# Maple integration test file: "7 Inverse hyperbolic functions\7.3 Inverse hyperbolic tangent\7.3.2 (d x)^m (a+b arctanh(c x^n))^p.txt"

lst:=[

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

# Integrands of the form (d x)^m (a+b ArcTanh[c x^1])^p

# Integrands of the form x^m (a+b ArcTanh[c x])^p
[x^5*(a+b*arctanh(c*x)),x,4,1/6*b*x/c^5+1/18*b*x^3/c^3+1/30*b*x^5/c-1/6*b*arctanh(c*x)/c^6+1/6*x^6*(a+b*arctanh(c*x))],
[x^4*(a+b*arctanh(c*x)),x,4,1/10*b*x^2/c^3+1/20*b*x^4/c+1/5*x^5*(a+b*arctanh(c*x))+1/10*b*log(1-c^2*x^2)/c^5],
[x^3*(a+b*arctanh(c*x)),x,4,1/4*b*x/c^3+1/12*b*x^3/c-1/4*b*arctanh(c*x)/c^4+1/4*x^4*(a+b*arctanh(c*x))],
[x^2*(a+b*arctanh(c*x)),x,4,1/6*b*x^2/c+1/3*x^3*(a+b*arctanh(c*x))+1/6*b*log(1-c^2*x^2)/c^3],
[x*(a+b*arctanh(c*x)),x,3,1/2*b*x/c-1/2*b*arctanh(c*x)/c^2+1/2*x^2*(a+b*arctanh(c*x))],
[a+b*arctanh(c*x),x,3,a*x+b*x*arctanh(c*x)+1/2*b*log(1-c^2*x^2)/c],
[(a+b*arctanh(c*x))/x,x,1,a*log(x)-1/2*b*polylog(2,-c*x)+1/2*b*polylog(2,c*x)],
[(a+b*arctanh(c*x))/x^2,x,5,(-a-b*arctanh(c*x))/x+b*c*log(x)-1/2*b*c*log(1-c^2*x^2)],
[(a+b*arctanh(c*x))/x^3,x,3,-1/2*b*c/x+1/2*b*c^2*arctanh(c*x)+1/2*(-a-b*arctanh(c*x))/x^2],
[(a+b*arctanh(c*x))/x^4,x,4,-1/6*b*c/x^2+1/3*(-a-b*arctanh(c*x))/x^3+1/3*b*c^3*log(x)-1/6*b*c^3*log(1-c^2*x^2)],
[(a+b*arctanh(c*x))/x^5,x,4,-1/12*b*c/x^3-1/4*b*c^3/x+1/4*b*c^4*arctanh(c*x)+1/4*(-a-b*arctanh(c*x))/x^4],
[(a+b*arctanh(c*x))/x^6,x,4,-1/20*b*c/x^4-1/10*b*c^3/x^2+1/5*(-a-b*arctanh(c*x))/x^5+1/5*b*c^5*log(x)-1/10*b*c^5*log(1-c^2*x^2)],
[x^5*(a+b*arctanh(c*x))^2,x,16,1/3*a*b*x/c^5+4/45*b^2*x^2/c^4+1/60*b^2*x^4/c^2+1/3*b^2*x*arctanh(c*x)/c^5+1/9*b*x^3*(a+b*arctanh(c*x))/c^3+1/15*b*x^5*(a+b*arctanh(c*x))/c-1/6*(a+b*arctanh(c*x))^2/c^6+1/6*x^6*(a+b*arctanh(c*x))^2+23/90*b^2*log(1-c^2*x^2)/c^6],
[x^4*(a+b*arctanh(c*x))^2,x,14,3/10*b^2*x/c^4+1/30*b^2*x^3/c^2-3/10*b^2*arctanh(c*x)/c^5+1/5*b*x^2*(a+b*arctanh(c*x))/c^3+1/10*b*x^4*(a+b*arctanh(c*x))/c+1/5*(a+b*arctanh(c*x))^2/c^5+1/5*x^5*(a+b*arctanh(c*x))^2-2/5*b*(a+b*arctanh(c*x))*log(2/(1-c*x))/c^5-1/5*b^2*polylog(2,1+(-2)/(1-c*x))/c^5],
[x^3*(a+b*arctanh(c*x))^2,x,11,1/2*a*b*x/c^3+1/12*b^2*x^2/c^2+1/2*b^2*x*arctanh(c*x)/c^3+1/6*b*x^3*(a+b*arctanh(c*x))/c-1/4*(a+b*arctanh(c*x))^2/c^4+1/4*x^4*(a+b*arctanh(c*x))^2+1/3*b^2*log(1-c^2*x^2)/c^4],
[x^2*(a+b*arctanh(c*x))^2,x,9,1/3*b^2*x/c^2-1/3*b^2*arctanh(c*x)/c^3+1/3*b*x^2*(a+b*arctanh(c*x))/c+1/3*(a+b*arctanh(c*x))^2/c^3+1/3*x^3*(a+b*arctanh(c*x))^2-2/3*b*(a+b*arctanh(c*x))*log(2/(1-c*x))/c^3-1/3*b^2*polylog(2,1+(-2)/(1-c*x))/c^3],
[x*(a+b*arctanh(c*x))^2,x,6,a*b*x/c+b^2*x*arctanh(c*x)/c-1/2*(a+b*arctanh(c*x))^2/c^2+1/2*x^2*(a+b*arctanh(c*x))^2+1/2*b^2*log(1-c^2*x^2)/c^2],
[(a+b*arctanh(c*x))^2,x,5,(a+b*arctanh(c*x))^2/c+x*(a+b*arctanh(c*x))^2-2*b*(a+b*arctanh(c*x))*log(2/(1-c*x))/c-b^2*polylog(2,1+(-2)/(1-c*x))/c],
[(a+b*arctanh(c*x))^2/x,x,6,2*(a+b*arctanh(c*x))^2*arctanh(1+(-2)/(1-c*x))-b*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1-c*x))+b*(a+b*arctanh(c*x))*polylog(2,-1+2/(1-c*x))+1/2*b^2*polylog(3,1+(-2)/(1-c*x))-1/2*b^2*polylog(3,-1+2/(1-c*x))],
[(a+b*arctanh(c*x))^2/x^2,x,4,c*(a+b*arctanh(c*x))^2-(a+b*arctanh(c*x))^2/x+2*b*c*(a+b*arctanh(c*x))*log(2+(-2)/(1+c*x))-b^2*c*polylog(2,-1+2/(1+c*x))],
[(a+b*arctanh(c*x))^2/x^3,x,8,-b*c*(a+b*arctanh(c*x))/x+1/2*c^2*(a+b*arctanh(c*x))^2-1/2*(a+b*arctanh(c*x))^2/x^2+b^2*c^2*log(x)-1/2*b^2*c^2*log(1-c^2*x^2)],
[(a+b*arctanh(c*x))^2/x^4,x,8,-1/3*b^2*c^2/x+1/3*b^2*c^3*arctanh(c*x)-1/3*b*c*(a+b*arctanh(c*x))/x^2+1/3*c^3*(a+b*arctanh(c*x))^2-1/3*(a+b*arctanh(c*x))^2/x^3+2/3*b*c^3*(a+b*arctanh(c*x))*log(2+(-2)/(1+c*x))-1/3*b^2*c^3*polylog(2,-1+2/(1+c*x))],
[(a+b*arctanh(c*x))^2/x^5,x,13,-1/12*b^2*c^2/x^2-1/6*b*c*(a+b*arctanh(c*x))/x^3-1/2*b*c^3*(a+b*arctanh(c*x))/x+1/4*c^4*(a+b*arctanh(c*x))^2-1/4*(a+b*arctanh(c*x))^2/x^4+2/3*b^2*c^4*log(x)-1/3*b^2*c^4*log(1-c^2*x^2)],
[x^5*(a+b*arctanh(c*x))^3,x,33,19/60*b^3*x/c^5+1/60*b^3*x^3/c^3-19/60*b^3*arctanh(c*x)/c^6+4/15*b^2*x^2*(a+b*arctanh(c*x))/c^4+1/20*b^2*x^4*(a+b*arctanh(c*x))/c^2+23/30*b*(a+b*arctanh(c*x))^2/c^6+1/2*b*x*(a+b*arctanh(c*x))^2/c^5+1/6*b*x^3*(a+b*arctanh(c*x))^2/c^3+1/10*b*x^5*(a+b*arctanh(c*x))^2/c-1/6*(a+b*arctanh(c*x))^3/c^6+1/6*x^6*(a+b*arctanh(c*x))^3-23/15*b^2*(a+b*arctanh(c*x))*log(2/(1-c*x))/c^6-23/30*b^3*polylog(2,1+(-2)/(1-c*x))/c^6],
[x^4*(a+b*arctanh(c*x))^3,x,24,9/10*a*b^2*x/c^4+1/20*b^3*x^2/c^3+9/10*b^3*x*arctanh(c*x)/c^4+1/10*b^2*x^3*(a+b*arctanh(c*x))/c^2-9/20*b*(a+b*arctanh(c*x))^2/c^5+3/10*b*x^2*(a+b*arctanh(c*x))^2/c^3+3/20*b*x^4*(a+b*arctanh(c*x))^2/c+1/5*(a+b*arctanh(c*x))^3/c^5+1/5*x^5*(a+b*arctanh(c*x))^3-3/5*b*(a+b*arctanh(c*x))^2*log(2/(1-c*x))/c^5+1/2*b^3*log(1-c^2*x^2)/c^5-3/5*b^2*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1-c*x))/c^5+3/10*b^3*polylog(3,1+(-2)/(1-c*x))/c^5],
[x^3*(a+b*arctanh(c*x))^3,x,18,1/4*b^3*x/c^3-1/4*b^3*arctanh(c*x)/c^4+1/4*b^2*x^2*(a+b*arctanh(c*x))/c^2+b*(a+b*arctanh(c*x))^2/c^4+3/4*b*x*(a+b*arctanh(c*x))^2/c^3+1/4*b*x^3*(a+b*arctanh(c*x))^2/c-1/4*(a+b*arctanh(c*x))^3/c^4+1/4*x^4*(a+b*arctanh(c*x))^3-2*b^2*(a+b*arctanh(c*x))*log(2/(1-c*x))/c^4-b^3*polylog(2,1+(-2)/(1-c*x))/c^4],
[x^2*(a+b*arctanh(c*x))^3,x,12,a*b^2*x/c^2+b^3*x*arctanh(c*x)/c^2-1/2*b*(a+b*arctanh(c*x))^2/c^3+1/2*b*x^2*(a+b*arctanh(c*x))^2/c+1/3*(a+b*arctanh(c*x))^3/c^3+1/3*x^3*(a+b*arctanh(c*x))^3-b*(a+b*arctanh(c*x))^2*log(2/(1-c*x))/c^3+1/2*b^3*log(1-c^2*x^2)/c^3-b^2*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1-c*x))/c^3+1/2*b^3*polylog(3,1+(-2)/(1-c*x))/c^3],
[x*(a+b*arctanh(c*x))^3,x,8,3/2*b*(a+b*arctanh(c*x))^2/c^2+3/2*b*x*(a+b*arctanh(c*x))^2/c-1/2*(a+b*arctanh(c*x))^3/c^2+1/2*x^2*(a+b*arctanh(c*x))^3-3*b^2*(a+b*arctanh(c*x))*log(2/(1-c*x))/c^2-3/2*b^3*polylog(2,1+(-2)/(1-c*x))/c^2],
[(a+b*arctanh(c*x))^3,x,5,(a+b*arctanh(c*x))^3/c+x*(a+b*arctanh(c*x))^3-3*b*(a+b*arctanh(c*x))^2*log(2/(1-c*x))/c-3*b^2*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1-c*x))/c+3/2*b^3*polylog(3,1+(-2)/(1-c*x))/c],
[(a+b*arctanh(c*x))^3/x,x,8,2*(a+b*arctanh(c*x))^3*arctanh(1+(-2)/(1-c*x))-3/2*b*(a+b*arctanh(c*x))^2*polylog(2,1+(-2)/(1-c*x))+3/2*b*(a+b*arctanh(c*x))^2*polylog(2,-1+2/(1-c*x))+3/2*b^2*(a+b*arctanh(c*x))*polylog(3,1+(-2)/(1-c*x))-3/2*b^2*(a+b*arctanh(c*x))*polylog(3,-1+2/(1-c*x))-3/4*b^3*polylog(4,1+(-2)/(1-c*x))+3/4*b^3*polylog(4,-1+2/(1-c*x))],
[(a+b*arctanh(c*x))^3/x^2,x,5,c*(a+b*arctanh(c*x))^3-(a+b*arctanh(c*x))^3/x+3*b*c*(a+b*arctanh(c*x))^2*log(2+(-2)/(1+c*x))-3*b^2*c*(a+b*arctanh(c*x))*polylog(2,-1+2/(1+c*x))-3/2*b^3*c*polylog(3,-1+2/(1+c*x))],
[(a+b*arctanh(c*x))^3/x^3,x,7,3/2*b*c^2*(a+b*arctanh(c*x))^2-3/2*b*c*(a+b*arctanh(c*x))^2/x+1/2*c^2*(a+b*arctanh(c*x))^3-1/2*(a+b*arctanh(c*x))^3/x^2+3*b^2*c^2*(a+b*arctanh(c*x))*log(2+(-2)/(1+c*x))-3/2*b^3*c^2*polylog(2,-1+2/(1+c*x))],
[(a+b*arctanh(c*x))^3/x^4,x,14,-b^2*c^2*(a+b*arctanh(c*x))/x+1/2*b*c^3*(a+b*arctanh(c*x))^2-1/2*b*c*(a+b*arctanh(c*x))^2/x^2+1/3*c^3*(a+b*arctanh(c*x))^3-1/3*(a+b*arctanh(c*x))^3/x^3+b^3*c^3*log(x)-1/2*b^3*c^3*log(1-c^2*x^2)+b*c^3*(a+b*arctanh(c*x))^2*log(2+(-2)/(1+c*x))-b^2*c^3*(a+b*arctanh(c*x))*polylog(2,-1+2/(1+c*x))-1/2*b^3*c^3*polylog(3,-1+2/(1+c*x))],
[(a+b*arctanh(c*x))^3/x^5,x,16,-1/4*b^3*c^3/x+1/4*b^3*c^4*arctanh(c*x)-1/4*b^2*c^2*(a+b*arctanh(c*x))/x^2+b*c^4*(a+b*arctanh(c*x))^2-1/4*b*c*(a+b*arctanh(c*x))^2/x^3-3/4*b*c^3*(a+b*arctanh(c*x))^2/x+1/4*c^4*(a+b*arctanh(c*x))^3-1/4*(a+b*arctanh(c*x))^3/x^4+2*b^2*c^4*(a+b*arctanh(c*x))*log(2+(-2)/(1+c*x))-b^3*c^4*polylog(2,-1+2/(1+c*x))],

# Integrands of the form (d x)^(m/2) (a+b ArcTanh[c x])^p
[(d*x)^(5/2)*(a+b*arctanh(c*x)),x,7,4/35*b*(d*x)^(5/2)/c-2/7*b*d^(5/2)*arctan(sqrt(c)*sqrt(d*x)/sqrt(d))/c^(7/2)+2/7*(d*x)^(7/2)*(a+b*arctanh(c*x))/d-2/7*b*d^(5/2)*arctanh(sqrt(c)*sqrt(d*x)/sqrt(d))/c^(7/2)+4/7*b*d^2*sqrt(d*x)/c^3],
[(d*x)^(3/2)*(a+b*arctanh(c*x)),x,6,4/15*b*(d*x)^(3/2)/c+2/5*b*d^(3/2)*arctan(sqrt(c)*sqrt(d*x)/sqrt(d))/c^(5/2)+2/5*(d*x)^(5/2)*(a+b*arctanh(c*x))/d-2/5*b*d^(3/2)*arctanh(sqrt(c)*sqrt(d*x)/sqrt(d))/c^(5/2)],
[(d*x)^(1/2)*(a+b*arctanh(c*x)),x,6,2/3*(d*x)^(3/2)*(a+b*arctanh(c*x))/d-2/3*b*arctan(sqrt(c)*sqrt(d*x)/sqrt(d))*sqrt(d)/c^(3/2)-2/3*b*arctanh(sqrt(c)*sqrt(d*x)/sqrt(d))*sqrt(d)/c^(3/2)+4/3*b*sqrt(d*x)/c],
[(a+b*arctanh(c*x))/(d*x)^(1/2),x,5,2*b*arctan(sqrt(c)*sqrt(d*x)/sqrt(d))/(sqrt(c)*sqrt(d))-2*b*arctanh(sqrt(c)*sqrt(d*x)/sqrt(d))/(sqrt(c)*sqrt(d))+2*(a+b*arctanh(c*x))*sqrt(d*x)/d],
[(a+b*arctanh(c*x))/(d*x)^(3/2),x,5,2*b*arctan(sqrt(c)*sqrt(d*x)/sqrt(d))*sqrt(c)/d^(3/2)+2*b*arctanh(sqrt(c)*sqrt(d*x)/sqrt(d))*sqrt(c)/d^(3/2)-2*(a+b*arctanh(c*x))/(d*sqrt(d*x))],
[(a+b*arctanh(c*x))/(d*x)^(5/2),x,6,-2/3*b*c^(3/2)*arctan(sqrt(c)*sqrt(d*x)/sqrt(d))/d^(5/2)-2/3*(a+b*arctanh(c*x))/(d*(d*x)^(3/2))+2/3*b*c^(3/2)*arctanh(sqrt(c)*sqrt(d*x)/sqrt(d))/d^(5/2)-4/3*b*c/(d^2*sqrt(d*x))],
[(a+b*arctanh(c*x))/(d*x)^(7/2),x,6,-4/15*b*c/(d^2*(d*x)^(3/2))+2/5*b*c^(5/2)*arctan(sqrt(c)*sqrt(d*x)/sqrt(d))/d^(7/2)-2/5*(a+b*arctanh(c*x))/(d*(d*x)^(5/2))+2/5*b*c^(5/2)*arctanh(sqrt(c)*sqrt(d*x)/sqrt(d))/d^(7/2)],
[(a+b*arctanh(c*x))/(d*x)^(9/2),x,7,-4/35*b*c/(d^2*(d*x)^(5/2))-2/7*b*c^(7/2)*arctan(sqrt(c)*sqrt(d*x)/sqrt(d))/d^(9/2)-2/7*(a+b*arctanh(c*x))/(d*(d*x)^(7/2))+2/7*b*c^(7/2)*arctanh(sqrt(c)*sqrt(d*x)/sqrt(d))/d^(9/2)-4/7*b*c^3/(d^4*sqrt(d*x))],

# Integrands of the form (d x)^m (a+b ArcTanh[c x])^p when m symbolic
[(d*x)^m*(a+b*arctanh(c*x))^3,x,0,Unintegrable((d*x)^m*(a+b*arctanh(c*x))^3,x)],
[(d*x)^m*(a+b*arctanh(c*x))^2,x,0,Unintegrable((d*x)^m*(a+b*arctanh(c*x))^2,x)],
[(d*x)^m*(a+b*arctanh(c*x)),x,2,(d*x)^(1+m)*(a+b*arctanh(c*x))/(d*(1+m))-b*c*(d*x)^(2+m)*hypergeom([1,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)/(d^2*(1+m)*(2+m))],
[(d*x)^m/(a+b*arctanh(c*x)),x,0,Unintegrable((d*x)^m/(a+b*arctanh(c*x)),x)],
[(d*x)^m/(a+b*arctanh(c*x))^2,x,0,Unintegrable((d*x)^m/(a+b*arctanh(c*x))^2,x)],

# Integrands of the form (d x)^m (a + b ArcTanh[c x])^p with p symbolic
[(a+b*arctanh(c*x))^p,x,0,Unintegrable((a+b*arctanh(c*x))^p,x)],
[(d*x)^m*(a+b*arctanh(c*x))^p,x,0,Unintegrable((d*x)^m*(a+b*arctanh(c*x))^p,x)],

# Integrands of the form (d x)^m (a+b ArcTanh[c x^2])^p

# Integrands of the form x^m (a+b ArcTanh[c x^2])^p
[x^7*(a+b*arctanh(c*x^2)),x,5,1/8*b*x^2/c^3+1/24*b*x^6/c-1/8*b*arctanh(c*x^2)/c^4+1/8*x^8*(a+b*arctanh(c*x^2))],
[x^5*(a+b*arctanh(c*x^2)),x,4,1/12*b*x^4/c+1/6*x^6*(a+b*arctanh(c*x^2))+1/12*b*log(1-c^2*x^4)/c^3],
[x^3*(a+b*arctanh(c*x^2)),x,4,1/4*b*x^2/c-1/4*b*arctanh(c*x^2)/c^2+1/4*x^4*(a+b*arctanh(c*x^2))],
[x*(a+b*arctanh(c*x^2)),x,2,1/2*x^2*(a+b*arctanh(c*x^2))+1/4*b*log(1-c^2*x^4)/c],
[(a+b*arctanh(c*x^2))/x,x,2,a*log(x)-1/4*b*polylog(2,-c*x^2)+1/4*b*polylog(2,c*x^2)],
[(a+b*arctanh(c*x^2))/x^3,x,5,1/2*(-a-b*arctanh(c*x^2))/x^2+b*c*log(x)-1/4*b*c*log(1-c^2*x^4)],
[(a+b*arctanh(c*x^2))/x^5,x,4,-1/4*b*c/x^2+1/4*b*c^2*arctanh(c*x^2)+1/4*(-a-b*arctanh(c*x^2))/x^4],
[(a+b*arctanh(c*x^2))/x^7,x,4,-1/12*b*c/x^4+1/6*(-a-b*arctanh(c*x^2))/x^6+1/3*b*c^3*log(x)-1/12*b*c^3*log(1-c^2*x^4)],
[x^4*(a+b*arctanh(c*x^2)),x,5,2/15*b*x^3/c+1/5*b*arctan(x*sqrt(c))/c^(5/2)+1/5*x^5*(a+b*arctanh(c*x^2))-1/5*b*arctanh(x*sqrt(c))/c^(5/2)],
[x^2*(a+b*arctanh(c*x^2)),x,5,2/3*b*x/c-1/3*b*arctan(x*sqrt(c))/c^(3/2)+1/3*x^3*(a+b*arctanh(c*x^2))-1/3*b*arctanh(x*sqrt(c))/c^(3/2)],
[a+b*arctanh(c*x^2),x,5,a*x+b*x*arctanh(c*x^2)+b*arctan(x*sqrt(c))/sqrt(c)-b*arctanh(x*sqrt(c))/sqrt(c)],
[(a+b*arctanh(c*x^2))/x^2,x,4,(-a-b*arctanh(c*x^2))/x+b*arctan(x*sqrt(c))*sqrt(c)+b*arctanh(x*sqrt(c))*sqrt(c)],
[(a+b*arctanh(c*x^2))/x^4,x,5,-2/3*b*c/x-1/3*b*c^(3/2)*arctan(x*sqrt(c))+1/3*(-a-b*arctanh(c*x^2))/x^3+1/3*b*c^(3/2)*arctanh(x*sqrt(c))],
[(a+b*arctanh(c*x^2))/x^6,x,5,-2/15*b*c/x^3+1/5*b*c^(5/2)*arctan(x*sqrt(c))+1/5*(-a-b*arctanh(c*x^2))/x^5+1/5*b*c^(5/2)*arctanh(x*sqrt(c))],
[x^7*(a+b*arctanh(c*x^2))^2,x,12,1/4*a*b*x^2/c^3+1/24*b^2*x^4/c^2+1/4*b^2*x^2*arctanh(c*x^2)/c^3+1/12*b*x^6*(a+b*arctanh(c*x^2))/c-1/8*(a+b*arctanh(c*x^2))^2/c^4+1/8*x^8*(a+b*arctanh(c*x^2))^2+1/6*b^2*log(1-c^2*x^4)/c^4],
[x^5*(a+b*arctanh(c*x^2))^2,x,10,1/6*b^2*x^2/c^2-1/6*b^2*arctanh(c*x^2)/c^3+1/6*b*x^4*(a+b*arctanh(c*x^2))/c+1/6*(a+b*arctanh(c*x^2))^2/c^3+1/6*x^6*(a+b*arctanh(c*x^2))^2-1/3*b*(a+b*arctanh(c*x^2))*log(2/(1-c*x^2))/c^3-1/6*b^2*polylog(2,1+(-2)/(1-c*x^2))/c^3],
[x^3*(a+b*arctanh(c*x^2))^2,x,7,1/2*a*b*x^2/c+1/2*b^2*x^2*arctanh(c*x^2)/c-1/4*(a+b*arctanh(c*x^2))^2/c^2+1/4*x^4*(a+b*arctanh(c*x^2))^2+1/4*b^2*log(1-c^2*x^4)/c^2],
[x*(a+b*arctanh(c*x^2))^2,x,6,1/2*(a+b*arctanh(c*x^2))^2/c+1/2*x^2*(a+b*arctanh(c*x^2))^2-b*(a+b*arctanh(c*x^2))*log(2/(1-c*x^2))/c-1/2*b^2*polylog(2,1+(-2)/(1-c*x^2))/c],
[(a+b*arctanh(c*x^2))^2/x,x,7,(a+b*arctanh(c*x^2))^2*arctanh(1+(-2)/(1-c*x^2))-1/2*b*(a+b*arctanh(c*x^2))*polylog(2,1+(-2)/(1-c*x^2))+1/2*b*(a+b*arctanh(c*x^2))*polylog(2,-1+2/(1-c*x^2))+1/4*b^2*polylog(3,1+(-2)/(1-c*x^2))-1/4*b^2*polylog(3,-1+2/(1-c*x^2))],
[(a+b*arctanh(c*x^2))^2/x^3,x,5,1/2*c*(a+b*arctanh(c*x^2))^2-1/2*(a+b*arctanh(c*x^2))^2/x^2+b*c*(a+b*arctanh(c*x^2))*log(2+(-2)/(1+c*x^2))-1/2*b^2*c*polylog(2,-1+2/(1+c*x^2))],
[(a+b*arctanh(c*x^2))^2/x^5,x,9,-1/2*b*c*(a+b*arctanh(c*x^2))/x^2+1/4*c^2*(a+b*arctanh(c*x^2))^2-1/4*(a+b*arctanh(c*x^2))^2/x^4+b^2*c^2*log(x)-1/4*b^2*c^2*log(1-c^2*x^4)],
[x^4*(a+b*arctanh(c*x^2))^2,x,102,8/15*b^2*x/c^2+2/15*a*b*x^3/c-2/25*a*b*x^5+2/5*a*b*arctan(x*sqrt(c))/c^(5/2)-4/15*b^2*arctan(x*sqrt(c))/c^(5/2)+1/5*I*b^2*arctan(x*sqrt(c))^2/c^(5/2)-4/15*b^2*arctanh(x*sqrt(c))/c^(5/2)-1/5*b^2*arctanh(x*sqrt(c))^2/c^(5/2)-1/15*b^2*x^3*log(1-c*x^2)/c+1/25*b^2*x^5*log(1-c*x^2)-1/5*b^2*arctan(x*sqrt(c))*log(1-c*x^2)/c^(5/2)+1/15*b*x^3*(2*a-b*log(1-c*x^2))/c+1/25*b*x^5*(2*a-b*log(1-c*x^2))-1/5*b*arctanh(x*sqrt(c))*(2*a-b*log(1-c*x^2))/c^(5/2)+1/20*x^5*(2*a-b*log(1-c*x^2))^2+2/15*b^2*x^3*log(1+c*x^2)/c+1/5*a*b*x^5*log(1+c*x^2)+1/5*b^2*arctan(x*sqrt(c))*log(1+c*x^2)/c^(5/2)-1/5*b^2*arctanh(x*sqrt(c))*log(1+c*x^2)/c^(5/2)-1/10*b^2*x^5*log(1-c*x^2)*log(1+c*x^2)+1/20*b^2*x^5*log(1+c*x^2)^2+2/5*b^2*arctanh(x*sqrt(c))*log(2/(1-x*sqrt(c)))/c^(5/2)-2/5*b^2*arctan(x*sqrt(c))*log(2/(1-I*x*sqrt(c)))/c^(5/2)+1/5*b^2*arctan(x*sqrt(c))*log((1+I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))/c^(5/2)+2/5*b^2*arctan(x*sqrt(c))*log(2/(1+I*x*sqrt(c)))/c^(5/2)-2/5*b^2*arctanh(x*sqrt(c))*log(2/(1+x*sqrt(c)))/c^(5/2)+1/5*b^2*arctanh(x*sqrt(c))*log(-2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))/c^(5/2)+1/5*b^2*arctanh(x*sqrt(c))*log(2*(1+x*sqrt(-c))*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+x*sqrt(c))))/c^(5/2)+1/5*b^2*arctan(x*sqrt(c))*log((1-I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))/c^(5/2)+1/5*b^2*polylog(2,1+(-2)/(1-x*sqrt(c)))/c^(5/2)+1/5*I*b^2*polylog(2,1+(-2)/(1-I*x*sqrt(c)))/c^(5/2)-1/10*I*b^2*polylog(2,1+(-1-I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))/c^(5/2)+1/5*I*b^2*polylog(2,1+(-2)/(1+I*x*sqrt(c)))/c^(5/2)+1/5*b^2*polylog(2,1+(-2)/(1+x*sqrt(c)))/c^(5/2)-1/10*b^2*polylog(2,1+2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))/c^(5/2)-1/10*b^2*polylog(2,1-2*(1+x*sqrt(-c))*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+x*sqrt(c))))/c^(5/2)-1/10*I*b^2*polylog(2,1+(-1+I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))/c^(5/2)],
[x^2*(a+b*arctanh(c*x^2))^2,x,86,4/3*a*b*x/c-2/9*a*b*x^3-2/3*a*b*arctan(x*sqrt(c))/c^(3/2)+4/3*b^2*arctan(x*sqrt(c))/c^(3/2)-1/3*I*b^2*arctan(x*sqrt(c))^2/c^(3/2)-4/3*b^2*arctanh(x*sqrt(c))/c^(3/2)-1/3*b^2*arctanh(x*sqrt(c))^2/c^(3/2)-2/3*b^2*x*log(1-c*x^2)/c+1/9*b^2*x^3*log(1-c*x^2)+1/3*b^2*arctan(x*sqrt(c))*log(1-c*x^2)/c^(3/2)+1/9*b*x^3*(2*a-b*log(1-c*x^2))-1/3*b*arctanh(x*sqrt(c))*(2*a-b*log(1-c*x^2))/c^(3/2)+1/12*x^3*(2*a-b*log(1-c*x^2))^2+2/3*b^2*x*log(1+c*x^2)/c+1/3*a*b*x^3*log(1+c*x^2)-1/3*b^2*arctan(x*sqrt(c))*log(1+c*x^2)/c^(3/2)-1/3*b^2*arctanh(x*sqrt(c))*log(1+c*x^2)/c^(3/2)-1/6*b^2*x^3*log(1-c*x^2)*log(1+c*x^2)+1/12*b^2*x^3*log(1+c*x^2)^2+2/3*b^2*arctanh(x*sqrt(c))*log(2/(1-x*sqrt(c)))/c^(3/2)+2/3*b^2*arctan(x*sqrt(c))*log(2/(1-I*x*sqrt(c)))/c^(3/2)-1/3*b^2*arctan(x*sqrt(c))*log((1+I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))/c^(3/2)-2/3*b^2*arctan(x*sqrt(c))*log(2/(1+I*x*sqrt(c)))/c^(3/2)-2/3*b^2*arctanh(x*sqrt(c))*log(2/(1+x*sqrt(c)))/c^(3/2)+1/3*b^2*arctanh(x*sqrt(c))*log(-2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))/c^(3/2)+1/3*b^2*arctanh(x*sqrt(c))*log(2*(1+x*sqrt(-c))*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+x*sqrt(c))))/c^(3/2)-1/3*b^2*arctan(x*sqrt(c))*log((1-I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))/c^(3/2)+1/3*b^2*polylog(2,1+(-2)/(1-x*sqrt(c)))/c^(3/2)-1/3*I*b^2*polylog(2,1+(-2)/(1-I*x*sqrt(c)))/c^(3/2)+1/6*I*b^2*polylog(2,1+(-1-I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))/c^(3/2)-1/3*I*b^2*polylog(2,1+(-2)/(1+I*x*sqrt(c)))/c^(3/2)+1/3*b^2*polylog(2,1+(-2)/(1+x*sqrt(c)))/c^(3/2)-1/6*b^2*polylog(2,1+2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))/c^(3/2)-1/6*b^2*polylog(2,1-2*(1+x*sqrt(-c))*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+x*sqrt(c))))/c^(3/2)+1/6*I*b^2*polylog(2,1+(-1+I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))/c^(3/2)],
[(a+b*arctanh(c*x^2))^2,x,69,a^2*x-a*b*x*log(1-c*x^2)+1/4*b^2*x*log(1-c*x^2)^2+a*b*x*log(1+c*x^2)-1/2*b^2*x*log(1-c*x^2)*log(1+c*x^2)+1/4*b^2*x*log(1+c*x^2)^2+2*a*b*arctan(x*sqrt(c))/sqrt(c)+I*b^2*arctan(x*sqrt(c))^2/sqrt(c)-2*a*b*arctanh(x*sqrt(c))/sqrt(c)-b^2*arctanh(x*sqrt(c))^2/sqrt(c)-b^2*arctan(x*sqrt(c))*log(1-c*x^2)/sqrt(c)+b^2*arctanh(x*sqrt(c))*log(1-c*x^2)/sqrt(c)+b^2*arctan(x*sqrt(c))*log(1+c*x^2)/sqrt(c)-b^2*arctanh(x*sqrt(c))*log(1+c*x^2)/sqrt(c)+2*b^2*arctanh(x*sqrt(c))*log(2/(1-x*sqrt(c)))/sqrt(c)-2*b^2*arctan(x*sqrt(c))*log(2/(1-I*x*sqrt(c)))/sqrt(c)+b^2*arctan(x*sqrt(c))*log((1+I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))/sqrt(c)+2*b^2*arctan(x*sqrt(c))*log(2/(1+I*x*sqrt(c)))/sqrt(c)-2*b^2*arctanh(x*sqrt(c))*log(2/(1+x*sqrt(c)))/sqrt(c)+b^2*arctanh(x*sqrt(c))*log(-2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))/sqrt(c)+b^2*arctanh(x*sqrt(c))*log(2*(1+x*sqrt(-c))*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+x*sqrt(c))))/sqrt(c)+b^2*arctan(x*sqrt(c))*log((1-I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))/sqrt(c)+b^2*polylog(2,1+(-2)/(1-x*sqrt(c)))/sqrt(c)+I*b^2*polylog(2,1+(-2)/(1-I*x*sqrt(c)))/sqrt(c)-1/2*I*b^2*polylog(2,1+(-1-I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))/sqrt(c)+I*b^2*polylog(2,1+(-2)/(1+I*x*sqrt(c)))/sqrt(c)+b^2*polylog(2,1+(-2)/(1+x*sqrt(c)))/sqrt(c)-1/2*b^2*polylog(2,1+2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))/sqrt(c)-1/2*b^2*polylog(2,1-2*(1+x*sqrt(-c))*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+x*sqrt(c))))/sqrt(c)-1/2*I*b^2*polylog(2,1+(-1+I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))/sqrt(c)],
[(a+b*arctanh(c*x^2))^2/x^2,x,47,-1/4*(2*a-b*log(1-c*x^2))^2/x-a*b*log(1+c*x^2)/x+1/2*b^2*log(1-c*x^2)*log(1+c*x^2)/x-1/4*b^2*log(1+c*x^2)^2/x+2*a*b*arctan(x*sqrt(c))*sqrt(c)+I*b^2*arctan(x*sqrt(c))^2*sqrt(c)+b^2*arctanh(x*sqrt(c))^2*sqrt(c)-b^2*arctan(x*sqrt(c))*log(1-c*x^2)*sqrt(c)+b*arctanh(x*sqrt(c))*(2*a-b*log(1-c*x^2))*sqrt(c)+b^2*arctan(x*sqrt(c))*log(1+c*x^2)*sqrt(c)+b^2*arctanh(x*sqrt(c))*log(1+c*x^2)*sqrt(c)-2*b^2*arctanh(x*sqrt(c))*log(2/(1-x*sqrt(c)))*sqrt(c)-2*b^2*arctan(x*sqrt(c))*log(2/(1-I*x*sqrt(c)))*sqrt(c)+b^2*arctan(x*sqrt(c))*log((1+I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))*sqrt(c)+2*b^2*arctan(x*sqrt(c))*log(2/(1+I*x*sqrt(c)))*sqrt(c)+2*b^2*arctanh(x*sqrt(c))*log(2/(1+x*sqrt(c)))*sqrt(c)-b^2*arctanh(x*sqrt(c))*log(-2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))*sqrt(c)-b^2*arctanh(x*sqrt(c))*log(2*(1+x*sqrt(-c))*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+x*sqrt(c))))*sqrt(c)+b^2*arctan(x*sqrt(c))*log((1-I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))*sqrt(c)-b^2*polylog(2,1+(-2)/(1-x*sqrt(c)))*sqrt(c)+I*b^2*polylog(2,1+(-2)/(1-I*x*sqrt(c)))*sqrt(c)-1/2*I*b^2*polylog(2,1+(-1-I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))*sqrt(c)+I*b^2*polylog(2,1+(-2)/(1+I*x*sqrt(c)))*sqrt(c)-b^2*polylog(2,1+(-2)/(1+x*sqrt(c)))*sqrt(c)+1/2*b^2*polylog(2,1+2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))*sqrt(c)+1/2*b^2*polylog(2,1-2*(1+x*sqrt(-c))*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+x*sqrt(c))))*sqrt(c)-1/2*I*b^2*polylog(2,1+(-1+I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))*sqrt(c)],
[(a+b*arctanh(c*x^2))^2/x^4,x,64,-2/3*a*b*c/x-2/3*a*b*c^(3/2)*arctan(x*sqrt(c))+4/3*b^2*c^(3/2)*arctan(x*sqrt(c))-1/3*I*b^2*c^(3/2)*arctan(x*sqrt(c))^2+4/3*b^2*c^(3/2)*arctanh(x*sqrt(c))+1/3*b^2*c^(3/2)*arctanh(x*sqrt(c))^2+1/3*b^2*c*log(1-c*x^2)/x+1/3*b^2*c^(3/2)*arctan(x*sqrt(c))*log(1-c*x^2)-1/3*b*c*(2*a-b*log(1-c*x^2))/x+1/3*b*c^(3/2)*arctanh(x*sqrt(c))*(2*a-b*log(1-c*x^2))-1/12*(2*a-b*log(1-c*x^2))^2/x^3-1/3*a*b*log(1+c*x^2)/x^3-2/3*b^2*c*log(1+c*x^2)/x-1/3*b^2*c^(3/2)*arctan(x*sqrt(c))*log(1+c*x^2)+1/3*b^2*c^(3/2)*arctanh(x*sqrt(c))*log(1+c*x^2)+1/6*b^2*log(1-c*x^2)*log(1+c*x^2)/x^3-1/12*b^2*log(1+c*x^2)^2/x^3-2/3*b^2*c^(3/2)*arctanh(x*sqrt(c))*log(2/(1-x*sqrt(c)))+2/3*b^2*c^(3/2)*arctan(x*sqrt(c))*log(2/(1-I*x*sqrt(c)))-1/3*b^2*c^(3/2)*arctan(x*sqrt(c))*log((1+I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))-2/3*b^2*c^(3/2)*arctan(x*sqrt(c))*log(2/(1+I*x*sqrt(c)))+2/3*b^2*c^(3/2)*arctanh(x*sqrt(c))*log(2/(1+x*sqrt(c)))-1/3*b^2*c^(3/2)*arctanh(x*sqrt(c))*log(-2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))-1/3*b^2*c^(3/2)*arctanh(x*sqrt(c))*log(2*(1+x*sqrt(-c))*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+x*sqrt(c))))-1/3*b^2*c^(3/2)*arctan(x*sqrt(c))*log((1-I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))-1/3*b^2*c^(3/2)*polylog(2,1+(-2)/(1-x*sqrt(c)))-1/3*I*b^2*c^(3/2)*polylog(2,1+(-2)/(1-I*x*sqrt(c)))+1/6*I*b^2*c^(3/2)*polylog(2,1+(-1-I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))-1/3*I*b^2*c^(3/2)*polylog(2,1+(-2)/(1+I*x*sqrt(c)))-1/3*b^2*c^(3/2)*polylog(2,1+(-2)/(1+x*sqrt(c)))+1/6*b^2*c^(3/2)*polylog(2,1+2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))+1/6*b^2*c^(3/2)*polylog(2,1-2*(1+x*sqrt(-c))*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+x*sqrt(c))))+1/6*I*b^2*c^(3/2)*polylog(2,1+(-1+I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))],
[(a+b*arctanh(c*x^2))^2/x^6,x,77,-2/15*a*b*c/x^3+2/5*a*b*c^2/x-8/15*b^2*c^2/x+2/5*a*b*c^(5/2)*arctan(x*sqrt(c))-4/15*b^2*c^(5/2)*arctan(x*sqrt(c))+1/5*I*b^2*c^(5/2)*arctan(x*sqrt(c))^2+4/15*b^2*c^(5/2)*arctanh(x*sqrt(c))+1/5*b^2*c^(5/2)*arctanh(x*sqrt(c))^2+1/15*b^2*c*log(1-c*x^2)/x^3-1/5*b^2*c^2*log(1-c*x^2)/x-1/5*b^2*c^(5/2)*arctan(x*sqrt(c))*log(1-c*x^2)-1/15*b*c*(2*a-b*log(1-c*x^2))/x^3-1/5*b*c^2*(2*a-b*log(1-c*x^2))/x+1/5*b*c^(5/2)*arctanh(x*sqrt(c))*(2*a-b*log(1-c*x^2))-1/20*(2*a-b*log(1-c*x^2))^2/x^5-1/5*a*b*log(1+c*x^2)/x^5-2/15*b^2*c*log(1+c*x^2)/x^3+1/5*b^2*c^(5/2)*arctan(x*sqrt(c))*log(1+c*x^2)+1/5*b^2*c^(5/2)*arctanh(x*sqrt(c))*log(1+c*x^2)+1/10*b^2*log(1-c*x^2)*log(1+c*x^2)/x^5-1/20*b^2*log(1+c*x^2)^2/x^5-2/5*b^2*c^(5/2)*arctanh(x*sqrt(c))*log(2/(1-x*sqrt(c)))-2/5*b^2*c^(5/2)*arctan(x*sqrt(c))*log(2/(1-I*x*sqrt(c)))+1/5*b^2*c^(5/2)*arctan(x*sqrt(c))*log((1+I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))+2/5*b^2*c^(5/2)*arctan(x*sqrt(c))*log(2/(1+I*x*sqrt(c)))+2/5*b^2*c^(5/2)*arctanh(x*sqrt(c))*log(2/(1+x*sqrt(c)))-1/5*b^2*c^(5/2)*arctanh(x*sqrt(c))*log(-2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))-1/5*b^2*c^(5/2)*arctanh(x*sqrt(c))*log(2*(1+x*sqrt(-c))*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+x*sqrt(c))))+1/5*b^2*c^(5/2)*arctan(x*sqrt(c))*log((1-I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))-1/5*b^2*c^(5/2)*polylog(2,1+(-2)/(1-x*sqrt(c)))+1/5*I*b^2*c^(5/2)*polylog(2,1+(-2)/(1-I*x*sqrt(c)))-1/10*I*b^2*c^(5/2)*polylog(2,1+(-1-I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))+1/5*I*b^2*c^(5/2)*polylog(2,1+(-2)/(1+I*x*sqrt(c)))-1/5*b^2*c^(5/2)*polylog(2,1+(-2)/(1+x*sqrt(c)))+1/10*b^2*c^(5/2)*polylog(2,1+2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))+1/10*b^2*c^(5/2)*polylog(2,1-2*(1+x*sqrt(-c))*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+x*sqrt(c))))-1/10*I*b^2*c^(5/2)*polylog(2,1+(-1+I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))],
[x^3*(a+b*arctanh(c*x^2))^3,x,9,3/4*b*(a+b*arctanh(c*x^2))^2/c^2+3/4*b*x^2*(a+b*arctanh(c*x^2))^2/c-1/4*(a+b*arctanh(c*x^2))^3/c^2+1/4*x^4*(a+b*arctanh(c*x^2))^3-3/2*b^2*(a+b*arctanh(c*x^2))*log(2/(1-c*x^2))/c^2-3/4*b^3*polylog(2,1+(-2)/(1-c*x^2))/c^2],
[x*(a+b*arctanh(c*x^2))^3,x,6,1/2*(a+b*arctanh(c*x^2))^3/c+1/2*x^2*(a+b*arctanh(c*x^2))^3-3/2*b*(a+b*arctanh(c*x^2))^2*log(2/(1-c*x^2))/c-3/2*b^2*(a+b*arctanh(c*x^2))*polylog(2,1+(-2)/(1-c*x^2))/c+3/4*b^3*polylog(3,1+(-2)/(1-c*x^2))/c],
[(a+b*arctanh(c*x^2))^3/x,x,9,(a+b*arctanh(c*x^2))^3*arctanh(1+(-2)/(1-c*x^2))-3/4*b*(a+b*arctanh(c*x^2))^2*polylog(2,1+(-2)/(1-c*x^2))+3/4*b*(a+b*arctanh(c*x^2))^2*polylog(2,-1+2/(1-c*x^2))+3/4*b^2*(a+b*arctanh(c*x^2))*polylog(3,1+(-2)/(1-c*x^2))-3/4*b^2*(a+b*arctanh(c*x^2))*polylog(3,-1+2/(1-c*x^2))-3/8*b^3*polylog(4,1+(-2)/(1-c*x^2))+3/8*b^3*polylog(4,-1+2/(1-c*x^2))],
[(a+b*arctanh(c*x^2))^3/x^3,x,6,1/2*c*(a+b*arctanh(c*x^2))^3-1/2*(a+b*arctanh(c*x^2))^3/x^2+3/2*b*c*(a+b*arctanh(c*x^2))^2*log(2+(-2)/(1+c*x^2))-3/2*b^2*c*(a+b*arctanh(c*x^2))*polylog(2,-1+2/(1+c*x^2))-3/4*b^3*c*polylog(3,-1+2/(1+c*x^2))],
[(a+b*arctanh(c*x^2))^3/x^5,x,8,3/4*b*c^2*(a+b*arctanh(c*x^2))^2-3/4*b*c*(a+b*arctanh(c*x^2))^2/x^2+1/4*c^2*(a+b*arctanh(c*x^2))^3-1/4*(a+b*arctanh(c*x^2))^3/x^4+3/2*b^2*c^2*(a+b*arctanh(c*x^2))*log(2+(-2)/(1+c*x^2))-3/4*b^3*c^2*polylog(2,-1+2/(1+c*x^2))],
#  {x^2*(a + b*ArcTan[c*x^2])^3, x, 86, 0}
# {x^0*(a + b*ArcTan[c*x^2])^3, x, 69, 0}
# {(a + b*ArcTan[c*x^2])^3/x^2, x, 47, 0}
# {(a + b*ArcTan[c*x^2])^3/x^4, x, 64, 0}

# {(a + b*ArcTan[c*x^2])^3/x^6, x, 77, 0} 

# Integrands of the form (d x)^(m/2) (a+b ArcTanh[c x^2])^p
[(d*x)^(5/2)*(a+b*arctanh(c*x^2)),x,16,8/21*b*d*(d*x)^(3/2)/c+2/7*b*d^(5/2)*arctan(c^(1/4)*sqrt(d*x)/sqrt(d))/c^(7/4)+2/7*(d*x)^(7/2)*(a+b*arctanh(c*x^2))/d-2/7*b*d^(5/2)*arctanh(c^(1/4)*sqrt(d*x)/sqrt(d))/c^(7/4)-1/7*b*d^(5/2)*log(sqrt(d)+x*sqrt(c)*sqrt(d)-c^(1/4)*sqrt(2)*sqrt(d*x))/(c^(7/4)*sqrt(2))+1/7*b*d^(5/2)*log(sqrt(d)+x*sqrt(c)*sqrt(d)+c^(1/4)*sqrt(2)*sqrt(d*x))/(c^(7/4)*sqrt(2))+1/7*b*d^(5/2)*arctan(1-c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/c^(7/4)-1/7*b*d^(5/2)*arctan(1+c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/c^(7/4)],
[(d*x)^(3/2)*(a+b*arctanh(c*x^2)),x,16,-2/5*b*d^(3/2)*arctan(c^(1/4)*sqrt(d*x)/sqrt(d))/c^(5/4)+2/5*(d*x)^(5/2)*(a+b*arctanh(c*x^2))/d-2/5*b*d^(3/2)*arctanh(c^(1/4)*sqrt(d*x)/sqrt(d))/c^(5/4)+1/5*b*d^(3/2)*log(sqrt(d)+x*sqrt(c)*sqrt(d)-c^(1/4)*sqrt(2)*sqrt(d*x))/(c^(5/4)*sqrt(2))-1/5*b*d^(3/2)*log(sqrt(d)+x*sqrt(c)*sqrt(d)+c^(1/4)*sqrt(2)*sqrt(d*x))/(c^(5/4)*sqrt(2))+1/5*b*d^(3/2)*arctan(1-c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/c^(5/4)-1/5*b*d^(3/2)*arctan(1+c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/c^(5/4)+8/5*b*d*sqrt(d*x)/c],
[(d*x)^(1/2)*(a+b*arctanh(c*x^2)),x,15,2/3*(d*x)^(3/2)*(a+b*arctanh(c*x^2))/d+2/3*b*arctan(c^(1/4)*sqrt(d*x)/sqrt(d))*sqrt(d)/c^(3/4)-2/3*b*arctanh(c^(1/4)*sqrt(d*x)/sqrt(d))*sqrt(d)/c^(3/4)+1/3*b*log(sqrt(d)+x*sqrt(c)*sqrt(d)-c^(1/4)*sqrt(2)*sqrt(d*x))*sqrt(d)/(c^(3/4)*sqrt(2))-1/3*b*log(sqrt(d)+x*sqrt(c)*sqrt(d)+c^(1/4)*sqrt(2)*sqrt(d*x))*sqrt(d)/(c^(3/4)*sqrt(2))-1/3*b*arctan(1-c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)*sqrt(d)/c^(3/4)+1/3*b*arctan(1+c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)*sqrt(d)/c^(3/4)],
[(a+b*arctanh(c*x^2))/(d*x)^(1/2),x,15,-2*b*arctan(c^(1/4)*sqrt(d*x)/sqrt(d))/(c^(1/4)*sqrt(d))-2*b*arctanh(c^(1/4)*sqrt(d*x)/sqrt(d))/(c^(1/4)*sqrt(d))-b*log(sqrt(d)+x*sqrt(c)*sqrt(d)-c^(1/4)*sqrt(2)*sqrt(d*x))/(c^(1/4)*sqrt(2)*sqrt(d))+b*log(sqrt(d)+x*sqrt(c)*sqrt(d)+c^(1/4)*sqrt(2)*sqrt(d*x))/(c^(1/4)*sqrt(2)*sqrt(d))-b*arctan(1-c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/(c^(1/4)*sqrt(d))+b*arctan(1+c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/(c^(1/4)*sqrt(d))+2*(a+b*arctanh(c*x^2))*sqrt(d*x)/d],
[(a+b*arctanh(c*x^2))/(d*x)^(3/2),x,15,-2*b*c^(1/4)*arctan(c^(1/4)*sqrt(d*x)/sqrt(d))/d^(3/2)+2*b*c^(1/4)*arctanh(c^(1/4)*sqrt(d*x)/sqrt(d))/d^(3/2)+b*c^(1/4)*log(sqrt(d)+x*sqrt(c)*sqrt(d)-c^(1/4)*sqrt(2)*sqrt(d*x))/(d^(3/2)*sqrt(2))-b*c^(1/4)*log(sqrt(d)+x*sqrt(c)*sqrt(d)+c^(1/4)*sqrt(2)*sqrt(d*x))/(d^(3/2)*sqrt(2))-b*c^(1/4)*arctan(1-c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/d^(3/2)+b*c^(1/4)*arctan(1+c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/d^(3/2)-2*(a+b*arctanh(c*x^2))/(d*sqrt(d*x))],
[(a+b*arctanh(c*x^2))/(d*x)^(5/2),x,15,2/3*b*c^(3/4)*arctan(c^(1/4)*sqrt(d*x)/sqrt(d))/d^(5/2)-2/3*(a+b*arctanh(c*x^2))/(d*(d*x)^(3/2))+2/3*b*c^(3/4)*arctanh(c^(1/4)*sqrt(d*x)/sqrt(d))/d^(5/2)-1/3*b*c^(3/4)*log(sqrt(d)+x*sqrt(c)*sqrt(d)-c^(1/4)*sqrt(2)*sqrt(d*x))/(d^(5/2)*sqrt(2))+1/3*b*c^(3/4)*log(sqrt(d)+x*sqrt(c)*sqrt(d)+c^(1/4)*sqrt(2)*sqrt(d*x))/(d^(5/2)*sqrt(2))-1/3*b*c^(3/4)*arctan(1-c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/d^(5/2)+1/3*b*c^(3/4)*arctan(1+c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/d^(5/2)],
[(a+b*arctanh(c*x^2))/(d*x)^(7/2),x,16,-2/5*b*c^(5/4)*arctan(c^(1/4)*sqrt(d*x)/sqrt(d))/d^(7/2)-2/5*(a+b*arctanh(c*x^2))/(d*(d*x)^(5/2))+2/5*b*c^(5/4)*arctanh(c^(1/4)*sqrt(d*x)/sqrt(d))/d^(7/2)-1/5*b*c^(5/4)*log(sqrt(d)+x*sqrt(c)*sqrt(d)-c^(1/4)*sqrt(2)*sqrt(d*x))/(d^(7/2)*sqrt(2))+1/5*b*c^(5/4)*log(sqrt(d)+x*sqrt(c)*sqrt(d)+c^(1/4)*sqrt(2)*sqrt(d*x))/(d^(7/2)*sqrt(2))+1/5*b*c^(5/4)*arctan(1-c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/d^(7/2)-1/5*b*c^(5/4)*arctan(1+c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/d^(7/2)-8/5*b*c/(d^3*sqrt(d*x))],
[(a+b*arctanh(c*x^2))/(d*x)^(9/2),x,16,-8/21*b*c/(d^3*(d*x)^(3/2))+2/7*b*c^(7/4)*arctan(c^(1/4)*sqrt(d*x)/sqrt(d))/d^(9/2)-2/7*(a+b*arctanh(c*x^2))/(d*(d*x)^(7/2))+2/7*b*c^(7/4)*arctanh(c^(1/4)*sqrt(d*x)/sqrt(d))/d^(9/2)+1/7*b*c^(7/4)*log(sqrt(d)+x*sqrt(c)*sqrt(d)-c^(1/4)*sqrt(2)*sqrt(d*x))/(d^(9/2)*sqrt(2))-1/7*b*c^(7/4)*log(sqrt(d)+x*sqrt(c)*sqrt(d)+c^(1/4)*sqrt(2)*sqrt(d*x))/(d^(9/2)*sqrt(2))+1/7*b*c^(7/4)*arctan(1-c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/d^(9/2)-1/7*b*c^(7/4)*arctan(1+c^(1/4)*sqrt(2)*sqrt(d*x)/sqrt(d))*sqrt(2)/d^(9/2)],
[(d*x)^(1/2)*(a+b*arctanh(c*x^2))^2,x,238,-8/9*a*b*x*sqrt(d*x)+4/9*b^2*x*log(1-c*x^2)*sqrt(d*x)+4/9*b*x*(2*a-b*log(1-c*x^2))*sqrt(d*x)+1/6*x*(2*a-b*log(1-c*x^2))^2*sqrt(d*x)+2/3*a*b*x*log(1+c*x^2)*sqrt(d*x)-1/3*b^2*x*log(1-c*x^2)*log(1+c*x^2)*sqrt(d*x)+1/6*b^2*x*log(1+c*x^2)^2*sqrt(d*x)-2/3*I*b^2*arctan((-c)^(1/4)*sqrt(x))^2*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-2/3*I*b^2*arctan(c^(1/4)*sqrt(x))^2*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*b^2*arctanh((-c)^(1/4)*sqrt(x))^2*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-2/3*b^2*arctanh(c^(1/4)*sqrt(x))^2*sqrt(d*x)/(c^(3/4)*sqrt(x))+2/3*b^2*arctan((-c)^(1/4)*sqrt(x))*log(1-c*x^2)*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-2/3*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(1-c*x^2)*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+2/3*b*arctan(c^(1/4)*sqrt(x))*(2*a-b*log(1-c*x^2))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*b*arctanh(c^(1/4)*sqrt(x))*(2*a-b*log(1-c*x^2))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*b^2*arctan((-c)^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+2/3*b^2*arctan(c^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(d*x)/(c^(3/4)*sqrt(x))+2/3*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-2/3*b^2*arctanh(c^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(d*x)/(c^(3/4)*sqrt(x))+4/3*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(2/(1-(-c)^(1/4)*sqrt(x)))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+4/3*b^2*arctan((-c)^(1/4)*sqrt(x))*log(2/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+2/3*b^2*arctan((-c)^(1/4)*sqrt(x))*log((1+I)*(1-(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-4/3*b^2*arctan((-c)^(1/4)*sqrt(x))*log(2/(1+I*(-c)^(1/4)*sqrt(x)))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-4/3*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(2/(1+(-c)^(1/4)*sqrt(x)))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+2/3*b^2*arctan((-c)^(1/4)*sqrt(x))*log((1-I)*(1+(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+4/3*b^2*arctanh(c^(1/4)*sqrt(x))*log(2/(1-c^(1/4)*sqrt(x)))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*b^2*arctan((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+2/3*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+4/3*b^2*arctan(c^(1/4)*sqrt(x))*log(2/(1-I*c^(1/4)*sqrt(x)))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*b^2*arctan(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)-c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*b^2*arctan(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)+c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(d*x)/(c^(3/4)*sqrt(x))+2/3*b^2*arctan(c^(1/4)*sqrt(x))*log((1+I)*(1-c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(d*x)/(c^(3/4)*sqrt(x))-4/3*b^2*arctan(c^(1/4)*sqrt(x))*log(2/(1+I*c^(1/4)*sqrt(x)))*sqrt(d*x)/(c^(3/4)*sqrt(x))-4/3*b^2*arctanh(c^(1/4)*sqrt(x))*log(2/(1+c^(1/4)*sqrt(x)))*sqrt(d*x)/(c^(3/4)*sqrt(x))+2/3*b^2*arctanh(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(d*x)/(c^(3/4)*sqrt(x))+2/3*b^2*arctanh(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*b^2*arctan((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+2/3*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+2/3*b^2*arctan(c^(1/4)*sqrt(x))*log((1-I)*(1+c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*b^2*arctan(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(-c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(-2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+2/3*b^2*arctanh(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*b^2*arctan(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+2/3*b^2*arctanh(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*b^2*arctan((-c)^(1/4)*sqrt(x))*log(-2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+2/3*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(-2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-2/3*b^2*arctanh(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(c)))))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*b^2*arctan((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+2/3*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-2/3*b^2*arctanh(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(c)))))*sqrt(d*x)/(c^(3/4)*sqrt(x))+2/3*b^2*polylog(2,1+(-2)/(1-(-c)^(1/4)*sqrt(x)))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-2/3*I*b^2*polylog(2,1+(-2)/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-1/3*I*b^2*polylog(2,1+(-1-I)*(1-(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-2/3*I*b^2*polylog(2,1+(-2)/(1+I*(-c)^(1/4)*sqrt(x)))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+2/3*b^2*polylog(2,1+(-2)/(1+(-c)^(1/4)*sqrt(x)))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-1/3*I*b^2*polylog(2,1+(-1+I)*(1+(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+2/3*b^2*polylog(2,1+(-2)/(1-c^(1/4)*sqrt(x)))*sqrt(d*x)/(c^(3/4)*sqrt(x))+1/3*I*b^2*polylog(2,1-2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-1/3*b^2*polylog(2,1-2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-2/3*I*b^2*polylog(2,1+(-2)/(1-I*c^(1/4)*sqrt(x)))*sqrt(d*x)/(c^(3/4)*sqrt(x))+1/3*I*b^2*polylog(2,1+2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)-c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(d*x)/(c^(3/4)*sqrt(x))+1/3*I*b^2*polylog(2,1-2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)+c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(d*x)/(c^(3/4)*sqrt(x))-1/3*I*b^2*polylog(2,1+(-1-I)*(1-c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*I*b^2*polylog(2,1+(-2)/(1+I*c^(1/4)*sqrt(x)))*sqrt(d*x)/(c^(3/4)*sqrt(x))+2/3*b^2*polylog(2,1+(-2)/(1+c^(1/4)*sqrt(x)))*sqrt(d*x)/(c^(3/4)*sqrt(x))-1/3*b^2*polylog(2,1+2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(d*x)/(c^(3/4)*sqrt(x))-1/3*b^2*polylog(2,1-2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(d*x)/(c^(3/4)*sqrt(x))+1/3*I*b^2*polylog(2,1-2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-1/3*b^2*polylog(2,1-2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-1/3*I*b^2*polylog(2,1+(-1+I)*(1+c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(d*x)/(c^(3/4)*sqrt(x))+1/3*I*b^2*polylog(2,1+2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(-c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(d*x)/(c^(3/4)*sqrt(x))+1/3*b^2*polylog(2,1+2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-1/3*b^2*polylog(2,1+2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(d*x)/(c^(3/4)*sqrt(x))+1/3*I*b^2*polylog(2,1-2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(d*x)/(c^(3/4)*sqrt(x))+1/3*b^2*polylog(2,1-2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-1/3*b^2*polylog(2,1-2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(d*x)/(c^(3/4)*sqrt(x))+1/3*I*b^2*polylog(2,1+2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-1/3*b^2*polylog(2,1+2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+1/3*b^2*polylog(2,1+2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(c)))))*sqrt(d*x)/(c^(3/4)*sqrt(x))+1/3*I*b^2*polylog(2,1-2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))-1/3*b^2*polylog(2,1-2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(d*x)/((-c)^(3/4)*sqrt(x))+1/3*b^2*polylog(2,1-2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(c)))))*sqrt(d*x)/(c^(3/4)*sqrt(x))-2/3*a*b*arctan(1-c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(d*x)/(c^(3/4)*sqrt(x))+2/3*a*b*arctan(1+c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(d*x)/(c^(3/4)*sqrt(x))+1/3*a*b*log(1+x*sqrt(c)-c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(d*x)/(c^(3/4)*sqrt(x))-1/3*a*b*log(1+x*sqrt(c)+c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(d*x)/(c^(3/4)*sqrt(x))],
[(a+b*arctanh(c*x^2))^2/(d*x)^(1/2),x,241,2*a^2*x/sqrt(d*x)-2*a*b*x*log(1-c*x^2)/sqrt(d*x)+1/2*b^2*x*log(1-c*x^2)^2/sqrt(d*x)+2*a*b*x*log(1+c*x^2)/sqrt(d*x)-b^2*x*log(1-c*x^2)*log(1+c*x^2)/sqrt(d*x)+1/2*b^2*x*log(1+c*x^2)^2/sqrt(d*x)+2*I*b^2*arctan((-c)^(1/4)*sqrt(x))^2*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-4*a*b*arctan(c^(1/4)*sqrt(x))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*I*b^2*arctan(c^(1/4)*sqrt(x))^2*sqrt(x)/(c^(1/4)*sqrt(d*x))-2*b^2*arctanh((-c)^(1/4)*sqrt(x))^2*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-4*a*b*arctanh(c^(1/4)*sqrt(x))*sqrt(x)/(c^(1/4)*sqrt(d*x))-2*b^2*arctanh(c^(1/4)*sqrt(x))^2*sqrt(x)/(c^(1/4)*sqrt(d*x))-2*b^2*arctan((-c)^(1/4)*sqrt(x))*log(1-c*x^2)*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+2*b^2*arctan(c^(1/4)*sqrt(x))*log(1-c*x^2)*sqrt(x)/(c^(1/4)*sqrt(d*x))-2*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(1-c*x^2)*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+2*b^2*arctanh(c^(1/4)*sqrt(x))*log(1-c*x^2)*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*arctan((-c)^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-2*b^2*arctan(c^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-2*b^2*arctanh(c^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(x)/(c^(1/4)*sqrt(d*x))+4*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(2/(1-(-c)^(1/4)*sqrt(x)))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-4*b^2*arctan((-c)^(1/4)*sqrt(x))*log(2/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-2*b^2*arctan((-c)^(1/4)*sqrt(x))*log((1+I)*(1-(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+4*b^2*arctan((-c)^(1/4)*sqrt(x))*log(2/(1+I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-4*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(2/(1+(-c)^(1/4)*sqrt(x)))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-2*b^2*arctan((-c)^(1/4)*sqrt(x))*log((1-I)*(1+(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+4*b^2*arctanh(c^(1/4)*sqrt(x))*log(2/(1-c^(1/4)*sqrt(x)))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*arctan((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+2*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-4*b^2*arctan(c^(1/4)*sqrt(x))*log(2/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*arctan(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)-c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*arctan(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)+c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(x)/(c^(1/4)*sqrt(d*x))-2*b^2*arctan(c^(1/4)*sqrt(x))*log((1+I)*(1-c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(c^(1/4)*sqrt(d*x))+4*b^2*arctan(c^(1/4)*sqrt(x))*log(2/(1+I*c^(1/4)*sqrt(x)))*sqrt(x)/(c^(1/4)*sqrt(d*x))-4*b^2*arctanh(c^(1/4)*sqrt(x))*log(2/(1+c^(1/4)*sqrt(x)))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*arctanh(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*arctanh(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*arctan((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+2*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-2*b^2*arctan(c^(1/4)*sqrt(x))*log((1-I)*(1+c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*arctan(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(-c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(x)/(c^(1/4)*sqrt(d*x))-2*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(-2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+2*b^2*arctanh(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*arctan(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(x)/(c^(1/4)*sqrt(d*x))-2*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+2*b^2*arctanh(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*arctan((-c)^(1/4)*sqrt(x))*log(-2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+2*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(-2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-2*b^2*arctanh(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*arctan((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+2*b^2*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-2*b^2*arctanh(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*polylog(2,1+(-2)/(1-(-c)^(1/4)*sqrt(x)))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+2*I*b^2*polylog(2,1+(-2)/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+I*b^2*polylog(2,1+(-1-I)*(1-(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+2*I*b^2*polylog(2,1+(-2)/(1+I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+2*b^2*polylog(2,1+(-2)/(1+(-c)^(1/4)*sqrt(x)))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+I*b^2*polylog(2,1+(-1+I)*(1+(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+2*b^2*polylog(2,1+(-2)/(1-c^(1/4)*sqrt(x)))*sqrt(x)/(c^(1/4)*sqrt(d*x))-I*b^2*polylog(2,1-2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-b^2*polylog(2,1-2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+2*I*b^2*polylog(2,1+(-2)/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(c^(1/4)*sqrt(d*x))-I*b^2*polylog(2,1+2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)-c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(x)/(c^(1/4)*sqrt(d*x))-I*b^2*polylog(2,1-2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)+c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(x)/(c^(1/4)*sqrt(d*x))+I*b^2*polylog(2,1+(-1-I)*(1-c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*I*b^2*polylog(2,1+(-2)/(1+I*c^(1/4)*sqrt(x)))*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*b^2*polylog(2,1+(-2)/(1+c^(1/4)*sqrt(x)))*sqrt(x)/(c^(1/4)*sqrt(d*x))-b^2*polylog(2,1+2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(x)/(c^(1/4)*sqrt(d*x))-b^2*polylog(2,1-2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(x)/(c^(1/4)*sqrt(d*x))-I*b^2*polylog(2,1-2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-b^2*polylog(2,1-2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+I*b^2*polylog(2,1+(-1+I)*(1+c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(c^(1/4)*sqrt(d*x))-I*b^2*polylog(2,1+2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(-c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(x)/(c^(1/4)*sqrt(d*x))+b^2*polylog(2,1+2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-b^2*polylog(2,1+2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(c^(1/4)*sqrt(d*x))-I*b^2*polylog(2,1-2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(x)/(c^(1/4)*sqrt(d*x))+b^2*polylog(2,1-2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-b^2*polylog(2,1-2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(c^(1/4)*sqrt(d*x))-I*b^2*polylog(2,1+2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-b^2*polylog(2,1+2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+b^2*polylog(2,1+2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(c^(1/4)*sqrt(d*x))-I*b^2*polylog(2,1-2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))-b^2*polylog(2,1-2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/((-c)^(1/4)*sqrt(d*x))+b^2*polylog(2,1-2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(c^(1/4)*sqrt(d*x))-2*a*b*arctan(1-c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(x)/(c^(1/4)*sqrt(d*x))+2*a*b*arctan(1+c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(x)/(c^(1/4)*sqrt(d*x))-a*b*log(1+x*sqrt(c)-c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(x)/(c^(1/4)*sqrt(d*x))+a*b*log(1+x*sqrt(c)+c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(x)/(c^(1/4)*sqrt(d*x))],
[(a+b*arctanh(c*x^2))^2/(d*x)^(3/2),x,197,-1/2*(2*a-b*log(1-c*x^2))^2/(d*sqrt(d*x))-2*a*b*log(1+c*x^2)/(d*sqrt(d*x))+b^2*log(1-c*x^2)*log(1+c*x^2)/(d*sqrt(d*x))-1/2*b^2*log(1+c*x^2)^2/(d*sqrt(d*x))+2*I*b^2*(-c)^(1/4)*arctan((-c)^(1/4)*sqrt(x))^2*sqrt(x)/(d*sqrt(d*x))+2*I*b^2*c^(1/4)*arctan(c^(1/4)*sqrt(x))^2*sqrt(x)/(d*sqrt(d*x))+2*b^2*(-c)^(1/4)*arctanh((-c)^(1/4)*sqrt(x))^2*sqrt(x)/(d*sqrt(d*x))+2*b^2*c^(1/4)*arctanh(c^(1/4)*sqrt(x))^2*sqrt(x)/(d*sqrt(d*x))-2*b^2*(-c)^(1/4)*arctan((-c)^(1/4)*sqrt(x))*log(1-c*x^2)*sqrt(x)/(d*sqrt(d*x))+2*b^2*(-c)^(1/4)*arctanh((-c)^(1/4)*sqrt(x))*log(1-c*x^2)*sqrt(x)/(d*sqrt(d*x))-2*b*c^(1/4)*arctan(c^(1/4)*sqrt(x))*(2*a-b*log(1-c*x^2))*sqrt(x)/(d*sqrt(d*x))+2*b*c^(1/4)*arctanh(c^(1/4)*sqrt(x))*(2*a-b*log(1-c*x^2))*sqrt(x)/(d*sqrt(d*x))+2*b^2*(-c)^(1/4)*arctan((-c)^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(x)/(d*sqrt(d*x))-2*b^2*c^(1/4)*arctan(c^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(x)/(d*sqrt(d*x))-2*b^2*(-c)^(1/4)*arctanh((-c)^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(x)/(d*sqrt(d*x))+2*b^2*c^(1/4)*arctanh(c^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(x)/(d*sqrt(d*x))-4*b^2*(-c)^(1/4)*arctanh((-c)^(1/4)*sqrt(x))*log(2/(1-(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))-4*b^2*(-c)^(1/4)*arctan((-c)^(1/4)*sqrt(x))*log(2/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))-2*b^2*(-c)^(1/4)*arctan((-c)^(1/4)*sqrt(x))*log((1+I)*(1-(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))+4*b^2*(-c)^(1/4)*arctan((-c)^(1/4)*sqrt(x))*log(2/(1+I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))+4*b^2*(-c)^(1/4)*arctanh((-c)^(1/4)*sqrt(x))*log(2/(1+(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))-2*b^2*(-c)^(1/4)*arctan((-c)^(1/4)*sqrt(x))*log((1-I)*(1+(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))-4*b^2*c^(1/4)*arctanh(c^(1/4)*sqrt(x))*log(2/(1-c^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))+2*b^2*(-c)^(1/4)*arctan((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))-2*b^2*(-c)^(1/4)*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))-4*b^2*c^(1/4)*arctan(c^(1/4)*sqrt(x))*log(2/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))+2*b^2*c^(1/4)*arctan(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)-c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))+2*b^2*c^(1/4)*arctan(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)+c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))-2*b^2*c^(1/4)*arctan(c^(1/4)*sqrt(x))*log((1+I)*(1-c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))+4*b^2*c^(1/4)*arctan(c^(1/4)*sqrt(x))*log(2/(1+I*c^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))+4*b^2*c^(1/4)*arctanh(c^(1/4)*sqrt(x))*log(2/(1+c^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))-2*b^2*c^(1/4)*arctanh(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))-2*b^2*c^(1/4)*arctanh(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))+2*b^2*(-c)^(1/4)*arctan((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))-2*b^2*(-c)^(1/4)*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))-2*b^2*c^(1/4)*arctan(c^(1/4)*sqrt(x))*log((1-I)*(1+c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))+2*b^2*c^(1/4)*arctan(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(-c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(x)/(d*sqrt(d*x))+2*b^2*(-c)^(1/4)*arctanh((-c)^(1/4)*sqrt(x))*log(-2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d*sqrt(d*x))-2*b^2*c^(1/4)*arctanh(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d*sqrt(d*x))+2*b^2*c^(1/4)*arctan(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(x)/(d*sqrt(d*x))+2*b^2*(-c)^(1/4)*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d*sqrt(d*x))-2*b^2*c^(1/4)*arctanh(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d*sqrt(d*x))+2*b^2*(-c)^(1/4)*arctan((-c)^(1/4)*sqrt(x))*log(-2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(x)/(d*sqrt(d*x))-2*b^2*(-c)^(1/4)*arctanh((-c)^(1/4)*sqrt(x))*log(-2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d*sqrt(d*x))+2*b^2*c^(1/4)*arctanh(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d*sqrt(d*x))+2*b^2*(-c)^(1/4)*arctan((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(x)/(d*sqrt(d*x))-2*b^2*(-c)^(1/4)*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d*sqrt(d*x))+2*b^2*c^(1/4)*arctanh(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d*sqrt(d*x))-2*b^2*(-c)^(1/4)*polylog(2,1+(-2)/(1-(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))+2*I*b^2*(-c)^(1/4)*polylog(2,1+(-2)/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))+I*b^2*(-c)^(1/4)*polylog(2,1+(-1-I)*(1-(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))+2*I*b^2*(-c)^(1/4)*polylog(2,1+(-2)/(1+I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))-2*b^2*(-c)^(1/4)*polylog(2,1+(-2)/(1+(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))+I*b^2*(-c)^(1/4)*polylog(2,1+(-1+I)*(1+(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))-2*b^2*c^(1/4)*polylog(2,1+(-2)/(1-c^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))-I*b^2*(-c)^(1/4)*polylog(2,1-2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))+b^2*(-c)^(1/4)*polylog(2,1-2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))+2*I*b^2*c^(1/4)*polylog(2,1+(-2)/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))-I*b^2*c^(1/4)*polylog(2,1+2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)-c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))-I*b^2*c^(1/4)*polylog(2,1-2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)+c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))+I*b^2*c^(1/4)*polylog(2,1+(-1-I)*(1-c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))+2*I*b^2*c^(1/4)*polylog(2,1+(-2)/(1+I*c^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))-2*b^2*c^(1/4)*polylog(2,1+(-2)/(1+c^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))+b^2*c^(1/4)*polylog(2,1+2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))+b^2*c^(1/4)*polylog(2,1-2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))-I*b^2*(-c)^(1/4)*polylog(2,1-2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))+b^2*(-c)^(1/4)*polylog(2,1-2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d*sqrt(d*x))+I*b^2*c^(1/4)*polylog(2,1+(-1+I)*(1+c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(d*sqrt(d*x))-I*b^2*c^(1/4)*polylog(2,1+2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(-c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(x)/(d*sqrt(d*x))-b^2*(-c)^(1/4)*polylog(2,1+2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d*sqrt(d*x))+b^2*c^(1/4)*polylog(2,1+2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d*sqrt(d*x))-I*b^2*c^(1/4)*polylog(2,1-2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(x)/(d*sqrt(d*x))-b^2*(-c)^(1/4)*polylog(2,1-2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d*sqrt(d*x))+b^2*c^(1/4)*polylog(2,1-2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d*sqrt(d*x))-I*b^2*(-c)^(1/4)*polylog(2,1+2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(x)/(d*sqrt(d*x))+b^2*(-c)^(1/4)*polylog(2,1+2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d*sqrt(d*x))-b^2*c^(1/4)*polylog(2,1+2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d*sqrt(d*x))-I*b^2*(-c)^(1/4)*polylog(2,1-2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(x)/(d*sqrt(d*x))+b^2*(-c)^(1/4)*polylog(2,1-2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d*sqrt(d*x))-b^2*c^(1/4)*polylog(2,1-2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d*sqrt(d*x))-2*a*b*c^(1/4)*arctan(1-c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(x)/(d*sqrt(d*x))+2*a*b*c^(1/4)*arctan(1+c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(x)/(d*sqrt(d*x))+a*b*c^(1/4)*log(1+x*sqrt(c)-c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(x)/(d*sqrt(d*x))-a*b*c^(1/4)*log(1+x*sqrt(c)+c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(x)/(d*sqrt(d*x))],
[(a+b*arctanh(c*x^2))^2/(d*x)^(5/2),x,197,-1/6*(2*a-b*log(1-c*x^2))^2/(d^2*x*sqrt(d*x))-2/3*a*b*log(1+c*x^2)/(d^2*x*sqrt(d*x))+1/3*b^2*log(1-c*x^2)*log(1+c*x^2)/(d^2*x*sqrt(d*x))-1/6*b^2*log(1+c*x^2)^2/(d^2*x*sqrt(d*x))-2/3*I*b^2*(-c)^(3/4)*arctan((-c)^(1/4)*sqrt(x))^2*sqrt(x)/(d^2*sqrt(d*x))-2/3*I*b^2*c^(3/4)*arctan(c^(1/4)*sqrt(x))^2*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*(-c)^(3/4)*arctanh((-c)^(1/4)*sqrt(x))^2*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*c^(3/4)*arctanh(c^(1/4)*sqrt(x))^2*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*(-c)^(3/4)*arctan((-c)^(1/4)*sqrt(x))*log(1-c*x^2)*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*(-c)^(3/4)*arctanh((-c)^(1/4)*sqrt(x))*log(1-c*x^2)*sqrt(x)/(d^2*sqrt(d*x))+2/3*b*c^(3/4)*arctan(c^(1/4)*sqrt(x))*(2*a-b*log(1-c*x^2))*sqrt(x)/(d^2*sqrt(d*x))+2/3*b*c^(3/4)*arctanh(c^(1/4)*sqrt(x))*(2*a-b*log(1-c*x^2))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*(-c)^(3/4)*arctan((-c)^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*c^(3/4)*arctan(c^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*(-c)^(3/4)*arctanh((-c)^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*c^(3/4)*arctanh(c^(1/4)*sqrt(x))*log(1+c*x^2)*sqrt(x)/(d^2*sqrt(d*x))-4/3*b^2*(-c)^(3/4)*arctanh((-c)^(1/4)*sqrt(x))*log(2/(1-(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))+4/3*b^2*(-c)^(3/4)*arctan((-c)^(1/4)*sqrt(x))*log(2/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*(-c)^(3/4)*arctan((-c)^(1/4)*sqrt(x))*log((1+I)*(1-(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-4/3*b^2*(-c)^(3/4)*arctan((-c)^(1/4)*sqrt(x))*log(2/(1+I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))+4/3*b^2*(-c)^(3/4)*arctanh((-c)^(1/4)*sqrt(x))*log(2/(1+(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*(-c)^(3/4)*arctan((-c)^(1/4)*sqrt(x))*log((1-I)*(1+(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-4/3*b^2*c^(3/4)*arctanh(c^(1/4)*sqrt(x))*log(2/(1-c^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*(-c)^(3/4)*arctan((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*(-c)^(3/4)*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))+4/3*b^2*c^(3/4)*arctan(c^(1/4)*sqrt(x))*log(2/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*c^(3/4)*arctan(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)-c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*c^(3/4)*arctan(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)+c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*c^(3/4)*arctan(c^(1/4)*sqrt(x))*log((1+I)*(1-c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-4/3*b^2*c^(3/4)*arctan(c^(1/4)*sqrt(x))*log(2/(1+I*c^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))+4/3*b^2*c^(3/4)*arctanh(c^(1/4)*sqrt(x))*log(2/(1+c^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*c^(3/4)*arctanh(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*c^(3/4)*arctanh(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*(-c)^(3/4)*arctan((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*(-c)^(3/4)*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*c^(3/4)*arctan(c^(1/4)*sqrt(x))*log((1-I)*(1+c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*c^(3/4)*arctan(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(-c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*(-c)^(3/4)*arctanh((-c)^(1/4)*sqrt(x))*log(-2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*c^(3/4)*arctanh(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*c^(3/4)*arctan(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*(-c)^(3/4)*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*c^(3/4)*arctanh(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*(-c)^(3/4)*arctan((-c)^(1/4)*sqrt(x))*log(-2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*(-c)^(3/4)*arctanh((-c)^(1/4)*sqrt(x))*log(-2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*c^(3/4)*arctanh(c^(1/4)*sqrt(x))*log(-2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*(-c)^(3/4)*arctan((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*(-c)^(3/4)*arctanh((-c)^(1/4)*sqrt(x))*log(2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d^2*sqrt(d*x))+2/3*b^2*c^(3/4)*arctanh(c^(1/4)*sqrt(x))*log(2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*(-c)^(3/4)*polylog(2,1+(-2)/(1-(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-2/3*I*b^2*(-c)^(3/4)*polylog(2,1+(-2)/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-1/3*I*b^2*(-c)^(3/4)*polylog(2,1+(-1-I)*(1-(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-2/3*I*b^2*(-c)^(3/4)*polylog(2,1+(-2)/(1+I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*(-c)^(3/4)*polylog(2,1+(-2)/(1+(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-1/3*I*b^2*(-c)^(3/4)*polylog(2,1+(-1+I)*(1+(-c)^(1/4)*sqrt(x))/(1-I*(-c)^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*c^(3/4)*polylog(2,1+(-2)/(1-c^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))+1/3*I*b^2*(-c)^(3/4)*polylog(2,1-2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))+1/3*b^2*(-c)^(3/4)*polylog(2,1-2*(-c)^(1/4)*(1-c^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*I*b^2*c^(3/4)*polylog(2,1+(-2)/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))+1/3*I*b^2*c^(3/4)*polylog(2,1+2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)-c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))+1/3*I*b^2*c^(3/4)*polylog(2,1-2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/((I*(-c)^(1/4)+c^(1/4))*(1-I*c^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))-1/3*I*b^2*c^(3/4)*polylog(2,1+(-1-I)*(1-c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-2/3*I*b^2*c^(3/4)*polylog(2,1+(-2)/(1+I*c^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))-2/3*b^2*c^(3/4)*polylog(2,1+(-2)/(1+c^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))+1/3*b^2*c^(3/4)*polylog(2,1+2*c^(1/4)*(1-(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)-c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))+1/3*b^2*c^(3/4)*polylog(2,1-2*c^(1/4)*(1+(-c)^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+c^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))+1/3*I*b^2*(-c)^(3/4)*polylog(2,1-2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+I*c^(1/4))*(1-I*(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))+1/3*b^2*(-c)^(3/4)*polylog(2,1-2*(-c)^(1/4)*(1+c^(1/4)*sqrt(x))/(((-c)^(1/4)+c^(1/4))*(1+(-c)^(1/4)*sqrt(x))))*sqrt(x)/(d^2*sqrt(d*x))-1/3*I*b^2*c^(3/4)*polylog(2,1+(-1+I)*(1+c^(1/4)*sqrt(x))/(1-I*c^(1/4)*sqrt(x)))*sqrt(x)/(d^2*sqrt(d*x))+1/3*I*b^2*c^(3/4)*polylog(2,1+2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(-c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(x)/(d^2*sqrt(d*x))-1/3*b^2*(-c)^(3/4)*polylog(2,1+2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d^2*sqrt(d*x))+1/3*b^2*c^(3/4)*polylog(2,1+2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d^2*sqrt(d*x))+1/3*I*b^2*c^(3/4)*polylog(2,1-2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1-I*c^(1/4)*sqrt(x))*(c^(1/4)+I*sqrt(-sqrt(-c)))))*sqrt(x)/(d^2*sqrt(d*x))-1/3*b^2*(-c)^(3/4)*polylog(2,1-2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d^2*sqrt(d*x))+1/3*b^2*c^(3/4)*polylog(2,1-2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(-c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(-c)))))*sqrt(x)/(d^2*sqrt(d*x))+1/3*I*b^2*(-c)^(3/4)*polylog(2,1+2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(x)/(d^2*sqrt(d*x))+1/3*b^2*(-c)^(3/4)*polylog(2,1+2*(-c)^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*(-(-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d^2*sqrt(d*x))-1/3*b^2*c^(3/4)*polylog(2,1+2*c^(1/4)*(1-sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(-c^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d^2*sqrt(d*x))+1/3*I*b^2*(-c)^(3/4)*polylog(2,1-2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1-I*(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+I*sqrt(-sqrt(c)))))*sqrt(x)/(d^2*sqrt(d*x))+1/3*b^2*(-c)^(3/4)*polylog(2,1-2*(-c)^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+(-c)^(1/4)*sqrt(x))*((-c)^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d^2*sqrt(d*x))-1/3*b^2*c^(3/4)*polylog(2,1-2*c^(1/4)*(1+sqrt(x)*sqrt(-sqrt(c)))/((1+c^(1/4)*sqrt(x))*(c^(1/4)+sqrt(-sqrt(c)))))*sqrt(x)/(d^2*sqrt(d*x))-2/3*a*b*c^(3/4)*arctan(1-c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(x)/(d^2*sqrt(d*x))+2/3*a*b*c^(3/4)*arctan(1+c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(x)/(d^2*sqrt(d*x))-1/3*a*b*c^(3/4)*log(1+x*sqrt(c)-c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(x)/(d^2*sqrt(d*x))+1/3*a*b*c^(3/4)*log(1+x*sqrt(c)+c^(1/4)*sqrt(2)*sqrt(x))*sqrt(2)*sqrt(x)/(d^2*sqrt(d*x))],

# Integrands of the form (d x)^m (a+b ArcTanh[c x^2])^p when m symbolic
[(d*x)^m*(a+b*arctanh(c*x^2))^3,x,0,Unintegrable((d*x)^m*(a+b*arctanh(c*x^2))^3,x)],
[(d*x)^m*(a+b*arctanh(c*x^2))^2,x,0,Unintegrable((d*x)^m*(a+b*arctanh(c*x^2))^2,x)],
[(d*x)^m*(a+b*arctanh(c*x^2)),x,2,(d*x)^(1+m)*(a+b*arctanh(c*x^2))/(d*(1+m))-2*b*c*(d*x)^(3+m)*hypergeom([1,1/4*(3+m)],[1/4*(7+m)],c^2*x^4)/(d^3*(1+m)*(3+m))],
[(d*x)^m/(a+b*arctanh(c*x^2)),x,0,Unintegrable((d*x)^m/(a+b*arctanh(c*x^2)),x)],
[(d*x)^m/(a+b*arctanh(c*x^2))^2,x,0,Unintegrable((d*x)^m/(a+b*arctanh(c*x^2))^2,x)],

# Integrands of the form (d x)^m (a+b ArcTanh[c x^3])^p

# Integrands of the form x^m (a+b ArcTanh[c x^3])^p
[x^11*(a+b*arctanh(c*x^3)),x,5,1/12*b*x^3/c^3+1/36*b*x^9/c-1/12*b*arctanh(c*x^3)/c^4+1/12*x^12*(a+b*arctanh(c*x^3))],
[x^8*(a+b*arctanh(c*x^3)),x,4,1/18*b*x^6/c+1/9*x^9*(a+b*arctanh(c*x^3))+1/18*b*log(1-c^2*x^6)/c^3],
[x^5*(a+b*arctanh(c*x^3)),x,4,1/6*b*x^3/c-1/6*b*arctanh(c*x^3)/c^2+1/6*x^6*(a+b*arctanh(c*x^3))],
[x^2*(a+b*arctanh(c*x^3)),x,2,1/3*x^3*(a+b*arctanh(c*x^3))+1/6*b*log(1-c^2*x^6)/c],
[(a+b*arctanh(c*x^3))/x,x,2,a*log(x)-1/6*b*polylog(2,-c*x^3)+1/6*b*polylog(2,c*x^3)],
[(a+b*arctanh(c*x^3))/x^4,x,5,1/3*(-a-b*arctanh(c*x^3))/x^3+b*c*log(x)-1/6*b*c*log(1-c^2*x^6)],
[(a+b*arctanh(c*x^3))/x^7,x,4,-1/6*b*c/x^3+1/6*b*c^2*arctanh(c*x^3)+1/6*(-a-b*arctanh(c*x^3))/x^6],
[(a+b*arctanh(c*x^3))/x^10,x,4,-1/18*b*c/x^6+1/9*(-a-b*arctanh(c*x^3))/x^9+1/3*b*c^3*log(x)-1/18*b*c^3*log(1-c^2*x^6)],
[x^3*(a+b*arctanh(c*x^3)),x,12,3/4*b*x/c-1/4*b*arctanh(c^(1/3)*x)/c^(4/3)+1/4*x^4*(a+b*arctanh(c*x^3))+1/16*b*log(1-c^(1/3)*x+c^(2/3)*x^2)/c^(4/3)-1/16*b*log(1+c^(1/3)*x+c^(2/3)*x^2)/c^(4/3)+1/8*b*arctan(1/sqrt(3)-2*c^(1/3)*x/sqrt(3))*sqrt(3)/c^(4/3)-1/8*b*arctan(1/sqrt(3)+2*c^(1/3)*x/sqrt(3))*sqrt(3)/c^(4/3)],
[a+b*arctanh(c*x^3),x,9,a*x+b*x*arctanh(c*x^3)+1/2*b*log(1-c^(2/3)*x^2)/c^(1/3)-1/4*b*log(1+c^(2/3)*x^2+c^(4/3)*x^4)/c^(1/3)+1/2*b*arctan((1+2*c^(2/3)*x^2)/sqrt(3))*sqrt(3)/c^(1/3)],
[(a+b*arctanh(c*x^3))/x^3,x,11,1/2*b*c^(2/3)*arctanh(c^(1/3)*x)+1/2*(-a-b*arctanh(c*x^3))/x^2-1/8*b*c^(2/3)*log(1-c^(1/3)*x+c^(2/3)*x^2)+1/8*b*c^(2/3)*log(1+c^(1/3)*x+c^(2/3)*x^2)-1/4*b*c^(2/3)*arctan(1/sqrt(3)-2*c^(1/3)*x/sqrt(3))*sqrt(3)+1/4*b*c^(2/3)*arctan(1/sqrt(3)+2*c^(1/3)*x/sqrt(3))*sqrt(3)],
[(a+b*arctanh(c*x^3))/x^6,x,9,-3/10*b*c/x^2+1/5*(-a-b*arctanh(c*x^3))/x^5-1/10*b*c^(5/3)*log(1-c^(2/3)*x^2)+1/20*b*c^(5/3)*log(1+c^(2/3)*x^2+c^(4/3)*x^4)-1/10*b*c^(5/3)*arctan((1+2*c^(2/3)*x^2)/sqrt(3))*sqrt(3)],
[x^7*(a+b*arctanh(c*x^3)),x,12,3/40*b*x^5/c-1/8*b*arctanh(c^(1/3)*x)/c^(8/3)+1/8*x^8*(a+b*arctanh(c*x^3))+1/32*b*log(1-c^(1/3)*x+c^(2/3)*x^2)/c^(8/3)-1/32*b*log(1+c^(1/3)*x+c^(2/3)*x^2)/c^(8/3)-1/16*b*arctan(1/sqrt(3)-2*c^(1/3)*x/sqrt(3))*sqrt(3)/c^(8/3)+1/16*b*arctan(1/sqrt(3)+2*c^(1/3)*x/sqrt(3))*sqrt(3)/c^(8/3)],
[x^4*(a+b*arctanh(c*x^3)),x,9,3/10*b*x^2/c+1/5*x^5*(a+b*arctanh(c*x^3))+1/10*b*log(1-c^(2/3)*x^2)/c^(5/3)-1/20*b*log(1+c^(2/3)*x^2+c^(4/3)*x^4)/c^(5/3)-1/10*b*arctan((1+2*c^(2/3)*x^2)/sqrt(3))*sqrt(3)/c^(5/3)],
[x*(a+b*arctanh(c*x^3)),x,11,-1/2*b*arctanh(c^(1/3)*x)/c^(2/3)+1/2*x^2*(a+b*arctanh(c*x^3))+1/8*b*log(1-c^(1/3)*x+c^(2/3)*x^2)/c^(2/3)-1/8*b*log(1+c^(1/3)*x+c^(2/3)*x^2)/c^(2/3)-1/4*b*arctan(1/sqrt(3)-2*c^(1/3)*x/sqrt(3))*sqrt(3)/c^(2/3)+1/4*b*arctan(1/sqrt(3)+2*c^(1/3)*x/sqrt(3))*sqrt(3)/c^(2/3)],
[(a+b*arctanh(c*x^3))/x^2,x,8,(-a-b*arctanh(c*x^3))/x-1/2*b*c^(1/3)*log(1-c^(2/3)*x^2)+1/4*b*c^(1/3)*log(1+c^(2/3)*x^2+c^(4/3)*x^4)+1/2*b*c^(1/3)*arctan((1+2*c^(2/3)*x^2)/sqrt(3))*sqrt(3)],
[(a+b*arctanh(c*x^3))/x^5,x,12,-3/4*b*c/x+1/4*b*c^(4/3)*arctanh(c^(1/3)*x)+1/4*(-a-b*arctanh(c*x^3))/x^4-1/16*b*c^(4/3)*log(1-c^(1/3)*x+c^(2/3)*x^2)+1/16*b*c^(4/3)*log(1+c^(1/3)*x+c^(2/3)*x^2)+1/8*b*c^(4/3)*arctan(1/sqrt(3)-2*c^(1/3)*x/sqrt(3))*sqrt(3)-1/8*b*c^(4/3)*arctan(1/sqrt(3)+2*c^(1/3)*x/sqrt(3))*sqrt(3)],
[x^11*(a+b*arctanh(c*x^3))^2,x,12,1/6*a*b*x^3/c^3+1/36*b^2*x^6/c^2+1/6*b^2*x^3*arctanh(c*x^3)/c^3+1/18*b*x^9*(a+b*arctanh(c*x^3))/c-1/12*(a+b*arctanh(c*x^3))^2/c^4+1/12*x^12*(a+b*arctanh(c*x^3))^2+1/9*b^2*log(1-c^2*x^6)/c^4],
[x^8*(a+b*arctanh(c*x^3))^2,x,10,1/9*b^2*x^3/c^2-1/9*b^2*arctanh(c*x^3)/c^3+1/9*b*x^6*(a+b*arctanh(c*x^3))/c+1/9*(a+b*arctanh(c*x^3))^2/c^3+1/9*x^9*(a+b*arctanh(c*x^3))^2-2/9*b*(a+b*arctanh(c*x^3))*log(2/(1-c*x^3))/c^3-1/9*b^2*polylog(2,1+(-2)/(1-c*x^3))/c^3],
[x^5*(a+b*arctanh(c*x^3))^2,x,7,1/3*a*b*x^3/c+1/3*b^2*x^3*arctanh(c*x^3)/c-1/6*(a+b*arctanh(c*x^3))^2/c^2+1/6*x^6*(a+b*arctanh(c*x^3))^2+1/6*b^2*log(1-c^2*x^6)/c^2],
[x^2*(a+b*arctanh(c*x^3))^2,x,6,1/3*(a+b*arctanh(c*x^3))^2/c+1/3*x^3*(a+b*arctanh(c*x^3))^2-2/3*b*(a+b*arctanh(c*x^3))*log(2/(1-c*x^3))/c-1/3*b^2*polylog(2,1+(-2)/(1-c*x^3))/c],
[(a+b*arctanh(c*x^3))^2/x,x,7,2/3*(a+b*arctanh(c*x^3))^2*arctanh(1+(-2)/(1-c*x^3))-1/3*b*(a+b*arctanh(c*x^3))*polylog(2,1+(-2)/(1-c*x^3))+1/3*b*(a+b*arctanh(c*x^3))*polylog(2,-1+2/(1-c*x^3))+1/6*b^2*polylog(3,1+(-2)/(1-c*x^3))-1/6*b^2*polylog(3,-1+2/(1-c*x^3))],
[(a+b*arctanh(c*x^3))^2/x^4,x,5,1/3*c*(a+b*arctanh(c*x^3))^2-1/3*(a+b*arctanh(c*x^3))^2/x^3+2/3*b*c*(a+b*arctanh(c*x^3))*log(2+(-2)/(1+c*x^3))-1/3*b^2*c*polylog(2,-1+2/(1+c*x^3))],
[(a+b*arctanh(c*x^3))^2/x^7,x,9,-1/3*b*c*(a+b*arctanh(c*x^3))/x^3+1/6*c^2*(a+b*arctanh(c*x^3))^2-1/6*(a+b*arctanh(c*x^3))^2/x^6+b^2*c^2*log(x)-1/6*b^2*c^2*log(1-c^2*x^6)],
[(a+b*arctanh(c*x^3))^2/x^10,x,9,-1/9*b^2*c^2/x^3+1/9*b^2*c^3*arctanh(c*x^3)-1/9*b*c*(a+b*arctanh(c*x^3))/x^6+1/9*c^3*(a+b*arctanh(c*x^3))^2-1/9*(a+b*arctanh(c*x^3))^2/x^9+2/9*b*c^3*(a+b*arctanh(c*x^3))*log(2+(-2)/(1+c*x^3))-1/9*b^2*c^3*polylog(2,-1+2/(1+c*x^3))],
#  {x^3*(a + b*ArcTanh[c*x^3])^2, x, 44, 0}
# {x^0*(a + b*ArcTanh[c*x^3])^2, x, 69, 0}
# {(a + b*ArcTanh[c*x^3])^2/x^3, x, 24, 0}
# {(a + b*ArcTanh[c*x^3])^2/x^6, x, 77, 0}
# {x^1*(a + b*ArcTanh[c*x^3])^2, x, 28, 0}
# {(a + b*ArcTanh[c*x^3])^2/x^2, x, 47, 0}

# {(a + b*ArcTanh[c*x^3])^2/x^5, x, 46, 0} 
[x^8*(a+b*arctanh(c*x^3))^3,x,13,1/3*a*b^2*x^3/c^2+1/3*b^3*x^3*arctanh(c*x^3)/c^2-1/6*b*(a+b*arctanh(c*x^3))^2/c^3+1/6*b*x^6*(a+b*arctanh(c*x^3))^2/c+1/9*(a+b*arctanh(c*x^3))^3/c^3+1/9*x^9*(a+b*arctanh(c*x^3))^3-1/3*b*(a+b*arctanh(c*x^3))^2*log(2/(1-c*x^3))/c^3+1/6*b^3*log(1-c^2*x^6)/c^3-1/3*b^2*(a+b*arctanh(c*x^3))*polylog(2,1+(-2)/(1-c*x^3))/c^3+1/6*b^3*polylog(3,1+(-2)/(1-c*x^3))/c^3],
[x^5*(a+b*arctanh(c*x^3))^3,x,9,1/2*b*(a+b*arctanh(c*x^3))^2/c^2+1/2*b*x^3*(a+b*arctanh(c*x^3))^2/c-1/6*(a+b*arctanh(c*x^3))^3/c^2+1/6*x^6*(a+b*arctanh(c*x^3))^3-b^2*(a+b*arctanh(c*x^3))*log(2/(1-c*x^3))/c^2-1/2*b^3*polylog(2,1+(-2)/(1-c*x^3))/c^2],
[x^2*(a+b*arctanh(c*x^3))^3,x,6,1/3*(a+b*arctanh(c*x^3))^3/c+1/3*x^3*(a+b*arctanh(c*x^3))^3-b*(a+b*arctanh(c*x^3))^2*log(2/(1-c*x^3))/c-b^2*(a+b*arctanh(c*x^3))*polylog(2,1+(-2)/(1-c*x^3))/c+1/2*b^3*polylog(3,1+(-2)/(1-c*x^3))/c],
[(a+b*arctanh(c*x^3))^3/x,x,9,2/3*(a+b*arctanh(c*x^3))^3*arctanh(1+(-2)/(1-c*x^3))-1/2*b*(a+b*arctanh(c*x^3))^2*polylog(2,1+(-2)/(1-c*x^3))+1/2*b*(a+b*arctanh(c*x^3))^2*polylog(2,-1+2/(1-c*x^3))+1/2*b^2*(a+b*arctanh(c*x^3))*polylog(3,1+(-2)/(1-c*x^3))-1/2*b^2*(a+b*arctanh(c*x^3))*polylog(3,-1+2/(1-c*x^3))-1/4*b^3*polylog(4,1+(-2)/(1-c*x^3))+1/4*b^3*polylog(4,-1+2/(1-c*x^3))],
[(a+b*arctanh(c*x^3))^3/x^4,x,6,1/3*c*(a+b*arctanh(c*x^3))^3-1/3*(a+b*arctanh(c*x^3))^3/x^3+b*c*(a+b*arctanh(c*x^3))^2*log(2+(-2)/(1+c*x^3))-b^2*c*(a+b*arctanh(c*x^3))*polylog(2,-1+2/(1+c*x^3))-1/2*b^3*c*polylog(3,-1+2/(1+c*x^3))],
[(a+b*arctanh(c*x^3))^3/x^7,x,8,1/2*b*c^2*(a+b*arctanh(c*x^3))^2-1/2*b*c*(a+b*arctanh(c*x^3))^2/x^3+1/6*c^2*(a+b*arctanh(c*x^3))^3-1/6*(a+b*arctanh(c*x^3))^3/x^6+b^2*c^2*(a+b*arctanh(c*x^3))*log(2+(-2)/(1+c*x^3))-1/2*b^3*c^2*polylog(2,-1+2/(1+c*x^3))],
#  {x^3*(a + b*ArcTanh[c*x^3])^3, x, 44, 0}
# {x^0*(a + b*ArcTanh[c*x^3])^3, x, 69, 0}
# {(a + b*ArcTanh[c*x^3])^3/x^3, x, 24, 0}
# {(a + b*ArcTanh[c*x^3])^3/x^6, x, 77, 0}
# {x^1*(a + b*ArcTanh[c*x^3])^3, x, 28, 0}
# {(a + b*ArcTanh[c*x^3])^3/x^2, x, 47, 0}

# {(a + b*ArcTanh[c*x^3])^3/x^5, x, 46, 0} 

# Integrands of the form (d x)^m (a+b ArcTanh[c x^3])^p when m symbolic
[(d*x)^m*(a+b*arctanh(c*x^3))^3,x,0,Unintegrable((d*x)^m*(a+b*arctanh(c*x^3))^3,x)],
[(d*x)^m*(a+b*arctanh(c*x^3))^2,x,0,Unintegrable((d*x)^m*(a+b*arctanh(c*x^3))^2,x)],
[(d*x)^m*(a+b*arctanh(c*x^3)),x,2,(d*x)^(1+m)*(a+b*arctanh(c*x^3))/(d*(1+m))-3*b*c*(d*x)^(4+m)*hypergeom([1,1/6*(4+m)],[1/6*(10+m)],c^2*x^6)/(d^4*(1+m)*(4+m))],
[(d*x)^m/(a+b*arctanh(c*x^3)),x,0,Unintegrable((d*x)^m/(a+b*arctanh(c*x^3)),x)],
[(d*x)^m/(a+b*arctanh(c*x^3))^2,x,0,Unintegrable((d*x)^m/(a+b*arctanh(c*x^3))^2,x)],

# Integrands of the form (d x)^m (a+b ArcTanh[c/x^1])^p

# Integrands of the form x^m (a+b ArcTanh[c/x])^p
[x^3*(a+b*arctanh(c/x)),x,5,1/4*b*c^3*x+1/12*b*c*x^3+1/4*x^4*(a+b*arctanh(c/x))-1/4*b*c^4*arctanh(x/c)],
[x^2*(a+b*arctanh(c/x)),x,5,1/6*b*c*x^2+1/3*x^3*(a+b*arctanh(c/x))+1/6*b*c^3*log(c^2-x^2)],
[x*(a+b*arctanh(c/x)),x,4,1/2*b*c*x+1/2*x^2*(a+b*arctanh(c/x))-1/2*b*c^2*arctanh(x/c)],
[a+b*arctanh(c/x),x,4,a*x+b*x*arctanh(c/x)+1/2*b*c*log(c^2-x^2)],
[(a+b*arctanh(c/x))/x,x,2,a*log(x)+1/2*b*polylog(2,-c/x)-1/2*b*polylog(2,c/x)],
[(a+b*arctanh(c/x))/x^2,x,2,(-a-b*arctanh(c/x))/x-1/2*b*log(1-c^2/x^2)/c],
[(a+b*arctanh(c/x))/x^3,x,4,-1/2*b/(c*x)+1/2*(-a-b*arctanh(c/x))/x^2+1/2*b*arctanh(x/c)/c^2],
[(a+b*arctanh(c/x))/x^4,x,5,-1/6*b/(c*x^2)+1/3*(-a-b*arctanh(c/x))/x^3+1/3*b*log(x)/c^3-1/6*b*log(c^2-x^2)/c^3],
[x^3*(a+b*arctanh(c/x))^2,x,14,1/12*b^2*c^2*x^2+1/2*b*c^3*x*(a+b*arccoth(x/c))+1/6*b*c*x^3*(a+b*arccoth(x/c))-1/4*c^4*(a+b*arccoth(x/c))^2+1/4*x^4*(a+b*arccoth(x/c))^2+1/3*b^2*c^4*log(1-c^2/x^2)+2/3*b^2*c^4*log(x)],
[x^2*(a+b*arctanh(c/x))^2,x,9,1/3*b^2*c^2*x-1/3*b^2*c^3*arccoth(x/c)+1/3*b*c*x^2*(a+b*arccoth(x/c))-1/3*c^3*(a+b*arccoth(x/c))^2+1/3*x^3*(a+b*arccoth(x/c))^2-2/3*b*c^3*(a+b*arccoth(x/c))*log(2+(-2)/(1+c/x))+1/3*b^2*c^3*polylog(2,-1+2/(1+c/x))],
[x*(a+b*arctanh(c/x))^2,x,9,b*c*x*(a+b*arccoth(x/c))-1/2*c^2*(a+b*arccoth(x/c))^2+1/2*x^2*(a+b*arccoth(x/c))^2+1/2*b^2*c^2*log(1-c^2/x^2)+b^2*c^2*log(x)],
[(a+b*arctanh(c/x))^2,x,6,c*(a+b*arccoth(x/c))^2+x*(a+b*arccoth(x/c))^2-2*b*c*(a+b*arccoth(x/c))*log(2*c/(c-x))-b^2*c*polylog(2,(-c-x)/(c-x))],
[(a+b*arctanh(c/x))^2/x,x,7,-2*(a+b*arccoth(x/c))^2*arctanh(1+(-2)/(1-c/x))+b*(a+b*arccoth(x/c))*polylog(2,1+(-2)/(1-c/x))-b*(a+b*arccoth(x/c))*polylog(2,-1+2/(1-c/x))-1/2*b^2*polylog(3,1+(-2)/(1-c/x))+1/2*b^2*polylog(3,-1+2/(1-c/x))],
[(a+b*arctanh(c/x))^2/x^2,x,6,-(a+b*arccoth(x/c))^2/c-(a+b*arccoth(x/c))^2/x+2*b*(a+b*arccoth(x/c))*log(2/(1-c/x))/c+b^2*polylog(2,1+(-2)/(1-c/x))/c],
[(a+b*arctanh(c/x))^2/x^3,x,7,-a*b/(c*x)-b^2*arccoth(x/c)/(c*x)+1/2*(a+b*arccoth(x/c))^2/c^2-1/2*(a+b*arccoth(x/c))^2/x^2-1/2*b^2*log(1-c^2/x^2)/c^2],
[x^3*(a+b*arctanh(c/x))^3,x,17,1/4*b^3*c^3*x-1/4*b^3*c^4*arccoth(x/c)+1/4*b^2*c^2*x^2*(a+b*arccoth(x/c))-b*c^4*(a+b*arccoth(x/c))^2+3/4*b*c^3*x*(a+b*arccoth(x/c))^2+1/4*b*c*x^3*(a+b*arccoth(x/c))^2-1/4*c^4*(a+b*arccoth(x/c))^3+1/4*x^4*(a+b*arccoth(x/c))^3-2*b^2*c^4*(a+b*arccoth(x/c))*log(2+(-2)/(1+c/x))+b^3*c^4*polylog(2,-1+2/(1+c/x))],
[x^2*(a+b*arctanh(c/x))^3,x,15,b^2*c^2*x*(a+b*arccoth(x/c))-1/2*b*c^3*(a+b*arccoth(x/c))^2+1/2*b*c*x^2*(a+b*arccoth(x/c))^2-1/3*c^3*(a+b*arccoth(x/c))^3+1/3*x^3*(a+b*arccoth(x/c))^3-b*c^3*(a+b*arccoth(x/c))^2*log(2+(-2)/(1+c/x))+1/2*b^3*c^3*log(1-c^2/x^2)+b^3*c^3*log(x)+b^2*c^3*(a+b*arccoth(x/c))*polylog(2,-1+2/(1+c/x))+1/2*b^3*c^3*polylog(3,-1+2/(1+c/x))],
[x*(a+b*arctanh(c/x))^3,x,8,-3/2*b*c^2*(a+b*arccoth(x/c))^2+3/2*b*c*x*(a+b*arccoth(x/c))^2-1/2*c^2*(a+b*arccoth(x/c))^3+1/2*x^2*(a+b*arccoth(x/c))^3-3*b^2*c^2*(a+b*arccoth(x/c))*log(2+(-2)/(1+c/x))+3/2*b^3*c^2*polylog(2,-1+2/(1+c/x))],
[(a+b*arctanh(c/x))^3,x,6,c*(a+b*arccoth(x/c))^3+x*(a+b*arccoth(x/c))^3-3*b*c*(a+b*arccoth(x/c))^2*log(2*c/(c-x))-3*b^2*c*(a+b*arccoth(x/c))*polylog(2,1-2*c/(c-x))+3/2*b^3*c*polylog(3,1-2*c/(c-x))],
[(a+b*arctanh(c/x))^3/x,x,9,-2*(a+b*arccoth(x/c))^3*arctanh(1+(-2)/(1-c/x))+3/2*b*(a+b*arccoth(x/c))^2*polylog(2,1+(-2)/(1-c/x))-3/2*b*(a+b*arccoth(x/c))^2*polylog(2,-1+2/(1-c/x))-3/2*b^2*(a+b*arccoth(x/c))*polylog(3,1+(-2)/(1-c/x))+3/2*b^2*(a+b*arccoth(x/c))*polylog(3,-1+2/(1-c/x))+3/4*b^3*polylog(4,1+(-2)/(1-c/x))-3/4*b^3*polylog(4,-1+2/(1-c/x))],
[(a+b*arctanh(c/x))^3/x^2,x,6,-(a+b*arccoth(x/c))^3/c-(a+b*arccoth(x/c))^3/x+3*b*(a+b*arccoth(x/c))^2*log(2/(1-c/x))/c+3*b^2*(a+b*arccoth(x/c))*polylog(2,1+(-2)/(1-c/x))/c-3/2*b^3*polylog(3,1+(-2)/(1-c/x))/c],
[(a+b*arctanh(c/x))^3/x^3,x,9,-3/2*b*(a+b*arccoth(x/c))^2/c^2-3/2*b*(a+b*arccoth(x/c))^2/(c*x)+1/2*(a+b*arccoth(x/c))^3/c^2-1/2*(a+b*arccoth(x/c))^3/x^2+3*b^2*(a+b*arccoth(x/c))*log(2/(1-c/x))/c^2+3/2*b^3*polylog(2,1+(-2)/(1-c/x))/c^2],

# Integrands of the form (d x)^m (a+b ArcTanh[c/x^2])^p

# Integrands of the form x^m (a+b ArcTanh[c/x^2])^p
[x^7*(a+b*arctanh(c/x^2)),x,6,1/8*b*c^3*x^2+1/24*b*c*x^6+1/8*x^8*(a+b*arctanh(c/x^2))-1/8*b*c^4*arctanh(x^2/c)],
[x^5*(a+b*arctanh(c/x^2)),x,5,1/12*b*c*x^4+1/6*x^6*(a+b*arctanh(c/x^2))+1/12*b*c^3*log(c^2-x^4)],
[x^3*(a+b*arctanh(c/x^2)),x,5,1/4*b*c*x^2+1/4*x^4*(a+b*arctanh(c/x^2))-1/4*b*c^2*arctanh(x^2/c)],
[x*(a+b*arctanh(c/x^2)),x,3,1/2*x^2*(a+b*arctanh(c/x^2))+1/4*b*c*log(c^2-x^4)],
[(a+b*arctanh(c/x^2))/x,x,2,a*log(x)+1/4*b*polylog(2,-c/x^2)-1/4*b*polylog(2,c/x^2)],
[(a+b*arctanh(c/x^2))/x^3,x,2,1/2*(-a-b*arctanh(c/x^2))/x^2-1/4*b*log(1-c^2/x^4)/c],
[(a+b*arctanh(c/x^2))/x^5,x,5,-1/4*b/(c*x^2)+1/4*(-a-b*arctanh(c/x^2))/x^4+1/4*b*arctanh(x^2/c)/c^2],
[(a+b*arctanh(c/x^2))/x^7,x,5,-1/12*b/(c*x^4)+1/6*(-a-b*arctanh(c/x^2))/x^6+1/3*b*log(x)/c^3-1/12*b*log(c^2-x^4)/c^3],
[x^4*(a+b*arctanh(c/x^2)),x,6,2/15*b*c*x^3+1/5*b*c^(5/2)*arctan(x/sqrt(c))+1/5*x^5*(a+b*arctanh(c/x^2))-1/5*b*c^(5/2)*arctanh(x/sqrt(c))],
[x^2*(a+b*arctanh(c/x^2)),x,6,2/3*b*c*x-1/3*b*c^(3/2)*arctan(x/sqrt(c))+1/3*x^3*(a+b*arctanh(c/x^2))-1/3*b*c^(3/2)*arctanh(x/sqrt(c))],
[a+b*arctanh(c/x^2),x,6,a*x+b*x*arctanh(c/x^2)+b*arctan(x/sqrt(c))*sqrt(c)-b*arctanh(x/sqrt(c))*sqrt(c)],
[(a+b*arctanh(c/x^2))/x^2,x,5,(-a-b*arctanh(c/x^2))/x+b*arctan(x/sqrt(c))/sqrt(c)+b*arctanh(x/sqrt(c))/sqrt(c)],
[(a+b*arctanh(c/x^2))/x^4,x,6,-2/3*b/(c*x)-1/3*b*arctan(x/sqrt(c))/c^(3/2)+1/3*(-a-b*arctanh(c/x^2))/x^3+1/3*b*arctanh(x/sqrt(c))/c^(3/2)],
[(a+b*arctanh(c/x^2))/x^6,x,6,-2/15*b/(c*x^3)+1/5*b*arctan(x/sqrt(c))/c^(5/2)+1/5*(-a-b*arctanh(c/x^2))/x^5+1/5*b*arctanh(x/sqrt(c))/c^(5/2)],
[x^3*(a+b*arctanh(c/x^2))^2,x,9,1/2*b*c*x^2*(a+b*arccoth(x^2/c))-1/4*c^2*(a+b*arccoth(x^2/c))^2+1/4*x^4*(a+b*arccoth(x^2/c))^2+1/4*b^2*c^2*log(1-c^2/x^4)+b^2*c^2*log(x)],
[x*(a+b*arctanh(c/x^2))^2,x,5,-1/2*c*(a+b*arccoth(x^2/c))^2+1/2*x^2*(a+b*arccoth(x^2/c))^2-b*c*(a+b*arccoth(x^2/c))*log(2+(-2)/(1+c/x^2))+1/2*b^2*c*polylog(2,-1+2/(1+c/x^2))],
[(a+b*arctanh(c/x^2))^2/x,x,7,-(a+b*arccoth(x^2/c))^2*arctanh(1+(-2)/(1-c/x^2))+1/2*b*(a+b*arccoth(x^2/c))*polylog(2,1+(-2)/(1-c/x^2))-1/2*b*(a+b*arccoth(x^2/c))*polylog(2,-1+2/(1-c/x^2))-1/4*b^2*polylog(3,1+(-2)/(1-c/x^2))+1/4*b^2*polylog(3,-1+2/(1-c/x^2))],
[(a+b*arctanh(c/x^2))^2/x^3,x,6,-1/2*(a+b*arccoth(x^2/c))^2/c-1/2*(a+b*arccoth(x^2/c))^2/x^2+b*(a+b*arccoth(x^2/c))*log(2/(1-c/x^2))/c+1/2*b^2*polylog(2,1+(-2)/(1-c/x^2))/c],
[(a+b*arctanh(c/x^2))^2/x^5,x,7,-1/2*a*b/(c*x^2)-1/2*b^2*arccoth(x^2/c)/(c*x^2)+1/4*(a+b*arccoth(x^2/c))^2/c^2-1/4*(a+b*arccoth(x^2/c))^2/x^4-1/4*b^2*log(1-c^2/x^4)/c^2],
[x^4*(a+b*arctanh(c/x^2))^2,x,98,8/15*b^2*c^2*x+2/15*a*b*c*x^3+2/5*a*b*c^(5/2)*arctan(x/sqrt(c))-4/15*b^2*c^(5/2)*arctan(x/sqrt(c))-1/5*I*b^2*c^(5/2)*arctan(x/sqrt(c))^2-4/15*b^2*c^(5/2)*arctanh(x/sqrt(c))+1/5*b^2*c^(5/2)*arctanh(x/sqrt(c))^2-1/15*b^2*c*x^3*log(1-c/x^2)-1/5*b^2*c^(5/2)*arctan(x/sqrt(c))*log(1-c/x^2)+1/15*b*c*x^3*(2*a-b*log(1-c/x^2))-1/5*b*c^(5/2)*arctanh(x/sqrt(c))*(2*a-b*log(1-c/x^2))+1/20*x^5*(2*a-b*log(1-c/x^2))^2+2/15*b^2*c*x^3*log(1+c/x^2)+1/5*a*b*x^5*log(1+c/x^2)+1/5*b^2*c^(5/2)*arctan(x/sqrt(c))*log(1+c/x^2)-1/5*b^2*c^(5/2)*arctanh(x/sqrt(c))*log(1+c/x^2)-1/10*b^2*x^5*log(1-c/x^2)*log(1+c/x^2)+1/20*b^2*x^5*log(1+c/x^2)^2-2/5*b^2*c^(5/2)*arctan(x/sqrt(c))*log(2*sqrt(c)/(-I*x+sqrt(c)))+1/5*b^2*c^(5/2)*arctan(x/sqrt(c))*log((1+I)*(-x+sqrt(c))/(-I*x+sqrt(c)))-2/5*b^2*c^(5/2)*arctanh(x/sqrt(c))*log(2*sqrt(c)/(x+sqrt(c)))+1/5*b^2*c^(5/2)*arctanh(x/sqrt(c))*log(2*(-x+sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(x+sqrt(c))))+1/5*b^2*c^(5/2)*arctan(x/sqrt(c))*log((1-I)*(x+sqrt(c))/(-I*x+sqrt(c)))+1/5*b^2*c^(5/2)*arctanh(x/sqrt(c))*log(2*(x+sqrt(-c))*sqrt(c)/((x+sqrt(c))*(sqrt(-c)+sqrt(c))))+2/5*b^2*c^(5/2)*arctan(x/sqrt(c))*log(2-2*sqrt(c)/(-I*x+sqrt(c)))+2/5*b^2*c^(5/2)*arctanh(x/sqrt(c))*log(2-2*sqrt(c)/(x+sqrt(c)))+1/5*b^2*c^(5/2)*polylog(2,-x/sqrt(c))-1/5*I*b^2*c^(5/2)*polylog(2,-I*x/sqrt(c))+1/5*I*b^2*c^(5/2)*polylog(2,I*x/sqrt(c))-1/5*b^2*c^(5/2)*polylog(2,x/sqrt(c))+1/5*I*b^2*c^(5/2)*polylog(2,1-2*sqrt(c)/(-I*x+sqrt(c)))-1/5*I*b^2*c^(5/2)*polylog(2,-1+2*sqrt(c)/(-I*x+sqrt(c)))-1/10*I*b^2*c^(5/2)*polylog(2,1+(-1-I)*(-x+sqrt(c))/(-I*x+sqrt(c)))+1/5*b^2*c^(5/2)*polylog(2,1-2*sqrt(c)/(x+sqrt(c)))-1/5*b^2*c^(5/2)*polylog(2,-1+2*sqrt(c)/(x+sqrt(c)))-1/10*b^2*c^(5/2)*polylog(2,1-2*(-x+sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(x+sqrt(c))))-1/10*I*b^2*c^(5/2)*polylog(2,1+(-1+I)*(x+sqrt(c))/(-I*x+sqrt(c)))-1/10*b^2*c^(5/2)*polylog(2,1-2*(x+sqrt(-c))*sqrt(c)/((x+sqrt(c))*(sqrt(-c)+sqrt(c))))],
[x^2*(a+b*arctanh(c/x^2))^2,x,80,4/3*a*b*c*x-2/3*a*b*c^(3/2)*arctan(x/sqrt(c))+4/3*b^2*c^(3/2)*arctan(x/sqrt(c))+1/3*I*b^2*c^(3/2)*arctan(x/sqrt(c))^2-4/3*b^2*c^(3/2)*arctanh(x/sqrt(c))+1/3*b^2*c^(3/2)*arctanh(x/sqrt(c))^2-2/3*b^2*c*x*log(1-c/x^2)+1/3*b^2*c^(3/2)*arctan(x/sqrt(c))*log(1-c/x^2)-1/3*b*c^(3/2)*arctanh(x/sqrt(c))*(2*a-b*log(1-c/x^2))+1/12*x^3*(2*a-b*log(1-c/x^2))^2+2/3*b^2*c*x*log(1+c/x^2)+1/3*a*b*x^3*log(1+c/x^2)-1/3*b^2*c^(3/2)*arctan(x/sqrt(c))*log(1+c/x^2)-1/3*b^2*c^(3/2)*arctanh(x/sqrt(c))*log(1+c/x^2)-1/6*b^2*x^3*log(1-c/x^2)*log(1+c/x^2)+1/12*b^2*x^3*log(1+c/x^2)^2+2/3*b^2*c^(3/2)*arctan(x/sqrt(c))*log(2*sqrt(c)/(-I*x+sqrt(c)))-1/3*b^2*c^(3/2)*arctan(x/sqrt(c))*log((1+I)*(-x+sqrt(c))/(-I*x+sqrt(c)))-2/3*b^2*c^(3/2)*arctanh(x/sqrt(c))*log(2*sqrt(c)/(x+sqrt(c)))+1/3*b^2*c^(3/2)*arctanh(x/sqrt(c))*log(2*(-x+sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(x+sqrt(c))))-1/3*b^2*c^(3/2)*arctan(x/sqrt(c))*log((1-I)*(x+sqrt(c))/(-I*x+sqrt(c)))+1/3*b^2*c^(3/2)*arctanh(x/sqrt(c))*log(2*(x+sqrt(-c))*sqrt(c)/((x+sqrt(c))*(sqrt(-c)+sqrt(c))))-2/3*b^2*c^(3/2)*arctan(x/sqrt(c))*log(2-2*sqrt(c)/(-I*x+sqrt(c)))+2/3*b^2*c^(3/2)*arctanh(x/sqrt(c))*log(2-2*sqrt(c)/(x+sqrt(c)))+1/3*b^2*c^(3/2)*polylog(2,-x/sqrt(c))+1/3*I*b^2*c^(3/2)*polylog(2,-I*x/sqrt(c))-1/3*I*b^2*c^(3/2)*polylog(2,I*x/sqrt(c))-1/3*b^2*c^(3/2)*polylog(2,x/sqrt(c))-1/3*I*b^2*c^(3/2)*polylog(2,1-2*sqrt(c)/(-I*x+sqrt(c)))+1/3*I*b^2*c^(3/2)*polylog(2,-1+2*sqrt(c)/(-I*x+sqrt(c)))+1/6*I*b^2*c^(3/2)*polylog(2,1+(-1-I)*(-x+sqrt(c))/(-I*x+sqrt(c)))+1/3*b^2*c^(3/2)*polylog(2,1-2*sqrt(c)/(x+sqrt(c)))-1/3*b^2*c^(3/2)*polylog(2,-1+2*sqrt(c)/(x+sqrt(c)))-1/6*b^2*c^(3/2)*polylog(2,1-2*(-x+sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(x+sqrt(c))))+1/6*I*b^2*c^(3/2)*polylog(2,1+(-1+I)*(x+sqrt(c))/(-I*x+sqrt(c)))-1/6*b^2*c^(3/2)*polylog(2,1-2*(x+sqrt(-c))*sqrt(c)/((x+sqrt(c))*(sqrt(-c)+sqrt(c))))],
[(a+b*arctanh(c/x^2))^2,x,100,a^2*x-a*b*x*log(1-c/x^2)+1/4*b^2*x*log(1-c/x^2)^2+a*b*x*log(1+c/x^2)-1/2*b^2*x*log(1-c/x^2)*log(1+c/x^2)+1/4*b^2*x*log(1+c/x^2)^2-1/2*b^2*log(1+c/x^2)*log(-x+sqrt(-c))*sqrt(-c)-b^2*log(x/sqrt(-c))*log(-x+sqrt(-c))*sqrt(-c)+1/4*b^2*log(-x+sqrt(-c))^2*sqrt(-c)+1/2*b^2*log(1+c/x^2)*log(x+sqrt(-c))*sqrt(-c)+b^2*log(-x/sqrt(-c))*log(x+sqrt(-c))*sqrt(-c)-1/2*b^2*log(1/2*(-x+sqrt(-c))/sqrt(-c))*log(x+sqrt(-c))*sqrt(-c)-1/4*b^2*log(x+sqrt(-c))^2*sqrt(-c)+1/2*b^2*log(-x+sqrt(-c))*log(1/2*(x+sqrt(-c))/sqrt(-c))*sqrt(-c)+1/2*b^2*polylog(2,1/2*(1-x/sqrt(-c)))*sqrt(-c)-b^2*polylog(2,1-x/sqrt(-c))*sqrt(-c)+b^2*polylog(2,1+x/sqrt(-c))*sqrt(-c)-1/2*b^2*polylog(2,1/2*(c-x*sqrt(-c))/c)*sqrt(-c)+2*a*b*arctan(x/sqrt(c))*sqrt(c)-2*a*b*arctanh(x/sqrt(c))*sqrt(c)-b^2*arctan(x/sqrt(c))*log(1-c/x^2)*sqrt(c)-b^2*arctanh(x/sqrt(c))*log(1+c/x^2)*sqrt(c)-1/2*b^2*log(1-c/x^2)*log(-x+sqrt(c))*sqrt(c)-b^2*log(x/sqrt(c))*log(-x+sqrt(c))*sqrt(c)+1/4*b^2*log(-x+sqrt(c))^2*sqrt(c)-2*b^2*arctan(x/sqrt(c))*log(2*sqrt(c)/(-I*x+sqrt(c)))*sqrt(c)+b^2*arctan(x/sqrt(c))*log((1+I)*(-x+sqrt(c))/(-I*x+sqrt(c)))*sqrt(c)-2*b^2*arctanh(x/sqrt(c))*log(2*sqrt(c)/(x+sqrt(c)))*sqrt(c)+b^2*arctanh(x/sqrt(c))*log(2*(-x+sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(x+sqrt(c))))*sqrt(c)+1/2*b^2*log(1-c/x^2)*log(x+sqrt(c))*sqrt(c)+b^2*log(-x/sqrt(c))*log(x+sqrt(c))*sqrt(c)-1/2*b^2*log(1/2*(-x+sqrt(c))/sqrt(c))*log(x+sqrt(c))*sqrt(c)-1/4*b^2*log(x+sqrt(c))^2*sqrt(c)+1/2*b^2*log(-x+sqrt(c))*log(1/2*(x+sqrt(c))/sqrt(c))*sqrt(c)+b^2*arctan(x/sqrt(c))*log((1-I)*(x+sqrt(c))/(-I*x+sqrt(c)))*sqrt(c)+b^2*arctanh(x/sqrt(c))*log(2*(x+sqrt(-c))*sqrt(c)/((x+sqrt(c))*(sqrt(-c)+sqrt(c))))*sqrt(c)-b^2*polylog(2,1-x/sqrt(c))*sqrt(c)+1/2*b^2*polylog(2,1/2-1/2*x/sqrt(c))*sqrt(c)+b^2*polylog(2,1+x/sqrt(c))*sqrt(c)+b^2*polylog(2,-x/sqrt(c))*sqrt(c)-I*b^2*polylog(2,-I*x/sqrt(c))*sqrt(c)+I*b^2*polylog(2,I*x/sqrt(c))*sqrt(c)-b^2*polylog(2,x/sqrt(c))*sqrt(c)-1/2*b^2*polylog(2,1/2*(x+sqrt(c))/sqrt(c))*sqrt(c)+I*b^2*polylog(2,1-2*sqrt(c)/(-I*x+sqrt(c)))*sqrt(c)-1/2*I*b^2*polylog(2,1+(-1-I)*(-x+sqrt(c))/(-I*x+sqrt(c)))*sqrt(c)+b^2*polylog(2,1-2*sqrt(c)/(x+sqrt(c)))*sqrt(c)-1/2*b^2*polylog(2,1-2*(-x+sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(x+sqrt(c))))*sqrt(c)-1/2*I*b^2*polylog(2,1+(-1+I)*(x+sqrt(c))/(-I*x+sqrt(c)))*sqrt(c)-1/2*b^2*polylog(2,1-2*(x+sqrt(-c))*sqrt(c)/((x+sqrt(c))*(sqrt(-c)+sqrt(c))))*sqrt(c)],
[(a+b*arctanh(c/x^2))^2/x^2,x,72,2*a*b/x-b^2*log(1-c/x^2)/x-b*(2*a-b*log(1-c/x^2))/x-1/4*(2*a-b*log(1-c/x^2))^2/x-a*b*log(1+c/x^2)/x+1/2*b^2*log(1-c/x^2)*log(1+c/x^2)/x-1/4*b^2*log(1+c/x^2)^2/x-2*a*b*arccot(x/sqrt(c))/sqrt(c)-2*b^2*arccot(x/sqrt(c))/sqrt(c)-2*b^2*arccoth(x/sqrt(c))/sqrt(c)-2*b^2*arctan(x/sqrt(c))/sqrt(c)-I*b^2*arctan(x/sqrt(c))^2/sqrt(c)+2*b^2*arctanh(x/sqrt(c))/sqrt(c)-b^2*arctanh(x/sqrt(c))^2/sqrt(c)+b^2*arccot(x/sqrt(c))*log(1-c/x^2)/sqrt(c)+b*arctanh(x/sqrt(c))*(2*a-b*log(1-c/x^2))/sqrt(c)+b^2*arccoth(x/sqrt(c))*log(1+c/x^2)/sqrt(c)+b^2*arctan(x/sqrt(c))*log(1+c/x^2)/sqrt(c)+2*b^2*arccot(x/sqrt(c))*log(2/(1-I*sqrt(c)/x))/sqrt(c)-b^2*arccot(x/sqrt(c))*log((1+I)*(1-sqrt(c)/x)/(1-I*sqrt(c)/x))/sqrt(c)+2*b^2*arccoth(x/sqrt(c))*log(2/(1+sqrt(c)/x))/sqrt(c)-b^2*arccoth(x/sqrt(c))*log(-2*(1-sqrt(-c)/x)*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+sqrt(c)/x)))/sqrt(c)-b^2*arccoth(x/sqrt(c))*log(2*(1+sqrt(-c)/x)*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+sqrt(c)/x)))/sqrt(c)-b^2*arccot(x/sqrt(c))*log((1-I)*(1+sqrt(c)/x)/(1-I*sqrt(c)/x))/sqrt(c)+2*b^2*arctan(x/sqrt(c))*log(2-2*sqrt(c)/(-I*x+sqrt(c)))/sqrt(c)-2*b^2*arctanh(x/sqrt(c))*log(2-2*sqrt(c)/(x+sqrt(c)))/sqrt(c)-I*b^2*polylog(2,-1+2*sqrt(c)/(-I*x+sqrt(c)))/sqrt(c)+b^2*polylog(2,-1+2*sqrt(c)/(x+sqrt(c)))/sqrt(c)-I*b^2*polylog(2,1+(-2)/(1-I*sqrt(c)/x))/sqrt(c)+1/2*I*b^2*polylog(2,1+(-1-I)*(1-sqrt(c)/x)/(1-I*sqrt(c)/x))/sqrt(c)-b^2*polylog(2,1+(-2)/(1+sqrt(c)/x))/sqrt(c)+1/2*b^2*polylog(2,1+2*(1-sqrt(-c)/x)*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+sqrt(c)/x)))/sqrt(c)+1/2*b^2*polylog(2,1-2*(1+sqrt(-c)/x)*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+sqrt(c)/x)))/sqrt(c)+1/2*I*b^2*polylog(2,1+(-1+I)*(1+sqrt(c)/x)/(1-I*sqrt(c)/x))/sqrt(c)],
[(a+b*arctanh(c/x^2))^2/x^4,x,105,2/9*a*b/x^3-2/3*a*b/(c*x)-2/3*a*b*arctan(x/sqrt(c))/c^(3/2)+4/3*b^2*arctan(x/sqrt(c))/c^(3/2)+1/3*I*b^2*arctan(x/sqrt(c))^2/c^(3/2)+4/3*b^2*arctanh(x/sqrt(c))/c^(3/2)-1/3*b^2*arctanh(x/sqrt(c))^2/c^(3/2)-1/9*b^2*log(1-c/x^2)/x^3+1/3*b^2*log(1-c/x^2)/(c*x)+1/3*b^2*arctan(x/sqrt(c))*log(1-c/x^2)/c^(3/2)-1/9*b*(2*a-b*log(1-c/x^2))/x^3-1/3*b*(2*a-b*log(1-c/x^2))/(c*x)+1/3*b*arctanh(x/sqrt(c))*(2*a-b*log(1-c/x^2))/c^(3/2)-1/12*(2*a-b*log(1-c/x^2))^2/x^3-1/3*a*b*log(1+c/x^2)/x^3-2/3*b^2*log(1+c/x^2)/(c*x)-1/3*b^2*arctan(x/sqrt(c))*log(1+c/x^2)/c^(3/2)+1/3*b^2*arctanh(x/sqrt(c))*log(1+c/x^2)/c^(3/2)+1/6*b^2*log(1-c/x^2)*log(1+c/x^2)/x^3-1/12*b^2*log(1+c/x^2)^2/x^3+2/3*b^2*arctan(x/sqrt(c))*log(2*sqrt(c)/(-I*x+sqrt(c)))/c^(3/2)-1/3*b^2*arctan(x/sqrt(c))*log((1+I)*(-x+sqrt(c))/(-I*x+sqrt(c)))/c^(3/2)+2/3*b^2*arctanh(x/sqrt(c))*log(2*sqrt(c)/(x+sqrt(c)))/c^(3/2)-1/3*b^2*arctanh(x/sqrt(c))*log(2*(-x+sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(x+sqrt(c))))/c^(3/2)-1/3*b^2*arctan(x/sqrt(c))*log((1-I)*(x+sqrt(c))/(-I*x+sqrt(c)))/c^(3/2)-1/3*b^2*arctanh(x/sqrt(c))*log(2*(x+sqrt(-c))*sqrt(c)/((x+sqrt(c))*(sqrt(-c)+sqrt(c))))/c^(3/2)-2/3*b^2*arctan(x/sqrt(c))*log(2-2*sqrt(c)/(-I*x+sqrt(c)))/c^(3/2)-2/3*b^2*arctanh(x/sqrt(c))*log(2-2*sqrt(c)/(x+sqrt(c)))/c^(3/2)-1/3*b^2*polylog(2,-x/sqrt(c))/c^(3/2)+1/3*I*b^2*polylog(2,-I*x/sqrt(c))/c^(3/2)-1/3*I*b^2*polylog(2,I*x/sqrt(c))/c^(3/2)+1/3*b^2*polylog(2,x/sqrt(c))/c^(3/2)-1/3*I*b^2*polylog(2,1-2*sqrt(c)/(-I*x+sqrt(c)))/c^(3/2)+1/3*I*b^2*polylog(2,-1+2*sqrt(c)/(-I*x+sqrt(c)))/c^(3/2)+1/6*I*b^2*polylog(2,1+(-1-I)*(-x+sqrt(c))/(-I*x+sqrt(c)))/c^(3/2)-1/3*b^2*polylog(2,1-2*sqrt(c)/(x+sqrt(c)))/c^(3/2)+1/3*b^2*polylog(2,-1+2*sqrt(c)/(x+sqrt(c)))/c^(3/2)+1/6*b^2*polylog(2,1-2*(-x+sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(x+sqrt(c))))/c^(3/2)+1/6*I*b^2*polylog(2,1+(-1+I)*(x+sqrt(c))/(-I*x+sqrt(c)))/c^(3/2)+1/6*b^2*polylog(2,1-2*(x+sqrt(-c))*sqrt(c)/((x+sqrt(c))*(sqrt(-c)+sqrt(c))))/c^(3/2)],
[(a+b*arctanh(c/x^2))^2/x^6,x,130,2/25*a*b/x^5-2/15*a*b/(c*x^3)+2/5*a*b/(c^2*x)-8/15*b^2/(c^2*x)+2/5*a*b*arctan(x/sqrt(c))/c^(5/2)-4/15*b^2*arctan(x/sqrt(c))/c^(5/2)-1/5*I*b^2*arctan(x/sqrt(c))^2/c^(5/2)+4/15*b^2*arctanh(x/sqrt(c))/c^(5/2)-1/5*b^2*arctanh(x/sqrt(c))^2/c^(5/2)-1/25*b^2*log(1-c/x^2)/x^5+1/15*b^2*log(1-c/x^2)/(c*x^3)-1/5*b^2*log(1-c/x^2)/(c^2*x)-1/5*b^2*arctan(x/sqrt(c))*log(1-c/x^2)/c^(5/2)-1/25*b*(2*a-b*log(1-c/x^2))/x^5-1/15*b*(2*a-b*log(1-c/x^2))/(c*x^3)-1/5*b*(2*a-b*log(1-c/x^2))/(c^2*x)+1/5*b*arctanh(x/sqrt(c))*(2*a-b*log(1-c/x^2))/c^(5/2)-1/20*(2*a-b*log(1-c/x^2))^2/x^5-1/5*a*b*log(1+c/x^2)/x^5-2/15*b^2*log(1+c/x^2)/(c*x^3)+1/5*b^2*arctan(x/sqrt(c))*log(1+c/x^2)/c^(5/2)+1/5*b^2*arctanh(x/sqrt(c))*log(1+c/x^2)/c^(5/2)+1/10*b^2*log(1-c/x^2)*log(1+c/x^2)/x^5-1/20*b^2*log(1+c/x^2)^2/x^5-2/5*b^2*arctan(x/sqrt(c))*log(2*sqrt(c)/(-I*x+sqrt(c)))/c^(5/2)+1/5*b^2*arctan(x/sqrt(c))*log((1+I)*(-x+sqrt(c))/(-I*x+sqrt(c)))/c^(5/2)+2/5*b^2*arctanh(x/sqrt(c))*log(2*sqrt(c)/(x+sqrt(c)))/c^(5/2)-1/5*b^2*arctanh(x/sqrt(c))*log(2*(-x+sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(x+sqrt(c))))/c^(5/2)+1/5*b^2*arctan(x/sqrt(c))*log((1-I)*(x+sqrt(c))/(-I*x+sqrt(c)))/c^(5/2)-1/5*b^2*arctanh(x/sqrt(c))*log(2*(x+sqrt(-c))*sqrt(c)/((x+sqrt(c))*(sqrt(-c)+sqrt(c))))/c^(5/2)+2/5*b^2*arctan(x/sqrt(c))*log(2-2*sqrt(c)/(-I*x+sqrt(c)))/c^(5/2)-2/5*b^2*arctanh(x/sqrt(c))*log(2-2*sqrt(c)/(x+sqrt(c)))/c^(5/2)-1/5*b^2*polylog(2,-x/sqrt(c))/c^(5/2)-1/5*I*b^2*polylog(2,-I*x/sqrt(c))/c^(5/2)+1/5*I*b^2*polylog(2,I*x/sqrt(c))/c^(5/2)+1/5*b^2*polylog(2,x/sqrt(c))/c^(5/2)+1/5*I*b^2*polylog(2,1-2*sqrt(c)/(-I*x+sqrt(c)))/c^(5/2)-1/5*I*b^2*polylog(2,-1+2*sqrt(c)/(-I*x+sqrt(c)))/c^(5/2)-1/10*I*b^2*polylog(2,1+(-1-I)*(-x+sqrt(c))/(-I*x+sqrt(c)))/c^(5/2)-1/5*b^2*polylog(2,1-2*sqrt(c)/(x+sqrt(c)))/c^(5/2)+1/5*b^2*polylog(2,-1+2*sqrt(c)/(x+sqrt(c)))/c^(5/2)+1/10*b^2*polylog(2,1-2*(-x+sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(x+sqrt(c))))/c^(5/2)-1/10*I*b^2*polylog(2,1+(-1+I)*(x+sqrt(c))/(-I*x+sqrt(c)))/c^(5/2)+1/10*b^2*polylog(2,1-2*(x+sqrt(-c))*sqrt(c)/((x+sqrt(c))*(sqrt(-c)+sqrt(c))))/c^(5/2)],

# Integrands of the form (d x)^(m/2) (a+b ArcTanh[c x^2])^p

# Integrands of the form (d x)^m (a+b ArcTanh[c x^2])^p when m symbolic
[(d*x)^m*(a+b*arctanh(c/x^2))^3,x,0,Unintegrable((d*x)^m*(a+b*arctanh(c/x^2))^3,x)],
[(d*x)^m*(a+b*arctanh(c/x^2))^2,x,0,Unintegrable((d*x)^m*(a+b*arctanh(c/x^2))^2,x)],
[(d*x)^m*(a+b*arctanh(c/x^2)),x,3,(d*x)^(1+m)*(a+b*arctanh(c/x^2))/(d*(1+m))-2*b*c*d*(d*x)^(-1+m)*hypergeom([1,1/4*(1-m)],[1/4*(5-m)],c^2/x^4)/(1-m^2)],
[(d*x)^m/(a+b*arctanh(c/x^2)),x,0,Unintegrable((d*x)^m/(a+b*arctanh(c/x^2)),x)],
[(d*x)^m/(a+b*arctanh(c/x^2))^2,x,0,Unintegrable((d*x)^m/(a+b*arctanh(c/x^2))^2,x)],

# Integrands of the form (d x)^m (a+b ArcTanh[c x^(1/2)])^p

# Integrands of the form x^m (a+b ArcTanh[c Sqrt[x]])^p
[x^3*(a+b*arctanh(c*sqrt(x))),x,7,1/12*b*x^(3/2)/c^5+1/20*b*x^(5/2)/c^3+1/28*b*x^(7/2)/c-1/4*b*arctanh(c*sqrt(x))/c^8+1/4*x^4*(a+b*arctanh(c*sqrt(x)))+1/4*b*sqrt(x)/c^7],
[x^2*(a+b*arctanh(c*sqrt(x))),x,6,1/9*b*x^(3/2)/c^3+1/15*b*x^(5/2)/c-1/3*b*arctanh(c*sqrt(x))/c^6+1/3*x^3*(a+b*arctanh(c*sqrt(x)))+1/3*b*sqrt(x)/c^5],
[x*(a+b*arctanh(c*sqrt(x))),x,5,1/6*b*x^(3/2)/c-1/2*b*arctanh(c*sqrt(x))/c^4+1/2*x^2*(a+b*arctanh(c*sqrt(x)))+1/2*b*sqrt(x)/c^3],
[a+b*arctanh(c*sqrt(x)),x,5,a*x-b*arctanh(c*sqrt(x))/c^2+b*x*arctanh(c*sqrt(x))+b*sqrt(x)/c],
[(a+b*arctanh(c*sqrt(x)))/x,x,2,a*log(x)-b*polylog(2,-c*sqrt(x))+b*polylog(2,c*sqrt(x))],
[(a+b*arctanh(c*sqrt(x)))/x^2,x,4,b*c^2*arctanh(c*sqrt(x))+(-a-b*arctanh(c*sqrt(x)))/x-b*c/sqrt(x)],
[(a+b*arctanh(c*sqrt(x)))/x^3,x,5,-1/6*b*c/x^(3/2)+1/2*b*c^4*arctanh(c*sqrt(x))+1/2*(-a-b*arctanh(c*sqrt(x)))/x^2-1/2*b*c^3/sqrt(x)],
[(a+b*arctanh(c*sqrt(x)))/x^4,x,6,-1/15*b*c/x^(5/2)-1/9*b*c^3/x^(3/2)+1/3*b*c^6*arctanh(c*sqrt(x))+1/3*(-a-b*arctanh(c*sqrt(x)))/x^3-1/3*b*c^5/sqrt(x)],
[x^3*(a+b*arctanh(c*sqrt(x)))^2,x,22,71/420*b^2*x/c^6+3/70*b^2*x^2/c^4+1/84*b^2*x^3/c^2+1/6*b*x^(3/2)*(a+b*arctanh(c*sqrt(x)))/c^5+1/10*b*x^(5/2)*(a+b*arctanh(c*sqrt(x)))/c^3+1/14*b*x^(7/2)*(a+b*arctanh(c*sqrt(x)))/c-1/4*(a+b*arctanh(c*sqrt(x)))^2/c^8+1/4*x^4*(a+b*arctanh(c*sqrt(x)))^2+44/105*b^2*log(1-c^2*x)/c^8+1/2*a*b*sqrt(x)/c^7+1/2*b^2*arctanh(c*sqrt(x))*sqrt(x)/c^7],
[x^2*(a+b*arctanh(c*sqrt(x)))^2,x,17,8/45*b^2*x/c^4+1/30*b^2*x^2/c^2+2/9*b*x^(3/2)*(a+b*arctanh(c*sqrt(x)))/c^3+2/15*b*x^(5/2)*(a+b*arctanh(c*sqrt(x)))/c-1/3*(a+b*arctanh(c*sqrt(x)))^2/c^6+1/3*x^3*(a+b*arctanh(c*sqrt(x)))^2+23/45*b^2*log(1-c^2*x)/c^6+2/3*a*b*sqrt(x)/c^5+2/3*b^2*arctanh(c*sqrt(x))*sqrt(x)/c^5],
[x*(a+b*arctanh(c*sqrt(x)))^2,x,12,1/6*b^2*x/c^2+1/3*b*x^(3/2)*(a+b*arctanh(c*sqrt(x)))/c-1/2*(a+b*arctanh(c*sqrt(x)))^2/c^4+1/2*x^2*(a+b*arctanh(c*sqrt(x)))^2+2/3*b^2*log(1-c^2*x)/c^4+a*b*sqrt(x)/c^3+b^2*arctanh(c*sqrt(x))*sqrt(x)/c^3],
[(a+b*arctanh(c*sqrt(x)))^2,x,7,-(a+b*arctanh(c*sqrt(x)))^2/c^2+x*(a+b*arctanh(c*sqrt(x)))^2+b^2*log(1-c^2*x)/c^2+2*a*b*sqrt(x)/c+2*b^2*arctanh(c*sqrt(x))*sqrt(x)/c],
[(a+b*arctanh(c*sqrt(x)))^2/x,x,7,4*(a+b*arctanh(c*sqrt(x)))^2*arctanh(1+(-2)/(1-c*sqrt(x)))-2*b*(a+b*arctanh(c*sqrt(x)))*polylog(2,1+(-2)/(1-c*sqrt(x)))+2*b*(a+b*arctanh(c*sqrt(x)))*polylog(2,-1+2/(1-c*sqrt(x)))+b^2*polylog(3,1+(-2)/(1-c*sqrt(x)))-b^2*polylog(3,-1+2/(1-c*sqrt(x)))],
[(a+b*arctanh(c*sqrt(x)))^2/x^2,x,9,c^2*(a+b*arctanh(c*sqrt(x)))^2-(a+b*arctanh(c*sqrt(x)))^2/x+b^2*c^2*log(x)-b^2*c^2*log(1-c^2*x)-2*b*c*(a+b*arctanh(c*sqrt(x)))/sqrt(x)],
[(a+b*arctanh(c*sqrt(x)))^2/x^3,x,14,-1/6*b^2*c^2/x-1/3*b*c*(a+b*arctanh(c*sqrt(x)))/x^(3/2)+1/2*c^4*(a+b*arctanh(c*sqrt(x)))^2-1/2*(a+b*arctanh(c*sqrt(x)))^2/x^2+2/3*b^2*c^4*log(x)-2/3*b^2*c^4*log(1-c^2*x)-b*c^3*(a+b*arctanh(c*sqrt(x)))/sqrt(x)],
[x^3*(a+b*arctanh(c*sqrt(x)))^3,x,54,23/420*b^3*x^(3/2)/c^5+1/140*b^3*x^(5/2)/c^3-47/70*b^3*arctanh(c*sqrt(x))/c^8+71/140*b^2*x*(a+b*arctanh(c*sqrt(x)))/c^6+9/70*b^2*x^2*(a+b*arctanh(c*sqrt(x)))/c^4+1/28*b^2*x^3*(a+b*arctanh(c*sqrt(x)))/c^2+44/35*b*(a+b*arctanh(c*sqrt(x)))^2/c^8+1/4*b*x^(3/2)*(a+b*arctanh(c*sqrt(x)))^2/c^5+3/20*b*x^(5/2)*(a+b*arctanh(c*sqrt(x)))^2/c^3+3/28*b*x^(7/2)*(a+b*arctanh(c*sqrt(x)))^2/c-1/4*(a+b*arctanh(c*sqrt(x)))^3/c^8+1/4*x^4*(a+b*arctanh(c*sqrt(x)))^3-88/35*b^2*(a+b*arctanh(c*sqrt(x)))*log(2/(1-c*sqrt(x)))/c^8-44/35*b^3*polylog(2,1+(-2)/(1-c*sqrt(x)))/c^8+47/70*b^3*sqrt(x)/c^7+3/4*b*(a+b*arctanh(c*sqrt(x)))^2*sqrt(x)/c^7],
[x^2*(a+b*arctanh(c*sqrt(x)))^3,x,34,1/30*b^3*x^(3/2)/c^3-19/30*b^3*arctanh(c*sqrt(x))/c^6+8/15*b^2*x*(a+b*arctanh(c*sqrt(x)))/c^4+1/10*b^2*x^2*(a+b*arctanh(c*sqrt(x)))/c^2+23/15*b*(a+b*arctanh(c*sqrt(x)))^2/c^6+1/3*b*x^(3/2)*(a+b*arctanh(c*sqrt(x)))^2/c^3+1/5*b*x^(5/2)*(a+b*arctanh(c*sqrt(x)))^2/c-1/3*(a+b*arctanh(c*sqrt(x)))^3/c^6+1/3*x^3*(a+b*arctanh(c*sqrt(x)))^3-46/15*b^2*(a+b*arctanh(c*sqrt(x)))*log(2/(1-c*sqrt(x)))/c^6-23/15*b^3*polylog(2,1+(-2)/(1-c*sqrt(x)))/c^6+19/30*b^3*sqrt(x)/c^5+b*(a+b*arctanh(c*sqrt(x)))^2*sqrt(x)/c^5],
[x*(a+b*arctanh(c*sqrt(x)))^3,x,19,-1/2*b^3*arctanh(c*sqrt(x))/c^4+1/2*b^2*x*(a+b*arctanh(c*sqrt(x)))/c^2+2*b*(a+b*arctanh(c*sqrt(x)))^2/c^4+1/2*b*x^(3/2)*(a+b*arctanh(c*sqrt(x)))^2/c-1/2*(a+b*arctanh(c*sqrt(x)))^3/c^4+1/2*x^2*(a+b*arctanh(c*sqrt(x)))^3-4*b^2*(a+b*arctanh(c*sqrt(x)))*log(2/(1-c*sqrt(x)))/c^4-2*b^3*polylog(2,1+(-2)/(1-c*sqrt(x)))/c^4+1/2*b^3*sqrt(x)/c^3+3/2*b*(a+b*arctanh(c*sqrt(x)))^2*sqrt(x)/c^3],
[(a+b*arctanh(c*sqrt(x)))^3,x,9,3*b*(a+b*arctanh(c*sqrt(x)))^2/c^2-(a+b*arctanh(c*sqrt(x)))^3/c^2+x*(a+b*arctanh(c*sqrt(x)))^3-6*b^2*(a+b*arctanh(c*sqrt(x)))*log(2/(1-c*sqrt(x)))/c^2-3*b^3*polylog(2,1+(-2)/(1-c*sqrt(x)))/c^2+3*b*(a+b*arctanh(c*sqrt(x)))^2*sqrt(x)/c],
[(a+b*arctanh(c*sqrt(x)))^3/x,x,9,4*(a+b*arctanh(c*sqrt(x)))^3*arctanh(1+(-2)/(1-c*sqrt(x)))-3*b*(a+b*arctanh(c*sqrt(x)))^2*polylog(2,1+(-2)/(1-c*sqrt(x)))+3*b*(a+b*arctanh(c*sqrt(x)))^2*polylog(2,-1+2/(1-c*sqrt(x)))+3*b^2*(a+b*arctanh(c*sqrt(x)))*polylog(3,1+(-2)/(1-c*sqrt(x)))-3*b^2*(a+b*arctanh(c*sqrt(x)))*polylog(3,-1+2/(1-c*sqrt(x)))-3/2*b^3*polylog(4,1+(-2)/(1-c*sqrt(x)))+3/2*b^3*polylog(4,-1+2/(1-c*sqrt(x)))],
[(a+b*arctanh(c*sqrt(x)))^3/x^2,x,8,3*b*c^2*(a+b*arctanh(c*sqrt(x)))^2+c^2*(a+b*arctanh(c*sqrt(x)))^3-(a+b*arctanh(c*sqrt(x)))^3/x+6*b^2*c^2*(a+b*arctanh(c*sqrt(x)))*log(2+(-2)/(1+c*sqrt(x)))-3*b^3*c^2*polylog(2,-1+2/(1+c*sqrt(x)))-3*b*c*(a+b*arctanh(c*sqrt(x)))^2/sqrt(x)],
[(a+b*arctanh(c*sqrt(x)))^3/x^3,x,17,1/2*b^3*c^4*arctanh(c*sqrt(x))-1/2*b^2*c^2*(a+b*arctanh(c*sqrt(x)))/x+2*b*c^4*(a+b*arctanh(c*sqrt(x)))^2-1/2*b*c*(a+b*arctanh(c*sqrt(x)))^2/x^(3/2)+1/2*c^4*(a+b*arctanh(c*sqrt(x)))^3-1/2*(a+b*arctanh(c*sqrt(x)))^3/x^2+4*b^2*c^4*(a+b*arctanh(c*sqrt(x)))*log(2+(-2)/(1+c*sqrt(x)))-2*b^3*c^4*polylog(2,-1+2/(1+c*sqrt(x)))-1/2*b^3*c^3/sqrt(x)-3/2*b*c^3*(a+b*arctanh(c*sqrt(x)))^2/sqrt(x)],

# Integrands of the form (d x)^(m/2) (a+b ArcTanh[c Sqrt[x]])^p
[x^(3/2)*arctanh(sqrt(x)),x,3,1/5*x+1/10*x^2+2/5*x^(5/2)*arctanh(sqrt(x))+1/5*log(1-x)],
[arctanh(sqrt(x))*sqrt(x),x,3,1/3*x+2/3*x^(3/2)*arctanh(sqrt(x))+1/3*log(1-x)],
[arctanh(sqrt(x))/sqrt(x),x,2,log(1-x)+2*arctanh(sqrt(x))*sqrt(x)],
[arctanh(sqrt(x))/x^(3/2),x,4,-log(1-x)+log(x)-2*arctanh(sqrt(x))/sqrt(x)],

# Integrands of the form (d x)^m (a+b ArcTanh[c x^(3/2)])^p

# Integrands of the form x^m (a+b ArcTanh[c x^(3/2)])^p
[x^3*(a+b*arctanh(c*x^(3/2))),x,13,3/20*b*x^(5/2)/c+1/4*x^4*(a+b*arctanh(c*x^(3/2)))-1/4*b*arctanh(c^(1/3)*sqrt(x))/c^(8/3)+1/16*b*log(1+c^(2/3)*x-c^(1/3)*sqrt(x))/c^(8/3)-1/16*b*log(1+c^(2/3)*x+c^(1/3)*sqrt(x))/c^(8/3)-1/8*b*arctan((1-2*c^(1/3)*sqrt(x))/sqrt(3))*sqrt(3)/c^(8/3)+1/8*b*arctan((1+2*c^(1/3)*sqrt(x))/sqrt(3))*sqrt(3)/c^(8/3)],
[x^2*(a+b*arctanh(c*x^(3/2))),x,5,1/3*b*x^(3/2)/c-1/3*b*arctanh(c*x^(3/2))/c^2+1/3*x^3*(a+b*arctanh(c*x^(3/2)))],
[x*(a+b*arctanh(c*x^(3/2))),x,13,1/2*x^2*(a+b*arctanh(c*x^(3/2)))-1/2*b*arctanh(c^(1/3)*sqrt(x))/c^(4/3)+1/8*b*log(1+c^(2/3)*x-c^(1/3)*sqrt(x))/c^(4/3)-1/8*b*log(1+c^(2/3)*x+c^(1/3)*sqrt(x))/c^(4/3)+1/4*b*arctan((1-2*c^(1/3)*sqrt(x))/sqrt(3))*sqrt(3)/c^(4/3)-1/4*b*arctan((1+2*c^(1/3)*sqrt(x))/sqrt(3))*sqrt(3)/c^(4/3)+3/2*b*sqrt(x)/c],
[a+b*arctanh(c*x^(3/2)),x,13,a*x+b*x*arctanh(c*x^(3/2))-b*arctanh(c^(1/3)*sqrt(x))/c^(2/3)+1/4*b*log(1+c^(2/3)*x-c^(1/3)*sqrt(x))/c^(2/3)-1/4*b*log(1+c^(2/3)*x+c^(1/3)*sqrt(x))/c^(2/3)-1/2*b*arctan((1-2*c^(1/3)*sqrt(x))/sqrt(3))*sqrt(3)/c^(2/3)+1/2*b*arctan((1+2*c^(1/3)*sqrt(x))/sqrt(3))*sqrt(3)/c^(2/3)],
[(a+b*arctanh(c*x^(3/2)))/x,x,2,a*log(x)-1/3*b*polylog(2,-c*x^(3/2))+1/3*b*polylog(2,c*x^(3/2))],
[(a+b*arctanh(c*x^(3/2)))/x^2,x,12,(-a-b*arctanh(c*x^(3/2)))/x+b*c^(2/3)*arctanh(c^(1/3)*sqrt(x))-1/4*b*c^(2/3)*log(1+c^(2/3)*x-c^(1/3)*sqrt(x))+1/4*b*c^(2/3)*log(1+c^(2/3)*x+c^(1/3)*sqrt(x))-1/2*b*c^(2/3)*arctan((1-2*c^(1/3)*sqrt(x))/sqrt(3))*sqrt(3)+1/2*b*c^(2/3)*arctan((1+2*c^(1/3)*sqrt(x))/sqrt(3))*sqrt(3)],
[(a+b*arctanh(c*x^(3/2)))/x^3,x,13,1/2*(-a-b*arctanh(c*x^(3/2)))/x^2+1/2*b*c^(4/3)*arctanh(c^(1/3)*sqrt(x))-1/8*b*c^(4/3)*log(1+c^(2/3)*x-c^(1/3)*sqrt(x))+1/8*b*c^(4/3)*log(1+c^(2/3)*x+c^(1/3)*sqrt(x))+1/4*b*c^(4/3)*arctan((1-2*c^(1/3)*sqrt(x))/sqrt(3))*sqrt(3)-1/4*b*c^(4/3)*arctan((1+2*c^(1/3)*sqrt(x))/sqrt(3))*sqrt(3)-3/2*b*c/sqrt(x)],
[(a+b*arctanh(c*x^(3/2)))/x^4,x,5,-1/3*b*c/x^(3/2)+1/3*b*c^2*arctanh(c*x^(3/2))+1/3*(-a-b*arctanh(c*x^(3/2)))/x^3],
[x^2*(a+b*arctanh(c*x^(3/2)))^2,x,7,2/3*a*b*x^(3/2)/c+2/3*b^2*x^(3/2)*arctanh(c*x^(3/2))/c-1/3*(a+b*arctanh(c*x^(3/2)))^2/c^2+1/3*x^3*(a+b*arctanh(c*x^(3/2)))^2+1/3*b^2*log(1-c^2*x^3)/c^2],
[(a+b*arctanh(c*x^(3/2)))^2/x,x,7,4/3*(a+b*arctanh(c*x^(3/2)))^2*arctanh(1+(-2)/(1-c*x^(3/2)))-2/3*b*(a+b*arctanh(c*x^(3/2)))*polylog(2,1+(-2)/(1-c*x^(3/2)))+2/3*b*(a+b*arctanh(c*x^(3/2)))*polylog(2,-1+2/(1-c*x^(3/2)))+1/3*b^2*polylog(3,1+(-2)/(1-c*x^(3/2)))-1/3*b^2*polylog(3,-1+2/(1-c*x^(3/2)))],
[(a+b*arctanh(c*x^(3/2)))^2/x^4,x,9,-2/3*b*c*(a+b*arctanh(c*x^(3/2)))/x^(3/2)+1/3*c^2*(a+b*arctanh(c*x^(3/2)))^2-1/3*(a+b*arctanh(c*x^(3/2)))^2/x^3+b^2*c^2*log(x)-1/3*b^2*c^2*log(1-c^2*x^3)],
# 
# {x^3*ArcTanh[c*x^(3/2)]^2, x, 272, (9*x)/(20*c^2) + (3*Sqrt[3]*ArcTan[(1 - 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/(20*c^(8/3)) + (3*Sqrt[3]*ArcTan[(1 + 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/(20*c^(8/3)) + (3*Log[1 - c^(1/3)*Sqrt[x]])/(20*c^(8/3)) + Log[1 - c^(1/3)*Sqrt[x]]^2/(16*c^(8/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(1/3) - c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3)))])/(8*c^(8/3)) + (Log[1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3) - c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3)))])/(8*c^(8/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + c^(1/3)*Sqrt[x])])/(8*c^(8/3)) + (3*Log[1 + c^(1/3)*Sqrt[x]])/(20*c^(8/3)) - (Log[(1/2)*(1 - c^(1/3)*Sqrt[x])]*Log[1 + c^(1/3)*Sqrt[x]])/(8*c^(8/3)) + (Log[((-1)^(1/3) - c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[1 + c^(1/3)*Sqrt[x]])/(8*c^(8/3)) - (Log[((-1)^(2/3) - c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))]*Log[1 + c^(1/3)*Sqrt[x]])/(8*c^(8/3)) + Log[1 + c^(1/3)*Sqrt[x]]^2/(16*c^(8/3)) - (Log[1 + c^(1/3)*Sqrt[x]]*Log[-(((-1)^(1/3) + c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3)))])/(8*c^(8/3)) + (Log[1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) + c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(8*c^(8/3)) + (Log[1 + c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3) + c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3)))])/(8*c^(8/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(2/3) + c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(8*c^(8/3)) + ((-1)^(1/3)*Log[-(((-1)^(1/3)*(1 - c^(1/3)*Sqrt[x]))/(1 - (-1)^(1/3)))]*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) - ((-1)^(1/3)*Log[((-1)^(1/3)*(1 + c^(1/3)*Sqrt[x]))/(1 + (-1)^(1/3))]*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) + ((-1)^(1/3)*Log[(-1)^(1/3) + c^(1/3)*Sqrt[x]]*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) - ((-1)^(1/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]^2)/(16*c^(8/3)) + ((-1)^(1/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])])/(8*c^(8/3)) - ((-1)^(1/3)*Log[((-1)^(1/3)*(1 - c^(1/3)*Sqrt[x]))/(1 + (-1)^(1/3))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) + ((-1)^(1/3)*Log[(-1)^(1/3) - c^(1/3)*Sqrt[x]]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) + ((-1)^(1/3)*Log[-(((-1)^(1/3)*(1 + c^(1/3)*Sqrt[x]))/(1 - (-1)^(1/3)))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) - ((-1)^(1/3)*Log[-(((-1)^(1/3)*((-1)^(1/3) + c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) + ((-1)^(1/3)*Log[(1/2)*(1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) - ((-1)^(1/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]^2)/(16*c^(8/3)) + ((-1)^(2/3)*Log[-(((-1)^(2/3)*(1 - c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) - ((-1)^(2/3)*Log[-(-1)^(2/3) - c^(1/3)*Sqrt[x]]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) - ((-1)^(2/3)*Log[((-1)^(2/3)*(1 + c^(1/3)*Sqrt[x]))/(1 + (-1)^(2/3))]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) + ((-1)^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]^2)/(16*c^(8/3)) - ((-1)^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(8*c^(8/3)) - ((-1)^(2/3)*Log[((-1)^(2/3)*(1 - c^(1/3)*Sqrt[x]))/(1 + (-1)^(2/3))]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) + ((-1)^(2/3)*Log[-(((-1)^(2/3)*(1 + c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) - ((-1)^(2/3)*Log[-(-1)^(2/3) + c^(1/3)*Sqrt[x]]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) - ((-1)^(2/3)*Log[(1/2)*(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) + ((-1)^(2/3)*Log[((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(8*c^(8/3)) + ((-1)^(2/3)*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]]^2)/(16*c^(8/3)) - ((-1)^(2/3)*Log[((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(8*c^(8/3)) - ((-1)^(1/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))])/(8*c^(8/3)) + ((-1)^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(8*c^(8/3)) - ((-1)^(2/3)*Log[(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(8*c^(8/3)) - (3*Log[1 - c^(1/3)*Sqrt[x] + c^(2/3)*x])/(40*c^(8/3)) - (3*Log[1 + c^(1/3)*Sqrt[x] + c^(2/3)*x])/(40*c^(8/3)) - (3*x^(5/2)*Log[1 - c*x^(3/2)])/(20*c) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(8*c^(8/3)) + (Log[1 + c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(8*c^(8/3)) - ((-1)^(1/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(8*c^(8/3)) + ((-1)^(1/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(8*c^(8/3)) - ((-1)^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(8*c^(8/3)) + ((-1)^(2/3)*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(8*c^(8/3)) + (1/16)*x^4*Log[1 - c*x^(3/2)]^2 + (3*x^(5/2)*Log[1 + c*x^(3/2)])/(20*c) + (Log[1 - c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(8*c^(8/3)) - (Log[1 + c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(8*c^(8/3)) + ((-1)^(1/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(8*c^(8/3)) - ((-1)^(1/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(8*c^(8/3)) + ((-1)^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(8*c^(8/3)) - ((-1)^(2/3)*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(8*c^(8/3)) - (1/8)*x^4*Log[1 - c*x^(3/2)]*Log[1 + c*x^(3/2)] + (1/16)*x^4*Log[1 + c*x^(3/2)]^2 - PolyLog[2, (1/2)*(1 - c^(1/3)*Sqrt[x])]/(8*c^(8/3)) - PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))]/(8*c^(8/3)) + PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]/(8*c^(8/3)) + PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))]/(8*c^(8/3)) - PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))]/(8*c^(8/3)) + ((-1)^(1/3)*PolyLog[2, 1/(1 + (-1)^(2/3)) - c^(1/3)*Sqrt[x]])/(8*c^(8/3)) - PolyLog[2, (1/2)*(1 + c^(1/3)*Sqrt[x])]/(8*c^(8/3)) - PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))]/(8*c^(8/3)) + PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]/(8*c^(8/3)) + PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))]/(8*c^(8/3)) - PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))]/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog[2, 1/(1 - (-1)^(1/3)) + c^(1/3)*Sqrt[x]])/(8*c^(8/3)) + ((-1)^(1/3)*PolyLog[2, 1/(1 + (-1)^(2/3)) + c^(1/3)*Sqrt[x]])/(8*c^(8/3)) + ((-1)^(1/3)*PolyLog[2, (1/2)*(1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])])/(8*c^(8/3)) + ((-1)^(1/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))])/(8*c^(8/3)) - ((-1)^(1/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(8*c^(8/3)) - ((-1)^(1/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(8*c^(8/3)) + ((-1)^(1/3)*PolyLog[2, (1/2)*(1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])])/(8*c^(8/3)) + ((-1)^(1/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))])/(8*c^(8/3)) - ((-1)^(1/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(8*c^(8/3)) - ((-1)^(1/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog[2, (1/2)*(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(8*c^(8/3)) + ((-1)^(2/3)*PolyLog[2, (1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog[2, (1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog[2, ((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog[2, (1/2)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))])/(8*c^(8/3)) + ((-1)^(2/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(8*c^(8/3)) - ((-1)^(2/3)*PolyLog[2, ((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(8*c^(8/3))}
# {x^0*ArcTanh[c*x^(3/2)]^2, x, 200, Log[1 - c^(1/3)*Sqrt[x]]^2/(4*c^(2/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(1/3) - c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3)))])/(2*c^(2/3)) + (Log[1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3) - c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3)))])/(2*c^(2/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + c^(1/3)*Sqrt[x])])/(2*c^(2/3)) - (Log[(1/2)*(1 - c^(1/3)*Sqrt[x])]*Log[1 + c^(1/3)*Sqrt[x]])/(2*c^(2/3)) + (Log[((-1)^(1/3) - c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[1 + c^(1/3)*Sqrt[x]])/(2*c^(2/3)) - (Log[((-1)^(2/3) - c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))]*Log[1 + c^(1/3)*Sqrt[x]])/(2*c^(2/3)) + Log[1 + c^(1/3)*Sqrt[x]]^2/(4*c^(2/3)) - (Log[1 + c^(1/3)*Sqrt[x]]*Log[-(((-1)^(1/3) + c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3)))])/(2*c^(2/3)) + (Log[1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) + c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(2*c^(2/3)) + (Log[1 + c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3) + c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3)))])/(2*c^(2/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(2/3) + c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(2*c^(2/3)) + ((-1)^(1/3)*Log[-(((-1)^(1/3)*(1 - c^(1/3)*Sqrt[x]))/(1 - (-1)^(1/3)))]*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) - ((-1)^(1/3)*Log[((-1)^(1/3)*(1 + c^(1/3)*Sqrt[x]))/(1 + (-1)^(1/3))]*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) + ((-1)^(1/3)*Log[(-1)^(1/3) + c^(1/3)*Sqrt[x]]*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) - ((-1)^(1/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]^2)/(4*c^(2/3)) + ((-1)^(1/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])])/(2*c^(2/3)) - ((-1)^(1/3)*Log[((-1)^(1/3)*(1 - c^(1/3)*Sqrt[x]))/(1 + (-1)^(1/3))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) + ((-1)^(1/3)*Log[(-1)^(1/3) - c^(1/3)*Sqrt[x]]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) + ((-1)^(1/3)*Log[-(((-1)^(1/3)*(1 + c^(1/3)*Sqrt[x]))/(1 - (-1)^(1/3)))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) - ((-1)^(1/3)*Log[-(((-1)^(1/3)*((-1)^(1/3) + c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) + ((-1)^(1/3)*Log[(1/2)*(1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) - ((-1)^(1/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]^2)/(4*c^(2/3)) + ((-1)^(2/3)*Log[-(((-1)^(2/3)*(1 - c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) - ((-1)^(2/3)*Log[-(-1)^(2/3) - c^(1/3)*Sqrt[x]]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) - ((-1)^(2/3)*Log[((-1)^(2/3)*(1 + c^(1/3)*Sqrt[x]))/(1 + (-1)^(2/3))]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) + ((-1)^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]^2)/(4*c^(2/3)) - ((-1)^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(2*c^(2/3)) - ((-1)^(2/3)*Log[((-1)^(2/3)*(1 - c^(1/3)*Sqrt[x]))/(1 + (-1)^(2/3))]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) + ((-1)^(2/3)*Log[-(((-1)^(2/3)*(1 + c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) - ((-1)^(2/3)*Log[-(-1)^(2/3) + c^(1/3)*Sqrt[x]]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) - ((-1)^(2/3)*Log[(1/2)*(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) + ((-1)^(2/3)*Log[((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(2*c^(2/3)) + ((-1)^(2/3)*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]]^2)/(4*c^(2/3)) - ((-1)^(2/3)*Log[((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(2*c^(2/3)) - ((-1)^(1/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))])/(2*c^(2/3)) + ((-1)^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(2*c^(2/3)) - ((-1)^(2/3)*Log[(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(2*c^(2/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(2*c^(2/3)) + (Log[1 + c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(2*c^(2/3)) - ((-1)^(1/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(2*c^(2/3)) + ((-1)^(1/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(2*c^(2/3)) - ((-1)^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(2*c^(2/3)) + ((-1)^(2/3)*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(2*c^(2/3)) + (1/4)*x*Log[1 - c*x^(3/2)]^2 + (Log[1 - c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(2*c^(2/3)) - (Log[1 + c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(2*c^(2/3)) + ((-1)^(1/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(2*c^(2/3)) - ((-1)^(1/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(2*c^(2/3)) + ((-1)^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(2*c^(2/3)) - ((-1)^(2/3)*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(2*c^(2/3)) - (1/2)*x*Log[1 - c*x^(3/2)]*Log[1 + c*x^(3/2)] + (1/4)*x*Log[1 + c*x^(3/2)]^2 - PolyLog[2, (1/2)*(1 - c^(1/3)*Sqrt[x])]/(2*c^(2/3)) - PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))]/(2*c^(2/3)) + PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]/(2*c^(2/3)) + PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))]/(2*c^(2/3)) - PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))]/(2*c^(2/3)) + ((-1)^(1/3)*PolyLog[2, 1/(1 + (-1)^(2/3)) - c^(1/3)*Sqrt[x]])/(2*c^(2/3)) - PolyLog[2, (1/2)*(1 + c^(1/3)*Sqrt[x])]/(2*c^(2/3)) - PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))]/(2*c^(2/3)) + PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]/(2*c^(2/3)) + PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))]/(2*c^(2/3)) - PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))]/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog[2, 1/(1 - (-1)^(1/3)) + c^(1/3)*Sqrt[x]])/(2*c^(2/3)) + ((-1)^(1/3)*PolyLog[2, 1/(1 + (-1)^(2/3)) + c^(1/3)*Sqrt[x]])/(2*c^(2/3)) + ((-1)^(1/3)*PolyLog[2, (1/2)*(1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])])/(2*c^(2/3)) + ((-1)^(1/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))])/(2*c^(2/3)) - ((-1)^(1/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(2*c^(2/3)) - ((-1)^(1/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(2*c^(2/3)) + ((-1)^(1/3)*PolyLog[2, (1/2)*(1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])])/(2*c^(2/3)) + ((-1)^(1/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))])/(2*c^(2/3)) - ((-1)^(1/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(2*c^(2/3)) - ((-1)^(1/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog[2, (1/2)*(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(2*c^(2/3)) + ((-1)^(2/3)*PolyLog[2, (1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog[2, (1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog[2, ((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog[2, (1/2)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))])/(2*c^(2/3)) + ((-1)^(2/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(2*c^(2/3)) - ((-1)^(2/3)*PolyLog[2, ((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(2*c^(2/3))}
# {ArcTanh[c*x^(3/2)]^2/x^3, x, 196, (-(3/2))*Sqrt[3]*c^(4/3)*ArcTan[(1 - 2*c^(1/3)*Sqrt[x])/Sqrt[3]] - (3/2)*Sqrt[3]*c^(4/3)*ArcTan[(1 + 2*c^(1/3)*Sqrt[x])/Sqrt[3]] - (3/2)*c^(4/3)*Log[1 - c^(1/3)*Sqrt[x]] - (1/8)*c^(4/3)*Log[1 - c^(1/3)*Sqrt[x]]^2 + (1/4)*c^(4/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(1/3) - c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3)))] - (1/4)*c^(4/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3) - c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3)))] + (1/4)*c^(4/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + c^(1/3)*Sqrt[x])] - (3/2)*c^(4/3)*Log[1 + c^(1/3)*Sqrt[x]] + (1/4)*c^(4/3)*Log[(1/2)*(1 - c^(1/3)*Sqrt[x])]*Log[1 + c^(1/3)*Sqrt[x]] - (1/4)*c^(4/3)*Log[((-1)^(1/3) - c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[1 + c^(1/3)*Sqrt[x]] + (1/4)*c^(4/3)*Log[((-1)^(2/3) - c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))]*Log[1 + c^(1/3)*Sqrt[x]] - (1/8)*c^(4/3)*Log[1 + c^(1/3)*Sqrt[x]]^2 + (1/4)*c^(4/3)*Log[1 + c^(1/3)*Sqrt[x]]*Log[-(((-1)^(1/3) + c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3)))] - (1/4)*c^(4/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) + c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/4)*c^(4/3)*Log[1 + c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3) + c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3)))] + (1/4)*c^(4/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(2/3) + c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))] - (1/4)*(-1)^(1/3)*c^(4/3)*Log[-(((-1)^(1/3)*(1 - c^(1/3)*Sqrt[x]))/(1 - (-1)^(1/3)))]*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]] + (1/4)*(-1)^(1/3)*c^(4/3)*Log[((-1)^(1/3)*(1 + c^(1/3)*Sqrt[x]))/(1 + (-1)^(1/3))]*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]] - (1/4)*(-1)^(1/3)*c^(4/3)*Log[(-1)^(1/3) + c^(1/3)*Sqrt[x]]*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]] + (1/8)*(-1)^(1/3)*c^(4/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]^2 - (1/4)*(-1)^(1/3)*c^(4/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])] + (1/4)*(-1)^(1/3)*c^(4/3)*Log[((-1)^(1/3)*(1 - c^(1/3)*Sqrt[x]))/(1 + (-1)^(1/3))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]] - (1/4)*(-1)^(1/3)*c^(4/3)*Log[(-1)^(1/3) - c^(1/3)*Sqrt[x]]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]] - (1/4)*(-1)^(1/3)*c^(4/3)*Log[-(((-1)^(1/3)*(1 + c^(1/3)*Sqrt[x]))/(1 - (-1)^(1/3)))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]] + (1/4)*(-1)^(1/3)*c^(4/3)*Log[-(((-1)^(1/3)*((-1)^(1/3) + c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]] - (1/4)*(-1)^(1/3)*c^(4/3)*Log[(1/2)*(1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]] + (1/8)*(-1)^(1/3)*c^(4/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]^2 - (1/4)*(-1)^(2/3)*c^(4/3)*Log[-(((-1)^(2/3)*(1 - c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]] + (1/4)*(-1)^(2/3)*c^(4/3)*Log[-(-1)^(2/3) - c^(1/3)*Sqrt[x]]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]] + (1/4)*(-1)^(2/3)*c^(4/3)*Log[((-1)^(2/3)*(1 + c^(1/3)*Sqrt[x]))/(1 + (-1)^(2/3))]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]] - (1/8)*(-1)^(2/3)*c^(4/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]^2 + (1/4)*(-1)^(2/3)*c^(4/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])] + (1/4)*(-1)^(2/3)*c^(4/3)*Log[((-1)^(2/3)*(1 - c^(1/3)*Sqrt[x]))/(1 + (-1)^(2/3))]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]] - (1/4)*(-1)^(2/3)*c^(4/3)*Log[-(((-1)^(2/3)*(1 + c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]] + (1/4)*(-1)^(2/3)*c^(4/3)*Log[-(-1)^(2/3) + c^(1/3)*Sqrt[x]]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]] + (1/4)*(-1)^(2/3)*c^(4/3)*Log[(1/2)*(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]] - (1/4)*(-1)^(2/3)*c^(4/3)*Log[((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]] - (1/8)*(-1)^(2/3)*c^(4/3)*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]]^2 + (1/4)*(-1)^(2/3)*c^(4/3)*Log[((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] + (1/4)*(-1)^(1/3)*c^(4/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))] - (1/4)*(-1)^(2/3)*c^(4/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] + (1/4)*(-1)^(2/3)*c^(4/3)*Log[(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] + (3/4)*c^(4/3)*Log[1 - c^(1/3)*Sqrt[x] + c^(2/3)*x] + (3/4)*c^(4/3)*Log[1 + c^(1/3)*Sqrt[x] + c^(2/3)*x] + (3*c*Log[1 - c*x^(3/2)])/(2*Sqrt[x]) + (1/4)*c^(4/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)] - (1/4)*c^(4/3)*Log[1 + c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)] + (1/4)*(-1)^(1/3)*c^(4/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)] - (1/4)*(-1)^(1/3)*c^(4/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)] + (1/4)*(-1)^(2/3)*c^(4/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)] - (1/4)*(-1)^(2/3)*c^(4/3)*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)] - Log[1 - c*x^(3/2)]^2/(8*x^2) - (3*c*Log[1 + c*x^(3/2)])/(2*Sqrt[x]) - (1/4)*c^(4/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)] + (1/4)*c^(4/3)*Log[1 + c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)] - (1/4)*(-1)^(1/3)*c^(4/3)*Log[1 - (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)] + (1/4)*(-1)^(1/3)*c^(4/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)] - (1/4)*(-1)^(2/3)*c^(4/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)] + (1/4)*(-1)^(2/3)*c^(4/3)*Log[1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)] + (Log[1 - c*x^(3/2)]*Log[1 + c*x^(3/2)])/(4*x^2) - Log[1 + c*x^(3/2)]^2/(8*x^2) + (1/4)*c^(4/3)*PolyLog[2, (1/2)*(1 - c^(1/3)*Sqrt[x])] + (1/4)*c^(4/3)*PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))] - (1/4)*c^(4/3)*PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/4)*c^(4/3)*PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))] + (1/4)*c^(4/3)*PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))] - (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog[2, 1/(1 + (-1)^(2/3)) - c^(1/3)*Sqrt[x]] + (1/4)*c^(4/3)*PolyLog[2, (1/2)*(1 + c^(1/3)*Sqrt[x])] + (1/4)*c^(4/3)*PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))] - (1/4)*c^(4/3)*PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/4)*c^(4/3)*PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))] + (1/4)*c^(4/3)*PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))] + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog[2, 1/(1 - (-1)^(1/3)) + c^(1/3)*Sqrt[x]] - (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog[2, 1/(1 + (-1)^(2/3)) + c^(1/3)*Sqrt[x]] - (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog[2, (1/2)*(1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])] - (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))] + (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] + (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))] - (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog[2, (1/2)*(1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])] - (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))] + (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] + (1/4)*(-1)^(1/3)*c^(4/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))] + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog[2, (1/2)*(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])] - (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog[2, (1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))] + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog[2, (1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))] + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog[2, ((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog[2, (1/2)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])] + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))] - (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))] + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))] + (1/4)*(-1)^(2/3)*c^(4/3)*PolyLog[2, ((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]}
# {x^4*ArcTanh[c*x^(3/2)]^2, x, 308, (9*x^2)/(70*c^2) - (24*Sqrt[3]*ArcTan[(1 - 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/(35*c^(10/3)) - (24*Sqrt[3]*ArcTan[(1 + 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/(35*c^(10/3)) + Log[-1 - c^(1/3)*Sqrt[x]]^2/(20*c^(10/3)) - (Log[-1 - c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 - c^(1/3)*Sqrt[x])])/(10*c^(10/3)) + (24*Log[1 - c^(1/3)*Sqrt[x]])/(35*c^(10/3)) + Log[1 - c^(1/3)*Sqrt[x]]^2/(20*c^(10/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(1/3) - c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3)))])/(10*c^(10/3)) + (Log[-1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) - c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(10*c^(10/3)) + (Log[1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3) - c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3)))])/(10*c^(10/3)) - (Log[-1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(2/3) - c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(10*c^(10/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + c^(1/3)*Sqrt[x])])/(10*c^(10/3)) + (24*Log[1 + c^(1/3)*Sqrt[x]])/(35*c^(10/3)) - (Log[-1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(1/3) + c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3)))])/(10*c^(10/3)) + (Log[1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) + c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(10*c^(10/3)) + (Log[-1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3) + c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3)))])/(10*c^(10/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(2/3) + c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(10*c^(10/3)) - ((-1)^(2/3)*Log[-(((-1)^(1/3)*(1 - c^(1/3)*Sqrt[x]))/(1 - (-1)^(1/3)))]*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) + ((-1)^(2/3)*Log[((-1)^(1/3)*(1 + c^(1/3)*Sqrt[x]))/(1 + (-1)^(1/3))]*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) - ((-1)^(2/3)*Log[(-1)^(1/3) + c^(1/3)*Sqrt[x]]*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) + ((-1)^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]^2)/(20*c^(10/3)) - ((-1)^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])])/(10*c^(10/3)) + ((-1)^(2/3)*Log[((-1)^(1/3)*(1 - c^(1/3)*Sqrt[x]))/(1 + (-1)^(1/3))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) - ((-1)^(2/3)*Log[(-1)^(1/3) - c^(1/3)*Sqrt[x]]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) - ((-1)^(2/3)*Log[-(((-1)^(1/3)*(1 + c^(1/3)*Sqrt[x]))/(1 - (-1)^(1/3)))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) + ((-1)^(2/3)*Log[-(((-1)^(1/3)*((-1)^(1/3) + c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) - ((-1)^(2/3)*Log[(1/2)*(1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) + ((-1)^(2/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]^2)/(20*c^(10/3)) + ((-1)^(1/3)*Log[((-1)^(2/3)*(1 - c^(1/3)*Sqrt[x]))/(1 + (-1)^(2/3))]*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) - ((-1)^(1/3)*Log[-(((-1)^(2/3)*(1 + c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) + ((-1)^(1/3)*Log[-(-1)^(2/3) + c^(1/3)*Sqrt[x]]*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) - ((-1)^(1/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]^2)/(20*c^(10/3)) + ((-1)^(1/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(10*c^(10/3)) - ((-1)^(1/3)*Log[-(((-1)^(2/3)*(1 - c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) + ((-1)^(1/3)*Log[-(-1)^(2/3) - c^(1/3)*Sqrt[x]]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) + ((-1)^(1/3)*Log[((-1)^(2/3)*(1 + c^(1/3)*Sqrt[x]))/(1 + (-1)^(2/3))]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(10*c^(10/3)) - ((-1)^(1/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]^2)/(20*c^(10/3)) - ((-1)^(1/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(10*c^(10/3)) + ((-1)^(1/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(10*c^(10/3)) + ((-1)^(1/3)*Log[((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(10*c^(10/3)) + ((-1)^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))])/(10*c^(10/3)) - ((-1)^(1/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(10*c^(10/3)) + ((-1)^(1/3)*Log[(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(10*c^(10/3)) - (12*Log[1 - c^(1/3)*Sqrt[x] + c^(2/3)*x])/(35*c^(10/3)) - (12*Log[1 + c^(1/3)*Sqrt[x] + c^(2/3)*x])/(35*c^(10/3)) - (3*Sqrt[x]*Log[1 - c*x^(3/2)])/(5*c^3) - (3*x^(7/2)*Log[1 - c*x^(3/2)])/(35*c) + (Log[-1 - c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(10*c^(10/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(10*c^(10/3)) + ((-1)^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(10*c^(10/3)) - ((-1)^(2/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(10*c^(10/3)) - ((-1)^(1/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(10*c^(10/3)) + ((-1)^(1/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(10*c^(10/3)) + (1/20)*x^5*Log[1 - c*x^(3/2)]^2 + (3*Sqrt[x]*Log[1 + c*x^(3/2)])/(5*c^3) + (3*x^(7/2)*Log[1 + c*x^(3/2)])/(35*c) - (Log[-1 - c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(10*c^(10/3)) + (Log[1 - c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(10*c^(10/3)) - ((-1)^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(10*c^(10/3)) + ((-1)^(2/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(10*c^(10/3)) + ((-1)^(1/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(10*c^(10/3)) - ((-1)^(1/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(10*c^(10/3)) - (1/10)*x^5*Log[1 - c*x^(3/2)]*Log[1 + c*x^(3/2)] + (1/20)*x^5*Log[1 + c*x^(3/2)]^2 - PolyLog[2, (1/2)*(1 - c^(1/3)*Sqrt[x])]/(10*c^(10/3)) - PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))]/(10*c^(10/3)) + PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]/(10*c^(10/3)) + PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))]/(10*c^(10/3)) - PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))]/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog[2, 1/(1 - (-1)^(1/3)) - c^(1/3)*Sqrt[x]])/(10*c^(10/3)) - ((-1)^(2/3)*PolyLog[2, 1/(1 + (-1)^(2/3)) - c^(1/3)*Sqrt[x]])/(10*c^(10/3)) - PolyLog[2, (1/2)*(1 + c^(1/3)*Sqrt[x])]/(10*c^(10/3)) - PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))]/(10*c^(10/3)) + PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]/(10*c^(10/3)) + PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))]/(10*c^(10/3)) - PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))]/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog[2, 1/(1 - (-1)^(1/3)) + c^(1/3)*Sqrt[x]])/(10*c^(10/3)) - ((-1)^(2/3)*PolyLog[2, 1/(1 + (-1)^(2/3)) + c^(1/3)*Sqrt[x]])/(10*c^(10/3)) - ((-1)^(2/3)*PolyLog[2, (1/2)*(1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])])/(10*c^(10/3)) - ((-1)^(2/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))])/(10*c^(10/3)) + ((-1)^(2/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(10*c^(10/3)) + ((-1)^(2/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(10*c^(10/3)) - ((-1)^(2/3)*PolyLog[2, (1/2)*(1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])])/(10*c^(10/3)) - ((-1)^(2/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))])/(10*c^(10/3)) + ((-1)^(2/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(10*c^(10/3)) + ((-1)^(2/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog[2, (1/2)*(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(10*c^(10/3)) - ((-1)^(1/3)*PolyLog[2, (1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog[2, (1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog[2, ((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog[2, (1/2)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(10*c^(10/3)) - ((-1)^(1/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(10*c^(10/3)) + ((-1)^(1/3)*PolyLog[2, ((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(10*c^(10/3))}
# {x^1*ArcTanh[c*x^(3/2)]^2, x, 236, -((3*Sqrt[3]*ArcTan[(1 - 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/(2*c^(4/3))) - (3*Sqrt[3]*ArcTan[(1 + 2*c^(1/3)*Sqrt[x])/Sqrt[3]])/(2*c^(4/3)) + Log[-1 - c^(1/3)*Sqrt[x]]^2/(8*c^(4/3)) - (Log[-1 - c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 - c^(1/3)*Sqrt[x])])/(4*c^(4/3)) + (3*Log[1 - c^(1/3)*Sqrt[x]])/(2*c^(4/3)) + Log[1 - c^(1/3)*Sqrt[x]]^2/(8*c^(4/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(1/3) - c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3)))])/(4*c^(4/3)) + (Log[-1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) - c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(4*c^(4/3)) + (Log[1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3) - c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3)))])/(4*c^(4/3)) - (Log[-1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(2/3) - c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(4*c^(4/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + c^(1/3)*Sqrt[x])])/(4*c^(4/3)) + (3*Log[1 + c^(1/3)*Sqrt[x]])/(2*c^(4/3)) - (Log[-1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(1/3) + c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3)))])/(4*c^(4/3)) + (Log[1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) + c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(4*c^(4/3)) + (Log[-1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3) + c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3)))])/(4*c^(4/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(2/3) + c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(4*c^(4/3)) - ((-1)^(2/3)*Log[-(((-1)^(1/3)*(1 - c^(1/3)*Sqrt[x]))/(1 - (-1)^(1/3)))]*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) + ((-1)^(2/3)*Log[((-1)^(1/3)*(1 + c^(1/3)*Sqrt[x]))/(1 + (-1)^(1/3))]*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) - ((-1)^(2/3)*Log[(-1)^(1/3) + c^(1/3)*Sqrt[x]]*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) + ((-1)^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]^2)/(8*c^(4/3)) - ((-1)^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])])/(4*c^(4/3)) + ((-1)^(2/3)*Log[((-1)^(1/3)*(1 - c^(1/3)*Sqrt[x]))/(1 + (-1)^(1/3))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) - ((-1)^(2/3)*Log[(-1)^(1/3) - c^(1/3)*Sqrt[x]]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) - ((-1)^(2/3)*Log[-(((-1)^(1/3)*(1 + c^(1/3)*Sqrt[x]))/(1 - (-1)^(1/3)))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) + ((-1)^(2/3)*Log[-(((-1)^(1/3)*((-1)^(1/3) + c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) - ((-1)^(2/3)*Log[(1/2)*(1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) + ((-1)^(2/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]^2)/(8*c^(4/3)) + ((-1)^(1/3)*Log[((-1)^(2/3)*(1 - c^(1/3)*Sqrt[x]))/(1 + (-1)^(2/3))]*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) - ((-1)^(1/3)*Log[-(((-1)^(2/3)*(1 + c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) + ((-1)^(1/3)*Log[-(-1)^(2/3) + c^(1/3)*Sqrt[x]]*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) - ((-1)^(1/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]^2)/(8*c^(4/3)) + ((-1)^(1/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(4*c^(4/3)) - ((-1)^(1/3)*Log[-(((-1)^(2/3)*(1 - c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) + ((-1)^(1/3)*Log[-(-1)^(2/3) - c^(1/3)*Sqrt[x]]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) + ((-1)^(1/3)*Log[((-1)^(2/3)*(1 + c^(1/3)*Sqrt[x]))/(1 + (-1)^(2/3))]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]])/(4*c^(4/3)) - ((-1)^(1/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]^2)/(8*c^(4/3)) - ((-1)^(1/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(4*c^(4/3)) + ((-1)^(1/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(4*c^(4/3)) + ((-1)^(1/3)*Log[((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(4*c^(4/3)) + ((-1)^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))])/(4*c^(4/3)) - ((-1)^(1/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(4*c^(4/3)) + ((-1)^(1/3)*Log[(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(4*c^(4/3)) - (3*Log[1 - c^(1/3)*Sqrt[x] + c^(2/3)*x])/(4*c^(4/3)) - (3*Log[1 + c^(1/3)*Sqrt[x] + c^(2/3)*x])/(4*c^(4/3)) - (3*Sqrt[x]*Log[1 - c*x^(3/2)])/(2*c) + (Log[-1 - c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(4*c^(4/3)) - (Log[1 - c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(4*c^(4/3)) + ((-1)^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(4*c^(4/3)) - ((-1)^(2/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(4*c^(4/3)) - ((-1)^(1/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(4*c^(4/3)) + ((-1)^(1/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)])/(4*c^(4/3)) + (1/8)*x^2*Log[1 - c*x^(3/2)]^2 + (3*Sqrt[x]*Log[1 + c*x^(3/2)])/(2*c) - (Log[-1 - c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(4*c^(4/3)) + (Log[1 - c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(4*c^(4/3)) - ((-1)^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(4*c^(4/3)) + ((-1)^(2/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(4*c^(4/3)) + ((-1)^(1/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(4*c^(4/3)) - ((-1)^(1/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)])/(4*c^(4/3)) - (1/4)*x^2*Log[1 - c*x^(3/2)]*Log[1 + c*x^(3/2)] + (1/8)*x^2*Log[1 + c*x^(3/2)]^2 - PolyLog[2, (1/2)*(1 - c^(1/3)*Sqrt[x])]/(4*c^(4/3)) - PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))]/(4*c^(4/3)) + PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]/(4*c^(4/3)) + PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))]/(4*c^(4/3)) - PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))]/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog[2, 1/(1 - (-1)^(1/3)) - c^(1/3)*Sqrt[x]])/(4*c^(4/3)) - ((-1)^(2/3)*PolyLog[2, 1/(1 + (-1)^(2/3)) - c^(1/3)*Sqrt[x]])/(4*c^(4/3)) - PolyLog[2, (1/2)*(1 + c^(1/3)*Sqrt[x])]/(4*c^(4/3)) - PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))]/(4*c^(4/3)) + PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]/(4*c^(4/3)) + PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))]/(4*c^(4/3)) - PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))]/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog[2, 1/(1 - (-1)^(1/3)) + c^(1/3)*Sqrt[x]])/(4*c^(4/3)) - ((-1)^(2/3)*PolyLog[2, 1/(1 + (-1)^(2/3)) + c^(1/3)*Sqrt[x]])/(4*c^(4/3)) - ((-1)^(2/3)*PolyLog[2, (1/2)*(1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])])/(4*c^(4/3)) - ((-1)^(2/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))])/(4*c^(4/3)) + ((-1)^(2/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(4*c^(4/3)) + ((-1)^(2/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(4*c^(4/3)) - ((-1)^(2/3)*PolyLog[2, (1/2)*(1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])])/(4*c^(4/3)) - ((-1)^(2/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))])/(4*c^(4/3)) + ((-1)^(2/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(4*c^(4/3)) + ((-1)^(2/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog[2, (1/2)*(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(4*c^(4/3)) - ((-1)^(1/3)*PolyLog[2, (1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog[2, (1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog[2, ((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog[2, (1/2)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])])/(4*c^(4/3)) - ((-1)^(1/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))])/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))])/(4*c^(4/3)) + ((-1)^(1/3)*PolyLog[2, ((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))])/(4*c^(4/3))}
# {ArcTanh[c*x^(3/2)]^2/x^2, x, 160, (-(1/4))*c^(2/3)*Log[-1 - c^(1/3)*Sqrt[x]]^2 + (1/2)*c^(2/3)*Log[-1 - c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 - c^(1/3)*Sqrt[x])] - (1/4)*c^(2/3)*Log[1 - c^(1/3)*Sqrt[x]]^2 + (1/2)*c^(2/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(1/3) - c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3)))] - (1/2)*c^(2/3)*Log[-1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) - c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/2)*c^(2/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3) - c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3)))] + (1/2)*c^(2/3)*Log[-1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(2/3) - c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))] + (1/2)*c^(2/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + c^(1/3)*Sqrt[x])] + (1/2)*c^(2/3)*Log[-1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(1/3) + c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3)))] - (1/2)*c^(2/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) + c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/2)*c^(2/3)*Log[-1 - c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3) + c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3)))] + (1/2)*c^(2/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[((-1)^(2/3) + c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))] + (1/2)*(-1)^(2/3)*c^(2/3)*Log[-(((-1)^(1/3)*(1 - c^(1/3)*Sqrt[x]))/(1 - (-1)^(1/3)))]*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]] - (1/2)*(-1)^(2/3)*c^(2/3)*Log[((-1)^(1/3)*(1 + c^(1/3)*Sqrt[x]))/(1 + (-1)^(1/3))]*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]] + (1/2)*(-1)^(2/3)*c^(2/3)*Log[(-1)^(1/3) + c^(1/3)*Sqrt[x]]*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]] - (1/4)*(-1)^(2/3)*c^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]^2 + (1/2)*(-1)^(2/3)*c^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])] - (1/2)*(-1)^(2/3)*c^(2/3)*Log[((-1)^(1/3)*(1 - c^(1/3)*Sqrt[x]))/(1 + (-1)^(1/3))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]] + (1/2)*(-1)^(2/3)*c^(2/3)*Log[(-1)^(1/3) - c^(1/3)*Sqrt[x]]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]] + (1/2)*(-1)^(2/3)*c^(2/3)*Log[-(((-1)^(1/3)*(1 + c^(1/3)*Sqrt[x]))/(1 - (-1)^(1/3)))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]] - (1/2)*(-1)^(2/3)*c^(2/3)*Log[-(((-1)^(1/3)*((-1)^(1/3) + c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]] + (1/2)*(-1)^(2/3)*c^(2/3)*Log[(1/2)*(1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])]*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]] - (1/4)*(-1)^(2/3)*c^(2/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]^2 - (1/2)*(-1)^(1/3)*c^(2/3)*Log[((-1)^(2/3)*(1 - c^(1/3)*Sqrt[x]))/(1 + (-1)^(2/3))]*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]] + (1/2)*(-1)^(1/3)*c^(2/3)*Log[-(((-1)^(2/3)*(1 + c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]] - (1/2)*(-1)^(1/3)*c^(2/3)*Log[-(-1)^(2/3) + c^(1/3)*Sqrt[x]]*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]] + (1/4)*(-1)^(1/3)*c^(2/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]^2 - (1/2)*(-1)^(1/3)*c^(2/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])] + (1/2)*(-1)^(1/3)*c^(2/3)*Log[-(((-1)^(2/3)*(1 - c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]] - (1/2)*(-1)^(1/3)*c^(2/3)*Log[-(-1)^(2/3) - c^(1/3)*Sqrt[x]]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]] - (1/2)*(-1)^(1/3)*c^(2/3)*Log[((-1)^(2/3)*(1 + c^(1/3)*Sqrt[x]))/(1 + (-1)^(2/3))]*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]] + (1/4)*(-1)^(1/3)*c^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]^2 + (1/2)*(-1)^(1/3)*c^(2/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/2)*(-1)^(1/3)*c^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[(1/2)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])] - (1/2)*(-1)^(1/3)*c^(2/3)*Log[((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/2)*(-1)^(2/3)*c^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[-(((-1)^(2/3)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x]))/(1 - (-1)^(2/3)))] + (1/2)*(-1)^(1/3)*c^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/2)*(-1)^(1/3)*c^(2/3)*Log[(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]*Log[((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/2)*c^(2/3)*Log[-1 - c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)] + (1/2)*c^(2/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)] - (1/2)*(-1)^(2/3)*c^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)] + (1/2)*(-1)^(2/3)*c^(2/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)] + (1/2)*(-1)^(1/3)*c^(2/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)] - (1/2)*(-1)^(1/3)*c^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 - c*x^(3/2)] - Log[1 - c*x^(3/2)]^2/(4*x) + (1/2)*c^(2/3)*Log[-1 - c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)] - (1/2)*c^(2/3)*Log[1 - c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)] + (1/2)*(-1)^(2/3)*c^(2/3)*Log[-1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)] - (1/2)*(-1)^(2/3)*c^(2/3)*Log[1 + (-1)^(1/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)] - (1/2)*(-1)^(1/3)*c^(2/3)*Log[-1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)] + (1/2)*(-1)^(1/3)*c^(2/3)*Log[1 - (-1)^(2/3)*c^(1/3)*Sqrt[x]]*Log[1 + c*x^(3/2)] + (Log[1 - c*x^(3/2)]*Log[1 + c*x^(3/2)])/(2*x) - Log[1 + c*x^(3/2)]^2/(4*x) + (1/2)*c^(2/3)*PolyLog[2, (1/2)*(1 - c^(1/3)*Sqrt[x])] + (1/2)*c^(2/3)*PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))] - (1/2)*c^(2/3)*PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/2)*c^(2/3)*PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))] + (1/2)*c^(2/3)*PolyLog[2, (1 - c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))] - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog[2, 1/(1 - (-1)^(1/3)) - c^(1/3)*Sqrt[x]] + (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog[2, 1/(1 + (-1)^(2/3)) - c^(1/3)*Sqrt[x]] + (1/2)*c^(2/3)*PolyLog[2, (1/2)*(1 + c^(1/3)*Sqrt[x])] + (1/2)*c^(2/3)*PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))] - (1/2)*c^(2/3)*PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/2)*c^(2/3)*PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))] + (1/2)*c^(2/3)*PolyLog[2, (1 + c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))] - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog[2, 1/(1 - (-1)^(1/3)) + c^(1/3)*Sqrt[x]] + (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog[2, 1/(1 + (-1)^(2/3)) + c^(1/3)*Sqrt[x]] + (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog[2, (1/2)*(1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])] + (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))] - (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog[2, (1 - (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))] + (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog[2, (1/2)*(1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])] + (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(1/3))] - (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/2)*(-1)^(2/3)*c^(2/3)*PolyLog[2, (1 + (-1)^(1/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))] - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog[2, (1/2)*(1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])] + (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog[2, (1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))] - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog[2, (1 - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))] - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog[2, ((-1)^(1/3) - (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))] - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog[2, (1/2)*(1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])] + (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 - (-1)^(2/3))] - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog[2, (1 + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(2/3))] - (1/2)*(-1)^(1/3)*c^(2/3)*PolyLog[2, ((-1)^(1/3) + (-1)^(2/3)*c^(1/3)*Sqrt[x])/(1 + (-1)^(1/3))]}

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

# Integrands of the form x^m (a+b ArcTanh[c x^n])^p
[x^2*(a+b*arctanh(c*x^n)),x,2,1/3*x^3*(a+b*arctanh(c*x^n))-1/3*b*c*n*x^(3+n)*hypergeom([1,1/2*(3+n)/n],[3/2*(1+n)/n],c^2*x^(2*n))/(3+n)],
[x*(a+b*arctanh(c*x^n)),x,2,1/2*x^2*(a+b*arctanh(c*x^n))-1/2*b*c*n*x^(2+n)*hypergeom([1,1/2*(2+n)/n],[1/2*(3+2/n)],c^2*x^(2*n))/(2+n)],
[a+b*arctanh(c*x^n),x,3,a*x+b*x*arctanh(c*x^n)-b*c*n*x^(1+n)*hypergeom([1,1/2*(1+n)/n],[1/2*(3+1/n)],c^2*x^(2*n))/(1+n)],
[(a+b*arctanh(c*x^n))/x,x,2,a*log(x)-1/2*b*polylog(2,-c*x^n)/n+1/2*b*polylog(2,c*x^n)/n],
[(a+b*arctanh(c*x^n))/x^2,x,2,(-a-b*arctanh(c*x^n))/x-b*c*n*x^(-1+n)*hypergeom([1,1/2*(-1+n)/n],[1/2*(3+(-1)/n)],c^2*x^(2*n))/(1-n)],
[(a+b*arctanh(c*x^n))/x^3,x,2,1/2*(-a-b*arctanh(c*x^n))/x^2-1/2*b*c*n*x^(-2+n)*hypergeom([1,1/2*(1+(-2)/n)],[1/2*(3+(-2)/n)],c^2*x^(2*n))/(2-n)],
[(a+b*arctanh(c*x^n))/x^4,x,2,1/3*(-a-b*arctanh(c*x^n))/x^3-1/3*b*c*n*x^(-3+n)*hypergeom([1,1/2*(-3+n)/n],[-3/2*(1-n)/n],c^2*x^(2*n))/(3-n)],
[x*(a+b*arctanh(c*x^n))^2,x,0,Unintegrable(x*(a+b*arctanh(c*x^n))^2,x)],
[(a+b*arctanh(c*x^n))^2,x,0,Unintegrable((a+b*arctanh(c*x^n))^2,x)],
[(a+b*arctanh(c*x^n))^2/x,x,7,2*(a+b*arctanh(c*x^n))^2*arctanh(1+(-2)/(1-c*x^n))/n-b*(a+b*arctanh(c*x^n))*polylog(2,1+(-2)/(1-c*x^n))/n+b*(a+b*arctanh(c*x^n))*polylog(2,-1+2/(1-c*x^n))/n+1/2*b^2*polylog(3,1+(-2)/(1-c*x^n))/n-1/2*b^2*polylog(3,-1+2/(1-c*x^n))/n],
[(a+b*arctanh(c*x^n))^2/x^2,x,0,Unintegrable((a+b*arctanh(c*x^n))^2/x^2,x)],
[(a+b*arctanh(c*x^n))^2/x^3,x,0,Unintegrable((a+b*arctanh(c*x^n))^2/x^3,x)],
[arctanh(a*x^n)/x,x,2,-1/2*polylog(2,-a*x^n)/n+1/2*polylog(2,a*x^n)/n],
[arctanh(a*x^5)/x,x,2,-1/10*polylog(2,-a*x^5)+1/10*polylog(2,a*x^5)],
[arctanh(1/x),x,3,x*arctanh(1/x)+1/2*log(1-x^2)],

# Integrands of the form (d x)^(m/2) (a+b ArcTanh[c x^n])^p

# Integrands of the form (d x)^m (a+b ArcTanh[c x^n])^p when m symbolic
[(d*x)^m*(a+b*arctanh(c*x^n))^3,x,0,Unintegrable((d*x)^m*(a+b*arctanh(c*x^n))^3,x)],
[(d*x)^m*(a+b*arctanh(c*x^n))^2,x,0,Unintegrable((d*x)^m*(a+b*arctanh(c*x^n))^2,x)],
[(d*x)^m*(a+b*arctanh(c*x^n)),x,3,x*(d*x)^m*(a+b*arctanh(c*x^n))/(1+m)-b*c*n*x^(1+n)*(d*x)^m*hypergeom([1,1/2*(1+m+n)/n],[1/2*(1+m+3*n)/n],c^2*x^(2*n))/((1+m)*(1+m+n))],
[(d*x)^m/(a+b*arctanh(c*x^n)),x,0,Unintegrable((d*x)^m/(a+b*arctanh(c*x^n)),x)],
[(d*x)^m/(a+b*arctanh(c*x^n))^2,x,0,Unintegrable((d*x)^m/(a+b*arctanh(c*x^n))^2,x)]]:
