# Maple integration test file: "7 Inverse hyperbolic functions\7.3 Inverse hyperbolic tangent\7.3.3 (d+e x)^m (a+b arctanh(c x^n))^p.txt"

lst:=[

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

# Integrands of the form (d+e x)^m (a+b ArcTanh[c x^1])^p
[(d+e*x)^4*(a+b*arctanh(c*x)),x,6,b*d*e*(2*c^2*d^2+e^2)*x/c^3+1/10*b*e^2*(10*c^2*d^2+e^2)*x^2/c^3+1/3*b*d*e^3*x^3/c+1/20*b*e^4*x^4/c+1/5*(d+e*x)^5*(a+b*arctanh(c*x))/e+1/10*b*(c*d+e)^5*log(1-c*x)/(c^5*e)-1/10*b*(c*d-e)^5*log(1+c*x)/(c^5*e)],
[(d+e*x)^3*(a+b*arctanh(c*x)),x,6,1/4*b*e*(6*c^2*d^2+e^2)*x/c^3+1/2*b*d*e^2*x^2/c+1/12*b*e^3*x^3/c+1/4*(d+e*x)^4*(a+b*arctanh(c*x))/e+1/8*b*(c*d+e)^4*log(1-c*x)/(c^4*e)-1/8*b*(c*d-e)^4*log(1+c*x)/(c^4*e)],
[(d+e*x)^2*(a+b*arctanh(c*x)),x,6,b*d*e*x/c+1/6*b*e^2*x^2/c+1/3*(d+e*x)^3*(a+b*arctanh(c*x))/e+1/6*b*(c*d+e)^3*log(1-c*x)/(c^3*e)-1/6*b*(c*d-e)^3*log(1+c*x)/(c^3*e)],
[(d+e*x)*(a+b*arctanh(c*x)),x,6,1/2*b*e*x/c+1/2*(d+e*x)^2*(a+b*arctanh(c*x))/e+1/4*b*(c*d+e)^2*log(1-c*x)/(c^2*e)-1/4*b*(c*d-e)^2*log(1+c*x)/(c^2*e)],
[(a+b*arctanh(c*x))/(d+e*x),x,4,-(a+b*arctanh(c*x))*log(2/(1+c*x))/e+(a+b*arctanh(c*x))*log(2*c*(d+e*x)/((c*d+e)*(1+c*x)))/e+1/2*b*polylog(2,1+(-2)/(1+c*x))/e-1/2*b*polylog(2,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/e],
[(a+b*arctanh(c*x))/(d+e*x)^2,x,6,(-a-b*arctanh(c*x))/(e*(d+e*x))-1/2*b*c*log(1-c*x)/(e*(c*d+e))+1/2*b*c*log(1+c*x)/((c*d-e)*e)-b*c*log(d+e*x)/(c^2*d^2-e^2)],
[(a+b*arctanh(c*x))/(d+e*x)^3,x,4,1/2*b*c/((c^2*d^2-e^2)*(d+e*x))+1/2*(-a-b*arctanh(c*x))/(e*(d+e*x)^2)-1/4*b*c^2*log(1-c*x)/(e*(c*d+e)^2)+1/4*b*c^2*log(1+c*x)/((c*d-e)^2*e)-b*c^3*d*log(d+e*x)/(c^2*d^2-e^2)^2],
[(a+b*arctanh(c*x))/(d+e*x)^4,x,4,1/6*b*c/((c^2*d^2-e^2)*(d+e*x)^2)+2/3*b*c^3*d/((c^2*d^2-e^2)^2*(d+e*x))+1/3*(-a-b*arctanh(c*x))/(e*(d+e*x)^3)-1/6*b*c^3*log(1-c*x)/(e*(c*d+e)^3)+1/6*b*c^3*log(1+c*x)/((c*d-e)^3*e)-1/3*b*c^3*(3*c^2*d^2+e^2)*log(d+e*x)/(c^2*d^2-e^2)^3],
[(d+e*x)^3*(a+b*arctanh(c*x))^2,x,19,b^2*d*e^2*x/c^2+1/2*a*b*e*(6*c^2*d^2+e^2)*x/c^3+1/12*b^2*e^3*x^2/c^2-b^2*d*e^2*arctanh(c*x)/c^3+1/2*b^2*e*(6*c^2*d^2+e^2)*x*arctanh(c*x)/c^3+b*d*e^2*x^2*(a+b*arctanh(c*x))/c+1/6*b*e^3*x^3*(a+b*arctanh(c*x))/c+d*(c^2*d^2+e^2)*(a+b*arctanh(c*x))^2/c^3-1/4*(c^4*d^4+6*c^2*d^2*e^2+e^4)*(a+b*arctanh(c*x))^2/(c^4*e)+1/4*(d+e*x)^4*(a+b*arctanh(c*x))^2/e-2*b*d*(c^2*d^2+e^2)*(a+b*arctanh(c*x))*log(2/(1-c*x))/c^3+1/12*b^2*e^3*log(1-c^2*x^2)/c^4+1/4*b^2*e*(6*c^2*d^2+e^2)*log(1-c^2*x^2)/c^4-b^2*d*(c^2*d^2+e^2)*polylog(2,1+(-2)/(1-c*x))/c^3],
[(d+e*x)^2*(a+b*arctanh(c*x))^2,x,15,2*a*b*d*e*x/c+1/3*b^2*e^2*x/c^2-1/3*b^2*e^2*arctanh(c*x)/c^3+2*b^2*d*e*x*arctanh(c*x)/c+1/3*b*e^2*x^2*(a+b*arctanh(c*x))/c+1/3*(3*c^2*d^2+e^2)*(a+b*arctanh(c*x))^2/c^3-1/3*d*(d^2+3*e^2/c^2)*(a+b*arctanh(c*x))^2/e+1/3*(d+e*x)^3*(a+b*arctanh(c*x))^2/e-2/3*b*(3*c^2*d^2+e^2)*(a+b*arctanh(c*x))*log(2/(1-c*x))/c^3+b^2*d*e*log(1-c^2*x^2)/c^2-1/3*b^2*(3*c^2*d^2+e^2)*polylog(2,1+(-2)/(1-c*x))/c^3],
[(d+e*x)*(a+b*arctanh(c*x))^2,x,12,a*b*e*x/c+b^2*e*x*arctanh(c*x)/c+d*(a+b*arctanh(c*x))^2/c-1/2*(d^2+e^2/c^2)*(a+b*arctanh(c*x))^2/e+1/2*(d+e*x)^2*(a+b*arctanh(c*x))^2/e-2*b*d*(a+b*arctanh(c*x))*log(2/(1-c*x))/c+1/2*b^2*e*log(1-c^2*x^2)/c^2-b^2*d*polylog(2,1+(-2)/(1-c*x))/c],
[(a+b*arctanh(c*x))^2/(d+e*x),x,1,-(a+b*arctanh(c*x))^2*log(2/(1+c*x))/e+(a+b*arctanh(c*x))^2*log(2*c*(d+e*x)/((c*d+e)*(1+c*x)))/e+b*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1+c*x))/e-b*(a+b*arctanh(c*x))*polylog(2,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/e+1/2*b^2*polylog(3,1+(-2)/(1+c*x))/e-1/2*b^2*polylog(3,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/e],
[(a+b*arctanh(c*x))^2/(d+e*x)^2,x,12,-(a+b*arctanh(c*x))^2/(e*(d+e*x))+b*c*(a+b*arctanh(c*x))*log(2/(1-c*x))/(e*(c*d+e))-b*c*(a+b*arctanh(c*x))*log(2/(1+c*x))/((c*d-e)*e)+2*b*c*(a+b*arctanh(c*x))*log(2/(1+c*x))/(c^2*d^2-e^2)-2*b*c*(a+b*arctanh(c*x))*log(2*c*(d+e*x)/((c*d+e)*(1+c*x)))/(c^2*d^2-e^2)+1/2*b^2*c*polylog(2,1+(-2)/(1-c*x))/(e*(c*d+e))+1/2*b^2*c*polylog(2,1+(-2)/(1+c*x))/((c*d-e)*e)-b^2*c*polylog(2,1+(-2)/(1+c*x))/(c^2*d^2-e^2)+b^2*c*polylog(2,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/(c^2*d^2-e^2)],
[(a+b*arctanh(c*x))^2/(d+e*x)^3,x,18,b*c*(a+b*arctanh(c*x))/((c^2*d^2-e^2)*(d+e*x))-1/2*(a+b*arctanh(c*x))^2/(e*(d+e*x)^2)+1/2*b*c^2*(a+b*arctanh(c*x))*log(2/(1-c*x))/(e*(c*d+e)^2)+1/2*b^2*c^2*log(1-c*x)/((c*d-e)*(c*d+e)^2)-1/2*b*c^2*(a+b*arctanh(c*x))*log(2/(1+c*x))/((c*d-e)^2*e)+2*b*c^3*d*(a+b*arctanh(c*x))*log(2/(1+c*x))/(c^2*d^2-e^2)^2-1/2*b^2*c^2*log(1+c*x)/((c*d-e)^2*(c*d+e))+b^2*c^2*e*log(d+e*x)/(c^2*d^2-e^2)^2-2*b*c^3*d*(a+b*arctanh(c*x))*log(2*c*(d+e*x)/((c*d+e)*(1+c*x)))/(c^2*d^2-e^2)^2+1/4*b^2*c^2*polylog(2,1+(-2)/(1-c*x))/(e*(c*d+e)^2)+1/4*b^2*c^2*polylog(2,1+(-2)/(1+c*x))/((c*d-e)^2*e)-b^2*c^3*d*polylog(2,1+(-2)/(1+c*x))/(c^2*d^2-e^2)^2+b^2*c^3*d*polylog(2,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/(c^2*d^2-e^2)^2],
[(d+e*x)^3*(a+b*arctanh(c*x))^3,x,29,3*a*b^2*d*e^2*x/c^2+1/4*b^3*e^3*x/c^3-1/4*b^3*e^3*arctanh(c*x)/c^4+3*b^3*d*e^2*x*arctanh(c*x)/c^2+1/4*b^2*e^3*x^2*(a+b*arctanh(c*x))/c^2-3/2*b*d*e^2*(a+b*arctanh(c*x))^2/c^3+1/4*b*e^3*(a+b*arctanh(c*x))^2/c^4+3/4*b*e*(6*c^2*d^2+e^2)*(a+b*arctanh(c*x))^2/c^4+3/4*b*e*(6*c^2*d^2+e^2)*x*(a+b*arctanh(c*x))^2/c^3+3/2*b*d*e^2*x^2*(a+b*arctanh(c*x))^2/c+1/4*b*e^3*x^3*(a+b*arctanh(c*x))^2/c+d*(c^2*d^2+e^2)*(a+b*arctanh(c*x))^3/c^3-1/4*(c^4*d^4+6*c^2*d^2*e^2+e^4)*(a+b*arctanh(c*x))^3/(c^4*e)+1/4*(d+e*x)^4*(a+b*arctanh(c*x))^3/e-1/2*b^2*e^3*(a+b*arctanh(c*x))*log(2/(1-c*x))/c^4-3/2*b^2*e*(6*c^2*d^2+e^2)*(a+b*arctanh(c*x))*log(2/(1-c*x))/c^4-3*b*d*(c^2*d^2+e^2)*(a+b*arctanh(c*x))^2*log(2/(1-c*x))/c^3+3/2*b^3*d*e^2*log(1-c^2*x^2)/c^3-1/4*b^3*e^3*polylog(2,1+(-2)/(1-c*x))/c^4-3/4*b^3*e*(6*c^2*d^2+e^2)*polylog(2,1+(-2)/(1-c*x))/c^4-3*b^2*d*(c^2*d^2+e^2)*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1-c*x))/c^3+3/2*b^3*d*(c^2*d^2+e^2)*polylog(3,1+(-2)/(1-c*x))/c^3],
[(d+e*x)^2*(a+b*arctanh(c*x))^3,x,20,a*b^2*e^2*x/c^2+b^3*e^2*x*arctanh(c*x)/c^2+3*b*d*e*(a+b*arctanh(c*x))^2/c^2-1/2*b*e^2*(a+b*arctanh(c*x))^2/c^3+3*b*d*e*x*(a+b*arctanh(c*x))^2/c+1/2*b*e^2*x^2*(a+b*arctanh(c*x))^2/c+1/3*(3*c^2*d^2+e^2)*(a+b*arctanh(c*x))^3/c^3-1/3*d*(d^2+3*e^2/c^2)*(a+b*arctanh(c*x))^3/e+1/3*(d+e*x)^3*(a+b*arctanh(c*x))^3/e-6*b^2*d*e*(a+b*arctanh(c*x))*log(2/(1-c*x))/c^2-b*(3*c^2*d^2+e^2)*(a+b*arctanh(c*x))^2*log(2/(1-c*x))/c^3+1/2*b^3*e^2*log(1-c^2*x^2)/c^3-3*b^3*d*e*polylog(2,1+(-2)/(1-c*x))/c^2-b^2*(3*c^2*d^2+e^2)*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1-c*x))/c^3+1/2*b^3*(3*c^2*d^2+e^2)*polylog(3,1+(-2)/(1-c*x))/c^3],
[(d+e*x)*(a+b*arctanh(c*x))^3,x,14,3/2*b*e*(a+b*arctanh(c*x))^2/c^2+3/2*b*e*x*(a+b*arctanh(c*x))^2/c+d*(a+b*arctanh(c*x))^3/c-1/2*(d^2+e^2/c^2)*(a+b*arctanh(c*x))^3/e+1/2*(d+e*x)^2*(a+b*arctanh(c*x))^3/e-3*b^2*e*(a+b*arctanh(c*x))*log(2/(1-c*x))/c^2-3*b*d*(a+b*arctanh(c*x))^2*log(2/(1-c*x))/c-3/2*b^3*e*polylog(2,1+(-2)/(1-c*x))/c^2-3*b^2*d*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1-c*x))/c+3/2*b^3*d*polylog(3,1+(-2)/(1-c*x))/c],
[(a+b*arctanh(c*x))^3/(d+e*x),x,1,-(a+b*arctanh(c*x))^3*log(2/(1+c*x))/e+(a+b*arctanh(c*x))^3*log(2*c*(d+e*x)/((c*d+e)*(1+c*x)))/e+3/2*b*(a+b*arctanh(c*x))^2*polylog(2,1+(-2)/(1+c*x))/e-3/2*b*(a+b*arctanh(c*x))^2*polylog(2,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/e+3/2*b^2*(a+b*arctanh(c*x))*polylog(3,1+(-2)/(1+c*x))/e-3/2*b^2*(a+b*arctanh(c*x))*polylog(3,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/e+3/4*b^3*polylog(4,1+(-2)/(1+c*x))/e-3/4*b^3*polylog(4,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/e],
[(a+b*arctanh(c*x))^3/(d+e*x)^2,x,9,-(a+b*arctanh(c*x))^3/(e*(d+e*x))+3/2*b*c*(a+b*arctanh(c*x))^2*log(2/(1-c*x))/(e*(c*d+e))-3/2*b*c*(a+b*arctanh(c*x))^2*log(2/(1+c*x))/((c*d-e)*e)+3*b*c*(a+b*arctanh(c*x))^2*log(2/(1+c*x))/(c^2*d^2-e^2)-3*b*c*(a+b*arctanh(c*x))^2*log(2*c*(d+e*x)/((c*d+e)*(1+c*x)))/(c^2*d^2-e^2)+3/2*b^2*c*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1-c*x))/(e*(c*d+e))+3/2*b^2*c*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1+c*x))/((c*d-e)*e)-3*b^2*c*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1+c*x))/(c^2*d^2-e^2)+3*b^2*c*(a+b*arctanh(c*x))*polylog(2,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/(c^2*d^2-e^2)-3/4*b^3*c*polylog(3,1+(-2)/(1-c*x))/(e*(c*d+e))+3/4*b^3*c*polylog(3,1+(-2)/(1+c*x))/((c*d-e)*e)-3/2*b^3*c*polylog(3,1+(-2)/(1+c*x))/(c^2*d^2-e^2)+3/2*b^3*c*polylog(3,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/(c^2*d^2-e^2)],
[(a+b*arctanh(c*x))^3/(d+e*x)^3,x,21,3/2*b*c*(a+b*arctanh(c*x))^2/((c^2*d^2-e^2)*(d+e*x))-1/2*(a+b*arctanh(c*x))^3/(e*(d+e*x)^2)-3/2*b^2*c^2*(a+b*arctanh(c*x))*log(2/(1-c*x))/((c*d-e)*(c*d+e)^2)+3/4*b*c^2*(a+b*arctanh(c*x))^2*log(2/(1-c*x))/(e*(c*d+e)^2)+3/2*b^2*c^2*(a+b*arctanh(c*x))*log(2/(1+c*x))/((c*d-e)^2*(c*d+e))-3*b^2*c^2*e*(a+b*arctanh(c*x))*log(2/(1+c*x))/(c^2*d^2-e^2)^2-3/4*b*c^2*(a+b*arctanh(c*x))^2*log(2/(1+c*x))/((c*d-e)^2*e)+3*b*c^3*d*(a+b*arctanh(c*x))^2*log(2/(1+c*x))/(c^2*d^2-e^2)^2+3*b^2*c^2*e*(a+b*arctanh(c*x))*log(2*c*(d+e*x)/((c*d+e)*(1+c*x)))/(c^2*d^2-e^2)^2-3*b*c^3*d*(a+b*arctanh(c*x))^2*log(2*c*(d+e*x)/((c*d+e)*(1+c*x)))/(c^2*d^2-e^2)^2-3/4*b^3*c^2*polylog(2,1+(-2)/(1-c*x))/((c*d-e)*(c*d+e)^2)+3/4*b^2*c^2*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1-c*x))/(e*(c*d+e)^2)-3/4*b^3*c^2*polylog(2,1+(-2)/(1+c*x))/((c*d-e)^2*(c*d+e))+3/2*b^3*c^2*e*polylog(2,1+(-2)/(1+c*x))/(c^2*d^2-e^2)^2+3/4*b^2*c^2*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1+c*x))/((c*d-e)^2*e)-3*b^2*c^3*d*(a+b*arctanh(c*x))*polylog(2,1+(-2)/(1+c*x))/(c^2*d^2-e^2)^2-3/2*b^3*c^2*e*polylog(2,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/(c^2*d^2-e^2)^2+3*b^2*c^3*d*(a+b*arctanh(c*x))*polylog(2,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/(c^2*d^2-e^2)^2-3/8*b^3*c^2*polylog(3,1+(-2)/(1-c*x))/(e*(c*d+e)^2)+3/8*b^3*c^2*polylog(3,1+(-2)/(1+c*x))/((c*d-e)^2*e)-3/2*b^3*c^3*d*polylog(3,1+(-2)/(1+c*x))/(c^2*d^2-e^2)^2+3/2*b^3*c^3*d*polylog(3,1-2*c*(d+e*x)/((c*d+e)*(1+c*x)))/(c^2*d^2-e^2)^2],
[(a+b*arctanh(c*x))/(1+2*c*x),x,4,1/2*(a-b*arctanh(1/2))*log(1/2*(-1-2*c*x)/d)/c-1/4*b*polylog(2,-1-2*c*x)/c+1/4*b*polylog(2,1/3*(1+2*c*x))/c,-1/2*(a+b*arctanh(c*x))*log(2/(1+c*x))/c+1/2*(a+b*arctanh(c*x))*log(2/3*(1+2*c*x)/(1+c*x))/c+1/4*b*polylog(2,1+(-2)/(1+c*x))/c-1/4*b*polylog(2,1-2/3*(1+2*c*x)/(1+c*x))/c],
[arctanh(x)/(1-x*sqrt(2)),x,4,-arctanh(1/sqrt(2))*log(1-x*sqrt(2))/sqrt(2)-1/2*polylog(2,(2*x-sqrt(2))/(2-sqrt(2)))/sqrt(2)+1/2*polylog(2,(-2*x+sqrt(2))/(2+sqrt(2)))/sqrt(2),arctanh(x)*log(2/(1+x))/sqrt(2)-arctanh(x)*log(-2*(1+sqrt(2))*(1-x*sqrt(2))/(1+x))/sqrt(2)-1/2*polylog(2,1+(-2)/(1+x))/sqrt(2)+1/2*polylog(2,1+2*(1+sqrt(2))*(1-x*sqrt(2))/(1+x))/sqrt(2)],

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

# Integrands of the form (d+e x)^m (a+b ArcTanh[c x^2])^p
[(d+e*x)^3*(a+b*arctanh(c*x^2)),x,13,2*b*d*e^2*x/c+1/4*b*e^3*x^2/c+b*d*(c*d^2-e^2)*arctan(x*sqrt(c))/c^(3/2)+1/4*(d+e*x)^4*(a+b*arctanh(c*x^2))/e-b*d*(c*d^2+e^2)*arctanh(x*sqrt(c))/c^(3/2)+1/8*b*(c^2*d^4+6*c*d^2*e^2+e^4)*log(1-c*x^2)/(c^2*e)-1/8*b*(c^2*d^4-6*c*d^2*e^2+e^4)*log(1+c*x^2)/(c^2*e)],
[(d+e*x)^2*(a+b*arctanh(c*x^2)),x,11,2/3*b*e^2*x/c+1/3*b*(3*c*d^2-e^2)*arctan(x*sqrt(c))/c^(3/2)+1/3*(d+e*x)^3*(a+b*arctanh(c*x^2))/e-1/3*b*(3*c*d^2+e^2)*arctanh(x*sqrt(c))/c^(3/2)+1/6*b*d*(c*d^2+3*e^2)*log(1-c*x^2)/(c*e)-1/6*b*d*(c*d^2-3*e^2)*log(1+c*x^2)/(c*e)],
[(d+e*x)*(a+b*arctanh(c*x^2)),x,10,1/2*(d+e*x)^2*(a+b*arctanh(c*x^2))/e+1/4*b*(c*d^2+e^2)*log(1-c*x^2)/(c*e)-1/4*b*(c*d^2-e^2)*log(1+c*x^2)/(c*e)+b*d*arctan(x*sqrt(c))/sqrt(c)-b*d*arctanh(x*sqrt(c))/sqrt(c)],
[(a+b*arctanh(c*x^2))/(d+e*x),x,19,(a+b*arctanh(c*x^2))*log(d+e*x)/e-1/2*b*log(d+e*x)*log(e*(1-x*sqrt(-c))/(e+d*sqrt(-c)))/e-1/2*b*log(d+e*x)*log(-e*(1+x*sqrt(-c))/(-e+d*sqrt(-c)))/e+1/2*b*log(d+e*x)*log(e*(1-x*sqrt(c))/(e+d*sqrt(c)))/e+1/2*b*log(d+e*x)*log(-e*(1+x*sqrt(c))/(-e+d*sqrt(c)))/e-1/2*b*polylog(2,(d+e*x)*sqrt(-c)/(-e+d*sqrt(-c)))/e-1/2*b*polylog(2,(d+e*x)*sqrt(-c)/(e+d*sqrt(-c)))/e+1/2*b*polylog(2,(d+e*x)*sqrt(c)/(-e+d*sqrt(c)))/e+1/2*b*polylog(2,(d+e*x)*sqrt(c)/(e+d*sqrt(c)))/e],
[(a+b*arctanh(c*x^2))/(d+e*x)^2,x,9,(-a-b*arctanh(c*x^2))/(e*(d+e*x))+2*b*c*d*e*log(d+e*x)/(c^2*d^4-e^4)-1/2*b*c*d*log(1-c*x^2)/(e*(c*d^2-e^2))+1/2*b*c*d*log(1+c*x^2)/(e*(c*d^2+e^2))+b*arctan(x*sqrt(c))*sqrt(c)/(c*d^2+e^2)-b*arctanh(x*sqrt(c))*sqrt(c)/(c*d^2-e^2)],
[(a+b*arctanh(c*x^2))/(d+e*x)^3,x,9,-b*c*d*e/((c^2*d^4-e^4)*(d+e*x))+b*c^(3/2)*d*arctan(x*sqrt(c))/(c*d^2+e^2)^2+1/2*(-a-b*arctanh(c*x^2))/(e*(d+e*x)^2)-b*c^(3/2)*d*arctanh(x*sqrt(c))/(c*d^2-e^2)^2+b*c*e*(3*c^2*d^4+e^4)*log(d+e*x)/(c^2*d^4-e^4)^2-1/4*b*c*(c*d^2+e^2)*log(1-c*x^2)/(e*(c*d^2-e^2)^2)+1/4*b*c*(c*d^2-e^2)*log(1+c*x^2)/(e*(c*d^2+e^2)^2)],

#  {(d + e*x)^2*(a + b*ArcTanh[c*x^2])^2, x, 163, a^2*d^2*x + (4*a*b*e^2*x)/(3*c) - (2/9)*a*b*e^2*x^3 + (2*a*b*d^2*ArcTan[Sqrt[c]*x])/Sqrt[c] - (2*a*b*e^2*ArcTan[Sqrt[c]*x])/(3*c^(3/2)) + (4*b^2*e^2*ArcTan[Sqrt[c]*x])/(3*c^(3/2)) + (I*b^2*d^2*ArcTan[Sqrt[c]*x]^2)/Sqrt[c] - (I*b^2*e^2*ArcTan[Sqrt[c]*x]^2)/(3*c^(3/2)) - (2*a*b*d^2*ArcTanh[Sqrt[c]*x])/Sqrt[c] - (4*b^2*e^2*ArcTanh[Sqrt[c]*x])/(3*c^(3/2)) - (b^2*d^2*ArcTanh[Sqrt[c]*x]^2)/Sqrt[c] - (b^2*e^2*ArcTanh[Sqrt[c]*x]^2)/(3*c^(3/2)) + (d*e*(a + b*ArcTanh[c*x^2])^2)/c + d*e*x^2*(a + b*ArcTanh[c*x^2])^2 + (2*b^2*d^2*ArcTanh[Sqrt[c]*x]*Log[2/(1 - Sqrt[c]*x)])/Sqrt[c] + (2*b^2*e^2*ArcTanh[Sqrt[c]*x]*Log[2/(1 - Sqrt[c]*x)])/(3*c^(3/2)) - (2*b^2*d^2*ArcTan[Sqrt[c]*x]*Log[2/(1 - I*Sqrt[c]*x)])/Sqrt[c] + (2*b^2*e^2*ArcTan[Sqrt[c]*x]*Log[2/(1 - I*Sqrt[c]*x)])/(3*c^(3/2)) + (b^2*d^2*ArcTan[Sqrt[c]*x]*Log[((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/Sqrt[c] - (b^2*e^2*ArcTan[Sqrt[c]*x]*Log[((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/(3*c^(3/2)) + (2*b^2*d^2*ArcTan[Sqrt[c]*x]*Log[2/(1 + I*Sqrt[c]*x)])/Sqrt[c] - (2*b^2*e^2*ArcTan[Sqrt[c]*x]*Log[2/(1 + I*Sqrt[c]*x)])/(3*c^(3/2)) - (2*b^2*d^2*ArcTanh[Sqrt[c]*x]*Log[2/(1 + Sqrt[c]*x)])/Sqrt[c] - (2*b^2*e^2*ArcTanh[Sqrt[c]*x]*Log[2/(1 + Sqrt[c]*x)])/(3*c^(3/2)) + (b^2*d^2*ArcTanh[Sqrt[c]*x]*Log[-((2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x)))])/Sqrt[c] + (b^2*e^2*ArcTanh[Sqrt[c]*x]*Log[-((2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x)))])/(3*c^(3/2)) + (b^2*d^2*ArcTanh[Sqrt[c]*x]*Log[(2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/Sqrt[c] + (b^2*e^2*ArcTanh[Sqrt[c]*x]*Log[(2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/(3*c^(3/2)) + (b^2*d^2*ArcTan[Sqrt[c]*x]*Log[((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/Sqrt[c] - (b^2*e^2*ArcTan[Sqrt[c]*x]*Log[((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/(3*c^(3/2)) - (2*b*d*e*(a + b*ArcTanh[c*x^2])*Log[2/(1 - c*x^2)])/c - a*b*d^2*x*Log[1 - c*x^2] - (2*b^2*e^2*x*Log[1 - c*x^2])/(3*c) + (1/9)*b^2*e^2*x^3*Log[1 - c*x^2] - (b^2*d^2*ArcTan[Sqrt[c]*x]*Log[1 - c*x^2])/Sqrt[c] + (b^2*e^2*ArcTan[Sqrt[c]*x]*Log[1 - c*x^2])/(3*c^(3/2)) + (b^2*d^2*ArcTanh[Sqrt[c]*x]*Log[1 - c*x^2])/Sqrt[c] + (1/4)*b^2*d^2*x*Log[1 - c*x^2]^2 + (1/9)*b*e^2*x^3*(2*a - b*Log[1 - c*x^2]) - (b*e^2*ArcTanh[Sqrt[c]*x]*(2*a - b*Log[1 - c*x^2]))/(3*c^(3/2)) + (1/12)*e^2*x^3*(2*a - b*Log[1 - c*x^2])^2 + a*b*d^2*x*Log[1 + c*x^2] + (2*b^2*e^2*x*Log[1 + c*x^2])/(3*c) + (1/3)*a*b*e^2*x^3*Log[1 + c*x^2] + (b^2*d^2*ArcTan[Sqrt[c]*x]*Log[1 + c*x^2])/Sqrt[c] - (b^2*e^2*ArcTan[Sqrt[c]*x]*Log[1 + c*x^2])/(3*c^(3/2)) - (b^2*d^2*ArcTanh[Sqrt[c]*x]*Log[1 + c*x^2])/Sqrt[c] - (b^2*e^2*ArcTanh[Sqrt[c]*x]*Log[1 + c*x^2])/(3*c^(3/2)) - (1/2)*b^2*d^2*x*Log[1 - c*x^2]*Log[1 + c*x^2] - (1/6)*b^2*e^2*x^3*Log[1 - c*x^2]*Log[1 + c*x^2] + (1/4)*b^2*d^2*x*Log[1 + c*x^2]^2 + (1/12)*b^2*e^2*x^3*Log[1 + c*x^2]^2 + (b^2*d^2*PolyLog[2, 1 - 2/(1 - Sqrt[c]*x)])/Sqrt[c] + (b^2*e^2*PolyLog[2, 1 - 2/(1 - Sqrt[c]*x)])/(3*c^(3/2)) + (I*b^2*d^2*PolyLog[2, 1 - 2/(1 - I*Sqrt[c]*x)])/Sqrt[c] - (I*b^2*e^2*PolyLog[2, 1 - 2/(1 - I*Sqrt[c]*x)])/(3*c^(3/2)) - (I*b^2*d^2*PolyLog[2, 1 - ((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/(2*Sqrt[c]) + (I*b^2*e^2*PolyLog[2, 1 - ((1 + I)*(1 - Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/(6*c^(3/2)) + (I*b^2*d^2*PolyLog[2, 1 - 2/(1 + I*Sqrt[c]*x)])/Sqrt[c] - (I*b^2*e^2*PolyLog[2, 1 - 2/(1 + I*Sqrt[c]*x)])/(3*c^(3/2)) + (b^2*d^2*PolyLog[2, 1 - 2/(1 + Sqrt[c]*x)])/Sqrt[c] + (b^2*e^2*PolyLog[2, 1 - 2/(1 + Sqrt[c]*x)])/(3*c^(3/2)) - (b^2*d^2*PolyLog[2, 1 + (2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/(2*Sqrt[c]) - (b^2*e^2*PolyLog[2, 1 + (2*Sqrt[c]*(1 - Sqrt[-c]*x))/((Sqrt[-c] - Sqrt[c])*(1 + Sqrt[c]*x))])/(6*c^(3/2)) - (b^2*d^2*PolyLog[2, 1 - (2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/(2*Sqrt[c]) - (b^2*e^2*PolyLog[2, 1 - (2*Sqrt[c]*(1 + Sqrt[-c]*x))/((Sqrt[-c] + Sqrt[c])*(1 + Sqrt[c]*x))])/(6*c^(3/2)) - (I*b^2*d^2*PolyLog[2, 1 - ((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/(2*Sqrt[c]) + (I*b^2*e^2*PolyLog[2, 1 - ((1 - I)*(1 + Sqrt[c]*x))/(1 - I*Sqrt[c]*x)])/(6*c^(3/2)) - (b^2*d*e*PolyLog[2, 1 - 2/(1 - c*x^2)])/c} 
[(d+e*x)*(a+b*arctanh(c*x^2))^2,x,77,a^2*d*x+1/2*e*(a+b*arctanh(c*x^2))^2/c+1/2*e*x^2*(a+b*arctanh(c*x^2))^2-b*e*(a+b*arctanh(c*x^2))*log(2/(1-c*x^2))/c-a*b*d*x*log(1-c*x^2)+1/4*b^2*d*x*log(1-c*x^2)^2+a*b*d*x*log(1+c*x^2)-1/2*b^2*d*x*log(1-c*x^2)*log(1+c*x^2)+1/4*b^2*d*x*log(1+c*x^2)^2-1/2*b^2*e*polylog(2,1+(-2)/(1-c*x^2))/c+2*a*b*d*arctan(x*sqrt(c))/sqrt(c)+I*b^2*d*arctan(x*sqrt(c))^2/sqrt(c)-2*a*b*d*arctanh(x*sqrt(c))/sqrt(c)-b^2*d*arctanh(x*sqrt(c))^2/sqrt(c)-b^2*d*arctan(x*sqrt(c))*log(1-c*x^2)/sqrt(c)+b^2*d*arctanh(x*sqrt(c))*log(1-c*x^2)/sqrt(c)+b^2*d*arctan(x*sqrt(c))*log(1+c*x^2)/sqrt(c)-b^2*d*arctanh(x*sqrt(c))*log(1+c*x^2)/sqrt(c)+2*b^2*d*arctanh(x*sqrt(c))*log(2/(1-x*sqrt(c)))/sqrt(c)-2*b^2*d*arctan(x*sqrt(c))*log(2/(1-I*x*sqrt(c)))/sqrt(c)+b^2*d*arctan(x*sqrt(c))*log((1+I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))/sqrt(c)+2*b^2*d*arctan(x*sqrt(c))*log(2/(1+I*x*sqrt(c)))/sqrt(c)-2*b^2*d*arctanh(x*sqrt(c))*log(2/(1+x*sqrt(c)))/sqrt(c)+b^2*d*arctanh(x*sqrt(c))*log(-2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))/sqrt(c)+b^2*d*arctanh(x*sqrt(c))*log(2*(1+x*sqrt(-c))*sqrt(c)/((sqrt(-c)+sqrt(c))*(1+x*sqrt(c))))/sqrt(c)+b^2*d*arctan(x*sqrt(c))*log((1-I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))/sqrt(c)+b^2*d*polylog(2,1+(-2)/(1-x*sqrt(c)))/sqrt(c)+I*b^2*d*polylog(2,1+(-2)/(1-I*x*sqrt(c)))/sqrt(c)-1/2*I*b^2*d*polylog(2,1+(-1-I)*(1-x*sqrt(c))/(1-I*x*sqrt(c)))/sqrt(c)+I*b^2*d*polylog(2,1+(-2)/(1+I*x*sqrt(c)))/sqrt(c)+b^2*d*polylog(2,1+(-2)/(1+x*sqrt(c)))/sqrt(c)-1/2*b^2*d*polylog(2,1+2*(1-x*sqrt(-c))*sqrt(c)/((sqrt(-c)-sqrt(c))*(1+x*sqrt(c))))/sqrt(c)-1/2*b^2*d*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*d*polylog(2,1+(-1+I)*(1+x*sqrt(c))/(1-I*x*sqrt(c)))/sqrt(c)],
[(a+b*arctanh(c*x^2))^2/(d+e*x),x,0,Unintegrable((a+b*arctanh(c*x^2))^2/(d+e*x),x)],
[(a+b*arctanh(c*x^2))^2/(d+e*x)^2,x,0,Unintegrable((a+b*arctanh(c*x^2))^2/(d+e*x)^2,x)],

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

# Integrands of the form (d+e x)^m (a+b ArcTanh[c x^3])^p
[(d+e*x)^2*(a+b*arctanh(c*x^3)),x,24,-b*d*e*arctanh(c^(1/3)*x)/c^(2/3)+1/3*(d+e*x)^3*(a+b*arctanh(c*x^3))/e+1/2*b*d^2*log(1-c^(2/3)*x^2)/c^(1/3)+1/4*b*d*e*log(1-c^(1/3)*x+c^(2/3)*x^2)/c^(2/3)-1/4*b*d*e*log(1+c^(1/3)*x+c^(2/3)*x^2)/c^(2/3)+1/6*b*(c*d^3+e^3)*log(1-c*x^3)/(c*e)-1/6*b*(c*d^3-e^3)*log(1+c*x^3)/(c*e)-1/4*b*d^2*log(1+c^(2/3)*x^2+c^(4/3)*x^4)/c^(1/3)-1/2*b*d*e*arctan(1/sqrt(3)-2*c^(1/3)*x/sqrt(3))*sqrt(3)/c^(2/3)+1/2*b*d*e*arctan(1/sqrt(3)+2*c^(1/3)*x/sqrt(3))*sqrt(3)/c^(2/3)+1/2*b*d^2*arctan((1+2*c^(2/3)*x^2)/sqrt(3))*sqrt(3)/c^(1/3)],
[(d+e*x)*(a+b*arctanh(c*x^3)),x,22,-1/2*b*e*arctanh(c^(1/3)*x)/c^(2/3)-1/2*b*d^2*arctanh(c*x^3)/e+1/2*(d+e*x)^2*(a+b*arctanh(c*x^3))/e+1/2*b*d*log(1-c^(2/3)*x^2)/c^(1/3)+1/8*b*e*log(1-c^(1/3)*x+c^(2/3)*x^2)/c^(2/3)-1/8*b*e*log(1+c^(1/3)*x+c^(2/3)*x^2)/c^(2/3)-1/4*b*d*log(1+c^(2/3)*x^2+c^(4/3)*x^4)/c^(1/3)-1/4*b*e*arctan(1/sqrt(3)-2*c^(1/3)*x/sqrt(3))*sqrt(3)/c^(2/3)+1/4*b*e*arctan(1/sqrt(3)+2*c^(1/3)*x/sqrt(3))*sqrt(3)/c^(2/3)+1/2*b*d*arctan((1+2*c^(2/3)*x^2)/sqrt(3))*sqrt(3)/c^(1/3)],
[(a+b*arctanh(c*x^3))/(d+e*x),x,25,(a+b*arctanh(c*x^3))*log(d+e*x)/e+1/2*b*log(e*(1-c^(1/3)*x)/(c^(1/3)*d+e))*log(d+e*x)/e-1/2*b*log(-e*(1+c^(1/3)*x)/(c^(1/3)*d-e))*log(d+e*x)/e+1/2*b*log(-e*((-1)^(1/3)+c^(1/3)*x)/(c^(1/3)*d-(-1)^(1/3)*e))*log(d+e*x)/e-1/2*b*log(-e*((-1)^(2/3)+c^(1/3)*x)/(c^(1/3)*d-(-1)^(2/3)*e))*log(d+e*x)/e+1/2*b*log((-1)^(2/3)*e*(1+(-1)^(1/3)*c^(1/3)*x)/(c^(1/3)*d+(-1)^(2/3)*e))*log(d+e*x)/e-1/2*b*log((-1)^(1/3)*e*(1+(-1)^(2/3)*c^(1/3)*x)/(c^(1/3)*d+(-1)^(1/3)*e))*log(d+e*x)/e-1/2*b*polylog(2,c^(1/3)*(d+e*x)/(c^(1/3)*d-e))/e+1/2*b*polylog(2,c^(1/3)*(d+e*x)/(c^(1/3)*d+e))/e+1/2*b*polylog(2,c^(1/3)*(d+e*x)/(c^(1/3)*d-(-1)^(1/3)*e))/e-1/2*b*polylog(2,c^(1/3)*(d+e*x)/(c^(1/3)*d+(-1)^(1/3)*e))/e-1/2*b*polylog(2,c^(1/3)*(d+e*x)/(c^(1/3)*d-(-1)^(2/3)*e))/e+1/2*b*polylog(2,c^(1/3)*(d+e*x)/(c^(1/3)*d+(-1)^(2/3)*e))/e],
[(a+b*arctanh(c*x^3))/(d+e*x)^2,x,19,(-a-b*arctanh(c*x^3))/(e*(d+e*x))+1/2*b*c^(1/3)*(c^(1/3)*d-e)*log(1-c^(1/3)*x)/(c*d^3+e^3)+1/2*b*c^(1/3)*(c^(1/3)*d+e)*log(1+c^(1/3)*x)/(c*d^3-e^3)-3*b*c*d^2*e^2*log(d+e*x)/(c^2*d^6-e^6)-1/4*b*c^(1/3)*(c^(1/3)*d+e)*log(1-c^(1/3)*x+c^(2/3)*x^2)/(c*d^3-e^3)-1/4*b*c^(1/3)*(c^(1/3)*d-e)*log(1+c^(1/3)*x+c^(2/3)*x^2)/(c*d^3+e^3)-1/2*b*c*d^2*log(1-c*x^3)/(e*(c*d^3+e^3))+1/2*b*c*d^2*log(1+c*x^3)/(e*(c*d^3-e^3))-1/2*b*c^(1/3)*arctan((1-2*c^(1/3)*x)/sqrt(3))*sqrt(3)/(c^(2/3)*d^2+c^(1/3)*d*e+e^2)-1/2*b*c^(1/3)*(c^(1/3)*d+e)*arctan((1+2*c^(1/3)*x)/sqrt(3))*sqrt(3)/(c*d^3+e^3)],

# Integrands of the form x^q (d+e x)^m (a+b ArcTanh[c x^(1/2)])^p with c^2 d+e=0
[x^3*(a+b*arctanh(c*sqrt(x)))/(1-c^2*x),x,19,-5/18*b*x^(3/2)/c^5-1/15*b*x^(5/2)/c^3+11/6*b*arctanh(c*sqrt(x))/c^8-x*(a+b*arctanh(c*sqrt(x)))/c^6-1/2*x^2*(a+b*arctanh(c*sqrt(x)))/c^4-1/3*x^3*(a+b*arctanh(c*sqrt(x)))/c^2-(a+b*arctanh(c*sqrt(x)))^2/(b*c^8)+2*(a+b*arctanh(c*sqrt(x)))*log(2/(1-c*sqrt(x)))/c^8+b*polylog(2,1+(-2)/(1-c*sqrt(x)))/c^8-11/6*b*sqrt(x)/c^7],
[x^2*(a+b*arctanh(c*sqrt(x)))/(1-c^2*x),x,14,-1/6*b*x^(3/2)/c^3+3/2*b*arctanh(c*sqrt(x))/c^6-x*(a+b*arctanh(c*sqrt(x)))/c^4-1/2*x^2*(a+b*arctanh(c*sqrt(x)))/c^2-(a+b*arctanh(c*sqrt(x)))^2/(b*c^6)+2*(a+b*arctanh(c*sqrt(x)))*log(2/(1-c*sqrt(x)))/c^6+b*polylog(2,1+(-2)/(1-c*sqrt(x)))/c^6-3/2*b*sqrt(x)/c^5],
[x*(a+b*arctanh(c*sqrt(x)))/(1-c^2*x),x,9,b*arctanh(c*sqrt(x))/c^4-x*(a+b*arctanh(c*sqrt(x)))/c^2-(a+b*arctanh(c*sqrt(x)))^2/(b*c^4)+2*(a+b*arctanh(c*sqrt(x)))*log(2/(1-c*sqrt(x)))/c^4+b*polylog(2,1+(-2)/(1-c*sqrt(x)))/c^4-b*sqrt(x)/c^3],
[(a+b*arctanh(c*sqrt(x)))/(1-c^2*x),x,5,-(a+b*arctanh(c*sqrt(x)))^2/(b*c^2)+2*(a+b*arctanh(c*sqrt(x)))*log(2/(1-c*sqrt(x)))/c^2+b*polylog(2,1+(-2)/(1-c*sqrt(x)))/c^2],
[(a+b*arctanh(c*sqrt(x)))/(x*(1-c^2*x)),x,5,(a+b*arctanh(c*sqrt(x)))^2/b+2*(a+b*arctanh(c*sqrt(x)))*log(2+(-2)/(1+c*sqrt(x)))-b*polylog(2,-1+2/(1+c*sqrt(x)))],
[(a+b*arctanh(c*sqrt(x)))/(x^2*(1-c^2*x)),x,9,b*c^2*arctanh(c*sqrt(x))+(-a-b*arctanh(c*sqrt(x)))/x+c^2*(a+b*arctanh(c*sqrt(x)))^2/b+2*c^2*(a+b*arctanh(c*sqrt(x)))*log(2+(-2)/(1+c*sqrt(x)))-b*c^2*polylog(2,-1+2/(1+c*sqrt(x)))-b*c/sqrt(x)],
[(a+b*arctanh(c*sqrt(x)))/(x^3*(1-c^2*x)),x,14,-1/6*b*c/x^(3/2)+3/2*b*c^4*arctanh(c*sqrt(x))+1/2*(-a-b*arctanh(c*sqrt(x)))/x^2-c^2*(a+b*arctanh(c*sqrt(x)))/x+c^4*(a+b*arctanh(c*sqrt(x)))^2/b+2*c^4*(a+b*arctanh(c*sqrt(x)))*log(2+(-2)/(1+c*sqrt(x)))-b*c^4*polylog(2,-1+2/(1+c*sqrt(x)))-3/2*b*c^3/sqrt(x)],
[(a+b*arctanh(c*sqrt(x)))/(x^4*(1-c^2*x)),x,20,-1/15*b*c/x^(5/2)-5/18*b*c^3/x^(3/2)+11/6*b*c^6*arctanh(c*sqrt(x))+1/3*(-a-b*arctanh(c*sqrt(x)))/x^3-1/2*c^2*(a+b*arctanh(c*sqrt(x)))/x^2-c^4*(a+b*arctanh(c*sqrt(x)))/x+c^6*(a+b*arctanh(c*sqrt(x)))^2/b+2*c^6*(a+b*arctanh(c*sqrt(x)))*log(2+(-2)/(1+c*sqrt(x)))-b*c^6*polylog(2,-1+2/(1+c*sqrt(x)))-11/6*b*c^5/sqrt(x)],

# Integrands of the form x^q (d+e x)^m (a+b ArcTanh[c x^(1/2)])^p
[x^2*(a+b*arctanh(c*sqrt(x)))/(d+e*x),x,20,1/6*b*x^(3/2)/(c*e)+b*d*arctanh(c*sqrt(x))/(c^2*e^2)-1/2*b*arctanh(c*sqrt(x))/(c^4*e)-d*x*(a+b*arctanh(c*sqrt(x)))/e^2+1/2*x^2*(a+b*arctanh(c*sqrt(x)))/e-2*d^2*(a+b*arctanh(c*sqrt(x)))*log(2/(1+c*sqrt(x)))/e^3+d^2*(a+b*arctanh(c*sqrt(x)))*log(2*c*(sqrt(-d)-sqrt(e)*sqrt(x))/((c*sqrt(-d)-sqrt(e))*(1+c*sqrt(x))))/e^3+d^2*(a+b*arctanh(c*sqrt(x)))*log(2*c*(sqrt(-d)+sqrt(e)*sqrt(x))/((c*sqrt(-d)+sqrt(e))*(1+c*sqrt(x))))/e^3+b*d^2*polylog(2,1+(-2)/(1+c*sqrt(x)))/e^3-1/2*b*d^2*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*sqrt(x))/((c*sqrt(-d)-sqrt(e))*(1+c*sqrt(x))))/e^3-1/2*b*d^2*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*sqrt(x))/((c*sqrt(-d)+sqrt(e))*(1+c*sqrt(x))))/e^3-b*d*sqrt(x)/(c*e^2)+1/2*b*sqrt(x)/(c^3*e)],
[x*(a+b*arctanh(c*sqrt(x)))/(d+e*x),x,15,-b*arctanh(c*sqrt(x))/(c^2*e)+x*(a+b*arctanh(c*sqrt(x)))/e+2*d*(a+b*arctanh(c*sqrt(x)))*log(2/(1+c*sqrt(x)))/e^2-d*(a+b*arctanh(c*sqrt(x)))*log(2*c*(sqrt(-d)-sqrt(e)*sqrt(x))/((c*sqrt(-d)-sqrt(e))*(1+c*sqrt(x))))/e^2-d*(a+b*arctanh(c*sqrt(x)))*log(2*c*(sqrt(-d)+sqrt(e)*sqrt(x))/((c*sqrt(-d)+sqrt(e))*(1+c*sqrt(x))))/e^2-b*d*polylog(2,1+(-2)/(1+c*sqrt(x)))/e^2+1/2*b*d*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*sqrt(x))/((c*sqrt(-d)-sqrt(e))*(1+c*sqrt(x))))/e^2+1/2*b*d*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*sqrt(x))/((c*sqrt(-d)+sqrt(e))*(1+c*sqrt(x))))/e^2+b*sqrt(x)/(c*e)],
[(a+b*arctanh(c*sqrt(x)))/(d+e*x),x,11,-2*(a+b*arctanh(c*sqrt(x)))*log(2/(1+c*sqrt(x)))/e+(a+b*arctanh(c*sqrt(x)))*log(2*c*(sqrt(-d)-sqrt(e)*sqrt(x))/((c*sqrt(-d)-sqrt(e))*(1+c*sqrt(x))))/e+(a+b*arctanh(c*sqrt(x)))*log(2*c*(sqrt(-d)+sqrt(e)*sqrt(x))/((c*sqrt(-d)+sqrt(e))*(1+c*sqrt(x))))/e+b*polylog(2,1+(-2)/(1+c*sqrt(x)))/e-1/2*b*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*sqrt(x))/((c*sqrt(-d)-sqrt(e))*(1+c*sqrt(x))))/e-1/2*b*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*sqrt(x))/((c*sqrt(-d)+sqrt(e))*(1+c*sqrt(x))))/e],
[(a+b*arctanh(c*sqrt(x)))/(x*(d+e*x)),x,15,a*log(x)/d+2*(a+b*arctanh(c*sqrt(x)))*log(2/(1+c*sqrt(x)))/d-(a+b*arctanh(c*sqrt(x)))*log(2*c*(sqrt(-d)-sqrt(e)*sqrt(x))/((c*sqrt(-d)-sqrt(e))*(1+c*sqrt(x))))/d-(a+b*arctanh(c*sqrt(x)))*log(2*c*(sqrt(-d)+sqrt(e)*sqrt(x))/((c*sqrt(-d)+sqrt(e))*(1+c*sqrt(x))))/d-b*polylog(2,-c*sqrt(x))/d+b*polylog(2,c*sqrt(x))/d-b*polylog(2,1+(-2)/(1+c*sqrt(x)))/d+1/2*b*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*sqrt(x))/((c*sqrt(-d)-sqrt(e))*(1+c*sqrt(x))))/d+1/2*b*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*sqrt(x))/((c*sqrt(-d)+sqrt(e))*(1+c*sqrt(x))))/d],
[(a+b*arctanh(c*sqrt(x)))/(x^2*(d+e*x)),x,19,b*c^2*arctanh(c*sqrt(x))/d+(-a-b*arctanh(c*sqrt(x)))/(d*x)-a*e*log(x)/d^2-2*e*(a+b*arctanh(c*sqrt(x)))*log(2/(1+c*sqrt(x)))/d^2+e*(a+b*arctanh(c*sqrt(x)))*log(2*c*(sqrt(-d)-sqrt(e)*sqrt(x))/((c*sqrt(-d)-sqrt(e))*(1+c*sqrt(x))))/d^2+e*(a+b*arctanh(c*sqrt(x)))*log(2*c*(sqrt(-d)+sqrt(e)*sqrt(x))/((c*sqrt(-d)+sqrt(e))*(1+c*sqrt(x))))/d^2+b*e*polylog(2,-c*sqrt(x))/d^2-b*e*polylog(2,c*sqrt(x))/d^2+b*e*polylog(2,1+(-2)/(1+c*sqrt(x)))/d^2-1/2*b*e*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*sqrt(x))/((c*sqrt(-d)-sqrt(e))*(1+c*sqrt(x))))/d^2-1/2*b*e*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*sqrt(x))/((c*sqrt(-d)+sqrt(e))*(1+c*sqrt(x))))/d^2-b*c/(d*sqrt(x))],
[(a+b*arctanh(c*sqrt(x)))/(x^3*(d+e*x)),x,24,-1/6*b*c/(d*x^(3/2))+1/2*b*c^4*arctanh(c*sqrt(x))/d-b*c^2*e*arctanh(c*sqrt(x))/d^2+1/2*(-a-b*arctanh(c*sqrt(x)))/(d*x^2)+e*(a+b*arctanh(c*sqrt(x)))/(d^2*x)+a*e^2*log(x)/d^3+2*e^2*(a+b*arctanh(c*sqrt(x)))*log(2/(1+c*sqrt(x)))/d^3-e^2*(a+b*arctanh(c*sqrt(x)))*log(2*c*(sqrt(-d)-sqrt(e)*sqrt(x))/((c*sqrt(-d)-sqrt(e))*(1+c*sqrt(x))))/d^3-e^2*(a+b*arctanh(c*sqrt(x)))*log(2*c*(sqrt(-d)+sqrt(e)*sqrt(x))/((c*sqrt(-d)+sqrt(e))*(1+c*sqrt(x))))/d^3-b*e^2*polylog(2,-c*sqrt(x))/d^3+b*e^2*polylog(2,c*sqrt(x))/d^3-b*e^2*polylog(2,1+(-2)/(1+c*sqrt(x)))/d^3+1/2*b*e^2*polylog(2,1-2*c*(sqrt(-d)-sqrt(e)*sqrt(x))/((c*sqrt(-d)-sqrt(e))*(1+c*sqrt(x))))/d^3+1/2*b*e^2*polylog(2,1-2*c*(sqrt(-d)+sqrt(e)*sqrt(x))/((c*sqrt(-d)+sqrt(e))*(1+c*sqrt(x))))/d^3-1/2*b*c^3/(d*sqrt(x))+b*c*e/(d^2*sqrt(x))]]:
