*x)-log(1+a+b*x)+log((1+a+b*x)/(a+b*x)))/c-1/2*arctan(x*sqrt(c)/sqrt(d))*(log(-1+a+b*x)-log((-1+a+b*x)/(a+b*x))-log(a+b*x))*sqrt(d)/c^(3/2)-1/2*arctan(x*sqrt(c)/sqrt(d))*(log(a+b*x)-log(1+a+b*x)+log((1+a+b*x)/(a+b*x)))*sqrt(d)/c^(3/2)+1/4*log(-1+a+b*x)*log(-b*(-x*sqrt(-c)+sqrt(d))/((1-a)*sqrt(-c)-b*sqrt(d)))*sqrt(d)/(-c)^(3/2)+1/4*log(1+a+b*x)*log(-b*(x*sqrt(-c)+sqrt(d))/((1+a)*sqrt(-c)-b*sqrt(d)))*sqrt(d)/(-c)^(3/2)-1/4*log(-1+a+b*x)*log(b*(x*sqrt(-c)+sqrt(d))/((1-a)*sqrt(-c)+b*sqrt(d)))*sqrt(d)/(-c)^(3/2)-1/4*log(1+a+b*x)*log(b*(-x*sqrt(-c)+sqrt(d))/((1+a)*sqrt(-c)+b*sqrt(d)))*sqrt(d)/(-c)^(3/2)+1/4*polylog(2,(1-a-b*x)*sqrt(-c)/((1-a)*sqrt(-c)-b*sqrt(d)))*sqrt(d)/(-c)^(3/2)+1/4*polylog(2,(1+a+b*x)*sqrt(-c)/((1+a)*sqrt(-c)-b*sqrt(d)))*sqrt(d)/(-c)^(3/2)-1/4*polylog(2,(1-a-b*x)*sqrt(-c)/((1-a)*sqrt(-c)+b*sqrt(d)))*sqrt(d)/(-c)^(3/2)-1/4*polylog(2,(1+a+b*x)*sqrt(-c)/((1+a)*sqrt(-c)+b*sqrt(d)))*sqrt(d)/(-c)^(3/2)],

#  {ArcCoth[a + b*x]/(c + d/x^3), x, 59, Log[1 - a - b*x]/(2*b*c) + Log[1 + a + b*x]/(2*b*c) - (d^(1/3)*Log[(c^(1/3)*(1 - a - b*x))/((1 - a)*c^(1/3) + b*d^(1/3))]*Log[-d^(1/3) - c^(1/3)*x])/(6*c^(4/3)) + (d^(1/3)*Log[(c^(1/3)*(1 + a + b*x))/((1 + a)*c^(1/3) - b*d^(1/3))]*Log[-d^(1/3) - c^(1/3)*x])/(6*c^(4/3)) + ((-1)^(1/3)*d^(1/3)*Log[(c^(1/3)*(1 - a - b*x))/((1 - a)*c^(1/3) - (-1)^(1/3)*b*d^(1/3))]*Log[(-1)^(1/3)*d^(1/3) - c^(1/3)*x])/(6*c^(4/3)) - ((-1)^(1/3)*d^(1/3)*Log[(c^(1/3)*(1 + a + b*x))/((1 + a)*c^(1/3) + (-1)^(1/3)*b*d^(1/3))]*Log[(-1)^(1/3)*d^(1/3) - c^(1/3)*x])/(6*c^(4/3)) - ((-1)^(2/3)*d^(1/3)*Log[(c^(1/3)*(1 - a - b*x))/((1 - a)*c^(1/3) + (-1)^(2/3)*b*d^(1/3))]*Log[(-(-1)^(2/3))*d^(1/3) - c^(1/3)*x])/(6*c^(4/3)) + ((-1)^(2/3)*d^(1/3)*Log[(c^(1/3)*(1 + a + b*x))/((1 + a)*c^(1/3) - (-1)^(2/3)*b*d^(1/3))]*Log[(-(-1)^(2/3))*d^(1/3) - c^(1/3)*x])/(6*c^(4/3)) - ((a + b*x)*Log[1 - 1/(a + b*x)])/(2*b*c) + (d^(1/3)*Log[-d^(1/3) - c^(1/3)*x]*Log[1 - 1/(a + b*x)])/(6*c^(4/3)) - ((-1)^(1/3)*d^(1/3)*Log[(-1)^(1/3)*d^(1/3) - c^(1/3)*x]*Log[1 - 1/(a + b*x)])/(6*c^(4/3)) + ((-1)^(2/3)*d^(1/3)*Log[(-(-1)^(2/3))*d^(1/3) - c^(1/3)*x]*Log[1 - 1/(a + b*x)])/(6*c^(4/3)) + ((a + b*x)*Log[1 + 1/(a + b*x)])/(2*b*c) - (d^(1/3)*Log[-d^(1/3) - c^(1/3)*x]*Log[1 + 1/(a + b*x)])/(6*c^(4/3)) + ((-1)^(1/3)*d^(1/3)*Log[(-1)^(1/3)*d^(1/3) - c^(1/3)*x]*Log[1 + 1/(a + b*x)])/(6*c^(4/3)) - ((-1)^(2/3)*d^(1/3)*Log[(-(-1)^(2/3))*d^(1/3) - c^(1/3)*x]*Log[1 + 1/(a + b*x)])/(6*c^(4/3)) + (d^(1/3)*PolyLog[2, -((b*(d^(1/3) + c^(1/3)*x))/((1 + a)*c^(1/3) - b*d^(1/3)))])/(6*c^(4/3)) - (d^(1/3)*PolyLog[2, (b*(d^(1/3) + c^(1/3)*x))/((1 - a)*c^(1/3) + b*d^(1/3))])/(6*c^(4/3)) + ((-1)^(2/3)*d^(1/3)*PolyLog[2, -((b*((-1)^(2/3)*d^(1/3) + c^(1/3)*x))/((1 + a)*c^(1/3) - (-1)^(2/3)*b*d^(1/3)))])/(6*c^(4/3)) - ((-1)^(2/3)*d^(1/3)*PolyLog[2, (b*((-1)^(2/3)*d^(1/3) + c^(1/3)*x))/((1 - a)*c^(1/3) + (-1)^(2/3)*b*d^(1/3))])/(6*c^(4/3)) + ((-1)^(1/3)*d^(1/3)*PolyLog[2, -(((-1)^(1/3)*b*(d^(1/3) + (-1)^(2/3)*c^(1/3)*x))/((1 - a)*c^(1/3) - (-1)^(1/3)*b*d^(1/3)))])/(6*c^(4/3)) - ((-1)^(1/3)*d^(1/3)*PolyLog[2, ((-1)^(1/3)*b*(d^(1/3) + (-1)^(2/3)*c^(1/3)*x))/((1 + a)*c^(1/3) + (-1)^(1/3)*b*d^(1/3))])/(6*c^(4/3))} 

#  {ArcCoth[a + b*x]/(a + b*x^(3/2)), x, 131, ((1 - 1/Sqrt[1 + a^(-1)])*Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x])/(Sqrt[-1 - a] + a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) + ((1 + 1/Sqrt[1 + a^(-1)])*Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x])/(Sqrt[-1 - a] + a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 - 1/Sqrt[1 + a^(-1)])*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x])/(Sqrt[-1 - a] - (-1)^(1/3)*a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 + 1/Sqrt[1 + a^(-1)])*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x])/(Sqrt[-1 - a] - (-1)^(1/3)*a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 - 1/Sqrt[1 + a^(-1)])*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x])/(Sqrt[-1 - a] + (-1)^(2/3)*a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 + 1/Sqrt[1 + a^(-1)])*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x])/(Sqrt[-1 - a] + (-1)^(2/3)*a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) - (Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[1 - a] - Sqrt[b]*Sqrt[x])/(Sqrt[1 - a] + a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[1 - a] - Sqrt[b]*Sqrt[x])/(Sqrt[1 - a] - (-1)^(1/3)*a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[1 - a] - Sqrt[b]*Sqrt[x])/(Sqrt[1 - a] + (-1)^(2/3)*a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) - (Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] - Sqrt[b]*Sqrt[x])/(Sqrt[-a] + a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) - ((Sqrt[1 - a] - Sqrt[-a])*Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] - Sqrt[b]*Sqrt[x])/(Sqrt[-a] + a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) - ((Sqrt[1 - a] + Sqrt[-a])*a^(2/3)*Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] - Sqrt[b]*Sqrt[x])/(Sqrt[-a] + a^(1/3)*b^(1/6))])/(6*(-a)^(3/2)*b^(2/3)) - ((-1)^(2/3)*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] - Sqrt[b]*Sqrt[x])/(Sqrt[-a] - (-1)^(1/3)*a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*(Sqrt[1 - a] - Sqrt[-a])*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] - Sqrt[b]*Sqrt[x])/(Sqrt[-a] - (-1)^(1/3)*a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(Sqrt[1 - a] + Sqrt[-a])*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] - Sqrt[b]*Sqrt[x])/(Sqrt[-a] - (-1)^(1/3)*a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] - Sqrt[b]*Sqrt[x])/(Sqrt[-a] + (-1)^(2/3)*a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*(Sqrt[1 - a] - Sqrt[-a])*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] - Sqrt[b]*Sqrt[x])/(Sqrt[-a] + (-1)^(2/3)*a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(Sqrt[1 - a] + Sqrt[-a])*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] - Sqrt[b]*Sqrt[x])/(Sqrt[-a] + (-1)^(2/3)*a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) + ((1 - 1/Sqrt[1 + a^(-1)])*Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x])/(Sqrt[-1 - a] - a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) + ((1 + 1/Sqrt[1 + a^(-1)])*Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x])/(Sqrt[-1 - a] - a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 - 1/Sqrt[1 + a^(-1)])*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x])/(Sqrt[-1 - a] + (-1)^(1/3)*a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 + 1/Sqrt[1 + a^(-1)])*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x])/(Sqrt[-1 - a] + (-1)^(1/3)*a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 - 1/Sqrt[1 + a^(-1)])*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x])/(Sqrt[-1 - a] - (-1)^(2/3)*a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 + 1/Sqrt[1 + a^(-1)])*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x])/(Sqrt[-1 - a] - (-1)^(2/3)*a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) - (Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[1 - a] + Sqrt[b]*Sqrt[x])/(Sqrt[1 - a] - a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[1 - a] + Sqrt[b]*Sqrt[x])/(Sqrt[1 - a] + (-1)^(1/3)*a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[1 - a] + Sqrt[b]*Sqrt[x])/(Sqrt[1 - a] - (-1)^(2/3)*a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) - (Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] + Sqrt[b]*Sqrt[x])/(Sqrt[-a] - a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) - ((Sqrt[1 - a] - Sqrt[-a])*Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] + Sqrt[b]*Sqrt[x])/(Sqrt[-a] - a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) - ((Sqrt[1 - a] + Sqrt[-a])*a^(2/3)*Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] + Sqrt[b]*Sqrt[x])/(Sqrt[-a] - a^(1/3)*b^(1/6))])/(6*(-a)^(3/2)*b^(2/3)) - ((-1)^(2/3)*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] + Sqrt[b]*Sqrt[x])/(Sqrt[-a] + (-1)^(1/3)*a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*(Sqrt[1 - a] - Sqrt[-a])*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] + Sqrt[b]*Sqrt[x])/(Sqrt[-a] + (-1)^(1/3)*a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(Sqrt[1 - a] + Sqrt[-a])*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] + Sqrt[b]*Sqrt[x])/(Sqrt[-a] + (-1)^(1/3)*a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] + Sqrt[b]*Sqrt[x])/(Sqrt[-a] - (-1)^(2/3)*a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*(Sqrt[1 - a] - Sqrt[-a])*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] + Sqrt[b]*Sqrt[x])/(Sqrt[-a] - (-1)^(2/3)*a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(Sqrt[1 - a] + Sqrt[-a])*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[(Sqrt[-a] + Sqrt[b]*Sqrt[x])/(Sqrt[-a] - (-1)^(2/3)*a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) + (Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[1 - (a + b*x)^(-1)])/(3*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[1 - (a + b*x)^(-1)])/(3*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[1 - (a + b*x)^(-1)])/(3*a^(1/3)*b^(2/3)) - (Log[-a^(1/3) - b^(1/3)*Sqrt[x]]*Log[1 + (a + b*x)^(-1)])/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*Log[(-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]]*Log[1 + (a + b*x)^(-1)])/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*Log[-((-1)^(2/3)*a^(1/3)) - b^(1/3)*Sqrt[x]]*Log[1 + (a + b*x)^(-1)])/(3*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 - 1/Sqrt[1 + a^(-1)])*PolyLog[2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]))/(Sqrt[-1 - a] - (-1)^(1/3)*a^(1/3)*b^(1/6)))])/(6*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 + 1/Sqrt[1 + a^(-1)])*PolyLog[2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]))/(Sqrt[-1 - a] - (-1)^(1/3)*a^(1/3)*b^(1/6)))])/(6*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*PolyLog[2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]))/(Sqrt[1 - a] - (-1)^(1/3)*a^(1/3)*b^(1/6)))])/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*PolyLog[2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]))/(Sqrt[-a] - (-1)^(1/3)*a^(1/3)*b^(1/6)))])/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*(Sqrt[1 - a] - Sqrt[-a])*PolyLog[2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]))/(Sqrt[-a] - (-1)^(1/3)*a^(1/3)*b^(1/6)))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(Sqrt[1 - a] + Sqrt[-a])*PolyLog[2, -((b^(1/6)*((-1)^(1/3)*a^(1/3) - b^(1/3)*Sqrt[x]))/(Sqrt[-a] - (-1)^(1/3)*a^(1/3)*b^(1/6)))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) + ((1 - 1/Sqrt[1 + a^(-1)])*PolyLog[2, -((b^(1/6)*(a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-1 - a] - a^(1/3)*b^(1/6)))])/(6*a^(1/3)*b^(2/3)) + ((1 + 1/Sqrt[1 + a^(-1)])*PolyLog[2, -((b^(1/6)*(a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-1 - a] - a^(1/3)*b^(1/6)))])/(6*a^(1/3)*b^(2/3)) - PolyLog[2, -((b^(1/6)*(a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[1 - a] - a^(1/3)*b^(1/6)))]/(3*a^(1/3)*b^(2/3)) - PolyLog[2, -((b^(1/6)*(a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-a] - a^(1/3)*b^(1/6)))]/(3*a^(1/3)*b^(2/3)) - ((Sqrt[1 - a] - Sqrt[-a])*PolyLog[2, -((b^(1/6)*(a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-a] - a^(1/3)*b^(1/6)))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) - ((Sqrt[1 - a] + Sqrt[-a])*a^(2/3)*PolyLog[2, -((b^(1/6)*(a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-a] - a^(1/3)*b^(1/6)))])/(6*(-a)^(3/2)*b^(2/3)) + ((1 - 1/Sqrt[1 + a^(-1)])*PolyLog[2, (b^(1/6)*(a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-1 - a] + a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) + ((1 + 1/Sqrt[1 + a^(-1)])*PolyLog[2, (b^(1/6)*(a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-1 - a] + a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) - PolyLog[2, (b^(1/6)*(a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[1 - a] + a^(1/3)*b^(1/6))]/(3*a^(1/3)*b^(2/3)) - PolyLog[2, (b^(1/6)*(a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-a] + a^(1/3)*b^(1/6))]/(3*a^(1/3)*b^(2/3)) - ((Sqrt[1 - a] - Sqrt[-a])*PolyLog[2, (b^(1/6)*(a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-a] + a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) - ((Sqrt[1 - a] + Sqrt[-a])*a^(2/3)*PolyLog[2, (b^(1/6)*(a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-a] + a^(1/3)*b^(1/6))])/(6*(-a)^(3/2)*b^(2/3)) - ((-1)^(1/3)*(1 - 1/Sqrt[1 + a^(-1)])*PolyLog[2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-1 - a] - (-1)^(2/3)*a^(1/3)*b^(1/6)))])/(6*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 + 1/Sqrt[1 + a^(-1)])*PolyLog[2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-1 - a] - (-1)^(2/3)*a^(1/3)*b^(1/6)))])/(6*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*PolyLog[2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[1 - a] - (-1)^(2/3)*a^(1/3)*b^(1/6)))])/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*PolyLog[2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-a] - (-1)^(2/3)*a^(1/3)*b^(1/6)))])/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*(Sqrt[1 - a] - Sqrt[-a])*PolyLog[2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-a] - (-1)^(2/3)*a^(1/3)*b^(1/6)))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(Sqrt[1 - a] + Sqrt[-a])*PolyLog[2, -((b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-a] - (-1)^(2/3)*a^(1/3)*b^(1/6)))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 - 1/Sqrt[1 + a^(-1)])*PolyLog[2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-1 - a] + (-1)^(2/3)*a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(1 + 1/Sqrt[1 + a^(-1)])*PolyLog[2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-1 - a] + (-1)^(2/3)*a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*PolyLog[2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[1 - a] + (-1)^(2/3)*a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*PolyLog[2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-a] + (-1)^(2/3)*a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) + ((-1)^(1/3)*(Sqrt[1 - a] - Sqrt[-a])*PolyLog[2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-a] + (-1)^(2/3)*a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) - ((-1)^(1/3)*(Sqrt[1 - a] + Sqrt[-a])*PolyLog[2, (b^(1/6)*((-1)^(2/3)*a^(1/3) + b^(1/3)*Sqrt[x]))/(Sqrt[-a] + (-1)^(2/3)*a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 - 1/Sqrt[1 + a^(-1)])*PolyLog[2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*Sqrt[x]))/(Sqrt[-1 - a] + (-1)^(1/3)*a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(1 + 1/Sqrt[1 + a^(-1)])*PolyLog[2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*Sqrt[x]))/(Sqrt[-1 - a] + (-1)^(1/3)*a^(1/3)*b^(1/6))])/(6*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*PolyLog[2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*Sqrt[x]))/(Sqrt[1 - a] + (-1)^(1/3)*a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*PolyLog[2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*Sqrt[x]))/(Sqrt[-a] + (-1)^(1/3)*a^(1/3)*b^(1/6))])/(3*a^(1/3)*b^(2/3)) - ((-1)^(2/3)*(Sqrt[1 - a] - Sqrt[-a])*PolyLog[2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*Sqrt[x]))/(Sqrt[-a] + (-1)^(1/3)*a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3)) + ((-1)^(2/3)*(Sqrt[1 - a] + Sqrt[-a])*PolyLog[2, ((-1)^(1/3)*b^(1/6)*(a^(1/3) + (-1)^(2/3)*b^(1/3)*Sqrt[x]))/(Sqrt[-a] + (-1)^(1/3)*a^(1/3)*b^(1/6))])/(6*Sqrt[-a]*a^(1/3)*b^(2/3))} 
[arccoth(a+b*x)/(c+d*sqrt(x)),x,55,c*log((-1+a+b*x)/(a+b*x))*log(c+d*sqrt(x))/d^2-c*log((1+a+b*x)/(a+b*x))*log(c+d*sqrt(x))/d^2+c*log(c+d*sqrt(x))*log(d*(sqrt(-1-a)-sqrt(b)*sqrt(x))/(d*sqrt(-1-a)+c*sqrt(b)))/d^2-c*log(c+d*sqrt(x))*log(d*(sqrt(1-a)-sqrt(b)*sqrt(x))/(d*sqrt(1-a)+c*sqrt(b)))/d^2+c*log(c+d*sqrt(x))*log(-d*(sqrt(-1-a)+sqrt(b)*sqrt(x))/(-d*sqrt(-1-a)+c*sqrt(b)))/d^2-c*log(c+d*sqrt(x))*log(-d*(sqrt(1-a)+sqrt(b)*sqrt(x))/(-d*sqrt(1-a)+c*sqrt(b)))/d^2+c*polylog(2,sqrt(b)*(c+d*sqrt(x))/(-d*sqrt(-1-a)+c*sqrt(b)))/d^2+c*polylog(2,sqrt(b)*(c+d*sqrt(x))/(d*sqrt(-1-a)+c*sqrt(b)))/d^2-c*polylog(2,sqrt(b)*(c+d*sqrt(x))/(-d*sqrt(1-a)+c*sqrt(b)))/d^2-c*polylog(2,sqrt(b)*(c+d*sqrt(x))/(d*sqrt(1-a)+c*sqrt(b)))/d^2-2*arctanh(sqrt(b)*sqrt(x)/sqrt(1-a))*sqrt(1-a)/(d*sqrt(b))+2*arctan(sqrt(b)*sqrt(x)/sqrt(1+a))*sqrt(1+a)/(d*sqrt(b))-log((-1+a+b*x)/(a+b*x))*sqrt(x)/d+log((1+a+b*x)/(a+b*x))*sqrt(x)/d],
[arccoth(a+b*x)/(c+d/sqrt(x)),x,65,1/2*(1-a)*log(1-a-b*x)/(b*c)-1/2*x*log((-1+a+b*x)/(a+b*x))/c+1/2*(1+a)*log(1+a+b*x)/(b*c)+1/2*x*log((1+a+b*x)/(a+b*x))/c-d^2*log((-1+a+b*x)/(a+b*x))*log(d+c*sqrt(x))/c^3+d^2*log((1+a+b*x)/(a+b*x))*log(d+c*sqrt(x))/c^3-d^2*log(d+c*sqrt(x))*log(c*(sqrt(-1-a)-sqrt(b)*sqrt(x))/(c*sqrt(-1-a)+d*sqrt(b)))/c^3+d^2*log(d+c*sqrt(x))*log(c*(sqrt(1-a)-sqrt(b)*sqrt(x))/(c*sqrt(1-a)+d*sqrt(b)))/c^3-d^2*log(d+c*sqrt(x))*log(c*(sqrt(-1-a)+sqrt(b)*sqrt(x))/(c*sqrt(-1-a)-d*sqrt(b)))/c^3+d^2*log(d+c*sqrt(x))*log(c*(sqrt(1-a)+sqrt(b)*sqrt(x))/(c*sqrt(1-a)-d*sqrt(b)))/c^3-d^2*polylog(2,-sqrt(b)*(d+c*sqrt(x))/(c*sqrt(-1-a)-d*sqrt(b)))/c^3+d^2*polylog(2,-sqrt(b)*(d+c*sqrt(x))/(c*sqrt(1-a)-d*sqrt(b)))/c^3-d^2*polylog(2,sqrt(b)*(d+c*sqrt(x))/(c*sqrt(-1-a)+d*sqrt(b)))/c^3+d^2*polylog(2,sqrt(b)*(d+c*sqrt(x))/(c*sqrt(1-a)+d*sqrt(b)))/c^3+2*d*arctanh(sqrt(b)*sqrt(x)/sqrt(1-a))*sqrt(1-a)/(c^2*sqrt(b))-2*d*arctan(sqrt(b)*sqrt(x)/sqrt(1+a))*sqrt(1+a)/(c^2*sqrt(b))+d*log((-1+a+b*x)/(a+b*x))*sqrt(x)/c^2-d*log((1+a+b*x)/(a+b*x))*sqrt(x)/c^2],

#  {ArcCoth[a + b*x]/(a + b/x^(3/2)), x, 145, -((1 - 1/Sqrt[1 + a^(-1)])*b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) + b^(5/6))])/(6*a^(5/3)) - ((1 + 1/Sqrt[1 + a^(-1)])*b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) + b^(5/6))])/(6*a^(5/3)) - ((-1)^(2/3)*(1 - 1/Sqrt[1 + a^(-1)])*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) - (-1)^(1/3)*b^(5/6))])/(6*a^(5/3)) - ((-1)^(2/3)*(1 + 1/Sqrt[1 + a^(-1)])*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) - (-1)^(1/3)*b^(5/6))])/(6*a^(5/3)) + ((-1)^(1/3)*(1 - 1/Sqrt[1 + a^(-1)])*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) + (-1)^(2/3)*b^(5/6))])/(6*a^(5/3)) + ((-1)^(1/3)*(1 + 1/Sqrt[1 + a^(-1)])*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) + (-1)^(2/3)*b^(5/6))])/(6*a^(5/3)) + (b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[1 - a]*a^(1/3) + b^(5/6))])/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[1 - a]*a^(1/3) - (-1)^(1/3)*b^(5/6))])/(3*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[1 - a] - Sqrt[b]*Sqrt[x]))/(Sqrt[1 - a]*a^(1/3) + (-1)^(2/3)*b^(5/6))])/(3*a^(5/3)) + (b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + b^(5/6))])/(3*a^(5/3)) + ((Sqrt[1 - a] - Sqrt[-a])*b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + b^(5/6))])/(6*Sqrt[-a]*a^(5/3)) - ((Sqrt[1 - a] + Sqrt[-a])*b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + b^(5/6))])/(6*Sqrt[-a]*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + (-1)^(2/3)*b^(5/6))])/(3*a^(5/3)) - ((-1)^(1/3)*(Sqrt[1 - a] - Sqrt[-a])*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + (-1)^(2/3)*b^(5/6))])/(6*Sqrt[-a]*a^(5/3)) - ((-1)^(1/3)*(Sqrt[1 - a] + Sqrt[-a])*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-a] - Sqrt[b]*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + (-1)^(2/3)*b^(5/6))])/(6*(-a)^(3/2)*a^(2/3)) + ((-1)^(2/3)*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[-((Sqrt[-a]*a^(1/3)*(Sqrt[-a] - Sqrt[b]*Sqrt[x]))/(a^(4/3) + (-1)^(1/3)*Sqrt[-a]*b^(5/6)))])/(3*a^(5/3)) + ((-1)^(2/3)*(Sqrt[1 - a] - Sqrt[-a])*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[-((Sqrt[-a]*a^(1/3)*(Sqrt[-a] - Sqrt[b]*Sqrt[x]))/(a^(4/3) + (-1)^(1/3)*Sqrt[-a]*b^(5/6)))])/(6*Sqrt[-a]*a^(5/3)) + ((-1)^(2/3)*(Sqrt[1 - a] + Sqrt[-a])*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[-((Sqrt[-a]*a^(1/3)*(Sqrt[-a] - Sqrt[b]*Sqrt[x]))/(a^(4/3) + (-1)^(1/3)*Sqrt[-a]*b^(5/6)))])/(6*(-a)^(3/2)*a^(2/3)) - ((1 - 1/Sqrt[1 + a^(-1)])*b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) - b^(5/6))])/(6*a^(5/3)) - ((1 + 1/Sqrt[1 + a^(-1)])*b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) - b^(5/6))])/(6*a^(5/3)) - ((-1)^(2/3)*(1 - 1/Sqrt[1 + a^(-1)])*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) + (-1)^(1/3)*b^(5/6))])/(6*a^(5/3)) - ((-1)^(2/3)*(1 + 1/Sqrt[1 + a^(-1)])*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) + (-1)^(1/3)*b^(5/6))])/(6*a^(5/3)) + ((-1)^(1/3)*(1 - 1/Sqrt[1 + a^(-1)])*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) - (-1)^(2/3)*b^(5/6))])/(6*a^(5/3)) + ((-1)^(1/3)*(1 + 1/Sqrt[1 + a^(-1)])*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) - (-1)^(2/3)*b^(5/6))])/(6*a^(5/3)) + (b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[1 - a]*a^(1/3) - b^(5/6))])/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[1 - a]*a^(1/3) + (-1)^(1/3)*b^(5/6))])/(3*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[1 - a] + Sqrt[b]*Sqrt[x]))/(Sqrt[1 - a]*a^(1/3) - (-1)^(2/3)*b^(5/6))])/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-a] + Sqrt[b]*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + (-1)^(1/3)*b^(5/6))])/(3*a^(5/3)) + ((-1)^(2/3)*(Sqrt[1 - a] - Sqrt[-a])*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-a] + Sqrt[b]*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + (-1)^(1/3)*b^(5/6))])/(6*Sqrt[-a]*a^(5/3)) + ((-1)^(2/3)*(Sqrt[1 - a] + Sqrt[-a])*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[(a^(1/3)*(Sqrt[-a] + Sqrt[b]*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + (-1)^(1/3)*b^(5/6))])/(6*(-a)^(3/2)*a^(2/3)) + (b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[-((Sqrt[-a]*a^(1/3)*(Sqrt[-a] + Sqrt[b]*Sqrt[x]))/(a^(4/3) + Sqrt[-a]*b^(5/6)))])/(3*a^(5/3)) + ((Sqrt[1 - a] - Sqrt[-a])*b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[-((Sqrt[-a]*a^(1/3)*(Sqrt[-a] + Sqrt[b]*Sqrt[x]))/(a^(4/3) + Sqrt[-a]*b^(5/6)))])/(6*Sqrt[-a]*a^(5/3)) - ((Sqrt[1 - a] + Sqrt[-a])*b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[-((Sqrt[-a]*a^(1/3)*(Sqrt[-a] + Sqrt[b]*Sqrt[x]))/(a^(4/3) + Sqrt[-a]*b^(5/6)))])/(6*Sqrt[-a]*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[-((Sqrt[-a]*a^(1/3)*(Sqrt[-a] + Sqrt[b]*Sqrt[x]))/(a^(4/3) + (-1)^(2/3)*Sqrt[-a]*b^(5/6)))])/(3*a^(5/3)) - ((-1)^(1/3)*(Sqrt[1 - a] - Sqrt[-a])*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[-((Sqrt[-a]*a^(1/3)*(Sqrt[-a] + Sqrt[b]*Sqrt[x]))/(a^(4/3) + (-1)^(2/3)*Sqrt[-a]*b^(5/6)))])/(6*Sqrt[-a]*a^(5/3)) - ((-1)^(1/3)*(Sqrt[1 - a] + Sqrt[-a])*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[-((Sqrt[-a]*a^(1/3)*(Sqrt[-a] + Sqrt[b]*Sqrt[x]))/(a^(4/3) + (-1)^(2/3)*Sqrt[-a]*b^(5/6)))])/(6*(-a)^(3/2)*a^(2/3)) + ((1 - a)*Log[1 - a - b*x])/(2*a*b) + ((1 + a)*Log[1 + a + b*x])/(2*a*b) - (x*Log[1 - (a + b*x)^(-1)])/(2*a) - (b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[1 - (a + b*x)^(-1)])/(3*a^(5/3)) - ((-1)^(2/3)*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[1 - (a + b*x)^(-1)])/(3*a^(5/3)) + ((-1)^(1/3)*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[1 - (a + b*x)^(-1)])/(3*a^(5/3)) + (x*Log[1 + (a + b*x)^(-1)])/(2*a) + (b^(2/3)*Log[-b^(1/3) - a^(1/3)*Sqrt[x]]*Log[1 + (a + b*x)^(-1)])/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*Log[(-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]]*Log[1 + (a + b*x)^(-1)])/(3*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*Log[-((-1)^(2/3)*b^(1/3)) - a^(1/3)*Sqrt[x]]*Log[1 + (a + b*x)^(-1)])/(3*a^(5/3)) - ((-1)^(2/3)*(1 - 1/Sqrt[1 + a^(-1)])*b^(2/3)*PolyLog[2, -((Sqrt[b]*((-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) - (-1)^(1/3)*b^(5/6)))])/(6*a^(5/3)) - ((-1)^(2/3)*(1 + 1/Sqrt[1 + a^(-1)])*b^(2/3)*PolyLog[2, -((Sqrt[b]*((-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) - (-1)^(1/3)*b^(5/6)))])/(6*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*PolyLog[2, -((Sqrt[b]*((-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]))/(Sqrt[1 - a]*a^(1/3) - (-1)^(1/3)*b^(5/6)))])/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*PolyLog[2, -((Sqrt[b]*((-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]))/(Sqrt[-a]*a^(1/3) - (-1)^(1/3)*b^(5/6)))])/(3*a^(5/3)) + ((-1)^(2/3)*(Sqrt[1 - a] - Sqrt[-a])*b^(2/3)*PolyLog[2, -((Sqrt[b]*((-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]))/(Sqrt[-a]*a^(1/3) - (-1)^(1/3)*b^(5/6)))])/(6*Sqrt[-a]*a^(5/3)) + ((-1)^(2/3)*(Sqrt[1 - a] + Sqrt[-a])*b^(2/3)*PolyLog[2, -((Sqrt[b]*((-1)^(1/3)*b^(1/3) - a^(1/3)*Sqrt[x]))/(Sqrt[-a]*a^(1/3) - (-1)^(1/3)*b^(5/6)))])/(6*(-a)^(3/2)*a^(2/3)) - ((1 - 1/Sqrt[1 + a^(-1)])*b^(2/3)*PolyLog[2, -((Sqrt[b]*(b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) - b^(5/6)))])/(6*a^(5/3)) - ((1 + 1/Sqrt[1 + a^(-1)])*b^(2/3)*PolyLog[2, -((Sqrt[b]*(b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) - b^(5/6)))])/(6*a^(5/3)) + (b^(2/3)*PolyLog[2, -((Sqrt[b]*(b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[1 - a]*a^(1/3) - b^(5/6)))])/(3*a^(5/3)) - ((1 - 1/Sqrt[1 + a^(-1)])*b^(2/3)*PolyLog[2, (Sqrt[b]*(b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) + b^(5/6))])/(6*a^(5/3)) - ((1 + 1/Sqrt[1 + a^(-1)])*b^(2/3)*PolyLog[2, (Sqrt[b]*(b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) + b^(5/6))])/(6*a^(5/3)) + (b^(2/3)*PolyLog[2, (Sqrt[b]*(b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[1 - a]*a^(1/3) + b^(5/6))])/(3*a^(5/3)) + (b^(2/3)*PolyLog[2, (Sqrt[b]*(b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + b^(5/6))])/(3*a^(5/3)) + ((Sqrt[1 - a] - Sqrt[-a])*b^(2/3)*PolyLog[2, (Sqrt[b]*(b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + b^(5/6))])/(6*Sqrt[-a]*a^(5/3)) - ((Sqrt[1 - a] + Sqrt[-a])*b^(2/3)*PolyLog[2, (Sqrt[b]*(b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + b^(5/6))])/(6*Sqrt[-a]*a^(5/3)) + (b^(2/3)*PolyLog[2, (Sqrt[b]*(b^(1/3) + a^(1/3)*Sqrt[x]))/(a^(4/3)/Sqrt[-a] + b^(5/6))])/(3*a^(5/3)) + ((Sqrt[1 - a] - Sqrt[-a])*b^(2/3)*PolyLog[2, (Sqrt[b]*(b^(1/3) + a^(1/3)*Sqrt[x]))/(a^(4/3)/Sqrt[-a] + b^(5/6))])/(6*Sqrt[-a]*a^(5/3)) - ((Sqrt[1 - a] + Sqrt[-a])*b^(2/3)*PolyLog[2, (Sqrt[b]*(b^(1/3) + a^(1/3)*Sqrt[x]))/(a^(4/3)/Sqrt[-a] + b^(5/6))])/(6*Sqrt[-a]*a^(5/3)) + ((-1)^(1/3)*(1 - 1/Sqrt[1 + a^(-1)])*b^(2/3)*PolyLog[2, -((Sqrt[b]*((-1)^(2/3)*b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) - (-1)^(2/3)*b^(5/6)))])/(6*a^(5/3)) + ((-1)^(1/3)*(1 + 1/Sqrt[1 + a^(-1)])*b^(2/3)*PolyLog[2, -((Sqrt[b]*((-1)^(2/3)*b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) - (-1)^(2/3)*b^(5/6)))])/(6*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*PolyLog[2, -((Sqrt[b]*((-1)^(2/3)*b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[1 - a]*a^(1/3) - (-1)^(2/3)*b^(5/6)))])/(3*a^(5/3)) + ((-1)^(1/3)*(1 - 1/Sqrt[1 + a^(-1)])*b^(2/3)*PolyLog[2, (Sqrt[b]*((-1)^(2/3)*b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) + (-1)^(2/3)*b^(5/6))])/(6*a^(5/3)) + ((-1)^(1/3)*(1 + 1/Sqrt[1 + a^(-1)])*b^(2/3)*PolyLog[2, (Sqrt[b]*((-1)^(2/3)*b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) + (-1)^(2/3)*b^(5/6))])/(6*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*PolyLog[2, (Sqrt[b]*((-1)^(2/3)*b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[1 - a]*a^(1/3) + (-1)^(2/3)*b^(5/6))])/(3*a^(5/3)) - ((-1)^(1/3)*b^(2/3)*PolyLog[2, (Sqrt[b]*((-1)^(2/3)*b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + (-1)^(2/3)*b^(5/6))])/(3*a^(5/3)) - ((-1)^(1/3)*(Sqrt[1 - a] - Sqrt[-a])*b^(2/3)*PolyLog[2, (Sqrt[b]*((-1)^(2/3)*b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + (-1)^(2/3)*b^(5/6))])/(6*Sqrt[-a]*a^(5/3)) - ((-1)^(1/3)*(Sqrt[1 - a] + Sqrt[-a])*b^(2/3)*PolyLog[2, (Sqrt[b]*((-1)^(2/3)*b^(1/3) + a^(1/3)*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + (-1)^(2/3)*b^(5/6))])/(6*(-a)^(3/2)*a^(2/3)) - ((-1)^(1/3)*b^(2/3)*PolyLog[2, (Sqrt[b]*((-1)^(2/3)*b^(1/3) + a^(1/3)*Sqrt[x]))/(a^(4/3)/Sqrt[-a] + (-1)^(2/3)*b^(5/6))])/(3*a^(5/3)) - ((-1)^(1/3)*(Sqrt[1 - a] - Sqrt[-a])*b^(2/3)*PolyLog[2, (Sqrt[b]*((-1)^(2/3)*b^(1/3) + a^(1/3)*Sqrt[x]))/(a^(4/3)/Sqrt[-a] + (-1)^(2/3)*b^(5/6))])/(6*Sqrt[-a]*a^(5/3)) - ((-1)^(1/3)*(Sqrt[1 - a] + Sqrt[-a])*b^(2/3)*PolyLog[2, (Sqrt[b]*((-1)^(2/3)*b^(1/3) + a^(1/3)*Sqrt[x]))/(a^(4/3)/Sqrt[-a] + (-1)^(2/3)*b^(5/6))])/(6*(-a)^(3/2)*a^(2/3)) - ((-1)^(2/3)*(1 - 1/Sqrt[1 + a^(-1)])*b^(2/3)*PolyLog[2, ((-1)^(1/3)*Sqrt[b]*(b^(1/3) + (-1)^(2/3)*a^(1/3)*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) + (-1)^(1/3)*b^(5/6))])/(6*a^(5/3)) - ((-1)^(2/3)*(1 + 1/Sqrt[1 + a^(-1)])*b^(2/3)*PolyLog[2, ((-1)^(1/3)*Sqrt[b]*(b^(1/3) + (-1)^(2/3)*a^(1/3)*Sqrt[x]))/(Sqrt[-1 - a]*a^(1/3) + (-1)^(1/3)*b^(5/6))])/(6*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*PolyLog[2, ((-1)^(1/3)*Sqrt[b]*(b^(1/3) + (-1)^(2/3)*a^(1/3)*Sqrt[x]))/(Sqrt[1 - a]*a^(1/3) + (-1)^(1/3)*b^(5/6))])/(3*a^(5/3)) + ((-1)^(2/3)*b^(2/3)*PolyLog[2, ((-1)^(1/3)*Sqrt[b]*(b^(1/3) + (-1)^(2/3)*a^(1/3)*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + (-1)^(1/3)*b^(5/6))])/(3*a^(5/3)) + ((-1)^(2/3)*(Sqrt[1 - a] - Sqrt[-a])*b^(2/3)*PolyLog[2, ((-1)^(1/3)*Sqrt[b]*(b^(1/3) + (-1)^(2/3)*a^(1/3)*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + (-1)^(1/3)*b^(5/6))])/(6*Sqrt[-a]*a^(5/3)) + ((-1)^(2/3)*(Sqrt[1 - a] + Sqrt[-a])*b^(2/3)*PolyLog[2, ((-1)^(1/3)*Sqrt[b]*(b^(1/3) + (-1)^(2/3)*a^(1/3)*Sqrt[x]))/(Sqrt[-a]*a^(1/3) + (-1)^(1/3)*b^(5/6))])/(6*(-a)^(3/2)*a^(2/3))} 

# Integrands of the form ArcCoth[a+b x] / (c+d x+e x^2)
[arccoth(d+e*x)/(a+b*x+c*x^2),x,12,arccoth(d+e*x)*log(2*e*(b+2*c*x-sqrt(b^2-4*a*c))/((1+d+e*x)*(2*c*(1-d)+e*(b-sqrt(b^2-4*a*c)))))/sqrt(b^2-4*a*c)-arccoth(d+e*x)*log(2*e*(b+2*c*x+sqrt(b^2-4*a*c))/((1+d+e*x)*(2*c*(1-d)+e*(b+sqrt(b^2-4*a*c)))))/sqrt(b^2-4*a*c)-1/2*polylog(2,1+2*(2*c*d-2*c*(d+e*x)-e*(b-sqrt(b^2-4*a*c)))/((1+d+e*x)*(2*c-2*c*d+b*e-e*sqrt(b^2-4*a*c))))/sqrt(b^2-4*a*c)+1/2*polylog(2,1+2*(2*c*d-2*c*(d+e*x)-e*(b+sqrt(b^2-4*a*c)))/((1+d+e*x)*(2*c*(1-d)+e*(b+sqrt(b^2-4*a*c)))))/sqrt(b^2-4*a*c)],

# Integrands of the form u ArcCoth[a x^n]

# Integrands of the form x^m ArcCoth[a x^n]

# n>0
[x^2*arccoth(sqrt(x)),x,6,1/9*x^(3/2)+1/15*x^(5/2)+1/3*x^3*arccoth(sqrt(x))-1/3*arctanh(sqrt(x))+1/3*sqrt(x)],
[x*arccoth(sqrt(x)),x,5,1/6*x^(3/2)+1/2*x^2*arccoth(sqrt(x))-1/2*arctanh(sqrt(x))+1/2*sqrt(x)],
[arccoth(sqrt(x)),x,4,x*arccoth(sqrt(x))-arctanh(sqrt(x))+sqrt(x)],
[arccoth(sqrt(x))/x,x,2,polylog(2,(-1)/sqrt(x))-polylog(2,1/sqrt(x))],
[arccoth(sqrt(x))/x^2,x,4,-arccoth(sqrt(x))/x+arctanh(sqrt(x))+(-1)/sqrt(x)],
[arccoth(sqrt(x))/x^3,x,5,(-1/6)/x^(3/2)-1/2*arccoth(sqrt(x))/x^2+1/2*arctanh(sqrt(x))+(-1/2)/sqrt(x)],
[x^(3/2)*arccoth(sqrt(x)),x,3,1/5*x+1/10*x^2+2/5*x^(5/2)*arccoth(sqrt(x))+1/5*log(1-x)],
[arccoth(sqrt(x))*sqrt(x),x,3,1/3*x+2/3*x^(3/2)*arccoth(sqrt(x))+1/3*log(1-x)],
[arccoth(sqrt(x))/sqrt(x),x,2,log(1-x)+2*arccoth(sqrt(x))*sqrt(x)],
[arccoth(sqrt(x))/x^(3/2),x,4,-log(1-x)+log(x)-2*arccoth(sqrt(x))/sqrt(x)],
[arccoth(a*x^5)/x,x,2,1/10*polylog(2,(-1)/(a*x^5))-1/10*polylog(2,1/(a*x^5))],

# n<0
[arccoth(1/x),x,3,x*arccoth(1/x)+1/2*log(1-x^2)],

# n symbolic
[arccoth(a*x^n)/x,x,2,1/2*polylog(2,(-1)/(a*x^n))/n-1/2*polylog(2,1/(a*x^n))/n],

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

# Integrands of the form (e+f x)^m (a+b ArcCoth[c+d x])^p when d e-c f=0
[(a+b*x)*arccoth(a+b*x),x,4,1/2*x+1/2*(a+b*x)^2*arccoth(a+b*x)/b-1/2*arctanh(a+b*x)/b],
[(a+b*x)^2*arccoth(a+b*x),x,5,1/6*(a+b*x)^2/b+1/3*(a+b*x)^3*arccoth(a+b*x)/b+1/6*log(1-(a+b*x)^2)/b],
[arccoth(a+b*x)/(a+b*x),x,2,1/2*polylog(2,(-1)/(a+b*x))/b-1/2*polylog(2,1/(a+b*x))/b],
[arccoth(a+b*x)/(a+b*x)^2,x,6,-arccoth(a+b*x)/(b*(a+b*x))+log(a+b*x)/b-1/2*log(1-(a+b*x)^2)/b],
[arccoth(1+x)/(2+2*x),x,3,1/4*polylog(2,(-1)/(1+x))-1/4*polylog(2,1/(1+x))],
[arccoth(a+b*x)/(a*d/b+d*x),x,3,1/2*polylog(2,(-1)/(a+b*x))/d-1/2*polylog(2,1/(a+b*x))/d],

# Integrands of the form (e+f x)^m (a+b ArcCoth[c+d x])^p
[(e+f*x)^3*(a+b*arccoth(c+d*x)),x,7,1/4*b*f*(6*d^2*e^2-12*c*d*e*f+(1+6*c^2)*f^2)*x/d^3+1/2*b*f^2*(d*e-c*f)*(c+d*x)^2/d^4+1/12*b*f^3*(c+d*x)^3/d^4+1/4*(e+f*x)^4*(a+b*arccoth(c+d*x))/f+1/8*b*(d*e+f-c*f)^4*log(1-c-d*x)/(d^4*f)-1/8*b*(d*e-f-c*f)^4*log(1+c+d*x)/(d^4*f)],
[(e+f*x)^2*(a+b*arccoth(c+d*x)),x,7,b*f*(d*e-c*f)*x/d^2+1/6*b*f^2*(c+d*x)^2/d^3+1/3*(e+f*x)^3*(a+b*arccoth(c+d*x))/f+1/6*b*(d*e+f-c*f)^3*log(1-c-d*x)/(d^3*f)-1/6*b*(d*e-(1+c)*f)^3*log(1+c+d*x)/(d^3*f)],
[(e+f*x)*(a+b*arccoth(c+d*x)),x,7,1/2*b*f*x/d+1/2*(e+f*x)^2*(a+b*arccoth(c+d*x))/f+1/4*b*(d*e+f-c*f)^2*log(1-c-d*x)/(d^2*f)-1/4*b*(d*e-(1+c)*f)^2*log(1+c+d*x)/(d^2*f)],
[a+b*arccoth(c+d*x),x,4,a*x+b*(c+d*x)*arccoth(c+d*x)/d+1/2*b*log(1-(c+d*x)^2)/d],
[(a+b*arccoth(c+d*x))/(e+f*x),x,5,-(a+b*arccoth(c+d*x))*log(2/(1+c+d*x))/f+(a+b*arccoth(c+d*x))*log(2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/f+1/2*b*polylog(2,1+(-2)/(1+c+d*x))/f-1/2*b*polylog(2,1-2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/f],
[(a+b*arccoth(c+d*x))/(e+f*x)^2,x,7,(-a-b*arccoth(c+d*x))/(f*(e+f*x))-1/2*b*d*log(1-c-d*x)/(f*(d*e+f-c*f))+1/2*b*d*log(1+c+d*x)/(f*(d*e-f-c*f))-b*d*log(e+f*x)/((d*e-f-c*f)*(d*e+f-c*f))],
[(a+b*arccoth(c+d*x))/(e+f*x)^3,x,5,1/2*b*d/((d*e-f-c*f)*(d*e+f-c*f)*(e+f*x))+1/2*(-a-b*arccoth(c+d*x))/(f*(e+f*x)^2)-1/4*b*d^2*log(1-c-d*x)/(f*(d*e+f-c*f)^2)+1/4*b*d^2*log(1+c+d*x)/(f*(d*e-f-c*f)^2)-b*d^2*(d*e-c*f)*log(e+f*x)/((d*e+f-c*f)^2*(d*e-(1+c)*f)^2)],
[(e+f*x)^2*(a+b*arccoth(c+d*x))^2,x,16,1/3*b^2*f^2*x/d^2+2*a*b*f*(d*e-c*f)*x/d^2+2*b^2*f*(d*e-c*f)*(c+d*x)*arccoth(c+d*x)/d^3+1/3*b*f^2*(c+d*x)^2*(a+b*arccoth(c+d*x))/d^3-1/3*(d*e-c*f)*(d^2*e^2-2*c*d*e*f+(3+c^2)*f^2)*(a+b*arccoth(c+d*x))^2/(d^3*f)+1/3*(3*d^2*e^2-6*c*d*e*f+(1+3*c^2)*f^2)*(a+b*arccoth(c+d*x))^2/d^3+1/3*(e+f*x)^3*(a+b*arccoth(c+d*x))^2/f-1/3*b^2*f^2*arctanh(c+d*x)/d^3-2/3*b*(3*d^2*e^2-6*c*d*e*f+(1+3*c^2)*f^2)*(a+b*arccoth(c+d*x))*log(2/(1-c-d*x))/d^3+b^2*f*(d*e-c*f)*log(1-(c+d*x)^2)/d^3-1/3*b^2*(3*d^2*e^2-6*c*d*e*f+(1+3*c^2)*f^2)*polylog(2,(-1-c-d*x)/(1-c-d*x))/d^3],
[(e+f*x)*(a+b*arccoth(c+d*x))^2,x,13,a*b*f*x/d+b^2*f*(c+d*x)*arccoth(c+d*x)/d^2+(d*e-c*f)*(a+b*arccoth(c+d*x))^2/d^2-1/2*(d^2*e^2-2*c*d*e*f+(1+c^2)*f^2)*(a+b*arccoth(c+d*x))^2/(d^2*f)+1/2*(e+f*x)^2*(a+b*arccoth(c+d*x))^2/f-2*b*(d*e-c*f)*(a+b*arccoth(c+d*x))*log(2/(1-c-d*x))/d^2+1/2*b^2*f*log(1-(c+d*x)^2)/d^2-b^2*(d*e-c*f)*polylog(2,(-1-c-d*x)/(1-c-d*x))/d^2],
[(a+b*arccoth(c+d*x))^2,x,6,(a+b*arccoth(c+d*x))^2/d+(c+d*x)*(a+b*arccoth(c+d*x))^2/d-2*b*(a+b*arccoth(c+d*x))*log(2/(1-c-d*x))/d-b^2*polylog(2,(-1-c-d*x)/(1-c-d*x))/d],
[(a+b*arccoth(c+d*x))^2/(e+f*x),x,2,-(a+b*arccoth(c+d*x))^2*log(2/(1+c+d*x))/f+(a+b*arccoth(c+d*x))^2*log(2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/f+b*(a+b*arccoth(c+d*x))*polylog(2,1+(-2)/(1+c+d*x))/f-b*(a+b*arccoth(c+d*x))*polylog(2,1-2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/f+1/2*b^2*polylog(3,1+(-2)/(1+c+d*x))/f-1/2*b^2*polylog(3,1-2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/f],
[(a+b*arccoth(c+d*x))^2/(e+f*x)^2,x,24,-(a+b*arccoth(c+d*x))^2/(f*(e+f*x))+b^2*d*arccoth(c+d*x)*log(2/(1-c-d*x))/(f*(d*e+f-c*f))-a*b*d*log(1-c-d*x)/(f*(d*e+f-c*f))-b^2*d*arccoth(c+d*x)*log(2/(1+c+d*x))/(f*(d*e-f-c*f))+2*b^2*d*arccoth(c+d*x)*log(2/(1+c+d*x))/((d*e-f-c*f)*(d*e+f-c*f))+a*b*d*log(1+c+d*x)/(f*(d*e-f-c*f))+2*a*b*d*log(e+f*x)/(f^2-(d*e-c*f)^2)-2*b^2*d*arccoth(c+d*x)*log(2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/((d*e-f-c*f)*(d*e+f-c*f))+1/2*b^2*d*polylog(2,(-1-c-d*x)/(1-c-d*x))/(f*(d*e+f-c*f))+1/2*b^2*d*polylog(2,1+(-2)/(1+c+d*x))/(f*(d*e-f-c*f))-b^2*d*polylog(2,1+(-2)/(1+c+d*x))/((d*e-f-c*f)*(d*e+f-c*f))+b^2*d*polylog(2,1-2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/((d*e-f-c*f)*(d*e+f-c*f))],
[(e+f*x)^2*(a+b*arccoth(c+d*x))^3,x,21,a*b^2*f^2*x/d^2+b^3*f^2*(c+d*x)*arccoth(c+d*x)/d^3-1/2*b*f^2*(a+b*arccoth(c+d*x))^2/d^3+3*b*f*(d*e-c*f)*(a+b*arccoth(c+d*x))^2/d^3+3*b*f*(d*e-c*f)*(c+d*x)*(a+b*arccoth(c+d*x))^2/d^3+1/2*b*f^2*(c+d*x)^2*(a+b*arccoth(c+d*x))^2/d^3-1/3*(d*e-c*f)*(d^2*e^2-2*c*d*e*f+(3+c^2)*f^2)*(a+b*arccoth(c+d*x))^3/(d^3*f)+1/3*(3*d^2*e^2-6*c*d*e*f+(1+3*c^2)*f^2)*(a+b*arccoth(c+d*x))^3/d^3+1/3*(e+f*x)^3*(a+b*arccoth(c+d*x))^3/f-6*b^2*f*(d*e-c*f)*(a+b*arccoth(c+d*x))*log(2/(1-c-d*x))/d^3-b*(3*d^2*e^2-6*c*d*e*f+(1+3*c^2)*f^2)*(a+b*arccoth(c+d*x))^2*log(2/(1-c-d*x))/d^3+1/2*b^3*f^2*log(1-(c+d*x)^2)/d^3-3*b^3*f*(d*e-c*f)*polylog(2,(-1-c-d*x)/(1-c-d*x))/d^3-b^2*(3*d^2*e^2-6*c*d*e*f+(1+3*c^2)*f^2)*(a+b*arccoth(c+d*x))*polylog(2,1+(-2)/(1-c-d*x))/d^3+1/2*b^3*(3*d^2*e^2-6*c*d*e*f+(1+3*c^2)*f^2)*polylog(3,1+(-2)/(1-c-d*x))/d^3],
[(e+f*x)*(a+b*arccoth(c+d*x))^3,x,15,3/2*b*f*(a+b*arccoth(c+d*x))^2/d^2+3/2*b*f*(c+d*x)*(a+b*arccoth(c+d*x))^2/d^2+(d*e-c*f)*(a+b*arccoth(c+d*x))^3/d^2-1/2*(d^2*e^2-2*c*d*e*f+(1+c^2)*f^2)*(a+b*arccoth(c+d*x))^3/(d^2*f)+1/2*(e+f*x)^2*(a+b*arccoth(c+d*x))^3/f-3*b^2*f*(a+b*arccoth(c+d*x))*log(2/(1-c-d*x))/d^2-3*b*(d*e-c*f)*(a+b*arccoth(c+d*x))^2*log(2/(1-c-d*x))/d^2-3/2*b^3*f*polylog(2,(-1-c-d*x)/(1-c-d*x))/d^2-3*b^2*(d*e-c*f)*(a+b*arccoth(c+d*x))*polylog(2,1+(-2)/(1-c-d*x))/d^2+3/2*b^3*(d*e-c*f)*polylog(3,1+(-2)/(1-c-d*x))/d^2],
[(a+b*arccoth(c+d*x))^3,x,6,(a+b*arccoth(c+d*x))^3/d+(c+d*x)*(a+b*arccoth(c+d*x))^3/d-3*b*(a+b*arccoth(c+d*x))^2*log(2/(1-c-d*x))/d-3*b^2*(a+b*arccoth(c+d*x))*polylog(2,1+(-2)/(1-c-d*x))/d+3/2*b^3*polylog(3,1+(-2)/(1-c-d*x))/d],
[(a+b*arccoth(c+d*x))^3/(e+f*x),x,2,-(a+b*arccoth(c+d*x))^3*log(2/(1+c+d*x))/f+(a+b*arccoth(c+d*x))^3*log(2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/f+3/2*b*(a+b*arccoth(c+d*x))^2*polylog(2,1+(-2)/(1+c+d*x))/f-3/2*b*(a+b*arccoth(c+d*x))^2*polylog(2,1-2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/f+3/2*b^2*(a+b*arccoth(c+d*x))*polylog(3,1+(-2)/(1+c+d*x))/f-3/2*b^2*(a+b*arccoth(c+d*x))*polylog(3,1-2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/f+3/4*b^3*polylog(4,1+(-2)/(1+c+d*x))/f-3/4*b^3*polylog(4,1-2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/f],
[(a+b*arccoth(c+d*x))^3/(e+f*x)^2,x,33,-(a+b*arccoth(c+d*x))^3/(f*(e+f*x))+3*a*b^2*d*arccoth(c+d*x)*log(2/(1-c-d*x))/(f*(d*e+f-c*f))+3/2*b^3*d*arccoth(c+d*x)^2*log(2/(1-c-d*x))/(f*(d*e+f-c*f))-3/2*a^2*b*d*log(1-c-d*x)/(f*(d*e+f-c*f))-3*a*b^2*d*arccoth(c+d*x)*log(2/(1+c+d*x))/(f*(d*e-f-c*f))+6*a*b^2*d*arccoth(c+d*x)*log(2/(1+c+d*x))/((d*e-f-c*f)*(d*e+f-c*f))-3/2*b^3*d*arccoth(c+d*x)^2*log(2/(1+c+d*x))/(f*(d*e-f-c*f))+3*b^3*d*arccoth(c+d*x)^2*log(2/(1+c+d*x))/((d*e-f-c*f)*(d*e+f-c*f))+3/2*a^2*b*d*log(1+c+d*x)/(f*(d*e-f-c*f))+3*a^2*b*d*log(e+f*x)/(f^2-(d*e-c*f)^2)-6*a*b^2*d*arccoth(c+d*x)*log(2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/((d*e-f-c*f)*(d*e+f-c*f))-3*b^3*d*arccoth(c+d*x)^2*log(2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/((d*e-f-c*f)*(d*e+f-c*f))+3/2*a*b^2*d*polylog(2,(-1-c-d*x)/(1-c-d*x))/(f*(d*e+f-c*f))+3/2*b^3*d*arccoth(c+d*x)*polylog(2,1+(-2)/(1-c-d*x))/(f*(d*e+f-c*f))+3/2*a*b^2*d*polylog(2,1+(-2)/(1+c+d*x))/(f*(d*e-f-c*f))-3*a*b^2*d*polylog(2,1+(-2)/(1+c+d*x))/((d*e-f-c*f)*(d*e+f-c*f))+3/2*b^3*d*arccoth(c+d*x)*polylog(2,1+(-2)/(1+c+d*x))/(f*(d*e-f-c*f))-3*b^3*d*arccoth(c+d*x)*polylog(2,1+(-2)/(1+c+d*x))/((d*e-f-c*f)*(d*e+f-c*f))+3*a*b^2*d*polylog(2,1-2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/((d*e-f-c*f)*(d*e+f-c*f))+3*b^3*d*arccoth(c+d*x)*polylog(2,1-2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/((d*e-f-c*f)*(d*e+f-c*f))-3/4*b^3*d*polylog(3,1+(-2)/(1-c-d*x))/(f*(d*e+f-c*f))+3/4*b^3*d*polylog(3,1+(-2)/(1+c+d*x))/(f*(d*e-f-c*f))-3/2*b^3*d*polylog(3,1+(-2)/(1+c+d*x))/((d*e-f-c*f)*(d*e+f-c*f))+3/2*b^3*d*polylog(3,1-2*d*(e+f*x)/((d*e+f-c*f)*(1+c+d*x)))/((d*e-f-c*f)*(d*e+f-c*f))],

# Integrands of the form (e+f x)^m (a+b ArcCoth[c+d x])^p with m symbolic
[(e+f*x)^m*(a+b*arccoth(c+d*x)),x,6,(e+f*x)^(1+m)*(a+b*arccoth(c+d*x))/(f*(1+m))+1/2*b*d*(e+f*x)^(2+m)*hypergeom([1,2+m],[3+m],d*(e+f*x)/(d*e-f-c*f))/(f*(d*e-(1+c)*f)*(1+m)*(2+m))-1/2*b*d*(e+f*x)^(2+m)*hypergeom([1,2+m],[3+m],d*(e+f*x)/(d*e+f-c*f))/(f*(d*e+f-c*f)*(1+m)*(2+m))],
[(e+f*x)^m*(a+b*arccoth(c+d*x))^2,x,1,Unintegrable((e+f*x)^m*(a+b*arccoth(c+d*x))^2,x)],
[(e+f*x)^m*(a+b*arccoth(c+d*x))^3,x,1,Unintegrable((e+f*x)^m*(a+b*arccoth(c+d*x))^3,x)],

# Integrands of the form u^m (a+b ArcCoth[Sqrt[1-c x]/Sqrt[1+c x]])^n
[(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))^n/(1-c^2*x^2),x,0,Unintegrable((a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))^n/(1-c^2*x^2),x)],
[(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))^3/(1-c^2*x^2),x,9,-2*arccoth(1+(-2)/(1-sqrt(1-c*x)/sqrt(1+c*x)))*(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))^3/c-3/2*b*(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))^2*polylog(2,1+(-2)/(1+sqrt(1-c*x)/sqrt(1+c*x)))/c+3/2*b*(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))^2*polylog(2,1-2*sqrt(1-c*x)/((1+sqrt(1-c*x)/sqrt(1+c*x))*sqrt(1+c*x)))/c-3/2*b^2*(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))*polylog(3,1+(-2)/(1+sqrt(1-c*x)/sqrt(1+c*x)))/c+3/2*b^2*(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))*polylog(3,1-2*sqrt(1-c*x)/((1+sqrt(1-c*x)/sqrt(1+c*x))*sqrt(1+c*x)))/c-3/4*b^3*polylog(4,1+(-2)/(1+sqrt(1-c*x)/sqrt(1+c*x)))/c+3/4*b^3*polylog(4,1-2*sqrt(1-c*x)/((1+sqrt(1-c*x)/sqrt(1+c*x))*sqrt(1+c*x)))/c],
[(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))^2/(1-c^2*x^2),x,7,-2*arccoth(1+(-2)/(1-sqrt(1-c*x)/sqrt(1+c*x)))*(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))^2/c-b*(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))*polylog(2,1+(-2)/(1+sqrt(1-c*x)/sqrt(1+c*x)))/c+b*(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))*polylog(2,1-2*sqrt(1-c*x)/((1+sqrt(1-c*x)/sqrt(1+c*x))*sqrt(1+c*x)))/c-1/2*b^2*polylog(3,1+(-2)/(1+sqrt(1-c*x)/sqrt(1+c*x)))/c+1/2*b^2*polylog(3,1-2*sqrt(1-c*x)/((1+sqrt(1-c*x)/sqrt(1+c*x))*sqrt(1+c*x)))/c],
[(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))/(1-c^2*x^2),x,2,-a*log(sqrt(1-c*x)/sqrt(1+c*x))/c-1/2*b*polylog(2,-sqrt(1+c*x)/sqrt(1-c*x))/c+1/2*b*polylog(2,sqrt(1+c*x)/sqrt(1-c*x))/c],
[1/((1-c^2*x^2)*(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))),x,0,Unintegrable(1/((1-c^2*x^2)*(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))),x)],
[1/((1-c^2*x^2)*(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))^2),x,0,Unintegrable(1/((1-c^2*x^2)*(a+b*arccoth(sqrt(1-c*x)/sqrt(1+c*x)))^2),x)],

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

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

# n>0
[x^m*arccoth(tanh(a+b*x)),x,2,-b*x^(2+m)/(2+3*m+m^2)+x^(1+m)*arccoth(tanh(a+b*x))/(1+m)],
[x^2*arccoth(tanh(a+b*x)),x,2,-1/12*b*x^4+1/3*x^3*arccoth(tanh(a+b*x))],
[x*arccoth(tanh(a+b*x)),x,2,-1/6*b*x^3+1/2*x^2*arccoth(tanh(a+b*x))],
[arccoth(tanh(a+b*x)),x,2,1/2*arccoth(tanh(a+b*x))^2/b],
[arccoth(tanh(a+b*x))/x,x,2,b*x-(b*x-arccoth(tanh(a+b*x)))*log(x)],
[arccoth(tanh(a+b*x))/x^2,x,2,-arccoth(tanh(a+b*x))/x+b*log(x)],
[arccoth(tanh(a+b*x))/x^3,x,2,-1/2*b/x-1/2*arccoth(tanh(a+b*x))/x^2],
[arccoth(tanh(a+b*x))/x^4,x,2,-1/6*b/x^2-1/3*arccoth(tanh(a+b*x))/x^3],
[x^m*arccoth(tanh(a+b*x))^2,x,3,2*b^2*x^(3+m)/(6+11*m+6*m^2+m^3)-2*b*x^(2+m)*arccoth(tanh(a+b*x))/(2+3*m+m^2)+x^(1+m)*arccoth(tanh(a+b*x))^2/(1+m)],
[x^3*arccoth(tanh(a+b*x))^2,x,3,1/60*b^2*x^6-1/10*b*x^5*arccoth(tanh(a+b*x))+1/4*x^4*arccoth(tanh(a+b*x))^2],
[x^2*arccoth(tanh(a+b*x))^2,x,3,1/30*b^2*x^5-1/6*b*x^4*arccoth(tanh(a+b*x))+1/3*x^3*arccoth(tanh(a+b*x))^2],
[x*arccoth(tanh(a+b*x))^2,x,3,1/3*x*arccoth(tanh(a+b*x))^3/b-1/12*arccoth(tanh(a+b*x))^4/b^2],
[arccoth(tanh(a+b*x))^2,x,2,1/3*arccoth(tanh(a+b*x))^3/b],
[arccoth(tanh(a+b*x))^2/x,x,3,-b*x*(b*x-arccoth(tanh(a+b*x)))+1/2*arccoth(tanh(a+b*x))^2+(b*x-arccoth(tanh(a+b*x)))^2*log(x)],
[arccoth(tanh(a+b*x))^2/x^2,x,3,2*b^2*x-arccoth(tanh(a+b*x))^2/x-2*b*(b*x-arccoth(tanh(a+b*x)))*log(x)],
[arccoth(tanh(a+b*x))^2/x^3,x,3,-b*arccoth(tanh(a+b*x))/x-1/2*arccoth(tanh(a+b*x))^2/x^2+b^2*log(x)],
[arccoth(tanh(a+b*x))^2/x^4,x,1,1/3*arccoth(tanh(a+b*x))^3/(x^3*(b*x-arccoth(tanh(a+b*x))))],
[arccoth(tanh(a+b*x))^2/x^5,x,2,1/12*b*arccoth(tanh(a+b*x))^3/(x^3*(b*x-arccoth(tanh(a+b*x)))^2)+1/4*arccoth(tanh(a+b*x))^3/(x^4*(b*x-arccoth(tanh(a+b*x))))],
[x^m*arccoth(tanh(a+b*x))^3,x,4,-6*b^3*x^(4+m)/((1+m)*(24+26*m+9*m^2+m^3))+6*b^2*x^(3+m)*arccoth(tanh(a+b*x))/(6+11*m+6*m^2+m^3)-3*b*x^(2+m)*arccoth(tanh(a+b*x))^2/(2+3*m+m^2)+x^(1+m)*arccoth(tanh(a+b*x))^3/(1+m)],
[x^4*arccoth(tanh(a+b*x))^3,x,4,-1/280*b^3*x^8+1/35*b^2*x^7*arccoth(tanh(a+b*x))-1/10*b*x^6*arccoth(tanh(a+b*x))^2+1/5*x^5*arccoth(tanh(a+b*x))^3],
[x^3*arccoth(tanh(a+b*x))^3,x,4,-1/140*b^3*x^7+1/20*b^2*x^6*arccoth(tanh(a+b*x))-3/20*b*x^5*arccoth(tanh(a+b*x))^2+1/4*x^4*arccoth(tanh(a+b*x))^3],
[x^2*arccoth(tanh(a+b*x))^3,x,4,1/4*x^2*arccoth(tanh(a+b*x))^4/b-1/10*x*arccoth(tanh(a+b*x))^5/b^2+1/60*arccoth(tanh(a+b*x))^6/b^3],
[x*arccoth(tanh(a+b*x))^3,x,3,1/4*x*arccoth(tanh(a+b*x))^4/b-1/20*arccoth(tanh(a+b*x))^5/b^2],
[arccoth(tanh(a+b*x))^3,x,2,1/4*arccoth(tanh(a+b*x))^4/b],
[arccoth(tanh(a+b*x))^3/x,x,4,b*x*(b*x-arccoth(tanh(a+b*x)))^2-1/2*(b*x-arccoth(tanh(a+b*x)))*arccoth(tanh(a+b*x))^2+1/3*arccoth(tanh(a+b*x))^3-(b*x-arccoth(tanh(a+b*x)))^3*log(x)],
[arccoth(tanh(a+b*x))^3/x^2,x,4,-3*b^2*x*(b*x-arccoth(tanh(a+b*x)))+3/2*b*arccoth(tanh(a+b*x))^2-arccoth(tanh(a+b*x))^3/x+3*b*(b*x-arccoth(tanh(a+b*x)))^2*log(x)],
[arccoth(tanh(a+b*x))^3/x^3,x,4,3*b^3*x-3/2*b*arccoth(tanh(a+b*x))^2/x-1/2*arccoth(tanh(a+b*x))^3/x^2-3*b^2*(b*x-arccoth(tanh(a+b*x)))*log(x)],
[arccoth(tanh(a+b*x))^3/x^4,x,4,-b^2*arccoth(tanh(a+b*x))/x-1/2*b*arccoth(tanh(a+b*x))^2/x^2-1/3*arccoth(tanh(a+b*x))^3/x^3+b^3*log(x)],
[arccoth(tanh(a+b*x))^3/x^5,x,1,1/4*arccoth(tanh(a+b*x))^4/(x^4*(b*x-arccoth(tanh(a+b*x))))],
[arccoth(tanh(a+b*x))^3/x^6,x,2,1/20*b*arccoth(tanh(a+b*x))^4/(x^4*(b*x-arccoth(tanh(a+b*x)))^2)+1/5*arccoth(tanh(a+b*x))^4/(x^5*(b*x-arccoth(tanh(a+b*x))))],

# n<0
[x^m/arccoth(tanh(a+b*x)),x,1,-x^(1+m)*hypergeom([1,1+m],[2+m],b*x/(b*x-arccoth(tanh(a+b*x))))/((1+m)*(b*x-arccoth(tanh(a+b*x))))],
[x^3/arccoth(tanh(a+b*x)),x,5,1/3*x^3/b+1/2*x^2*(b*x-arccoth(tanh(a+b*x)))/b^2+x*(b*x-arccoth(tanh(a+b*x)))^2/b^3+(b*x-arccoth(tanh(a+b*x)))^3*log(arccoth(tanh(a+b*x)))/b^4],
[x^2/arccoth(tanh(a+b*x)),x,4,1/2*x^2/b+x*(b*x-arccoth(tanh(a+b*x)))/b^2+(b*x-arccoth(tanh(a+b*x)))^2*log(arccoth(tanh(a+b*x)))/b^3],
[x/arccoth(tanh(a+b*x)),x,3,x/b+(b*x-arccoth(tanh(a+b*x)))*log(arccoth(tanh(a+b*x)))/b^2],
[1/arccoth(tanh(a+b*x)),x,2,log(arccoth(tanh(a+b*x)))/b],
[1/(x*arccoth(tanh(a+b*x))),x,4,-log(x)/(b*x-arccoth(tanh(a+b*x)))+log(arccoth(tanh(a+b*x)))/(b*x-arccoth(tanh(a+b*x)))],
[1/(x^2*arccoth(tanh(a+b*x))),x,5,1/(x*(b*x-arccoth(tanh(a+b*x))))-b*log(x)/(b*x-arccoth(tanh(a+b*x)))^2+b*log(arccoth(tanh(a+b*x)))/(b*x-arccoth(tanh(a+b*x)))^2],
[1/(x^3*arccoth(tanh(a+b*x))),x,6,b/(x*(b*x-arccoth(tanh(a+b*x)))^2)+1/2/(x^2*(b*x-arccoth(tanh(a+b*x))))-b^2*log(x)/(b*x-arccoth(tanh(a+b*x)))^3+b^2*log(arccoth(tanh(a+b*x)))/(b*x-arccoth(tanh(a+b*x)))^3],
[x^m/arccoth(tanh(a+b*x))^2,x,2,-x^m/(b*arccoth(tanh(a+b*x)))-x^m*hypergeom([1,m],[1+m],b*x/(b*x-arccoth(tanh(a+b*x))))/(b*(b*x-arccoth(tanh(a+b*x))))],
[x^4/arccoth(tanh(a+b*x))^2,x,6,4/3*x^3/b^2+2*x^2*(b*x-arccoth(tanh(a+b*x)))/b^3+4*x*(b*x-arccoth(tanh(a+b*x)))^2/b^4-x^4/(b*arccoth(tanh(a+b*x)))+4*(b*x-arccoth(tanh(a+b*x)))^3*log(arccoth(tanh(a+b*x)))/b^5],
[x^3/arccoth(tanh(a+b*x))^2,x,5,3/2*x^2/b^2+3*x*(b*x-arccoth(tanh(a+b*x)))/b^3-x^3/(b*arccoth(tanh(a+b*x)))+3*(b*x-arccoth(tanh(a+b*x)))^2*log(arccoth(tanh(a+b*x)))/b^4],
[x^2/arccoth(tanh(a+b*x))^2,x,4,2*x/b^2-x^2/(b*arccoth(tanh(a+b*x)))+2*(b*x-arccoth(tanh(a+b*x)))*log(arccoth(tanh(a+b*x)))/b^3],
[x/arccoth(tanh(a+b*x))^2,x,3,-x/(b*arccoth(tanh(a+b*x)))+log(arccoth(tanh(a+b*x)))/b^2],
[1/arccoth(tanh(a+b*x))^2,x,2,(-1)/(b*arccoth(tanh(a+b*x)))],
[1/(x*arccoth(tanh(a+b*x))^2),x,5,(-1)/((b*x-arccoth(tanh(a+b*x)))*arccoth(tanh(a+b*x)))+log(x)/(b*x-arccoth(tanh(a+b*x)))^2-log(arccoth(tanh(a+b*x)))/(b*x-arccoth(tanh(a+b*x)))^2],
[1/(x^2*arccoth(tanh(a+b*x))^2),x,6,-2*b/((b*x-arccoth(tanh(a+b*x)))^2*arccoth(tanh(a+b*x)))+1/(x*(b*x-arccoth(tanh(a+b*x)))*arccoth(tanh(a+b*x)))+2*b*log(x)/(b*x-arccoth(tanh(a+b*x)))^3-2*b*log(arccoth(tanh(a+b*x)))/(b*x-arccoth(tanh(a+b*x)))^3],
[1/(x^3*arccoth(tanh(a+b*x))^2),x,7,-3*b^2/((b*x-arccoth(tanh(a+b*x)))^3*arccoth(tanh(a+b*x)))+3/2*b/(x*(b*x-arccoth(tanh(a+b*x)))^2*arccoth(tanh(a+b*x)))+1/2/(x^2*(b*x-arccoth(tanh(a+b*x)))*arccoth(tanh(a+b*x)))+3*b^2*log(x)/(b*x-arccoth(tanh(a+b*x)))^4-3*b^2*log(arccoth(tanh(a+b*x)))/(b*x-arccoth(tanh(a+b*x)))^4],
[x^m/arccoth(tanh(a+b*x))^3,x,3,-1/2*x^m/(b*arccoth(tanh(a+b*x))^2)-1/2*m*x^(-1+m)/(b^2*arccoth(tanh(a+b*x)))-1/2*m*x^(-1+m)*hypergeom([1,-1+m],[m],b*x/(b*x-arccoth(tanh(a+b*x))))/(b^2*(b*x-arccoth(tanh(a+b*x))))],
[x^4/arccoth(tanh(a+b*x))^3,x,6,3*x^2/b^3+6*x*(b*x-arccoth(tanh(a+b*x)))/b^4-1/2*x^4/(b*arccoth(tanh(a+b*x))^2)-2*x^3/(b^2*arccoth(tanh(a+b*x)))+6*(b*x-arccoth(tanh(a+b*x)))^2*log(arccoth(tanh(a+b*x)))/b^5],
[x^3/arccoth(tanh(a+b*x))^3,x,5,3*x/b^3-1/2*x^3/(b*arccoth(tanh(a+b*x))^2)-3/2*x^2/(b^2*arccoth(tanh(a+b*x)))+3*(b*x-arccoth(tanh(a+b*x)))*log(arccoth(tanh(a+b*x)))/b^4],
[x^2/arccoth(tanh(a+b*x))^3,x,4,-1/2*x^2/(b*arccoth(tanh(a+b*x))^2)-x/(b^2*arccoth(tanh(a+b*x)))+log(arccoth(tanh(a+b*x)))/b^3],
[x/arccoth(tanh(a+b*x))^3,x,3,-1/2*x/(b*arccoth(tanh(a+b*x))^2)+(-1/2)/(b^2*arccoth(tanh(a+b*x)))],
[1/arccoth(tanh(a+b*x))^3,x,2,(-1/2)/(b*arccoth(tanh(a+b*x))^2)],
[1/(x*arccoth(tanh(a+b*x))^3),x,6,(-1/2)/((b*x-arccoth(tanh(a+b*x)))*arccoth(tanh(a+b*x))^2)+1/((b*x-arccoth(tanh(a+b*x)))^2*arccoth(tanh(a+b*x)))-log(x)/(b*x-arccoth(tanh(a+b*x)))^3+log(arccoth(tanh(a+b*x)))/(b*x-arccoth(tanh(a+b*x)))^3],
[1/(x^2*arccoth(tanh(a+b*x))^3),x,7,-3/2*b/((b*x-arccoth(tanh(a+b*x)))^2*arccoth(tanh(a+b*x))^2)+1/(x*(b*x-arccoth(tanh(a+b*x)))*arccoth(tanh(a+b*x))^2)+3*b/((b*x-arccoth(tanh(a+b*x)))^3*arccoth(tanh(a+b*x)))-3*b*log(x)/(b*x-arccoth(tanh(a+b*x)))^4+3*b*log(arccoth(tanh(a+b*x)))/(b*x-arccoth(tanh(a+b*x)))^4],
[1/(x^3*arccoth(tanh(a+b*x))^3),x,8,-3*b^2/((b*x-arccoth(tanh(a+b*x)))^3*arccoth(tanh(a+b*x))^2)+2*b/(x*(b*x-arccoth(tanh(a+b*x)))^2*arccoth(tanh(a+b*x))^2)+1/2/(x^2*(b*x-arccoth(tanh(a+b*x)))*arccoth(tanh(a+b*x))^2)+6*b^2/((b*x-arccoth(tanh(a+b*x)))^4*arccoth(tanh(a+b*x)))-6*b^2*log(x)/(b*x-arccoth(tanh(a+b*x)))^5+6*b^2*log(arccoth(tanh(a+b*x)))/(b*x-arccoth(tanh(a+b*x)))^5],

# n symbolic
[x^m*arccoth(tanh(a+b*x))^n,x,1,x^m*arccoth(tanh(a+b*x))^(1+n)*hypergeom([-m,1+n],[2+n],-arccoth(tanh(a+b*x))/(b*x-arccoth(tanh(a+b*x))))/(b*(1+n)*(b*x/(b*x-arccoth(tanh(a+b*x))))^m)],
[x^4*arccoth(tanh(a+b*x))^n,x,6,x^4*arccoth(tanh(a+b*x))^(1+n)/(b*(1+n))-4*x^3*arccoth(tanh(a+b*x))^(2+n)/(b^2*(1+n)*(2+n))+12*x^2*arccoth(tanh(a+b*x))^(3+n)/(b^3*(3+n)*(2+3*n+n^2))-24*x*arccoth(tanh(a+b*x))^(4+n)/(b^4*(4+5*n+n^2)*(6+5*n+n^2))+24*arccoth(tanh(a+b*x))^(5+n)/(b^5*(12+7*n+n^2)*(10+17*n+8*n^2+n^3))],
[x^3*arccoth(tanh(a+b*x))^n,x,5,x^3*arccoth(tanh(a+b*x))^(1+n)/(b*(1+n))-3*x^2*arccoth(tanh(a+b*x))^(2+n)/(b^2*(1+n)*(2+n))+6*x*arccoth(tanh(a+b*x))^(3+n)/(b^3*(3+n)*(2+3*n+n^2))-6*arccoth(tanh(a+b*x))^(4+n)/(b^4*(4+5*n+n^2)*(6+5*n+n^2))],
[x^2*arccoth(tanh(a+b*x))^n,x,4,x^2*arccoth(tanh(a+b*x))^(1+n)/(b*(1+n))-2*x*arccoth(tanh(a+b*x))^(2+n)/(b^2*(1+n)*(2+n))+2*arccoth(tanh(a+b*x))^(3+n)/(b^3*(3+n)*(2+3*n+n^2))],
[x*arccoth(tanh(a+b*x))^n,x,3,x*arccoth(tanh(a+b*x))^(1+n)/(b*(1+n))-arccoth(tanh(a+b*x))^(2+n)/(b^2*(1+n)*(2+n))],
[arccoth(tanh(a+b*x))^n,x,2,arccoth(tanh(a+b*x))^(1+n)/(b*(1+n))],
[arccoth(tanh(a+b*x))^n/x,x,1,arccoth(tanh(a+b*x))^(1+n)*hypergeom([1,1+n],[2+n],-arccoth(tanh(a+b*x))/(b*x-arccoth(tanh(a+b*x))))/((1+n)*(b*x-arccoth(tanh(a+b*x))))],
[arccoth(tanh(a+b*x))^n/x^2,x,2,-arccoth(tanh(a+b*x))^n/x+b*arccoth(tanh(a+b*x))^n*hypergeom([1,n],[1+n],-arccoth(tanh(a+b*x))/(b*x-arccoth(tanh(a+b*x))))/(b*x-arccoth(tanh(a+b*x)))],
[arccoth(tanh(a+b*x))^n/x^3,x,3,-1/2*b*n*arccoth(tanh(a+b*x))^(-1+n)/x-1/2*arccoth(tanh(a+b*x))^n/x^2+1/2*b^2*n*arccoth(tanh(a+b*x))^(-1+n)*hypergeom([1,-1+n],[n],-arccoth(tanh(a+b*x))/(b*x-arccoth(tanh(a+b*x))))/(b*x-arccoth(tanh(a+b*x)))],

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

# Integrands of the form x^m ArcCoth[Coth[a+b x]]^n
[x^m*arccoth(tanh(a+b*x)),x,2,-b*x^(2+m)/(2+3*m+m^2)+x^(1+m)*arccoth(tanh(a+b*x))/(1+m)],
[x^2*arccoth(coth(a+b*x)),x,2,-1/12*b*x^4+1/3*x^3*arccoth(coth(a+b*x))],
[x*arccoth(coth(a+b*x)),x,2,-1/6*b*x^3+1/2*x^2*arccoth(coth(a+b*x))],
[arccoth(coth(a+b*x)),x,2,1/2*arccoth(coth(a+b*x))^2/b],
[arccoth(coth(a+b*x))/x,x,2,b*x-(b*x-arccoth(coth(a+b*x)))*log(x)],
[arccoth(coth(a+b*x))/x^2,x,2,-arccoth(coth(a+b*x))/x+b*log(x)],
[arccoth(coth(a+b*x))/x^3,x,2,-1/2*b/x-1/2*arccoth(coth(a+b*x))/x^2],

# Integrands of the form x^m ArcCoth[c+d Hyper[a+b x]]

# Integrands of the form x^m ArcCoth[c+d Sinh[a+b x]]
#  {ArcCoth[Sinh[x]], x, 6, 0}
# {x*ArcCoth[Sinh[x]], x, 8, 0}

# {x^2*ArcCoth[Sinh[x]], x, 10, 0} 

# Integrands of the form x^m ArcCoth[c+d Cosh[a+b x]]
[arccoth(cosh(x)),x,6,x*arccoth(cosh(x))-2*x*arctanh(exp(x))-polylog(2,-exp(x))+polylog(2,exp(x))],
[x*arccoth(cosh(x)),x,8,1/2*x^2*arccoth(cosh(x))-x^2*arctanh(exp(x))-x*polylog(2,-exp(x))+x*polylog(2,exp(x))+polylog(3,-exp(x))-polylog(3,exp(x))],
[x^2*arccoth(cosh(x)),x,10,1/3*x^3*arccoth(cosh(x))-2/3*x^3*arctanh(exp(x))-x^2*polylog(2,-exp(x))+x^2*polylog(2,exp(x))+2*x*polylog(3,-exp(x))-2*x*polylog(3,exp(x))-2*polylog(4,-exp(x))+2*polylog(4,exp(x))],

# Integrands of the form x^m ArcCoth[c+d Tanh[a+b x]]
[x^2*arccoth(c+d*tanh(a+b*x)),x,11,1/3*x^3*arccoth(c+d*tanh(a+b*x))+1/6*x^3*log(1+(1-c-d)*exp(2*a+2*b*x)/(1-c+d))-1/6*x^3*log(1+(1+c+d)*exp(2*a+2*b*x)/(1+c-d))+1/4*x^2*polylog(2,-(1-c-d)*exp(2*a+2*b*x)/(1-c+d))/b-1/4*x^2*polylog(2,-(1+c+d)*exp(2*a+2*b*x)/(1+c-d))/b-1/4*x*polylog(3,-(1-c-d)*exp(2*a+2*b*x)/(1-c+d))/b^2+1/4*x*polylog(3,-(1+c+d)*exp(2*a+2*b*x)/(1+c-d))/b^2+1/8*polylog(4,-(1-c-d)*exp(2*a+2*b*x)/(1-c+d))/b^3-1/8*polylog(4,-(1+c+d)*exp(2*a+2*b*x)/(1+c-d))/b^3],
[x*arccoth(c+d*tanh(a+b*x)),x,9,1/2*x^2*arccoth(c+d*tanh(a+b*x))+1/4*x^2*log(1+(1-c-d)*exp(2*a+2*b*x)/(1-c+d))-1/4*x^2*log(1+(1+c+d)*exp(2*a+2*b*x)/(1+c-d))+1/4*x*polylog(2,-(1-c-d)*exp(2*a+2*b*x)/(1-c+d))/b-1/4*x*polylog(2,-(1+c+d)*exp(2*a+2*b*x)/(1+c-d))/b-1/8*polylog(3,-(1-c-d)*exp(2*a+2*b*x)/(1-c+d))/b^2+1/8*polylog(3,-(1+c+d)*exp(2*a+2*b*x)/(1+c-d))/b^2],
[arccoth(c+d*tanh(a+b*x)),x,7,x*arccoth(c+d*tanh(a+b*x))+1/2*x*log(1+(1-c-d)*exp(2*a+2*b*x)/(1-c+d))-1/2*x*log(1+(1+c+d)*exp(2*a+2*b*x)/(1+c-d))+1/4*polylog(2,-(1-c-d)*exp(2*a+2*b*x)/(1-c+d))/b-1/4*polylog(2,-(1+c+d)*exp(2*a+2*b*x)/(1+c-d))/b],
[arccoth(c+d*tanh(a+b*x))/x,x,0,CannotIntegrate(arccoth(c+d*tanh(a+b*x))/x,x)],
[x^3*arccoth(1+d+d*tanh(a+b*x)),x,8,1/20*b*x^5+1/4*x^4*arccoth(1+d+d*tanh(a+b*x))-1/8*x^4*log(1+(1+d)*exp(2*a+2*b*x))-1/4*x^3*polylog(2,-(1+d)*exp(2*a+2*b*x))/b+3/8*x^2*polylog(3,-(1+d)*exp(2*a+2*b*x))/b^2-3/8*x*polylog(4,-(1+d)*exp(2*a+2*b*x))/b^3+3/16*polylog(5,-(1+d)*exp(2*a+2*b*x))/b^4],
[x^2*arccoth(1+d+d*tanh(a+b*x)),x,7,1/12*b*x^4+1/3*x^3*arccoth(1+d+d*tanh(a+b*x))-1/6*x^3*log(1+(1+d)*exp(2*a+2*b*x))-1/4*x^2*polylog(2,-(1+d)*exp(2*a+2*b*x))/b+1/4*x*polylog(3,-(1+d)*exp(2*a+2*b*x))/b^2-1/8*polylog(4,-(1+d)*exp(2*a+2*b*x))/b^3],
[x*arccoth(1+d+d*tanh(a+b*x)),x,6,1/6*b*x^3+1/2*x^2*arccoth(1+d+d*tanh(a+b*x))-1/4*x^2*log(1+(1+d)*exp(2*a+2*b*x))-1/4*x*polylog(2,-(1+d)*exp(2*a+2*b*x))/b+1/8*polylog(3,-(1+d)*exp(2*a+2*b*x))/b^2],
[arccoth(1+d+d*tanh(a+b*x)),x,5,1/2*b*x^2+x*arccoth(1+d+d*tanh(a+b*x))-1/2*x*log(1+(1+d)*exp(2*a+2*b*x))-1/4*polylog(2,-(1+d)*exp(2*a+2*b*x))/b],
[arccoth(1+d+d*tanh(a+b*x))/x,x,0,CannotIntegrate(arccoth(1+d+d*tanh(a+b*x))/x,x)],
[x^3*arccoth(1-d-d*tanh(a+b*x)),x,8,1/20*b*x^5+1/4*x^4*arccoth(1-d-d*tanh(a+b*x))-1/8*x^4*log(1+(1-d)*exp(2*a+2*b*x))-1/4*x^3*polylog(2,-(1-d)*exp(2*a+2*b*x))/b+3/8*x^2*polylog(3,-(1-d)*exp(2*a+2*b*x))/b^2-3/8*x*polylog(4,-(1-d)*exp(2*a+2*b*x))/b^3+3/16*polylog(5,-(1-d)*exp(2*a+2*b*x))/b^4],
[x^2*arccoth(1-d-d*tanh(a+b*x)),x,7,1/12*b*x^4+1/3*x^3*arccoth(1-d-d*tanh(a+b*x))-1/6*x^3*log(1+(1-d)*exp(2*a+2*b*x))-1/4*x^2*polylog(2,-(1-d)*exp(2*a+2*b*x))/b+1/4*x*polylog(3,-(1-d)*exp(2*a+2*b*x))/b^2-1/8*polylog(4,-(1-d)*exp(2*a+2*b*x))/b^3],
[x*arccoth(1-d-d*tanh(a+b*x)),x,6,1/6*b*x^3+1/2*x^2*arccoth(1-d-d*tanh(a+b*x))-1/4*x^2*log(1+(1-d)*exp(2*a+2*b*x))-1/4*x*polylog(2,-(1-d)*exp(2*a+2*b*x))/b+1/8*polylog(3,-(1-d)*exp(2*a+2*b*x))/b^2],
[arccoth(1-d-d*tanh(a+b*x)),x,5,1/2*b*x^2+x*arccoth(1-d-d*tanh(a+b*x))-1/2*x*log(1+(1-d)*exp(2*a+2*b*x))-1/4*polylog(2,-(1-d)*exp(2*a+2*b*x))/b],
[arccoth(1-d-d*tanh(a+b*x))/x,x,0,CannotIntegrate(arccoth(1-d-d*tanh(a+b*x))/x,x)],

# Integrands of the form x^m ArcCoth[c+d Coth[a+b x]]
[x^2*arccoth(c+d*coth(a+b*x)),x,11,1/3*x^3*arccoth(c+d*coth(a+b*x))+1/6*x^3*log(1-(1-c-d)*exp(2*a+2*b*x)/(1-c+d))-1/6*x^3*log(1-(1+c+d)*exp(2*a+2*b*x)/(1+c-d))+1/4*x^2*polylog(2,(1-c-d)*exp(2*a+2*b*x)/(1-c+d))/b-1/4*x^2*polylog(2,(1+c+d)*exp(2*a+2*b*x)/(1+c-d))/b-1/4*x*polylog(3,(1-c-d)*exp(2*a+2*b*x)/(1-c+d))/b^2+1/4*x*polylog(3,(1+c+d)*exp(2*a+2*b*x)/(1+c-d))/b^2+1/8*polylog(4,(1-c-d)*exp(2*a+2*b*x)/(1-c+d))/b^3-1/8*polylog(4,(1+c+d)*exp(2*a+2*b*x)/(1+c-d))/b^3],
[x*arccoth(c+d*coth(a+b*x)),x,9,1/2*x^2*arccoth(c+d*coth(a+b*x))+1/4*x^2*log(1-(1-c-d)*exp(2*a+2*b*x)/(1-c+d))-1/4*x^2*log(1-(1+c+d)*exp(2*a+2*b*x)/(1+c-d))+1/4*x*polylog(2,(1-c-d)*exp(2*a+2*b*x)/(1-c+d))/b-1/4*x*polylog(2,(1+c+d)*exp(2*a+2*b*x)/(1+c-d))/b-1/8*polylog(3,(1-c-d)*exp(2*a+2*b*x)/(1-c+d))/b^2+1/8*polylog(3,(1+c+d)*exp(2*a+2*b*x)/(1+c-d))/b^2],
[arccoth(c+d*coth(a+b*x)),x,7,x*arccoth(c+d*coth(a+b*x))+1/2*x*log(1-(1-c-d)*exp(2*a+2*b*x)/(1-c+d))-1/2*x*log(1-(1+c+d)*exp(2*a+2*b*x)/(1+c-d))+1/4*polylog(2,(1-c-d)*exp(2*a+2*b*x)/(1-c+d))/b-1/4*polylog(2,(1+c+d)*exp(2*a+2*b*x)/(1+c-d))/b],
[arccoth(c+d*coth(a+b*x))/x,x,0,CannotIntegrate(arccoth(c+d*coth(a+b*x))/x,x)],
[x^3*arccoth(1+d+d*coth(a+b*x)),x,8,1/20*b*x^5+1/4*x^4*arccoth(1+d+d*coth(a+b*x))-1/8*x^4*log(1-(1+d)*exp(2*a+2*b*x))-1/4*x^3*polylog(2,(1+d)*exp(2*a+2*b*x))/b+3/8*x^2*polylog(3,(1+d)*exp(2*a+2*b*x))/b^2-3/8*x*polylog(4,(1+d)*exp(2*a+2*b*x))/b^3+3/16*polylog(5,(1+d)*exp(2*a+2*b*x))/b^4],
[x^2*arccoth(1+d+d*coth(a+b*x)),x,7,1/12*b*x^4+1/3*x^3*arccoth(1+d+d*coth(a+b*x))-1/6*x^3*log(1-(1+d)*exp(2*a+2*b*x))-1/4*x^2*polylog(2,(1+d)*exp(2*a+2*b*x))/b+1/4*x*polylog(3,(1+d)*exp(2*a+2*b*x))/b^2-1/8*polylog(4,(1+d)*exp(2*a+2*b*x))/b^3],
[x*arccoth(1+d+d*coth(a+b*x)),x,6,1/6*b*x^3+1/2*x^2*arccoth(1+d+d*coth(a+b*x))-1/4*x^2*log(1-(1+d)*exp(2*a+2*b*x))-1/4*x*polylog(2,(1+d)*exp(2*a+2*b*x))/b+1/8*polylog(3,(1+d)*exp(2*a+2*b*x))/b^2],
[arccoth(1+d+d*coth(a+b*x)),x,5,1/2*b*x^2+x*arccoth(1+d+d*coth(a+b*x))-1/2*x*log(1-(1+d)*exp(2*a+2*b*x))-1/4*polylog(2,(1+d)*exp(2*a+2*b*x))/b],
[arccoth(1+d+d*coth(a+b*x))/x,x,0,CannotIntegrate(arccoth(1+d+d*coth(a+b*x))/x,x)],
[x^3*arccoth(1-d-d*coth(a+b*x)),x,8,1/20*b*x^5+1/4*x^4*arccoth(1-d-d*coth(a+b*x))-1/8*x^4*log(1-(1-d)*exp(2*a+2*b*x))-1/4*x^3*polylog(2,(1-d)*exp(2*a+2*b*x))/b+3/8*x^2*polylog(3,(1-d)*exp(2*a+2*b*x))/b^2-3/8*x*polylog(4,(1-d)*exp(2*a+2*b*x))/b^3+3/16*polylog(5,(1-d)*exp(2*a+2*b*x))/b^4],
[x^2*arccoth(1-d-d*coth(a+b*x)),x,7,1/12*b*x^4+1/3*x^3*arccoth(1-d-d*coth(a+b*x))-1/6*x^3*log(1-(1-d)*exp(2*a+2*b*x))-1/4*x^2*polylog(2,(1-d)*exp(2*a+2*b*x))/b+1/4*x*polylog(3,(1-d)*exp(2*a+2*b*x))/b^2-1/8*polylog(4,(1-d)*exp(2*a+2*b*x))/b^3],
[x*arccoth(1-d-d*coth(a+b*x)),x,6,1/6*b*x^3+1/2*x^2*arccoth(1-d-d*coth(a+b*x))-1/4*x^2*log(1-(1-d)*exp(2*a+2*b*x))-1/4*x*polylog(2,(1-d)*exp(2*a+2*b*x))/b+1/8*polylog(3,(1-d)*exp(2*a+2*b*x))/b^2],
[arccoth(1-d-d*coth(a+b*x)),x,5,1/2*b*x^2+x*arccoth(1-d-d*coth(a+b*x))-1/2*x*log(1-(1-d)*exp(2*a+2*b*x))-1/4*polylog(2,(1-d)*exp(2*a+2*b*x))/b],
[arccoth(1-d-d*coth(a+b*x))/x,x,0,CannotIntegrate(arccoth(1-d-d*coth(a+b*x))/x,x)],

# Integrands of the form x^m ArcCoth[c+d Trig[a+b x]]

# Integrands of the form x^m ArcCoth[c+d Tan[a+b x]]
[(e+f*x)^3*arccoth(tan(a+b*x)),x,12,1/4*(e+f*x)^4*arccoth(tan(a+b*x))/f+1/4*I*(e+f*x)^4*arctan(exp(2*I*(a+b*x)))/f-1/4*I*(e+f*x)^3*polylog(2,-I*exp(2*I*(a+b*x)))/b+1/4*I*(e+f*x)^3*polylog(2,I*exp(2*I*(a+b*x)))/b+3/8*f*(e+f*x)^2*polylog(3,-I*exp(2*I*(a+b*x)))/b^2-3/8*f*(e+f*x)^2*polylog(3,I*exp(2*I*(a+b*x)))/b^2+3/8*I*f^2*(e+f*x)*polylog(4,-I*exp(2*I*(a+b*x)))/b^3-3/8*I*f^2*(e+f*x)*polylog(4,I*exp(2*I*(a+b*x)))/b^3-3/16*f^3*polylog(5,-I*exp(2*I*(a+b*x)))/b^4+3/16*f^3*polylog(5,I*exp(2*I*(a+b*x)))/b^4],
[(e+f*x)^2*arccoth(tan(a+b*x)),x,10,1/3*(e+f*x)^3*arccoth(tan(a+b*x))/f+1/3*I*(e+f*x)^3*arctan(exp(2*I*(a+b*x)))/f-1/4*I*(e+f*x)^2*polylog(2,-I*exp(2*I*(a+b*x)))/b+1/4*I*(e+f*x)^2*polylog(2,I*exp(2*I*(a+b*x)))/b+1/4*f*(e+f*x)*polylog(3,-I*exp(2*I*(a+b*x)))/b^2-1/4*f*(e+f*x)*polylog(3,I*exp(2*I*(a+b*x)))/b^2+1/8*I*f^2*polylog(4,-I*exp(2*I*(a+b*x)))/b^3-1/8*I*f^2*polylog(4,I*exp(2*I*(a+b*x)))/b^3],
[(e+f*x)*arccoth(tan(a+b*x)),x,8,1/2*(e+f*x)^2*arccoth(tan(a+b*x))/f+1/2*I*(e+f*x)^2*arctan(exp(2*I*(a+b*x)))/f-1/4*I*(e+f*x)*polylog(2,-I*exp(2*I*(a+b*x)))/b+1/4*I*(e+f*x)*polylog(2,I*exp(2*I*(a+b*x)))/b+1/8*f*polylog(3,-I*exp(2*I*(a+b*x)))/b^2-1/8*f*polylog(3,I*exp(2*I*(a+b*x)))/b^2],
[arccoth(tan(a+b*x)),x,6,x*arccoth(tan(a+b*x))+I*x*arctan(exp(2*I*(a+b*x)))-1/4*I*polylog(2,-I*exp(2*I*(a+b*x)))/b+1/4*I*polylog(2,I*exp(2*I*(a+b*x)))/b],
[arccoth(tan(a+b*x))/(e+f*x),x,0,CannotIntegrate(arccoth(tan(a+b*x))/(e+f*x),x)],
[x^2*arccoth(c+d*tan(a+b*x)),x,11,1/3*x^3*arccoth(c+d*tan(a+b*x))+1/6*x^3*log(1+(1-c+I*d)*exp(2*I*a+2*I*b*x)/(1-c-I*d))-1/6*x^3*log(1+(1+c-I*d)*exp(2*I*a+2*I*b*x)/(1+c+I*d))-1/4*I*x^2*polylog(2,-(1-c+I*d)*exp(2*I*a+2*I*b*x)/(1-c-I*d))/b+1/4*I*x^2*polylog(2,-(1+c-I*d)*exp(2*I*a+2*I*b*x)/(1+c+I*d))/b+1/4*x*polylog(3,-(1-c+I*d)*exp(2*I*a+2*I*b*x)/(1-c-I*d))/b^2-1/4*x*polylog(3,-(1+c-I*d)*exp(2*I*a+2*I*b*x)/(1+c+I*d))/b^2+1/8*I*polylog(4,-(1-c+I*d)*exp(2*I*a+2*I*b*x)/(1-c-I*d))/b^3-1/8*I*polylog(4,-(1+c-I*d)*exp(2*I*a+2*I*b*x)/(1+c+I*d))/b^3],
[x*arccoth(c+d*tan(a+b*x)),x,9,1/2*x^2*arccoth(c+d*tan(a+b*x))+1/4*x^2*log(1+(1-c+I*d)*exp(2*I*a+2*I*b*x)/(1-c-I*d))-1/4*x^2*log(1+(1+c-I*d)*exp(2*I*a+2*I*b*x)/(1+c+I*d))-1/4*I*x*polylog(2,-(1-c+I*d)*exp(2*I*a+2*I*b*x)/(1-c-I*d))/b+1/4*I*x*polylog(2,-(1+c-I*d)*exp(2*I*a+2*I*b*x)/(1+c+I*d))/b+1/8*polylog(3,-(1-c+I*d)*exp(2*I*a+2*I*b*x)/(1-c-I*d))/b^2-1/8*polylog(3,-(1+c-I*d)*exp(2*I*a+2*I*b*x)/(1+c+I*d))/b^2],
[arccoth(c+d*tan(a+b*x)),x,7,x*arccoth(c+d*tan(a+b*x))+1/2*x*log(1+(1-c+I*d)*exp(2*I*a+2*I*b*x)/(1-c-I*d))-1/2*x*log(1+(1+c-I*d)*exp(2*I*a+2*I*b*x)/(1+c+I*d))-1/4*I*polylog(2,-(1-c+I*d)*exp(2*I*a+2*I*b*x)/(1-c-I*d))/b+1/4*I*polylog(2,-(1+c-I*d)*exp(2*I*a+2*I*b*x)/(1+c+I*d))/b],
[arccoth(c+d*tan(a+b*x))/x,x,0,CannotIntegrate(arccoth(c+d*tan(a+b*x))/x,x)],
[x^2*arccoth(1-I*d+d*tan(a+b*x)),x,7,1/12*I*b*x^4+1/3*x^3*arccoth(1-I*d+d*tan(a+b*x))-1/6*x^3*log(1+(1-I*d)*exp(2*I*a+2*I*b*x))+1/4*I*x^2*polylog(2,-(1-I*d)*exp(2*I*a+2*I*b*x))/b-1/4*x*polylog(3,-(1-I*d)*exp(2*I*a+2*I*b*x))/b^2-1/8*I*polylog(4,-(1-I*d)*exp(2*I*a+2*I*b*x))/b^3],
[x*arccoth(1-I*d+d*tan(a+b*x)),x,6,1/6*I*b*x^3+1/2*x^2*arccoth(1-I*d+d*tan(a+b*x))-1/4*x^2*log(1+(1-I*d)*exp(2*I*a+2*I*b*x))+1/4*I*x*polylog(2,-(1-I*d)*exp(2*I*a+2*I*b*x))/b-1/8*polylog(3,-(1-I*d)*exp(2*I*a+2*I*b*x))/b^2],
[arccoth(1-I*d+d*tan(a+b*x)),x,5,1/2*I*b*x^2+x*arccoth(1-I*d+d*tan(a+b*x))-1/2*x*log(1+(1-I*d)*exp(2*I*a+2*I*b*x))+1/4*I*polylog(2,-(1-I*d)*exp(2*I*a+2*I*b*x))/b],
[arccoth(1-I*d+d*tan(a+b*x))/x,x,0,CannotIntegrate(arccoth(1-I*d+d*tan(a+b*x))/x,x)],
[x^2*arccoth(1+I*d-d*tan(a+b*x)),x,7,1/12*I*b*x^4+1/3*x^3*arccoth(1+I*d-d*tan(a+b*x))-1/6*x^3*log(1+(1+I*d)*exp(2*I*a+2*I*b*x))+1/4*I*x^2*polylog(2,-(1+I*d)*exp(2*I*a+2*I*b*x))/b-1/4*x*polylog(3,-(1+I*d)*exp(2*I*a+2*I*b*x))/b^2-1/8*I*polylog(4,-(1+I*d)*exp(2*I*a+2*I*b*x))/b^3],
[x*arccoth(1+I*d-d*tan(a+b*x)),x,6,1/6*I*b*x^3+1/2*x^2*arccoth(1+I*d-d*tan(a+b*x))-1/4*x^2*log(1+(1+I*d)*exp(2*I*a+2*I*b*x))+1/4*I*x*polylog(2,-(1+I*d)*exp(2*I*a+2*I*b*x))/b-1/8*polylog(3,-(1+I*d)*exp(2*I*a+2*I*b*x))/b^2],
[arccoth(1+I*d-d*tan(a+b*x)),x,5,1/2*I*b*x^2+x*arccoth(1+I*d-d*tan(a+b*x))-1/2*x*log(1+(1+I*d)*exp(2*I*a+2*I*b*x))+1/4*I*polylog(2,-(1+I*d)*exp(2*I*a+2*I*b*x))/b],
[arccoth(1+I*d-d*tan(a+b*x))/x,x,0,CannotIntegrate(arccoth(1+I*d-d*tan(a+b*x))/x,x)],

# Integrands of the form x^m ArcCoth[c+d Cot[a+b x]]
[(e+f*x)^3*arccoth(cot(a+b*x)),x,12,1/4*(e+f*x)^4*arccoth(cot(a+b*x))/f+1/4*I*(e+f*x)^4*arctan(exp(2*I*(a+b*x)))/f-1/4*I*(e+f*x)^3*polylog(2,-I*exp(2*I*(a+b*x)))/b+1/4*I*(e+f*x)^3*polylog(2,I*exp(2*I*(a+b*x)))/b+3/8*f*(e+f*x)^2*polylog(3,-I*exp(2*I*(a+b*x)))/b^2-3/8*f*(e+f*x)^2*polylog(3,I*exp(2*I*(a+b*x)))/b^2+3/8*I*f^2*(e+f*x)*polylog(4,-I*exp(2*I*(a+b*x)))/b^3-3/8*I*f^2*(e+f*x)*polylog(4,I*exp(2*I*(a+b*x)))/b^3-3/16*f^3*polylog(5,-I*exp(2*I*(a+b*x)))/b^4+3/16*f^3*polylog(5,I*exp(2*I*(a+b*x)))/b^4],
[(e+f*x)^2*arccoth(cot(a+b*x)),x,10,1/3*(e+f*x)^3*arccoth(cot(a+b*x))/f+1/3*I*(e+f*x)^3*arctan(exp(2*I*(a+b*x)))/f-1/4*I*(e+f*x)^2*polylog(2,-I*exp(2*I*(a+b*x)))/b+1/4*I*(e+f*x)^2*polylog(2,I*exp(2*I*(a+b*x)))/b+1/4*f*(e+f*x)*polylog(3,-I*exp(2*I*(a+b*x)))/b^2-1/4*f*(e+f*x)*polylog(3,I*exp(2*I*(a+b*x)))/b^2+1/8*I*f^2*polylog(4,-I*exp(2*I*(a+b*x)))/b^3-1/8*I*f^2*polylog(4,I*exp(2*I*(a+b*x)))/b^3],
[(e+f*x)*arccoth(cot(a+b*x)),x,8,1/2*(e+f*x)^2*arccoth(cot(a+b*x))/f+1/2*I*(e+f*x)^2*arctan(exp(2*I*(a+b*x)))/f-1/4*I*(e+f*x)*polylog(2,-I*exp(2*I*(a+b*x)))/b+1/4*I*(e+f*x)*polylog(2,I*exp(2*I*(a+b*x)))/b+1/8*f*polylog(3,-I*exp(2*I*(a+b*x)))/b^2-1/8*f*polylog(3,I*exp(2*I*(a+b*x)))/b^2],
[arccoth(cot(a+b*x)),x,6,x*arccoth(cot(a+b*x))+I*x*arctan(exp(2*I*(a+b*x)))-1/4*I*polylog(2,-I*exp(2*I*(a+b*x)))/b+1/4*I*polylog(2,I*exp(2*I*(a+b*x)))/b],
[arccoth(cot(a+b*x))/(e+f*x),x,0,CannotIntegrate(arccoth(cot(a+b*x))/(e+f*x),x)],
[x^2*arccoth(c+d*cot(a+b*x)),x,11,1/3*x^3*arccoth(c+d*cot(a+b*x))+1/6*x^3*log(1-(1-c-I*d)*exp(2*I*a+2*I*b*x)/(1-c+I*d))-1/6*x^3*log(1-(1+c+I*d)*exp(2*I*a+2*I*b*x)/(1+c-I*d))-1/4*I*x^2*polylog(2,(1-c-I*d)*exp(2*I*a+2*I*b*x)/(1-c+I*d))/b+1/4*I*x^2*polylog(2,(1+c+I*d)*exp(2*I*a+2*I*b*x)/(1+c-I*d))/b+1/4*x*polylog(3,(1-c-I*d)*exp(2*I*a+2*I*b*x)/(1-c+I*d))/b^2-1/4*x*polylog(3,(1+c+I*d)*exp(2*I*a+2*I*b*x)/(1+c-I*d))/b^2+1/8*I*polylog(4,(1-c-I*d)*exp(2*I*a+2*I*b*x)/(1-c+I*d))/b^3-1/8*I*polylog(4,(1+c+I*d)*exp(2*I*a+2*I*b*x)/(1+c-I*d))/b^3],
[x*arccoth(c+d*cot(a+b*x)),x,9,1/2*x^2*arccoth(c+d*cot(a+b*x))+1/4*x^2*log(1-(1-c-I*d)*exp(2*I*a+2*I*b*x)/(1-c+I*d))-1/4*x^2*log(1-(1+c+I*d)*exp(2*I*a+2*I*b*x)/(1+c-I*d))-1/4*I*x*polylog(2,(1-c-I*d)*exp(2*I*a+2*I*b*x)/(1-c+I*d))/b+1/4*I*x*polylog(2,(1+c+I*d)*exp(2*I*a+2*I*b*x)/(1+c-I*d))/b+1/8*polylog(3,(1-c-I*d)*exp(2*I*a+2*I*b*x)/(1-c+I*d))/b^2-1/8*polylog(3,(1+c+I*d)*exp(2*I*a+2*I*b*x)/(1+c-I*d))/b^2],
[arccoth(c+d*cot(a+b*x)),x,7,x*arccoth(c+d*cot(a+b*x))+1/2*x*log(1-(1-c-I*d)*exp(2*I*a+2*I*b*x)/(1-c+I*d))-1/2*x*log(1-(1+c+I*d)*exp(2*I*a+2*I*b*x)/(1+c-I*d))-1/4*I*polylog(2,(1-c-I*d)*exp(2*I*a+2*I*b*x)/(1-c+I*d))/b+1/4*I*polylog(2,(1+c+I*d)*exp(2*I*a+2*I*b*x)/(1+c-I*d))/b],
[arccoth(c+d*cot(a+b*x))/x,x,0,CannotIntegrate(arccoth(c+d*cot(a+b*x))/x,x)],
[x^2*arccoth(1+I*d+d*cot(a+b*x)),x,7,1/12*I*b*x^4+1/3*x^3*arccoth(1+I*d+d*cot(a+b*x))-1/6*x^3*log(1-(1+I*d)*exp(2*I*a+2*I*b*x))+1/4*I*x^2*polylog(2,(1+I*d)*exp(2*I*a+2*I*b*x))/b-1/4*x*polylog(3,(1+I*d)*exp(2*I*a+2*I*b*x))/b^2-1/8*I*polylog(4,(1+I*d)*exp(2*I*a+2*I*b*x))/b^3],
[x*arccoth(1+I*d+d*cot(a+b*x)),x,6,1/6*I*b*x^3+1/2*x^2*arccoth(1+I*d+d*cot(a+b*x))-1/4*x^2*log(1-(1+I*d)*exp(2*I*a+2*I*b*x))+1/4*I*x*polylog(2,(1+I*d)*exp(2*I*a+2*I*b*x))/b-1/8*polylog(3,(1+I*d)*exp(2*I*a+2*I*b*x))/b^2],
[arccoth(1+I*d+d*cot(a+b*x)),x,5,1/2*I*b*x^2+x*arccoth(1+I*d+d*cot(a+b*x))-1/2*x*log(1-(1+I*d)*exp(2*I*a+2*I*b*x))+1/4*I*polylog(2,(1+I*d)*exp(2*I*a+2*I*b*x))/b],
[arccoth(1+I*d+d*cot(a+b*x))/x,x,0,CannotIntegrate(arccoth(1+I*d+d*cot(a+b*x))/x,x)],
[x^2*arccoth(1-I*d-d*cot(a+b*x)),x,7,1/12*I*b*x^4+1/3*x^3*arccoth(1-I*d-d*cot(a+b*x))-1/6*x^3*log(1-(1-I*d)*exp(2*I*a+2*I*b*x))+1/4*I*x^2*polylog(2,(1-I*d)*exp(2*I*a+2*I*b*x))/b-1/4*x*polylog(3,(1-I*d)*exp(2*I*a+2*I*b*x))/b^2-1/8*I*polylog(4,(1-I*d)*exp(2*I*a+2*I*b*x))/b^3],
[x*arccoth(1-I*d-d*cot(a+b*x)),x,6,1/6*I*b*x^3+1/2*x^2*arccoth(1-I*d-d*cot(a+b*x))-1/4*x^2*log(1-(1-I*d)*exp(2*I*a+2*I*b*x))+1/4*I*x*polylog(2,(1-I*d)*exp(2*I*a+2*I*b*x))/b-1/8*polylog(3,(1-I*d)*exp(2*I*a+2*I*b*x))/b^2],
[arccoth(1-I*d-d*cot(a+b*x)),x,5,1/2*I*b*x^2+x*arccoth(1-I*d-d*cot(a+b*x))-1/2*x*log(1-(1-I*d)*exp(2*I*a+2*I*b*x))+1/4*I*polylog(2,(1-I*d)*exp(2*I*a+2*I*b*x))/b],
[arccoth(1-I*d-d*cot(a+b*x))/x,x,0,CannotIntegrate(arccoth(1-I*d-d*cot(a+b*x))/x,x)],

# Integrands of the form x^m (d+e Log[f x^m]) (a+b ArcCoth[c x^n])
[(a+b*arccoth(c*x^n))*(d+e*log(f*x^m))/x,x,11,a*d*log(x)+1/2*a*e*log(f*x^m)^2/m+1/2*b*d*polylog(2,(-1)/(c*x^n))/n+1/2*b*e*log(f*x^m)*polylog(2,(-1)/(c*x^n))/n-1/2*b*d*polylog(2,1/(c*x^n))/n-1/2*b*e*log(f*x^m)*polylog(2,1/(c*x^n))/n+1/2*b*e*m*polylog(3,(-1)/(c*x^n))/n^2-1/2*b*e*m*polylog(3,1/(c*x^n))/n^2],

# Integrands of the form x^m (d+e Log[f+g x^2]) (a+b ArcCoth[c x])
[x^5*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2)),x,18,1/36*b*(6*d-11*e)*x/c^5-23/45*b*e*x/c^5+1/108*b*(6*d-5*e)*x^3/c^3-8/135*b*e*x^3/c^3+1/90*b*(3*d-e)*x^5/c-1/75*b*e*x^5/c-1/6*e*x^2*(a+b*arccoth(c*x))/c^4-1/12*e*x^4*(a+b*arccoth(c*x))/c^2-1/18*e*x^6*(a+b*arccoth(c*x))-1/36*b*(6*d-11*e)*arctanh(c*x)/c^6+23/45*b*e*arctanh(c*x)/c^6+1/6*b*e*x*log(1-c^2*x^2)/c^5+1/18*b*e*x^3*log(1-c^2*x^2)/c^3+1/30*b*e*x^5*log(1-c^2*x^2)/c-1/6*e*(a+b*arccoth(c*x))*log(1-c^2*x^2)/c^6+1/6*x^6*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))],
[x^3*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2)),x,14,1/8*b*(2*d-3*e)*x/c^3-2/3*b*e*x/c^3+1/24*b*(2*d-e)*x^3/c-1/18*b*e*x^3/c-1/4*e*x^2*(a+b*arccoth(c*x))/c^2-1/8*e*x^4*(a+b*arccoth(c*x))-1/8*b*(2*d-3*e)*arctanh(c*x)/c^4+2/3*b*e*arctanh(c*x)/c^4+1/4*b*e*x*log(1-c^2*x^2)/c^3+1/12*b*e*x^3*log(1-c^2*x^2)/c-1/4*e*(a+b*arccoth(c*x))*log(1-c^2*x^2)/c^4+1/4*x^4*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))],
[x*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2)),x,7,1/2*b*(d-e)*x/c-b*e*x/c+1/2*d*x^2*(a+b*arccoth(c*x))-1/2*e*x^2*(a+b*arccoth(c*x))-1/2*b*(d-e)*arctanh(c*x)/c^2+b*e*arctanh(c*x)/c^2+1/2*b*e*x*log(1-c^2*x^2)/c-1/2*e*(1-c^2*x^2)*(a+b*arccoth(c*x))*log(1-c^2*x^2)/c^2],
[(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))/x,x,21,-1/2*b*e*log(1+1/(c*x))^2*log((-1)/(c*x))+1/2*b*e*log(1+(-1)/(c*x))^2*log(1/(c*x))+a*d*log(x)-b*e*log((c+1/x)/c)*polylog(2,(c+1/x)/c)+b*e*log(1+(-1)/(c*x))*polylog(2,1+(-1)/(c*x))+1/2*b*d*polylog(2,(-1)/(c*x))+1/2*b*e*log(-c^2*x^2)*polylog(2,(-1)/(c*x))-1/2*b*e*(log(1+(-1)/(c*x))+log(1+1/(c*x))+log(-c^2*x^2)-log(1-c^2*x^2))*polylog(2,(-1)/(c*x))-1/2*b*d*polylog(2,1/(c*x))-1/2*b*e*log(-c^2*x^2)*polylog(2,1/(c*x))+1/2*b*e*(log(1+(-1)/(c*x))+log(1+1/(c*x))+log(-c^2*x^2)-log(1-c^2*x^2))*polylog(2,1/(c*x))-1/2*a*e*polylog(2,c^2*x^2)+b*e*polylog(3,(c+1/x)/c)-b*e*polylog(3,1+(-1)/(c*x))+b*e*polylog(3,(-1)/(c*x))-b*e*polylog(3,1/(c*x))],
[(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))/x^3,x,13,-1/2*b*c^2*e*arccoth(c*x)^2-1/2*b*c^2*e*arctanh(c*x)^2-a*c^2*e*log(x)+b*c^2*e*arctanh(c*x)*log(2/(1-c*x))+1/2*(a+b)*c^2*e*log(1-c*x)+1/2*(a-b)*c^2*e*log(1+c*x)-1/2*b*c*(d+e*log(1-c^2*x^2))/x-1/2*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))/x^2+1/2*b*c^2*arctanh(c*x)*(d+e*log(1-c^2*x^2))-b*c^2*e*arccoth(c*x)*log(2+(-2)/(1+c*x))+1/2*b*c^2*e*polylog(2,1+(-2)/(1-c*x))+1/2*b*c^2*e*polylog(2,-1+2/(1+c*x))],
[(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))/x^5,x,17,1/4*a*c^2*e/x^2+5/12*b*c^3*e/x+1/4*b*c^2*e*arccoth(c*x)/x^2-1/4*b*c^4*e*arccoth(c*x)^2-1/4*b*c^4*e*arctanh(c*x)-1/4*b*c^4*e*arctanh(c*x)^2-1/2*a*c^4*e*log(x)+1/2*b*c^4*e*arctanh(c*x)*log(2/(1-c*x))+1/12*(3*a+4*b)*c^4*e*log(1-c*x)+1/12*(3*a-4*b)*c^4*e*log(1+c*x)-1/12*b*c*(d+e*log(1-c^2*x^2))/x^3-1/4*b*c^3*(d+e*log(1-c^2*x^2))/x-1/4*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))/x^4+1/4*b*c^4*arctanh(c*x)*(d+e*log(1-c^2*x^2))-1/2*b*c^4*e*arccoth(c*x)*log(2+(-2)/(1+c*x))+1/4*b*c^4*e*polylog(2,1+(-2)/(1-c*x))+1/4*b*c^4*e*polylog(2,-1+2/(1+c*x))],
[x^4*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2)),x,26,-2/5*a*e*x/c^4-77/300*b*e*x^2/c^3-2/15*a*e*x^3/c^2-9/200*b*e*x^4/c-2/25*a*e*x^5-2/5*b*e*x*arccoth(c*x)/c^4-2/15*b*e*x^3*arccoth(c*x)/c^2-2/25*b*e*x^5*arccoth(c*x)+1/5*b*e*arccoth(c*x)^2/c^5-1/20*(4*a+3*b)*e*log(1-c*x)/c^5+1/20*(4*a-3*b)*e*log(1+c*x)/c^5-23/75*b*e*log(1-c^2*x^2)/c^5-1/20*b*e*log(1-c^2*x^2)^2/c^5+1/10*b*x^2*(d+e*log(1-c^2*x^2))/c^3+1/20*b*x^4*(d+e*log(1-c^2*x^2))/c+1/5*x^5*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))+1/10*b*log(1-c^2*x^2)*(d+e*log(1-c^2*x^2))/c^5],
[x^2*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2)),x,21,-2/3*a*e*x/c^2-5/18*b*e*x^2/c-2/9*a*e*x^3-2/3*b*e*x*arccoth(c*x)/c^2-2/9*b*e*x^3*arccoth(c*x)+1/3*b*e*arccoth(c*x)^2/c^3-1/6*(2*a+b)*e*log(1-c*x)/c^3+1/6*(2*a-b)*e*log(1+c*x)/c^3-4/9*b*e*log(1-c^2*x^2)/c^3-1/12*b*e*log(1-c^2*x^2)^2/c^3+1/6*b*x^2*(d+e*log(1-c^2*x^2))/c+1/3*x^3*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))+1/6*b*log(1-c^2*x^2)*(d+e*log(1-c^2*x^2))/c^3],
[(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2)),x,9,-2*a*e*x-2*b*e*x*arccoth(c*x)+e*(a+b*arccoth(c*x))^2/(b*c)-b*e*log(1-c^2*x^2)/c+x*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))+1/4*b*(d+e*log(1-c^2*x^2))^2/(c*e)],
[(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))/x^2,x,6,-c*e*(a+b*arccoth(c*x))^2/b-(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))/x+1/2*b*c*(d+e*log(1-c^2*x^2))*log(1+(-1)/(1-c^2*x^2))-1/2*b*c*e*polylog(2,1/(1-c^2*x^2))],
[(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))/x^4,x,15,2/3*c^2*e*(a+b*arccoth(c*x))/x-1/3*c^3*e*(a+b*arccoth(c*x))^2/b-b*c^3*e*log(x)+1/3*b*c^3*e*log(1-c^2*x^2)-1/6*b*c*(1-c^2*x^2)*(d+e*log(1-c^2*x^2))/x^2-1/3*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))/x^3+1/6*b*c^3*(d+e*log(1-c^2*x^2))*log(1+(-1)/(1-c^2*x^2))-1/6*b*c^3*e*polylog(2,1/(1-c^2*x^2))],
[(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))/x^6,x,24,7/60*b*c^3*e/x^2+2/15*c^2*e*(a+b*arccoth(c*x))/x^3+2/5*c^4*e*(a+b*arccoth(c*x))/x-1/5*c^5*e*(a+b*arccoth(c*x))^2/b-5/6*b*c^5*e*log(x)+19/60*b*c^5*e*log(1-c^2*x^2)-1/20*b*c*(d+e*log(1-c^2*x^2))/x^4-1/10*b*c^3*(1-c^2*x^2)*(d+e*log(1-c^2*x^2))/x^2-1/5*(a+b*arccoth(c*x))*(d+e*log(1-c^2*x^2))/x^5+1/10*b*c^5*(d+e*log(1-c^2*x^2))*log(1+(-1)/(1-c^2*x^2))-1/10*b*c^5*e*polylog(2,1/(1-c^2*x^2))],
[x*(a+b*arccoth(c*x))*(d+e*log(f+g*x^2)),x,21,1/2*b*(d-e)*x/c-b*e*x/c+1/2*d*x^2*(a+b*arccoth(c*x))-1/2*e*x^2*(a+b*arccoth(c*x))-1/2*b*(d-e)*arctanh(c*x)/c^2-b*e*(c^2*f+g)*arctanh(c*x)*log(2/(1+c*x))/(c^2*g)+1/2*b*e*x*log(f+g*x^2)/c+1/2*e*(f+g*x^2)*(a+b*arccoth(c*x))*log(f+g*x^2)/g-1/2*b*e*(c^2*f+g)*arctanh(c*x)*log(f+g*x^2)/(c^2*g)+1/2*b*e*(c^2*f+g)*arctanh(c*x)*log(2*c*(sqrt(-f)-x*sqrt(g))/((1+c*x)*(c*sqrt(-f)-sqrt(g))))/(c^2*g)+1/2*b*e*(c^2*f+g)*arctanh(c*x)*log(2*c*(sqrt(-f)+x*sqrt(g))/((1+c*x)*(c*sqrt(-f)+sqrt(g))))/(c^2*g)+1/2*b*e*(c^2*f+g)*polylog(2,1+(-2)/(1+c*x))/(c^2*g)-1/4*b*e*(c^2*f+g)*polylog(2,1-2*c*(sqrt(-f)-x*sqrt(g))/((1+c*x)*(c*sqrt(-f)-sqrt(g))))/(c^2*g)-1/4*b*e*(c^2*f+g)*polylog(2,1-2*c*(sqrt(-f)+x*sqrt(g))/((1+c*x)*(c*sqrt(-f)+sqrt(g))))/(c^2*g)+b*e*arctan(x*sqrt(g)/sqrt(f))*sqrt(f)/(c*sqrt(g))],
[(a+b*arccoth(c*x))*(d+e*log(f+g*x^2)),x,38,-2*a*e*x-2*b*e*x*arccoth(c*x)-b*e*log(1-c^2*x^2)/c+x*(a+b*arccoth(c*x))*(d+e*log(f+g*x^2))+1/2*b*log(g*(1-c^2*x^2)/(c^2*f+g))*(d+e*log(f+g*x^2))/c+1/2*b*e*polylog(2,c^2*(f+g*x^2)/(c^2*f+g))/c+2*a*e*arctan(x*sqrt(g)/sqrt(f))*sqrt(f)/sqrt(g)-b*e*arctan(x*sqrt(g)/sqrt(f))*log(1+(-1)/(c*x))*sqrt(f)/sqrt(g)+b*e*arctan(x*sqrt(g)/sqrt(f))*log(1+1/(c*x))*sqrt(f)/sqrt(g)+b*e*arctan(x*sqrt(g)/sqrt(f))*log(-2*(1-c*x)*sqrt(f)*sqrt(g)/((I*c*sqrt(f)-sqrt(g))*(sqrt(f)-I*x*sqrt(g))))*sqrt(f)/sqrt(g)-b*e*arctan(x*sqrt(g)/sqrt(f))*log(2*(1+c*x)*sqrt(f)*sqrt(g)/((I*c*sqrt(f)+sqrt(g))*(sqrt(f)-I*x*sqrt(g))))*sqrt(f)/sqrt(g)-1/2*I*b*e*polylog(2,1+2*(1-c*x)*sqrt(f)*sqrt(g)/((I*c*sqrt(f)-sqrt(g))*(sqrt(f)-I*x*sqrt(g))))*sqrt(f)/sqrt(g)+1/2*I*b*e*polylog(2,1-2*(1+c*x)*sqrt(f)*sqrt(g)/((I*c*sqrt(f)+sqrt(g))*(sqrt(f)-I*x*sqrt(g))))*sqrt(f)/sqrt(g)],
[(a+b*arccoth(c*x))*(d+e*log(f+g*x^2))/x,x,6,b*e*CannotIntegrate(arccoth(c*x)*log(f+g*x^2)/x,x)+a*d*log(x)+1/2*a*e*log(-g*x^2/f)*log(f+g*x^2)+1/2*b*d*polylog(2,(-1)/(c*x))-1/2*b*d*polylog(2,1/(c*x))+1/2*a*e*polylog(2,1+g*x^2/f)],
[(a+b*arccoth(c*x))*(d+e*log(f+g*x^2))/x^2,x,38,-(a+b*arccoth(c*x))*(d+e*log(f+g*x^2))/x+1/2*b*c*log(-g*x^2/f)*(d+e*log(f+g*x^2))-1/2*b*c*log(g*(1-c^2*x^2)/(c^2*f+g))*(d+e*log(f+g*x^2))-1/2*b*c*e*polylog(2,c^2*(f+g*x^2)/(c^2*f+g))+1/2*b*c*e*polylog(2,1+g*x^2/f)+2*a*e*arctan(x*sqrt(g)/sqrt(f))*sqrt(g)/sqrt(f)-b*e*arctan(x*sqrt(g)/sqrt(f))*log(1+(-1)/(c*x))*sqrt(g)/sqrt(f)+b*e*arctan(x*sqrt(g)/sqrt(f))*log(1+1/(c*x))*sqrt(g)/sqrt(f)+b*e*arctan(x*sqrt(g)/sqrt(f))*log(-2*(1-c*x)*sqrt(f)*sqrt(g)/((I*c*sqrt(f)-sqrt(g))*(sqrt(f)-I*x*sqrt(g))))*sqrt(g)/sqrt(f)-b*e*arctan(x*sqrt(g)/sqrt(f))*log(2*(1+c*x)*sqrt(f)*sqrt(g)/((I*c*sqrt(f)+sqrt(g))*(sqrt(f)-I*x*sqrt(g))))*sqrt(g)/sqrt(f)-1/2*I*b*e*polylog(2,1+2*(1-c*x)*sqrt(f)*sqrt(g)/((I*c*sqrt(f)-sqrt(g))*(sqrt(f)-I*x*sqrt(g))))*sqrt(g)/sqrt(f)+1/2*I*b*e*polylog(2,1-2*(1+c*x)*sqrt(f)*sqrt(g)/((I*c*sqrt(f)+sqrt(g))*(sqrt(f)-I*x*sqrt(g))))*sqrt(g)/sqrt(f)],
[(a+b*arccoth(c*x))*(d+e*log(f+g*x^2))/x^3,x,32,a*e*g*log(x)/f+b*e*g*arccoth(c*x)*log(2/(1+c*x))/f+b*c^2*e*arctanh(c*x)*log(2/(1+c*x))-1/2*a*e*g*log(f+g*x^2)/f-1/2*b*c*(d+e*log(f+g*x^2))/x-1/2*(a+b*arccoth(c*x))*(d+e*log(f+g*x^2))/x^2+1/2*b*c^2*arctanh(c*x)*(d+e*log(f+g*x^2))-1/2*b*e*g*arccoth(c*x)*log(2*c*(sqrt(-f)-x*sqrt(g))/((1+c*x)*(c*sqrt(-f)-sqrt(g))))/f-1/2*b*c^2*e*arctanh(c*x)*log(2*c*(sqrt(-f)-x*sqrt(g))/((1+c*x)*(c*sqrt(-f)-sqrt(g))))-1/2*b*e*g*arccoth(c*x)*log(2*c*(sqrt(-f)+x*sqrt(g))/((1+c*x)*(c*sqrt(-f)+sqrt(g))))/f-1/2*b*c^2*e*arctanh(c*x)*log(2*c*(sqrt(-f)+x*sqrt(g))/((1+c*x)*(c*sqrt(-f)+sqrt(g))))+1/2*b*e*g*polylog(2,(-1)/(c*x))/f-1/2*b*e*g*polylog(2,1/(c*x))/f-1/2*b*c^2*e*polylog(2,1+(-2)/(1+c*x))-1/2*b*e*g*polylog(2,1+(-2)/(1+c*x))/f+1/4*b*c^2*e*polylog(2,1-2*c*(sqrt(-f)-x*sqrt(g))/((1+c*x)*(c*sqrt(-f)-sqrt(g))))+1/4*b*e*g*polylog(2,1-2*c*(sqrt(-f)-x*sqrt(g))/((1+c*x)*(c*sqrt(-f)-sqrt(g))))/f+1/4*b*c^2*e*polylog(2,1-2*c*(sqrt(-f)+x*sqrt(g))/((1+c*x)*(c*sqrt(-f)+sqrt(g))))+1/4*b*e*g*polylog(2,1-2*c*(sqrt(-f)+x*sqrt(g))/((1+c*x)*(c*sqrt(-f)+sqrt(g))))/f+b*c*e*arctan(x*sqrt(g)/sqrt(f))*sqrt(g)/sqrt(f)],

# Integrands involving inverse hyperbolic cotangents of exponentials
[arccoth(exp(x)),x,2,1/2*polylog(2,(-1)/exp(x))-1/2*polylog(2,exp(-x))],
[x*arccoth(exp(x)),x,7,1/2*x*polylog(2,(-1)/exp(x))-1/2*x*polylog(2,exp(-x))+1/2*polylog(3,(-1)/exp(x))-1/2*polylog(3,exp(-x))],
[x^2*arccoth(exp(x)),x,9,1/2*x^2*polylog(2,(-1)/exp(x))-1/2*x^2*polylog(2,exp(-x))+x*polylog(3,(-1)/exp(x))-x*polylog(3,exp(-x))+polylog(4,(-1)/exp(x))-polylog(4,exp(-x))],
[arccoth(exp(a+b*x)),x,2,1/2*polylog(2,-exp(-a-b*x))/b-1/2*polylog(2,exp(-a-b*x))/b],
[x*arccoth(exp(a+b*x)),x,7,1/2*x*polylog(2,-exp(-a-b*x))/b-1/2*x*polylog(2,exp(-a-b*x))/b+1/2*polylog(3,-exp(-a-b*x))/b^2-1/2*polylog(3,exp(-a-b*x))/b^2],
[x^2*arccoth(exp(a+b*x)),x,9,1/2*x^2*polylog(2,-exp(-a-b*x))/b-1/2*x^2*polylog(2,exp(-a-b*x))/b+x*polylog(3,-exp(-a-b*x))/b^2-x*polylog(3,exp(-a-b*x))/b^2+polylog(4,-exp(-a-b*x))/b^3-polylog(4,exp(-a-b*x))/b^3],
[arccoth(a+b*f^(c+d*x)),x,6,-arccoth(a+b*f^(c+d*x))*log(2/(1+a+b*f^(c+d*x)))/(d*log(f))+arccoth(a+b*f^(c+d*x))*log(2*b*f^(c+d*x)/((1-a)*(1+a+b*f^(c+d*x))))/(d*log(f))+1/2*polylog(2,1+(-2)/(1+a+b*f^(c+d*x)))/(d*log(f))-1/2*polylog(2,1-2*b*f^(c+d*x)/((1-a)*(1+a+b*f^(c+d*x))))/(d*log(f))],
[x*arccoth(a+b*f^(c+d*x)),x,25,1/4*x^2*log(1-b*f^(c+d*x)/(1-a))-1/4*x^2*log(1+b*f^(c+d*x)/(1+a))-1/4*x^2*log(1+(-1)/(a+b*f^(c+d*x)))+1/4*x^2*log(1+1/(a+b*f^(c+d*x)))+1/2*x*polylog(2,b*f^(c+d*x)/(1-a))/(d*log(f))-1/2*x*polylog(2,-b*f^(c+d*x)/(1+a))/(d*log(f))-1/2*polylog(3,b*f^(c+d*x)/(1-a))/(d^2*log(f)^2)+1/2*polylog(3,-b*f^(c+d*x)/(1+a))/(d^2*log(f)^2)],
[x^2*arccoth(a+b*f^(c+d*x)),x,29,1/6*x^3*log(1-b*f^(c+d*x)/(1-a))-1/6*x^3*log(1+b*f^(c+d*x)/(1+a))-1/6*x^3*log(1+(-1)/(a+b*f^(c+d*x)))+1/6*x^3*log(1+1/(a+b*f^(c+d*x)))+1/2*x^2*polylog(2,b*f^(c+d*x)/(1-a))/(d*log(f))-1/2*x^2*polylog(2,-b*f^(c+d*x)/(1+a))/(d*log(f))-x*polylog(3,b*f^(c+d*x)/(1-a))/(d^2*log(f)^2)+x*polylog(3,-b*f^(c+d*x)/(1+a))/(d^2*log(f)^2)+polylog(4,b*f^(c+d*x)/(1-a))/(d^3*log(f)^3)-polylog(4,-b*f^(c+d*x)/(1+a))/(d^3*log(f)^3)],

# Miscellaneous integrands involving inverse hyperbolic cotangents
[1/((a-a*x^2)*(b-2*b*arccoth(x))),x,1,-1/2*log(1-2*arccoth(x))/(a*b)],
[x^3*arccoth(a+b*x^4),x,4,1/4*(a+b*x^4)*arccoth(a+b*x^4)/b+1/8*log(1-(a+b*x^4)^2)/b],
[x^(-1+n)*arccoth(a+b*x^n),x,4,(a+b*x^n)*arccoth(a+b*x^n)/(b*n)+1/2*log(1-(a+b*x^n)^2)/(b*n)],
[exp(c*(a+b*x))*arccoth(sinh(a*c+b*c*x)),x,8,exp(a*c+b*c*x)*arccoth(sinh(c*(a+b*x)))/(b*c)+1/2*log(3-exp(2*c*(a+b*x))-2*sqrt(2))*(1-sqrt(2))/(b*c)+1/2*log(3-exp(2*c*(a+b*x))+2*sqrt(2))*(1+sqrt(2))/(b*c)],
[exp(c*(a+b*x))*arccoth(cosh(a*c+b*c*x)),x,5,exp(a*c+b*c*x)*arccoth(cosh(c*(a+b*x)))/(b*c)+log(1-exp(2*c*(a+b*x)))/(b*c)],
[exp(c*(a+b*x))*arccoth(tanh(a*c+b*c*x)),x,3,-exp(a*c+b*c*x)/(b*c)+exp(a*c+b*c*x)*arccoth(tanh(c*(a+b*x)))/(b*c)],
[exp(c*(a+b*x))*arccoth(coth(a*c+b*c*x)),x,3,-exp(a*c+b*c*x)/(b*c)+exp(a*c+b*c*x)*arccoth(coth(c*(a+b*x)))/(b*c)],
[exp(c*(a+b*x))*arccoth(sech(a*c+b*c*x)),x,5,exp(a*c+b*c*x)*arccoth(sech(c*(a+b*x)))/(b*c)+log(1-exp(2*c*(a+b*x)))/(b*c)],
[exp(c*(a+b*x))*arccoth(csch(a*c+b*c*x)),x,8,exp(a*c+b*c*x)*arccoth(csch(c*(a+b*x)))/(b*c)+1/2*log(3-exp(2*c*(a+b*x))-2*sqrt(2))*(1-sqrt(2))/(b*c)+1/2*log(3-exp(2*c*(a+b*x))+2*sqrt(2))*(1+sqrt(2))/(b*c)]]:
