# Maple integration test file: "7 Inverse hyperbolic functions\7.2 Inverse hyperbolic cosine\7.2.5 Inverse hyperbolic cosine functions.txt"

lst:=[

# Integrands of the form u (a+b ArcCosh[c x])^n

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

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

# n>0
[(d+e*x)^3*arccosh(c*x),x,5,-1/32*(8*c^4*d^4+24*c^2*d^2*e^2+3*e^4)*arccosh(c*x)/(c^4*e)+1/4*(d+e*x)^4*arccosh(c*x)/e-7/48*d*(d+e*x)^2*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/16*(d+e*x)^3*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/96*(4*d*(19*c^2*d^2+16*e^2)+e*(26*c^2*d^2+9*e^2)*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c^3],
[(d+e*x)^2*arccosh(c*x),x,4,-1/6*d*(2*d^2/e+3*e/c^2)*arccosh(c*x)+1/3*(d+e*x)^3*arccosh(c*x)/e-1/9*(d+e*x)^2*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/18*(4*(4*c^2*d^2+e^2)+5*c^2*d*e*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c^3],
[(d+e*x)*arccosh(c*x),x,4,-1/4*(2*d^2/e+e/c^2)*arccosh(c*x)+1/2*(d+e*x)^2*arccosh(c*x)/e-3/4*d*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/4*(d+e*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[arccosh(c*x)/(d+e*x),x,8,-1/2*arccosh(c*x)^2/e+arccosh(c*x)*log(1+e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/e+arccosh(c*x)*log(1+e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/e+polylog(2,-e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/e+polylog(2,-e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/e],
[arccosh(c*x)/(d+e*x)^2,x,3,-arccosh(c*x)/(e*(d+e*x))+2*c*arctanh(sqrt(c*d+e)*sqrt(1+c*x)/(sqrt(c*d-e)*sqrt(-1+c*x)))/(e*sqrt(c*d-e)*sqrt(c*d+e))],
[arccosh(c*x)/(d+e*x)^3,x,4,-1/2*arccosh(c*x)/(e*(d+e*x)^2)+c^3*d*arctanh(sqrt(c*d+e)*sqrt(1+c*x)/(sqrt(c*d-e)*sqrt(-1+c*x)))/((c*d-e)^(3/2)*e*(c*d+e)^(3/2))-1/2*c*sqrt(-1+c*x)*sqrt(1+c*x)/((c^2*d^2-e^2)*(d+e*x))],
[arccosh(c*x)/(d+e*x)^4,x,6,-1/3*arccosh(c*x)/(e*(d+e*x)^3)+1/3*c^3*(2*c^2*d^2+e^2)*arctanh(sqrt(c*d+e)*sqrt(1+c*x)/(sqrt(c*d-e)*sqrt(-1+c*x)))/((c*d-e)^(5/2)*e*(c*d+e)^(5/2))-1/6*c*sqrt(-1+c*x)*sqrt(1+c*x)/((c^2*d^2-e^2)*(d+e*x)^2)-1/2*c^3*d*sqrt(-1+c*x)*sqrt(1+c*x)/((c^2*d^2-e^2)^2*(d+e*x))],
[(d+e*x)^3*arccosh(c*x)^2,x,18,2*d^3*x+4/3*d*e^2*x/c^2+3/4*d^2*e*x^2+3/32*e^3*x^2/c^2+2/9*d*e^2*x^3+1/32*e^3*x^4-1/4*d^4*arccosh(c*x)^2/e-3/4*d^2*e*arccosh(c*x)^2/c^2-3/32*e^3*arccosh(c*x)^2/c^4+1/4*(d+e*x)^4*arccosh(c*x)^2/e-2*d^3*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c-4/3*d*e^2*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-3/2*d^2*e*x*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c-3/16*e^3*x*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-2/3*d*e^2*x^2*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/8*e^3*x^3*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(d+e*x)^2*arccosh(c*x)^2,x,13,2*d^2*x+4/9*e^2*x/c^2+1/2*d*e*x^2+2/27*e^2*x^3-1/3*d^3*arccosh(c*x)^2/e-1/2*d*e*arccosh(c*x)^2/c^2+1/3*(d+e*x)^3*arccosh(c*x)^2/e-2*d^2*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c-4/9*e^2*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-d*e*x*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c-2/9*e^2*x^2*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(d+e*x)*arccosh(c*x)^2,x,9,2*d*x+1/4*e*x^2-1/2*d^2*arccosh(c*x)^2/e-1/4*e*arccosh(c*x)^2/c^2+1/2*(d+e*x)^2*arccosh(c*x)^2/e-2*d*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/2*e*x*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[arccosh(c*x)^2/(d+e*x),x,10,-1/3*arccosh(c*x)^3/e+arccosh(c*x)^2*log(1+e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/e+arccosh(c*x)^2*log(1+e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/e+2*arccosh(c*x)*polylog(2,-e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/e+2*arccosh(c*x)*polylog(2,-e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/e-2*polylog(3,-e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/e-2*polylog(3,-e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/e],
[arccosh(c*x)^2/(d+e*x)^2,x,10,-arccosh(c*x)^2/(e*(d+e*x))+2*c*arccosh(c*x)*log(1+e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/(e*sqrt(c^2*d^2-e^2))-2*c*arccosh(c*x)*log(1+e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/(e*sqrt(c^2*d^2-e^2))+2*c*polylog(2,-e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/(e*sqrt(c^2*d^2-e^2))-2*c*polylog(2,-e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/(e*sqrt(c^2*d^2-e^2))],
[arccosh(c*x)^2/(d+e*x)^3,x,13,-1/2*arccosh(c*x)^2/(e*(d+e*x)^2)+c^2*log(d+e*x)/(e*(c^2*d^2-e^2))+c^3*d*arccosh(c*x)*log(1+e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/(e*(c^2*d^2-e^2)^(3/2))-c^3*d*arccosh(c*x)*log(1+e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/(e*(c^2*d^2-e^2)^(3/2))+c^3*d*polylog(2,-e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/(e*(c^2*d^2-e^2)^(3/2))-c^3*d*polylog(2,-e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/(e*(c^2*d^2-e^2)^(3/2))-c*(1+c*x)*arccosh(c*x)*sqrt((-1+c*x)/(1+c*x))/((c^2*d^2-e^2)*(d+e*x))],

# n<0

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

# n>0
[(d+e*x)^3*(a+b*arccosh(c*x)),x,5,-1/32*b*(8*c^4*d^4+24*c^2*d^2*e^2+3*e^4)*arccosh(c*x)/(c^4*e)+1/4*(d+e*x)^4*(a+b*arccosh(c*x))/e-7/48*b*d*(d+e*x)^2*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/16*b*(d+e*x)^3*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/96*b*(4*d*(19*c^2*d^2+16*e^2)+e*(26*c^2*d^2+9*e^2)*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c^3],
[(d+e*x)^2*(a+b*arccosh(c*x)),x,4,-1/6*b*d*(2*d^2+3*e^2/c^2)*arccosh(c*x)/e+1/3*(d+e*x)^3*(a+b*arccosh(c*x))/e-1/9*b*(d+e*x)^2*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/18*b*(4*(4*c^2*d^2+e^2)+5*c^2*d*e*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c^3],
[(d+e*x)*(a+b*arccosh(c*x)),x,4,-1/4*b*(2*d^2+e^2/c^2)*arccosh(c*x)/e+1/2*(d+e*x)^2*(a+b*arccosh(c*x))/e-3/4*b*d*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/4*b*(d+e*x)*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(a+b*arccosh(c*x))/(d+e*x),x,8,-1/2*(a+b*arccosh(c*x))^2/(b*e)+(a+b*arccosh(c*x))*log(1+e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/e+(a+b*arccosh(c*x))*log(1+e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/e+b*polylog(2,-e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/e+b*polylog(2,-e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/e],
[(a+b*arccosh(c*x))/(d+e*x)^2,x,3,(-a-b*arccosh(c*x))/(e*(d+e*x))+2*b*c*arctanh(sqrt(c*d+e)*sqrt(1+c*x)/(sqrt(c*d-e)*sqrt(-1+c*x)))/(e*sqrt(c*d-e)*sqrt(c*d+e))],
[(a+b*arccosh(c*x))/(d+e*x)^3,x,4,1/2*(-a-b*arccosh(c*x))/(e*(d+e*x)^2)+b*c^3*d*arctanh(sqrt(c*d+e)*sqrt(1+c*x)/(sqrt(c*d-e)*sqrt(-1+c*x)))/((c*d-e)^(3/2)*e*(c*d+e)^(3/2))-1/2*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/((c^2*d^2-e^2)*(d+e*x))],
[(a+b*arccosh(c*x))/(d+e*x)^4,x,6,1/3*(-a-b*arccosh(c*x))/(e*(d+e*x)^3)+1/3*b*c^3*(2*c^2*d^2+e^2)*arctanh(sqrt(c*d+e)*sqrt(1+c*x)/(sqrt(c*d-e)*sqrt(-1+c*x)))/((c*d-e)^(5/2)*e*(c*d+e)^(5/2))-1/6*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/((c^2*d^2-e^2)*(d+e*x)^2)-1/2*b*c^3*d*sqrt(-1+c*x)*sqrt(1+c*x)/((c^2*d^2-e^2)^2*(d+e*x))],
[(d+e*x)^3*(a+b*arccosh(c*x))^2,x,18,2*b^2*d^3*x+4/3*b^2*d*e^2*x/c^2+3/4*b^2*d^2*e*x^2+3/32*b^2*e^3*x^2/c^2+2/9*b^2*d*e^2*x^3+1/32*b^2*e^3*x^4-1/4*d^4*(a+b*arccosh(c*x))^2/e-3/4*d^2*e*(a+b*arccosh(c*x))^2/c^2-3/32*e^3*(a+b*arccosh(c*x))^2/c^4+1/4*(d+e*x)^4*(a+b*arccosh(c*x))^2/e-2*b*d^3*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c-4/3*b*d*e^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-3/2*b*d^2*e*x*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c-3/16*b*e^3*x*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-2/3*b*d*e^2*x^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/8*b*e^3*x^3*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(d+e*x)^2*(a+b*arccosh(c*x))^2,x,13,2*b^2*d^2*x+4/9*b^2*e^2*x/c^2+1/2*b^2*d*e*x^2+2/27*b^2*e^2*x^3-1/3*d^3*(a+b*arccosh(c*x))^2/e-1/2*d*e*(a+b*arccosh(c*x))^2/c^2+1/3*(d+e*x)^3*(a+b*arccosh(c*x))^2/e-2*b*d^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c-4/9*b*e^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-b*d*e*x*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c-2/9*b*e^2*x^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(d+e*x)*(a+b*arccosh(c*x))^2,x,9,2*b^2*d*x+1/4*b^2*e*x^2-1/2*d^2*(a+b*arccosh(c*x))^2/e-1/4*e*(a+b*arccosh(c*x))^2/c^2+1/2*(d+e*x)^2*(a+b*arccosh(c*x))^2/e-2*b*d*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/2*b*e*x*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(a+b*arccosh(c*x))^2/(d+e*x),x,10,-1/3*(a+b*arccosh(c*x))^3/(b*e)+(a+b*arccosh(c*x))^2*log(1+e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/e+(a+b*arccosh(c*x))^2*log(1+e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/e+2*b*(a+b*arccosh(c*x))*polylog(2,-e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/e+2*b*(a+b*arccosh(c*x))*polylog(2,-e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/e-2*b^2*polylog(3,-e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/e-2*b^2*polylog(3,-e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/e],
[(a+b*arccosh(c*x))^2/(d+e*x)^2,x,10,-(a+b*arccosh(c*x))^2/(e*(d+e*x))+2*b*c*(a+b*arccosh(c*x))*log(1+e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/(e*sqrt(c^2*d^2-e^2))-2*b*c*(a+b*arccosh(c*x))*log(1+e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/(e*sqrt(c^2*d^2-e^2))+2*b^2*c*polylog(2,-e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/(e*sqrt(c^2*d^2-e^2))-2*b^2*c*polylog(2,-e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/(e*sqrt(c^2*d^2-e^2))],
[(a+b*arccosh(c*x))^2/(d+e*x)^3,x,13,-1/2*(a+b*arccosh(c*x))^2/(e*(d+e*x)^2)+b^2*c^2*log(d+e*x)/(e*(c^2*d^2-e^2))+b*c^3*d*(a+b*arccosh(c*x))*log(1+e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/(e*(c^2*d^2-e^2)^(3/2))-b*c^3*d*(a+b*arccosh(c*x))*log(1+e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/(e*(c^2*d^2-e^2)^(3/2))+b^2*c^3*d*polylog(2,-e*exp(arccosh(c*x))/(c*d-sqrt(c^2*d^2-e^2)))/(e*(c^2*d^2-e^2)^(3/2))-b^2*c^3*d*polylog(2,-e*exp(arccosh(c*x))/(c*d+sqrt(c^2*d^2-e^2)))/(e*(c^2*d^2-e^2)^(3/2))-b*c*(1+c*x)*(a+b*arccosh(c*x))*sqrt((-1+c*x)/(1+c*x))/((c^2*d^2-e^2)*(d+e*x))],

# n<0
[(d+e*x)^3/(a+b*arccosh(c*x)),x,27,d^3*cosh(a/b)*Shi(a/b+arccosh(c*x))/(b*c)+3/4*d*e^2*cosh(a/b)*Shi(a/b+arccosh(c*x))/(b*c^3)+3/2*d^2*e*cosh(2*a/b)*Shi(2*a/b+2*arccosh(c*x))/(b*c^2)+1/4*e^3*cosh(2*a/b)*Shi(2*a/b+2*arccosh(c*x))/(b*c^4)+3/4*d*e^2*cosh(3*a/b)*Shi(3*a/b+3*arccosh(c*x))/(b*c^3)+1/8*e^3*cosh(4*a/b)*Shi(4*a/b+4*arccosh(c*x))/(b*c^4)-d^3*Chi(a/b+arccosh(c*x))*sinh(a/b)/(b*c)-3/4*d*e^2*Chi(a/b+arccosh(c*x))*sinh(a/b)/(b*c^3)-3/2*d^2*e*Chi(2*a/b+2*arccosh(c*x))*sinh(2*a/b)/(b*c^2)-1/4*e^3*Chi(2*a/b+2*arccosh(c*x))*sinh(2*a/b)/(b*c^4)-3/4*d*e^2*Chi(3*a/b+3*arccosh(c*x))*sinh(3*a/b)/(b*c^3)-1/8*e^3*Chi(4*a/b+4*arccosh(c*x))*sinh(4*a/b)/(b*c^4)],
[(d+e*x)^2/(a+b*arccosh(c*x)),x,17,d^2*cosh(a/b)*Shi(a/b+arccosh(c*x))/(b*c)+1/4*e^2*cosh(a/b)*Shi(a/b+arccosh(c*x))/(b*c^3)+d*e*cosh(2*a/b)*Shi(2*a/b+2*arccosh(c*x))/(b*c^2)+1/4*e^2*cosh(3*a/b)*Shi(3*a/b+3*arccosh(c*x))/(b*c^3)-d^2*Chi(a/b+arccosh(c*x))*sinh(a/b)/(b*c)-1/4*e^2*Chi(a/b+arccosh(c*x))*sinh(a/b)/(b*c^3)-d*e*Chi(2*a/b+2*arccosh(c*x))*sinh(2*a/b)/(b*c^2)-1/4*e^2*Chi(3*a/b+3*arccosh(c*x))*sinh(3*a/b)/(b*c^3)],
[(d+e*x)/(a+b*arccosh(c*x)),x,11,d*cosh(a/b)*Shi(a/b+arccosh(c*x))/(b*c)+1/2*e*cosh(2*a/b)*Shi(2*a/b+2*arccosh(c*x))/(b*c^2)-d*Chi(a/b+arccosh(c*x))*sinh(a/b)/(b*c)-1/2*e*Chi(2*a/b+2*arccosh(c*x))*sinh(2*a/b)/(b*c^2)],
[1/((d+e*x)*(a+b*arccosh(c*x))),x,0,Unintegrable(1/((d+e*x)*(a+b*arccosh(c*x))),x)],
[1/((d+e*x)^2*(a+b*arccosh(c*x))),x,0,Unintegrable(1/((d+e*x)^2*(a+b*arccosh(c*x))),x)],
[(d+e*x)^2/(a+b*arccosh(c*x))^2,x,19,d^2*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)/(b^2*c)+1/4*e^2*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)/(b^2*c^3)+2*d*e*Chi(2*(a+b*arccosh(c*x))/b)*cosh(2*a/b)/(b^2*c^2)+3/4*e^2*Chi(3*(a+b*arccosh(c*x))/b)*cosh(3*a/b)/(b^2*c^3)-d^2*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b^2*c)-1/4*e^2*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b^2*c^3)-2*d*e*Shi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)/(b^2*c^2)-3/4*e^2*Shi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)/(b^2*c^3)-d^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))-2*d*e*x*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))-e^2*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))],
[(d+e*x)/(a+b*arccosh(c*x))^2,x,11,d*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)/(b^2*c)+e*Chi(2*(a+b*arccosh(c*x))/b)*cosh(2*a/b)/(b^2*c^2)-d*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b^2*c)-e*Shi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)/(b^2*c^2)-d*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))-e*x*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))],
[1/((d+e*x)*(a+b*arccosh(c*x))^2),x,0,Unintegrable(1/((d+e*x)*(a+b*arccosh(c*x))^2),x)],
[1/((d+e*x)^2*(a+b*arccosh(c*x))^2),x,0,Unintegrable(1/((d+e*x)^2*(a+b*arccosh(c*x))^2),x)],

# Integrands of the form (d+e x)^m (a+b ArcCosh[c x])^n with m symbolic
[(d+e*x)^m*(a+b*arccosh(c*x))^3,x,1,(d+e*x)^(1+m)*(a+b*arccosh(c*x))^3/(e*(1+m))-3*b*c*Unintegrable((d+e*x)^(1+m)*(a+b*arccosh(c*x))^2/(sqrt(-1+c*x)*sqrt(1+c*x)),x)/(e*(1+m))],
[(d+e*x)^m*(a+b*arccosh(c*x))^2,x,1,(d+e*x)^(1+m)*(a+b*arccosh(c*x))^2/(e*(1+m))-2*b*c*Unintegrable((d+e*x)^(1+m)*(a+b*arccosh(c*x))/(sqrt(-1+c*x)*sqrt(1+c*x)),x)/(e*(1+m))],
[(d+e*x)^m*(a+b*arccosh(c*x)),x,3,(d+e*x)^(1+m)*(a+b*arccosh(c*x))/(e*(1+m))-b*(c*d+e)*(d+e*x)^m*AppellF1(1/2,1/2,-1-m,3/2,1/2*(1-c*x),e*(1-c*x)/(c*d+e))*sqrt(2)*sqrt(-1+c*x)/(c*e*(1+m)*(c*(d+e*x)/(c*d+e))^m)],
[(d+e*x)^m/(a+b*arccosh(c*x)),x,0,Unintegrable((d+e*x)^m/(a+b*arccosh(c*x)),x)],
[(d+e*x)^m/(a+b*arccosh(c*x))^2,x,0,Unintegrable((d+e*x)^m/(a+b*arccosh(c*x))^2,x)],

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

# Integrands of the form (d+e x^2)^p (a+b ArcCosh[c x])^n
[(c+d*x^2)^4*arccosh(a*x),x,6,c^4*x*arccosh(a*x)+4/3*c^3*d*x^3*arccosh(a*x)+6/5*c^2*d^2*x^5*arccosh(a*x)+4/7*c*d^3*x^7*arccosh(a*x)+1/9*d^4*x^9*arccosh(a*x)+1/315*(315*a^8*c^4+420*a^6*c^3*d+378*a^4*c^2*d^2+180*a^2*c*d^3+35*d^4)*(1-a^2*x^2)/(a^9*sqrt(-1+a*x)*sqrt(1+a*x))-4/945*d*(105*a^6*c^3+189*a^4*c^2*d+135*a^2*c*d^2+35*d^3)*(1-a^2*x^2)^2/(a^9*sqrt(-1+a*x)*sqrt(1+a*x))+2/525*d^2*(63*a^4*c^2+90*a^2*c*d+35*d^2)*(1-a^2*x^2)^3/(a^9*sqrt(-1+a*x)*sqrt(1+a*x))-4/441*d^3*(9*a^2*c+7*d)*(1-a^2*x^2)^4/(a^9*sqrt(-1+a*x)*sqrt(1+a*x))+1/81*d^4*(1-a^2*x^2)^5/(a^9*sqrt(-1+a*x)*sqrt(1+a*x))],
[(c+d*x^2)^3*arccosh(a*x),x,6,c^3*x*arccosh(a*x)+c^2*d*x^3*arccosh(a*x)+3/5*c*d^2*x^5*arccosh(a*x)+1/7*d^3*x^7*arccosh(a*x)+1/35*(35*a^6*c^3+35*a^4*c^2*d+21*a^2*c*d^2+5*d^3)*(1-a^2*x^2)/(a^7*sqrt(-1+a*x)*sqrt(1+a*x))-1/105*d*(35*a^4*c^2+42*a^2*c*d+15*d^2)*(1-a^2*x^2)^2/(a^7*sqrt(-1+a*x)*sqrt(1+a*x))+3/175*d^2*(7*a^2*c+5*d)*(1-a^2*x^2)^3/(a^7*sqrt(-1+a*x)*sqrt(1+a*x))-1/49*d^3*(1-a^2*x^2)^4/(a^7*sqrt(-1+a*x)*sqrt(1+a*x))],
[(c+d*x^2)^2*arccosh(a*x),x,6,c^2*x*arccosh(a*x)+2/3*c*d*x^3*arccosh(a*x)+1/5*d^2*x^5*arccosh(a*x)+1/15*(15*a^4*c^2+10*a^2*c*d+3*d^2)*(1-a^2*x^2)/(a^5*sqrt(-1+a*x)*sqrt(1+a*x))-2/45*d*(5*a^2*c+3*d)*(1-a^2*x^2)^2/(a^5*sqrt(-1+a*x)*sqrt(1+a*x))+1/25*d^2*(1-a^2*x^2)^3/(a^5*sqrt(-1+a*x)*sqrt(1+a*x))],
[(c+d*x^2)*arccosh(a*x),x,3,c*x*arccosh(a*x)+1/3*d*x^3*arccosh(a*x)-1/9*(9*a^2*c+2*d)*sqrt(-1+a*x)*sqrt(1+a*x)/a^3-1/9*d*x^2*sqrt(-1+a*x)*sqrt(1+a*x)/a],
[arccosh(a*x)/(c+d*x^2),x,18,1/2*arccosh(a*x)*log(1-exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)-sqrt(-a^2*c-d)))/(sqrt(-c)*sqrt(d))-1/2*arccosh(a*x)*log(1+exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)-sqrt(-a^2*c-d)))/(sqrt(-c)*sqrt(d))+1/2*arccosh(a*x)*log(1-exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)+sqrt(-a^2*c-d)))/(sqrt(-c)*sqrt(d))-1/2*arccosh(a*x)*log(1+exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)+sqrt(-a^2*c-d)))/(sqrt(-c)*sqrt(d))-1/2*polylog(2,-exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)-sqrt(-a^2*c-d)))/(sqrt(-c)*sqrt(d))+1/2*polylog(2,exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)-sqrt(-a^2*c-d)))/(sqrt(-c)*sqrt(d))-1/2*polylog(2,-exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)+sqrt(-a^2*c-d)))/(sqrt(-c)*sqrt(d))+1/2*polylog(2,exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)+sqrt(-a^2*c-d)))/(sqrt(-c)*sqrt(d))],
[arccosh(a*x)/(c+d*x^2)^2,x,26,-1/4*arccosh(a*x)*log(1-exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)-sqrt(-a^2*c-d)))/((-c)^(3/2)*sqrt(d))+1/4*arccosh(a*x)*log(1+exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)-sqrt(-a^2*c-d)))/((-c)^(3/2)*sqrt(d))-1/4*arccosh(a*x)*log(1-exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)+sqrt(-a^2*c-d)))/((-c)^(3/2)*sqrt(d))+1/4*arccosh(a*x)*log(1+exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)+sqrt(-a^2*c-d)))/((-c)^(3/2)*sqrt(d))+1/4*polylog(2,-exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)-sqrt(-a^2*c-d)))/((-c)^(3/2)*sqrt(d))-1/4*polylog(2,exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)-sqrt(-a^2*c-d)))/((-c)^(3/2)*sqrt(d))+1/4*polylog(2,-exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)+sqrt(-a^2*c-d)))/((-c)^(3/2)*sqrt(d))-1/4*polylog(2,exp(arccosh(a*x))*sqrt(d)/(a*sqrt(-c)+sqrt(-a^2*c-d)))/((-c)^(3/2)*sqrt(d))-1/4*arccosh(a*x)/(c*sqrt(d)*(sqrt(-c)-x*sqrt(d)))+1/4*arccosh(a*x)/(c*sqrt(d)*(sqrt(-c)+x*sqrt(d)))+1/2*a*arctanh(sqrt(1+a*x)*sqrt(a*sqrt(-c)-sqrt(d))/(sqrt(-1+a*x)*sqrt(a*sqrt(-c)+sqrt(d))))/(c*sqrt(d)*sqrt(a*sqrt(-c)-sqrt(d))*sqrt(a*sqrt(-c)+sqrt(d)))-1/2*a*arctanh(sqrt(1+a*x)*sqrt(a*sqrt(-c)+sqrt(d))/(sqrt(-1+a*x)*sqrt(a*sqrt(-c)-sqrt(d))))/(c*sqrt(d)*sqrt(a*sqrt(-c)-sqrt(d))*sqrt(a*sqrt(-c)+sqrt(d)))],

# Integrands of the form (d+e x^2)^(p/2) (a+b ArcCosh[c x])^n
[(c+d*x^2)^(1/2)*arccosh(a*x),x,0,Unintegrable(arccosh(a*x)*sqrt(c+d*x^2),x)],
[arccosh(a*x)/(c+d*x^2)^(1/2),x,0,Unintegrable(arccosh(a*x)/sqrt(c+d*x^2),x)],
[arccosh(a*x)/(c+d*x^2)^(3/2),x,7,-arctanh(sqrt(d)*sqrt(-1+a^2*x^2)/(a*sqrt(c+d*x^2)))*sqrt(-1+a^2*x^2)/(c*sqrt(d)*sqrt(-1+a*x)*sqrt(1+a*x))+x*arccosh(a*x)/(c*sqrt(c+d*x^2))],
[arccosh(a*x)/(c+d*x^2)^(5/2),x,8,1/3*x*arccosh(a*x)/(c*(c+d*x^2)^(3/2))-2/3*arctanh(sqrt(d)*sqrt(-1+a^2*x^2)/(a*sqrt(c+d*x^2)))*sqrt(-1+a^2*x^2)/(c^2*sqrt(d)*sqrt(-1+a*x)*sqrt(1+a*x))+2/3*x*arccosh(a*x)/(c^2*sqrt(c+d*x^2))+1/3*a*(1-a^2*x^2)/(c*(a^2*c+d)*sqrt(-1+a*x)*sqrt(1+a*x)*sqrt(c+d*x^2))],
[arccosh(a*x)/(c+d*x^2)^(7/2),x,9,1/5*x*arccosh(a*x)/(c*(c+d*x^2)^(5/2))+4/15*x*arccosh(a*x)/(c^2*(c+d*x^2)^(3/2))+1/15*a*(1-a^2*x^2)/(c*(a^2*c+d)*(c+d*x^2)^(3/2)*sqrt(-1+a*x)*sqrt(1+a*x))-8/15*arctanh(sqrt(d)*sqrt(-1+a^2*x^2)/(a*sqrt(c+d*x^2)))*sqrt(-1+a^2*x^2)/(c^3*sqrt(d)*sqrt(-1+a*x)*sqrt(1+a*x))+8/15*x*arccosh(a*x)/(c^3*sqrt(c+d*x^2))+2/15*a*(3*a^2*c+2*d)*(1-a^2*x^2)/(c^2*(a^2*c+d)^2*sqrt(-1+a*x)*sqrt(1+a*x)*sqrt(c+d*x^2))],
[arccosh(a*x)/(c+d*x^2)^(9/2),x,10,1/7*x*arccosh(a*x)/(c*(c+d*x^2)^(7/2))+6/35*x*arccosh(a*x)/(c^2*(c+d*x^2)^(5/2))+8/35*x*arccosh(a*x)/(c^3*(c+d*x^2)^(3/2))+1/35*a*(1-a^2*x^2)/(c*(a^2*c+d)*(c+d*x^2)^(5/2)*sqrt(-1+a*x)*sqrt(1+a*x))+2/105*a*(5*a^2*c+3*d)*(1-a^2*x^2)/(c^2*(a^2*c+d)^2*(c+d*x^2)^(3/2)*sqrt(-1+a*x)*sqrt(1+a*x))-16/35*arctanh(sqrt(d)*sqrt(-1+a^2*x^2)/(a*sqrt(c+d*x^2)))*sqrt(-1+a^2*x^2)/(c^4*sqrt(d)*sqrt(-1+a*x)*sqrt(1+a*x))+16/35*x*arccosh(a*x)/(c^4*sqrt(c+d*x^2))+4/105*a*(11*a^4*c^2+15*a^2*c*d+6*d^2)*(1-a^2*x^2)/(c^3*(a^2*c+d)^3*sqrt(-1+a*x)*sqrt(1+a*x)*sqrt(c+d*x^2))],

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

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

# p>0
[(f+g*x)^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2),x,17,1/2*f^3*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-3/8*f*g^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+3/4*f*g^2*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-f^2*g*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2-2/15*g^3*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^4-1/5*g^3*x^2*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+b*f^2*g*x*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))+2/15*b*g^3*x*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))-1/4*b*c*f^3*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3/16*b*f*g^2*x^2*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/3*b*c*f^2*g*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/45*b*g^3*x^3*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-3/16*b*c*f*g^2*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/25*b*c*g^3*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/4*f^3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*sqrt(-1+c*x)*sqrt(1+c*x))-3/16*f*g^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f+g*x)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2),x,14,1/2*f^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-1/8*g^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+1/4*g^2*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-2/3*f*g*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+2/3*b*f*g*x*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/4*b*c*f^2*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/16*b*g^2*x^2*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-2/9*b*c*f*g*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/16*b*c*g^2*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/4*f^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*sqrt(-1+c*x)*sqrt(1+c*x))-1/16*g^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f+g*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2),x,9,1/2*f*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-1/3*g*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+1/3*b*g*x*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/4*b*c*f*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/9*b*c*g*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/4*f*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f+g*x),x,23,a*(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(g*(1-c*x)*(1+c*x))+b*arccosh(c*x)*sqrt(d-c^2*d*x^2)/g-b*c*x*sqrt(d-c^2*d*x^2)/(g*sqrt(-1+c*x)*sqrt(1+c*x))-1/2*c*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*g*sqrt(-1+c*x)*sqrt(1+c*x))+1/2*(1-c^2*f^2/g^2)*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*(f+g*x)*sqrt(-1+c*x)*sqrt(1+c*x))-1/2*(1-c^2*x^2)*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*(f+g*x)*sqrt(-1+c*x)*sqrt(1+c*x))+b*arccosh(c*x)*log(1+exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(c^2*f^2-g^2)*sqrt(d-c^2*d*x^2)/(g^2*sqrt(-1+c*x)*sqrt(1+c*x))-b*arccosh(c*x)*log(1+exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(c^2*f^2-g^2)*sqrt(d-c^2*d*x^2)/(g^2*sqrt(-1+c*x)*sqrt(1+c*x))+b*polylog(2,-exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(c^2*f^2-g^2)*sqrt(d-c^2*d*x^2)/(g^2*sqrt(-1+c*x)*sqrt(1+c*x))-b*polylog(2,-exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(c^2*f^2-g^2)*sqrt(d-c^2*d*x^2)/(g^2*sqrt(-1+c*x)*sqrt(1+c*x))-a*arctanh((g+c^2*f*x)/(sqrt(c^2*f^2-g^2)*sqrt(-1+c^2*x^2)))*sqrt(c^2*f^2-g^2)*sqrt(-1+c^2*x^2)*sqrt(d-c^2*d*x^2)/(g^2*(1-c*x)*(1+c*x))],
[(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f+g*x)^2,x,38,-a*sqrt(d-c^2*d*x^2)/(g*(f+g*x))+a*c^3*f^2*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(g^2*(c^2*f^2-g^2)*sqrt(-1+c*x)*sqrt(1+c*x))+1/2*b*c^3*f^2*arccosh(c*x)^2*sqrt(d-c^2*d*x^2)/(g^2*(c^2*f^2-g^2)*sqrt(-1+c*x)*sqrt(1+c*x))-1/2*(g+c^2*f*x)^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*(c^2*f^2-g^2)*(f+g*x)^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/2*(1-c^2*x^2)*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*(f+g*x)^2*sqrt(-1+c*x)*sqrt(1+c*x))+b*c*log(f+g*x)*sqrt(d-c^2*d*x^2)/(g^2*sqrt(-1+c*x)*sqrt(1+c*x))-2*a*c^2*f*arctanh(sqrt(c*f+g)*sqrt(1+c*x)/(sqrt(c*f-g)*sqrt(-1+c*x)))*sqrt(d-c^2*d*x^2)/(g^2*sqrt(c*f-g)*sqrt(c*f+g)*sqrt(-1+c*x)*sqrt(1+c*x))-b*c^2*f*arccosh(c*x)*log(1+exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(d-c^2*d*x^2)/(g^2*sqrt(c^2*f^2-g^2)*sqrt(-1+c*x)*sqrt(1+c*x))+b*c^2*f*arccosh(c*x)*log(1+exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(d-c^2*d*x^2)/(g^2*sqrt(c^2*f^2-g^2)*sqrt(-1+c*x)*sqrt(1+c*x))-b*c^2*f*polylog(2,-exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(d-c^2*d*x^2)/(g^2*sqrt(c^2*f^2-g^2)*sqrt(-1+c*x)*sqrt(1+c*x))+b*c^2*f*polylog(2,-exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(d-c^2*d*x^2)/(g^2*sqrt(c^2*f^2-g^2)*sqrt(-1+c*x)*sqrt(1+c*x))-b*arccosh(c*x)*sqrt((-1+c*x)/(1+c*x))*sqrt(1+c*x)*sqrt(d-c^2*d*x^2)/(g*(f+g*x)*sqrt(-1+c*x))],
[(f+g*x)^3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x)),x,27,3/8*d*f^3*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-3/16*d*f*g^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+3/8*d*f*g^2*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+1/4*d*f^3*x*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+1/2*d*f*g^2*x^3*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-3/5*d*f^2*g*(1-c*x)^2*(1+c*x)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2-2/35*d*g^3*(1-c*x)^2*(1+c*x)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^4-1/7*d*g^3*x^2*(1-c*x)^2*(1+c*x)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+3/5*b*d*f^2*g*x*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))+2/35*b*d*g^3*x*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))-5/16*b*c*d*f^3*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3/32*b*d*f*g^2*x^2*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-2/5*b*c*d*f^2*g*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/105*b*d*g^3*x^3*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))+1/16*b*c^3*d*f^3*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-7/32*b*c*d*f*g^2*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3/25*b*c^3*d*f^2*g*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-8/175*b*c*d*g^3*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/12*b*c^3*d*f*g^2*x^6*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/49*b*c^3*d*g^3*x^7*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3/16*d*f^3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*sqrt(-1+c*x)*sqrt(1+c*x))-3/32*d*f*g^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f+g*x)^2*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x)),x,23,3/8*d*f^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-1/16*d*g^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+1/8*d*g^2*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+1/4*d*f^2*x*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+1/6*d*g^2*x^3*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-2/5*d*f*g*(1-c*x)^2*(1+c*x)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+2/5*b*d*f*g*x*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-5/16*b*c*d*f^2*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/32*b*d*g^2*x^2*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-4/15*b*c*d*f*g*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/16*b*c^3*d*f^2*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-7/96*b*c*d*g^2*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+2/25*b*c^3*d*f*g*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/36*b*c^3*d*g^2*x^6*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3/16*d*f^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*sqrt(-1+c*x)*sqrt(1+c*x))-1/32*d*g^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f+g*x)*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x)),x,14,3/8*d*f*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+1/4*d*f*x*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-1/5*d*g*(1-c*x)^2*(1+c*x)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+1/5*b*d*g*x*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-5/16*b*c*d*f*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2/15*b*c*d*g*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/16*b*c^3*d*f*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/25*b*c^3*d*g*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3/16*d*f*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/(f+g*x),x,-28,-a*d*(c*f-g)*(c*f+g)*sqrt(d-c^2*d*x^2)/g^3+1/6*a*d*(2+3*c*x-2*c^2*x^2)*sqrt(d-c^2*d*x^2)/g-b*d*(c*f-g)*(c*f+g)*arccosh(c*x)*sqrt(d-c^2*d*x^2)/g^3+1/6*b*d*(2+3*c*x-2*c^2*x^2)*arccosh(c*x)*sqrt(d-c^2*d*x^2)/g+1/2*c*d*(c*f-g)*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/g^2+b*c*d*(c*f-g)*(c*f+g)*x*sqrt(d-c^2*d*x^2)/(g^3*sqrt(-1+c*x)*sqrt(1+c*x))-1/4*b*c^2*d*(c*f-g)*x^2*sqrt(d-c^2*d*x^2)/(g^2*sqrt(-1+c*x)*sqrt(1+c*x))+1/36*b*c*d*x*(-12-9*c*x+4*c^2*x^2)*sqrt(d-c^2*d*x^2)/(g*sqrt(-1+c*x)*sqrt(1+c*x))-1/2*a*d*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(g*sqrt(-1+c*x)*sqrt(1+c*x))-1/4*b*d*arccosh(c*x)^2*sqrt(d-c^2*d*x^2)/(g*sqrt(-1+c*x)*sqrt(1+c*x))-1/4*d*(c*f-g)*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*g^2*sqrt(-1+c*x)*sqrt(1+c*x))+1/2*c*d*(c*f-g)*(c*f+g)*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*g^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/2*d*(c*f-g)^2*(c*f+g)^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*g^4*(f+g*x)*sqrt(-1+c*x)*sqrt(1+c*x))+1/2*d*(c*f-g)*(c*f+g)*(1-c^2*x^2)*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*g^2*(f+g*x)*sqrt(-1+c*x)*sqrt(1+c*x))-2*a*d*(c*f-g)^(3/2)*(c*f+g)^(3/2)*arctanh(sqrt(c*f+g)*sqrt(1+c*x)/(sqrt(c*f-g)*sqrt(-1+c*x)))*sqrt(d-c^2*d*x^2)/(g^4*sqrt(-1+c*x)*sqrt(1+c*x))-b*d*(c*f-g)*(c*f+g)*arccosh(c*x)*log(1+exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(c^2*f^2-g^2)*sqrt(d-c^2*d*x^2)/(g^4*sqrt(-1+c*x)*sqrt(1+c*x))+b*d*(c*f-g)*(c*f+g)*arccosh(c*x)*log(1+exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(c^2*f^2-g^2)*sqrt(d-c^2*d*x^2)/(g^4*sqrt(-1+c*x)*sqrt(1+c*x))-b*d*(c*f-g)*(c*f+g)*polylog(2,-exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(c^2*f^2-g^2)*sqrt(d-c^2*d*x^2)/(g^4*sqrt(-1+c*x)*sqrt(1+c*x))+b*d*(c*f-g)*(c*f+g)*polylog(2,-exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(c^2*f^2-g^2)*sqrt(d-c^2*d*x^2)/(g^4*sqrt(-1+c*x)*sqrt(1+c*x))],

#  {(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])/(f + g*x)^2, x, 0, 0} 
[(f+g*x)^3*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x)),x,35,5/16*d^2*f^3*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-15/128*d^2*f*g^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+15/64*d^2*f*g^2*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+5/24*d^2*f^3*x*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+5/16*d^2*f*g^2*x^3*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+1/6*d^2*f^3*x*(1-c*x)^2*(1+c*x)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+3/8*d^2*f*g^2*x^3*(1-c*x)^2*(1+c*x)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-3/7*d^2*f^2*g*(1-c*x)^3*(1+c*x)^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2-2/63*d^2*g^3*(1-c*x)^3*(1+c*x)^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^4-1/9*d^2*g^3*x^2*(1-c*x)^3*(1+c*x)^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+3/7*b*d^2*f^2*g*x*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))+2/63*b*d^2*g^3*x*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))-25/96*b*c*d^2*f^3*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+15/256*b*d^2*f*g^2*x^2*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-3/7*b*c*d^2*f^2*g*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/189*b*d^2*g^3*x^3*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))+5/96*b*c^3*d^2*f^3*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-59/256*b*c*d^2*f*g^2*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+9/35*b*c^3*d^2*f^2*g*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/21*b*c*d^2*g^3*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+17/96*b*c^3*d^2*f*g^2*x^6*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3/49*b*c^5*d^2*f^2*g*x^7*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+19/441*b*c^3*d^2*g^3*x^7*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3/64*b*c^5*d^2*f*g^2*x^8*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/81*b*c^5*d^2*g^3*x^9*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/36*b*d^2*f^3*(1-c^2*x^2)^3*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-5/32*d^2*f^3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*sqrt(-1+c*x)*sqrt(1+c*x))-15/256*d^2*f*g^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f+g*x)^2*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x)),x,31,5/16*d^2*f^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-5/128*d^2*g^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+5/64*d^2*g^2*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+5/24*d^2*f^2*x*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+5/48*d^2*g^2*x^3*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+1/6*d^2*f^2*x*(1-c*x)^2*(1+c*x)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+1/8*d^2*g^2*x^3*(1-c*x)^2*(1+c*x)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-2/7*d^2*f*g*(1-c*x)^3*(1+c*x)^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+2/7*b*d^2*f*g*x*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-25/96*b*c*d^2*f^2*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+5/256*b*d^2*g^2*x^2*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-2/7*b*c*d^2*f*g*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+5/96*b*c^3*d^2*f^2*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-59/768*b*c*d^2*g^2*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+6/35*b*c^3*d^2*f*g*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+17/288*b*c^3*d^2*g^2*x^6*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2/49*b*c^5*d^2*f*g*x^7*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/64*b*c^5*d^2*g^2*x^8*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/36*b*d^2*f^2*(1-c^2*x^2)^3*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-5/32*d^2*f^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*sqrt(-1+c*x)*sqrt(1+c*x))-5/256*d^2*g^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f+g*x)*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x)),x,17,5/16*d^2*f*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+5/24*d^2*f*x*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+1/6*d^2*f*x*(1-c*x)^2*(1+c*x)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-1/7*d^2*g*(1-c*x)^3*(1+c*x)^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+1/7*b*d^2*g*x*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-25/96*b*c*d^2*f*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/7*b*c*d^2*g*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+5/96*b*c^3*d^2*f*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3/35*b*c^3*d^2*g*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/49*b*c^5*d^2*g*x^7*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/36*b*d^2*f*(1-c^2*x^2)^3*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-5/32*d^2*f*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(f+g*x),x,39,a*d^2*(c^2*f^2-g^2)^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(g^5*(1-c*x)*(1+c*x))+b*d^2*(c^2*f^2-g^2)^2*arccosh(c*x)*sqrt(d-c^2*d*x^2)/g^5+1/8*c^2*d^2*f*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/g^2-1/2*c^2*d^2*f*(c^2*f^2-2*g^2)*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/g^4-1/4*c^4*d^2*f*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/g^2-2/15*d^2*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/g-1/3*d^2*(c^2*f^2-2*g^2)*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/g^3-1/5*c^2*d^2*x^2*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/g+2/15*b*c*d^2*x*sqrt(d-c^2*d*x^2)/(g*sqrt(-1+c*x)*sqrt(1+c*x))+1/3*b*c*d^2*(c^2*f^2-2*g^2)*x*sqrt(d-c^2*d*x^2)/(g^3*sqrt(-1+c*x)*sqrt(1+c*x))-b*c*d^2*(c^2*f^2-g^2)^2*x*sqrt(d-c^2*d*x^2)/(g^5*sqrt(-1+c*x)*sqrt(1+c*x))-1/16*b*c^3*d^2*f*x^2*sqrt(d-c^2*d*x^2)/(g^2*sqrt(-1+c*x)*sqrt(1+c*x))+1/4*b*c^3*d^2*f*(c^2*f^2-2*g^2)*x^2*sqrt(d-c^2*d*x^2)/(g^4*sqrt(-1+c*x)*sqrt(1+c*x))+1/45*b*c^3*d^2*x^3*sqrt(d-c^2*d*x^2)/(g*sqrt(-1+c*x)*sqrt(1+c*x))-1/9*b*c^3*d^2*(c^2*f^2-2*g^2)*x^3*sqrt(d-c^2*d*x^2)/(g^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/16*b*c^5*d^2*f*x^4*sqrt(d-c^2*d*x^2)/(g^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/25*b*c^5*d^2*x^5*sqrt(d-c^2*d*x^2)/(g*sqrt(-1+c*x)*sqrt(1+c*x))+1/16*c*d^2*f*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*g^2*sqrt(-1+c*x)*sqrt(1+c*x))+1/4*c*d^2*f*(c^2*f^2-2*g^2)*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*g^4*sqrt(-1+c*x)*sqrt(1+c*x))-1/2*c*d^2*(c^2*f^2-g^2)^2*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*g^5*sqrt(-1+c*x)*sqrt(1+c*x))-1/2*d^2*(c^2*f^2-g^2)^3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*g^6*(f+g*x)*sqrt(-1+c*x)*sqrt(1+c*x))-1/2*d^2*(c^2*f^2-g^2)^2*(1-c^2*x^2)*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c*g^4*(f+g*x)*sqrt(-1+c*x)*sqrt(1+c*x))+b*d^2*(c^2*f^2-g^2)^(5/2)*arccosh(c*x)*log(1+exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(d-c^2*d*x^2)/(g^6*sqrt(-1+c*x)*sqrt(1+c*x))-b*d^2*(c^2*f^2-g^2)^(5/2)*arccosh(c*x)*log(1+exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(d-c^2*d*x^2)/(g^6*sqrt(-1+c*x)*sqrt(1+c*x))+b*d^2*(c^2*f^2-g^2)^(5/2)*polylog(2,-exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(d-c^2*d*x^2)/(g^6*sqrt(-1+c*x)*sqrt(1+c*x))-b*d^2*(c^2*f^2-g^2)^(5/2)*polylog(2,-exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(d-c^2*d*x^2)/(g^6*sqrt(-1+c*x)*sqrt(1+c*x))-a*d^2*(c^2*f^2-g^2)^(5/2)*arctanh((g+c^2*f*x)/(sqrt(c^2*f^2-g^2)*sqrt(-1+c^2*x^2)))*sqrt(-1+c^2*x^2)*sqrt(d-c^2*d*x^2)/(g^6*(1-c*x)*(1+c*x))],

#  {(d - c^2*d*x^2)^(5/2)*(a + b*ArcCosh[c*x])/(f + g*x)^2, x, 0, 0} 

# p<0
[(f+g*x)^3*(a+b*arccosh(c*x))/sqrt(d-c^2*d*x^2),x,13,-3*f^2*g*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))/(c^2*sqrt(d-c^2*d*x^2))-2/3*g^3*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))/(c^4*sqrt(d-c^2*d*x^2))-3/2*f*g^2*x*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))/(c^2*sqrt(d-c^2*d*x^2))-1/3*g^3*x^2*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))/(c^2*sqrt(d-c^2*d*x^2))-3*b*f^2*g*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))-2/3*b*g^3*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*sqrt(d-c^2*d*x^2))-3/4*b*f*g^2*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))-1/9*b*g^3*x^3*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))+1/2*f^3*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*sqrt(d-c^2*d*x^2))+3/4*f*g^2*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^3*sqrt(d-c^2*d*x^2))],
[(f+g*x)^2*(a+b*arccosh(c*x))/sqrt(d-c^2*d*x^2),x,9,-2*f*g*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))/(c^2*sqrt(d-c^2*d*x^2))-1/2*g^2*x*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))/(c^2*sqrt(d-c^2*d*x^2))-2*b*f*g*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))-1/4*b*g^2*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))+1/2*f^2*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*sqrt(d-c^2*d*x^2))+1/4*g^2*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^3*sqrt(d-c^2*d*x^2))],
[(f+g*x)*(a+b*arccosh(c*x))/sqrt(d-c^2*d*x^2),x,6,-g*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))/(c^2*sqrt(d-c^2*d*x^2))-b*g*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))+1/2*f*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))/((f+g*x)*sqrt(d-c^2*d*x^2)),x,10,(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(sqrt(c^2*f^2-g^2)*sqrt(d-c^2*d*x^2))-(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(sqrt(c^2*f^2-g^2)*sqrt(d-c^2*d*x^2))+b*polylog(2,-exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(sqrt(c^2*f^2-g^2)*sqrt(d-c^2*d*x^2))-b*polylog(2,-exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(sqrt(c^2*f^2-g^2)*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))/((f+g*x)^2*sqrt(d-c^2*d*x^2)),x,13,-g*(1+c*x)^(3/2)*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt((-1+c*x)/(1+c*x))/((c^2*f^2-g^2)*(f+g*x)*sqrt(d-c^2*d*x^2))+b*c*log(f+g*x)*sqrt(-1+c*x)*sqrt(1+c*x)/((c^2*f^2-g^2)*sqrt(d-c^2*d*x^2))+c^2*f*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/((c^2*f^2-g^2)^(3/2)*sqrt(d-c^2*d*x^2))-c^2*f*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/((c^2*f^2-g^2)^(3/2)*sqrt(d-c^2*d*x^2))+b*c^2*f*polylog(2,-exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/((c^2*f^2-g^2)^(3/2)*sqrt(d-c^2*d*x^2))-b*c^2*f*polylog(2,-exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/((c^2*f^2-g^2)^(3/2)*sqrt(d-c^2*d*x^2))],
[(f+g*x)^3*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(3/2),x,21,-1/2*(c*f-g)^3*(1-c*x)*(a+b*arccosh(c*x))/(c^4*d*sqrt(d-c^2*d*x^2))+1/2*(c*f+g)^3*(1+c*x)*(a+b*arccosh(c*x))/(c^4*d*sqrt(d-c^2*d*x^2))+g^3*(1-c*x)*(1+c*x)*(a+b*arccosh(c*x))/(c^4*d*sqrt(d-c^2*d*x^2))+b*g^3*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d*sqrt(d-c^2*d*x^2))-3/2*f*g^2*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^3*d*sqrt(d-c^2*d*x^2))-1/2*b*(c*f-g)^3*log(2/(1+c*x))*sqrt((1-c*x)*(1+c*x))*sqrt(1-c^2*x^2)/(c^4*d*(1+c*x)*sqrt((-1+c*x)/(1+c*x))*sqrt(d-c^2*d*x^2))-1/2*b*(c*f+g)^3*log(2/(1+c*x))*sqrt((1-c*x)*(1+c*x))*sqrt(1-c^2*x^2)/(c^4*d*(1+c*x)*sqrt((-1+c*x)/(1+c*x))*sqrt(d-c^2*d*x^2))+b*(c*f+g)^3*log(sqrt((-1+c*x)/(1+c*x)))*sqrt((1-c*x)*(1+c*x))*sqrt(1-c^2*x^2)/(c^4*d*(1+c*x)*sqrt((-1+c*x)/(1+c*x))*sqrt(d-c^2*d*x^2))],
[(f+g*x)^2*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(3/2),x,19,-1/2*(c*f-g)^2*(1-c*x)*(a+b*arccosh(c*x))/(c^3*d*sqrt(d-c^2*d*x^2))+1/2*(c*f+g)^2*(1+c*x)*(a+b*arccosh(c*x))/(c^3*d*sqrt(d-c^2*d*x^2))-1/2*g^2*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^3*d*sqrt(d-c^2*d*x^2))-1/2*b*(c*f-g)^2*log(2/(1+c*x))*sqrt((1-c*x)*(1+c*x))*sqrt(1-c^2*x^2)/(c^3*d*(1+c*x)*sqrt((-1+c*x)/(1+c*x))*sqrt(d-c^2*d*x^2))-1/2*b*(c*f+g)^2*log(2/(1+c*x))*sqrt((1-c*x)*(1+c*x))*sqrt(1-c^2*x^2)/(c^3*d*(1+c*x)*sqrt((-1+c*x)/(1+c*x))*sqrt(d-c^2*d*x^2))+b*(c*f+g)^2*log(sqrt((-1+c*x)/(1+c*x)))*sqrt((1-c*x)*(1+c*x))*sqrt(1-c^2*x^2)/(c^3*d*(1+c*x)*sqrt((-1+c*x)/(1+c*x))*sqrt(d-c^2*d*x^2))],
[(f+g*x)*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(3/2),x,5,(g+c^2*f*x)*(a+b*arccosh(c*x))/(c^2*d*sqrt(d-c^2*d*x^2))-b*(c*f-g)*arctanh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*d*sqrt(d-c^2*d*x^2))-b*f*log(1-c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d*sqrt(d-c^2*d*x^2)),-(c*f-g)*(a+b*arccosh(c*x))/(c^2*d*sqrt(d-c^2*d*x^2))+f*(1+c*x)*(a+b*arccosh(c*x))/(c*d*sqrt(d-c^2*d*x^2))-b*(c*f-g)*arctanh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*d*sqrt(d-c^2*d*x^2))-b*f*log(1-c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))/((f+g*x)*(d-c^2*d*x^2)^(3/2)),x,27,-1/2*(1-c*x)*(a+b*arccosh(c*x))/(d*(c*f-g)*sqrt(d-c^2*d*x^2))+1/2*(1+c*x)*(a+b*arccosh(c*x))/(d*(c*f+g)*sqrt(d-c^2*d*x^2))-g^2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*(c^2*f^2-g^2)^(3/2)*sqrt(d-c^2*d*x^2))+g^2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*(c^2*f^2-g^2)^(3/2)*sqrt(d-c^2*d*x^2))-b*g^2*polylog(2,-exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*(c^2*f^2-g^2)^(3/2)*sqrt(d-c^2*d*x^2))+b*g^2*polylog(2,-exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*(c^2*f^2-g^2)^(3/2)*sqrt(d-c^2*d*x^2))-1/2*b*log(2/(1+c*x))*sqrt((1-c*x)*(1+c*x))*sqrt(1-c^2*x^2)/(d*(c*f-g)*(1+c*x)*sqrt((-1+c*x)/(1+c*x))*sqrt(d-c^2*d*x^2))-1/2*b*log(2/(1+c*x))*sqrt((1-c*x)*(1+c*x))*sqrt(1-c^2*x^2)/(d*(c*f+g)*(1+c*x)*sqrt((-1+c*x)/(1+c*x))*sqrt(d-c^2*d*x^2))+b*log(sqrt((-1+c*x)/(1+c*x)))*sqrt((1-c*x)*(1+c*x))*sqrt(1-c^2*x^2)/(d*(c*f+g)*(1+c*x)*sqrt((-1+c*x)/(1+c*x))*sqrt(d-c^2*d*x^2))],

#  {1/(d - c^2*d*x^2)^(3/2)*(a + b*ArcCosh[c*x])/(f + g*x)^2, x, 0, 0} 

# Integrands of the form (f+g x)^m (d1+c d1 x)^(p/2) (d2-c d2 x)^(p/2) (a+b ArcCosh[c x])^n
[(f+g*x)*(a+b*arccosh(c*x))^n/sqrt(1-c^2*x^2),x,7,f*(a+b*arccosh(c*x))^(1+n)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(1+n)*sqrt(1-c^2*x^2))+1/2*g*(a+b*arccosh(c*x))^n*GAMMA(1+n,(-a-b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*exp(a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(1-c^2*x^2))-1/2*exp(a/b)*g*(a+b*arccosh(c*x))^n*GAMMA(1+n,(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*((a+b*arccosh(c*x))/b)^n*sqrt(1-c^2*x^2))],
[(f+g*x)*(a+b*arccosh(c*x))^n/(sqrt(1-c*x)*sqrt(1+c*x)),x,7,f*(a+b*arccosh(c*x))^(1+n)*sqrt(-1+c*x)/(b*c*(1+n)*sqrt(1-c*x))+1/2*g*(a+b*arccosh(c*x))^n*GAMMA(1+n,(-a-b*arccosh(c*x))/b)*sqrt(-1+c*x)/(c^2*exp(a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(1-c*x))-1/2*exp(a/b)*g*(a+b*arccosh(c*x))^n*GAMMA(1+n,(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(c^2*((a+b*arccosh(c*x))/b)^n*sqrt(1-c*x))],
[(f+g*x)*(a+b*arccosh(c*x))^n/(sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)),x,7,f*(a+b*arccosh(c*x))^(1+n)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(1+n)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))+1/2*g*(a+b*arccosh(c*x))^n*GAMMA(1+n,(-a-b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*exp(a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))-1/2*exp(a/b)*g*(a+b*arccosh(c*x))^n*GAMMA(1+n,(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*((a+b*arccosh(c*x))/b)^n*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))],

# Integrands of the form Log[h (f + g x)^m] (d+e x^2)^p (a+b ArcCosh[c x])^n

# Integrands of the form Log[h (f + g x)^m] (d-c^2 d x^2)^(p/2) (a+b ArcCosh[c x])^n

# p>0

# p<0
[(a+b*arccosh(c*x))^n*log(h*(f+g*x)^m)/sqrt(1-c^2*x^2),x,1,sqrt(-1+c*x)*sqrt(1+c*x)*Unintegrable((a+b*arccosh(c*x))^n*log(h*(f+g*x)^m)/(sqrt(-1+c*x)*sqrt(1+c*x)),x)/sqrt(1-c^2*x^2)],

#  {Log[h*(f + g*x)^m]*(a + b*ArcCosh[c*x])^3/Sqrt[1 - c^2*x^2], x, 0, 0} 
[(a+b*arccosh(c*x))^2*log(h*(f+g*x)^m)/sqrt(1-c^2*x^2),x,14,1/12*m*(a+b*arccosh(c*x))^4*sqrt(-1+c*x)*sqrt(1+c*x)/(b^2*c*sqrt(1-c^2*x^2))+1/3*(a+b*arccosh(c*x))^3*log(h*(f+g*x)^m)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*sqrt(1-c^2*x^2))-1/3*m*(a+b*arccosh(c*x))^3*log(1+exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*sqrt(1-c^2*x^2))-1/3*m*(a+b*arccosh(c*x))^3*log(1+exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*sqrt(1-c^2*x^2))-m*(a+b*arccosh(c*x))^2*polylog(2,-exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(1-c^2*x^2))-m*(a+b*arccosh(c*x))^2*polylog(2,-exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(1-c^2*x^2))+2*b*m*(a+b*arccosh(c*x))*polylog(3,-exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(1-c^2*x^2))+2*b*m*(a+b*arccosh(c*x))*polylog(3,-exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(1-c^2*x^2))-2*b^2*m*polylog(4,-exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(1-c^2*x^2))-2*b^2*m*polylog(4,-exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(1-c^2*x^2))],
[(a+b*arccosh(c*x))*log(h*(f+g*x)^m)/sqrt(1-c^2*x^2),x,12,1/6*m*(a+b*arccosh(c*x))^3*sqrt(-1+c*x)*sqrt(1+c*x)/(b^2*c*sqrt(1-c^2*x^2))+1/2*(a+b*arccosh(c*x))^2*log(h*(f+g*x)^m)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*sqrt(1-c^2*x^2))-1/2*m*(a+b*arccosh(c*x))^2*log(1+exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*sqrt(1-c^2*x^2))-1/2*m*(a+b*arccosh(c*x))^2*log(1+exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*sqrt(1-c^2*x^2))-m*(a+b*arccosh(c*x))*polylog(2,-exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(1-c^2*x^2))-m*(a+b*arccosh(c*x))*polylog(2,-exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(1-c^2*x^2))+b*m*polylog(3,-exp(arccosh(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(1-c^2*x^2))+b*m*polylog(3,-exp(arccosh(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(1-c^2*x^2))],
[log(h*(f+g*x)^m)/sqrt(1-c^2*x^2),x,9,1/2*I*m*arcsin(c*x)^2/c+arcsin(c*x)*log(h*(f+g*x)^m)/c-m*arcsin(c*x)*log(1-I*exp(I*arcsin(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))/c-m*arcsin(c*x)*log(1-I*exp(I*arcsin(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))/c+I*m*polylog(2,I*exp(I*arcsin(c*x))*g/(c*f-sqrt(c^2*f^2-g^2)))/c+I*m*polylog(2,I*exp(I*arcsin(c*x))*g/(c*f+sqrt(c^2*f^2-g^2)))/c],
[log(h*(f+g*x)^m)/((a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x,1,sqrt(-1+c*x)*sqrt(1+c*x)*Unintegrable(log(h*(f+g*x)^m)/((a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)),x)/sqrt(1-c^2*x^2)],

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

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

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

# n>0
[x^3*arccosh(a+b*x),x,6,-1/32*(3+24*a^2+8*a^4)*arccosh(a+b*x)/b^4+1/4*x^4*arccosh(a+b*x)+7/48*a*x^2*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/b^2-1/16*x^3*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/b+1/96*(4*a*(16+19*a^2)-(9+26*a^2)*(a+b*x))*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/b^4],
[x^2*arccosh(a+b*x),x,5,1/6*a*(3+2*a^2)*arccosh(a+b*x)/b^3+1/3*x^3*arccosh(a+b*x)-1/9*x^2*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/b-1/18*(4+11*a^2-5*a*b*x)*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/b^3],
[x*arccosh(a+b*x),x,5,-1/4*(1+2*a^2)*arccosh(a+b*x)/b^2+1/2*x^2*arccosh(a+b*x)+3/4*a*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/b^2-1/4*x*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/b],
[arccosh(a+b*x),x,3,(a+b*x)*arccosh(a+b*x)/b-sqrt(-1+a+b*x)*sqrt(1+a+b*x)/b],
[arccosh(a+b*x)/x,x,9,-1/2*arccosh(a+b*x)^2+arccosh(a+b*x)*log(1-exp(arccosh(a+b*x))/(a-sqrt(-1+a^2)))+arccosh(a+b*x)*log(1-exp(arccosh(a+b*x))/(a+sqrt(-1+a^2)))+polylog(2,exp(arccosh(a+b*x))/(a-sqrt(-1+a^2)))+polylog(2,exp(arccosh(a+b*x))/(a+sqrt(-1+a^2)))],
[arccosh(a+b*x)/x^2,x,4,-arccosh(a+b*x)/x-2*b*arctan(sqrt(1-a)*sqrt(1+a+b*x)/(sqrt(1+a)*sqrt(-1+a+b*x)))/sqrt(1-a^2)],
[arccosh(a+b*x)/x^3,x,5,-1/2*arccosh(a+b*x)/x^2-a*b^2*arctan(sqrt(1-a)*sqrt(1+a+b*x)/(sqrt(1+a)*sqrt(-1+a+b*x)))/(1-a^2)^(3/2)+1/2*b*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/((1-a^2)*x)],
[arccosh(a+b*x)/x^4,x,7,-1/3*arccosh(a+b*x)/x^3-1/3*(1+2*a^2)*b^3*arctan(sqrt(1-a)*sqrt(1+a+b*x)/(sqrt(1+a)*sqrt(-1+a+b*x)))/(1-a^2)^(5/2)+1/6*b*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/((1-a^2)*x^2)+1/2*a*b^2*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/((1-a^2)^2*x)],

# n<0

# Integrands of the form x^m (a+b ArcCosh[c+d x])^(n/2)
[1/sqrt(a+b*arccosh(c+d*x)),x,7,-1/2*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*sqrt(b))+1/2*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(a/b)*sqrt(b))],
[1/sqrt(a-b*arccosh(c+d*x)),x,7,-1/2*exp(a/b)*erf(sqrt(a-b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*sqrt(b))+1/2*erfi(sqrt(a-b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(a/b)*sqrt(b))],

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

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

# n>0
[(c*e+d*e*x)^4*(a+b*arccosh(c+d*x)),x,8,1/5*e^4*(c+d*x)^5*(a+b*arccosh(c+d*x))/d-8/75*b*e^4*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-4/75*b*e^4*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-1/25*b*e^4*(c+d*x)^4*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(c*e+d*e*x)^3*(a+b*arccosh(c+d*x)),x,7,-3/32*b*e^3*arccosh(c+d*x)/d+1/4*e^3*(c+d*x)^4*(a+b*arccosh(c+d*x))/d-3/32*b*e^3*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-1/16*b*e^3*(c+d*x)^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(c*e+d*e*x)^2*(a+b*arccosh(c+d*x)),x,6,1/3*e^2*(c+d*x)^3*(a+b*arccosh(c+d*x))/d-2/9*b*e^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-1/9*b*e^2*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(c*e+d*e*x)*(a+b*arccosh(c+d*x)),x,5,-1/4*b*e*arccosh(c+d*x)/d+1/2*e*(c+d*x)^2*(a+b*arccosh(c+d*x))/d-1/4*b*e*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[a+b*arccosh(c+d*x),x,4,a*x+b*(c+d*x)*arccosh(c+d*x)/d-b*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(a+b*arccosh(c+d*x))/(c*e+d*e*x),x,7,1/2*(a+b*arccosh(c+d*x))^2/(b*d*e)+(a+b*arccosh(c+d*x))*log(1+exp(-2*arccosh(c+d*x)))/(d*e)-1/2*b*polylog(2,(-1)/exp(2*arccosh(c+d*x)))/(d*e)],
[(a+b*arccosh(c+d*x))/(c*e+d*e*x)^2,x,5,(-a-b*arccosh(c+d*x))/(d*e^2*(c+d*x))+b*arctan(sqrt(-1+c+d*x)*sqrt(1+c+d*x))/(d*e^2)],
[(a+b*arccosh(c+d*x))/(c*e+d*e*x)^3,x,4,1/2*(-a-b*arccosh(c+d*x))/(d*e^3*(c+d*x)^2)+1/2*b*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^3*(c+d*x))],
[(a+b*arccosh(c+d*x))/(c*e+d*e*x)^4,x,6,1/3*(-a-b*arccosh(c+d*x))/(d*e^4*(c+d*x)^3)+1/6*b*arctan(sqrt(-1+c+d*x)*sqrt(1+c+d*x))/(d*e^4)+1/6*b*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^4*(c+d*x)^2)],
[(a+b*arccosh(c+d*x))/(c*e+d*e*x)^5,x,6,1/4*(-a-b*arccosh(c+d*x))/(d*e^5*(c+d*x)^4)+1/12*b*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^5*(c+d*x)^3)+1/6*b*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^5*(c+d*x))],
[(a+b*arccosh(c+d*x))/(c*e+d*e*x)^6,x,8,1/5*(-a-b*arccosh(c+d*x))/(d*e^6*(c+d*x)^5)+3/40*b*arctan(sqrt(-1+c+d*x)*sqrt(1+c+d*x))/(d*e^6)+1/20*b*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^6*(c+d*x)^4)+3/40*b*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^6*(c+d*x)^2)],
[(c*e+d*e*x)^4*(a+b*arccosh(c+d*x))^2,x,9,16/75*b^2*e^4*x+8/225*b^2*e^4*(c+d*x)^3/d+2/125*b^2*e^4*(c+d*x)^5/d+1/5*e^4*(c+d*x)^5*(a+b*arccosh(c+d*x))^2/d-16/75*b*e^4*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-8/75*b*e^4*(c+d*x)^2*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-2/25*b*e^4*(c+d*x)^4*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(c*e+d*e*x)^3*(a+b*arccosh(c+d*x))^2,x,8,3/32*b^2*e^3*(c+d*x)^2/d+1/32*b^2*e^3*(c+d*x)^4/d-3/32*e^3*(a+b*arccosh(c+d*x))^2/d+1/4*e^3*(c+d*x)^4*(a+b*arccosh(c+d*x))^2/d-3/16*b*e^3*(c+d*x)*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-1/8*b*e^3*(c+d*x)^3*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(c*e+d*e*x)^2*(a+b*arccosh(c+d*x))^2,x,7,4/9*b^2*e^2*x+2/27*b^2*e^2*(c+d*x)^3/d+1/3*e^2*(c+d*x)^3*(a+b*arccosh(c+d*x))^2/d-4/9*b*e^2*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-2/9*b*e^2*(c+d*x)^2*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(c*e+d*e*x)*(a+b*arccosh(c+d*x))^2,x,6,1/4*b^2*e*(c+d*x)^2/d-1/4*e*(a+b*arccosh(c+d*x))^2/d+1/2*e*(c+d*x)^2*(a+b*arccosh(c+d*x))^2/d-1/2*b*e*(c+d*x)*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(a+b*arccosh(c+d*x))^2,x,4,2*b^2*x+(c+d*x)*(a+b*arccosh(c+d*x))^2/d-2*b*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(a+b*arccosh(c+d*x))^2/(c*e+d*e*x),x,8,1/3*(a+b*arccosh(c+d*x))^3/(b*d*e)+(a+b*arccosh(c+d*x))^2*log(1+exp(-2*arccosh(c+d*x)))/(d*e)-b*(a+b*arccosh(c+d*x))*polylog(2,(-1)/exp(2*arccosh(c+d*x)))/(d*e)-1/2*b^2*polylog(3,(-1)/exp(2*arccosh(c+d*x)))/(d*e)],
[(a+b*arccosh(c+d*x))^2/(c*e+d*e*x)^2,x,9,-(a+b*arccosh(c+d*x))^2/(d*e^2*(c+d*x))+4*b*(a+b*arccosh(c+d*x))*arctan(exp(arccosh(c+d*x)))/(d*e^2)-2*I*b^2*polylog(2,-I*exp(arccosh(c+d*x)))/(d*e^2)+2*I*b^2*polylog(2,I*exp(arccosh(c+d*x)))/(d*e^2)],
[(a+b*arccosh(c+d*x))^2/(c*e+d*e*x)^3,x,5,-1/2*(a+b*arccosh(c+d*x))^2/(d*e^3*(c+d*x)^2)-b^2*log(c+d*x)/(d*e^3)+b*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^3*(c+d*x))],
[(a+b*arccosh(c+d*x))^2/(c*e+d*e*x)^4,x,11,1/3*b^2/(d*e^4*(c+d*x))-1/3*(a+b*arccosh(c+d*x))^2/(d*e^4*(c+d*x)^3)+2/3*b*(a+b*arccosh(c+d*x))*arctan(exp(arccosh(c+d*x)))/(d*e^4)-1/3*I*b^2*polylog(2,-I*exp(arccosh(c+d*x)))/(d*e^4)+1/3*I*b^2*polylog(2,I*exp(arccosh(c+d*x)))/(d*e^4)+1/3*b*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^4*(c+d*x)^2)],
[(c*e+d*e*x)^4*(a+b*arccosh(c+d*x))^3,x,19,16/25*a*b^2*e^4*x+16/25*b^3*e^4*(c+d*x)*arccosh(c+d*x)/d+8/75*b^2*e^4*(c+d*x)^3*(a+b*arccosh(c+d*x))/d+6/125*b^2*e^4*(c+d*x)^5*(a+b*arccosh(c+d*x))/d+1/5*e^4*(c+d*x)^5*(a+b*arccosh(c+d*x))^3/d-4144/5625*b^3*e^4*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-272/5625*b^3*e^4*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-6/625*b^3*e^4*(c+d*x)^4*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-8/25*b*e^4*(a+b*arccosh(c+d*x))^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-4/25*b*e^4*(c+d*x)^2*(a+b*arccosh(c+d*x))^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-3/25*b*e^4*(c+d*x)^4*(a+b*arccosh(c+d*x))^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(c*e+d*e*x)^3*(a+b*arccosh(c+d*x))^3,x,14,-45/256*b^3*e^3*arccosh(c+d*x)/d+9/32*b^2*e^3*(c+d*x)^2*(a+b*arccosh(c+d*x))/d+3/32*b^2*e^3*(c+d*x)^4*(a+b*arccosh(c+d*x))/d-3/32*e^3*(a+b*arccosh(c+d*x))^3/d+1/4*e^3*(c+d*x)^4*(a+b*arccosh(c+d*x))^3/d-45/256*b^3*e^3*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-3/128*b^3*e^3*(c+d*x)^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-9/32*b*e^3*(c+d*x)*(a+b*arccosh(c+d*x))^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-3/16*b*e^3*(c+d*x)^3*(a+b*arccosh(c+d*x))^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(c*e+d*e*x)^2*(a+b*arccosh(c+d*x))^3,x,12,4/3*a*b^2*e^2*x+4/3*b^3*e^2*(c+d*x)*arccosh(c+d*x)/d+2/9*b^2*e^2*(c+d*x)^3*(a+b*arccosh(c+d*x))/d+1/3*e^2*(c+d*x)^3*(a+b*arccosh(c+d*x))^3/d-40/27*b^3*e^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-2/27*b^3*e^2*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-2/3*b*e^2*(a+b*arccosh(c+d*x))^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-1/3*b*e^2*(c+d*x)^2*(a+b*arccosh(c+d*x))^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(c*e+d*e*x)*(a+b*arccosh(c+d*x))^3,x,8,-3/8*b^3*e*arccosh(c+d*x)/d+3/4*b^2*e*(c+d*x)^2*(a+b*arccosh(c+d*x))/d-1/4*e*(a+b*arccosh(c+d*x))^3/d+1/2*e*(c+d*x)^2*(a+b*arccosh(c+d*x))^3/d-3/8*b^3*e*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-3/4*b*e*(c+d*x)*(a+b*arccosh(c+d*x))^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(a+b*arccosh(c+d*x))^3,x,6,6*a*b^2*x+6*b^3*(c+d*x)*arccosh(c+d*x)/d+(c+d*x)*(a+b*arccosh(c+d*x))^3/d-6*b^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-3*b*(a+b*arccosh(c+d*x))^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(a+b*arccosh(c+d*x))^3/(c*e+d*e*x),x,9,1/4*(a+b*arccosh(c+d*x))^4/(b*d*e)+(a+b*arccosh(c+d*x))^3*log(1+exp(-2*arccosh(c+d*x)))/(d*e)-3/2*b*(a+b*arccosh(c+d*x))^2*polylog(2,(-1)/exp(2*arccosh(c+d*x)))/(d*e)-3/2*b^2*(a+b*arccosh(c+d*x))*polylog(3,(-1)/exp(2*arccosh(c+d*x)))/(d*e)-3/4*b^3*polylog(4,(-1)/exp(2*arccosh(c+d*x)))/(d*e)],
[(a+b*arccosh(c+d*x))^3/(c*e+d*e*x)^2,x,11,-(a+b*arccosh(c+d*x))^3/(d*e^2*(c+d*x))+6*b*(a+b*arccosh(c+d*x))^2*arctan(exp(arccosh(c+d*x)))/(d*e^2)-6*I*b^2*(a+b*arccosh(c+d*x))*polylog(2,-I*exp(arccosh(c+d*x)))/(d*e^2)+6*I*b^2*(a+b*arccosh(c+d*x))*polylog(2,I*exp(arccosh(c+d*x)))/(d*e^2)+6*I*b^3*polylog(3,-I*exp(arccosh(c+d*x)))/(d*e^2)-6*I*b^3*polylog(3,I*exp(arccosh(c+d*x)))/(d*e^2)],
[(a+b*arccosh(c+d*x))^3/(c*e+d*e*x)^3,x,9,-3/2*b*(a+b*arccosh(c+d*x))^2/(d*e^3)-1/2*(a+b*arccosh(c+d*x))^3/(d*e^3*(c+d*x)^2)-3*b^2*(a+b*arccosh(c+d*x))*log(1+exp(-2*arccosh(c+d*x)))/(d*e^3)+3/2*b^3*polylog(2,(-1)/exp(2*arccosh(c+d*x)))/(d*e^3)+3/2*b*(a+b*arccosh(c+d*x))^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^3*(c+d*x))],
[(a+b*arccosh(c+d*x))^3/(c*e+d*e*x)^4,x,15,b^2*(a+b*arccosh(c+d*x))/(d*e^4*(c+d*x))-1/3*(a+b*arccosh(c+d*x))^3/(d*e^4*(c+d*x)^3)+b*(a+b*arccosh(c+d*x))^2*arctan(exp(arccosh(c+d*x)))/(d*e^4)-b^3*arctan(sqrt(-1+c+d*x)*sqrt(1+c+d*x))/(d*e^4)-I*b^2*(a+b*arccosh(c+d*x))*polylog(2,-I*exp(arccosh(c+d*x)))/(d*e^4)+I*b^2*(a+b*arccosh(c+d*x))*polylog(2,I*exp(arccosh(c+d*x)))/(d*e^4)+I*b^3*polylog(3,-I*exp(arccosh(c+d*x)))/(d*e^4)-I*b^3*polylog(3,I*exp(arccosh(c+d*x)))/(d*e^4)+1/2*b*(a+b*arccosh(c+d*x))^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^4*(c+d*x)^2)],
[(c*e+d*e*x)^3*(a+b*arccosh(c+d*x))^4,x,16,45/128*b^4*e^3*(c+d*x)^2/d+3/128*b^4*e^3*(c+d*x)^4/d-45/128*b^2*e^3*(a+b*arccosh(c+d*x))^2/d+9/16*b^2*e^3*(c+d*x)^2*(a+b*arccosh(c+d*x))^2/d+3/16*b^2*e^3*(c+d*x)^4*(a+b*arccosh(c+d*x))^2/d-3/32*e^3*(a+b*arccosh(c+d*x))^4/d+1/4*e^3*(c+d*x)^4*(a+b*arccosh(c+d*x))^4/d-45/64*b^3*e^3*(c+d*x)*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-3/32*b^3*e^3*(c+d*x)^3*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-3/8*b*e^3*(c+d*x)*(a+b*arccosh(c+d*x))^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-1/4*b*e^3*(c+d*x)^3*(a+b*arccosh(c+d*x))^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(c*e+d*e*x)^2*(a+b*arccosh(c+d*x))^4,x,13,160/27*b^4*e^2*x+8/81*b^4*e^2*(c+d*x)^3/d+8/3*b^2*e^2*(c+d*x)*(a+b*arccosh(c+d*x))^2/d+4/9*b^2*e^2*(c+d*x)^3*(a+b*arccosh(c+d*x))^2/d+1/3*e^2*(c+d*x)^3*(a+b*arccosh(c+d*x))^4/d-160/27*b^3*e^2*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-8/27*b^3*e^2*(c+d*x)^2*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-8/9*b*e^2*(a+b*arccosh(c+d*x))^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-4/9*b*e^2*(c+d*x)^2*(a+b*arccosh(c+d*x))^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(c*e+d*e*x)*(a+b*arccosh(c+d*x))^4,x,9,3/4*b^4*e*(c+d*x)^2/d-3/4*b^2*e*(a+b*arccosh(c+d*x))^2/d+3/2*b^2*e*(c+d*x)^2*(a+b*arccosh(c+d*x))^2/d-1/4*e*(a+b*arccosh(c+d*x))^4/d+1/2*e*(c+d*x)^2*(a+b*arccosh(c+d*x))^4/d-3/2*b^3*e*(c+d*x)*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-b*e*(c+d*x)*(a+b*arccosh(c+d*x))^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(a+b*arccosh(c+d*x))^4,x,6,24*b^4*x+12*b^2*(c+d*x)*(a+b*arccosh(c+d*x))^2/d+(c+d*x)*(a+b*arccosh(c+d*x))^4/d-24*b^3*(a+b*arccosh(c+d*x))*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-4*b*(a+b*arccosh(c+d*x))^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(a+b*arccosh(c+d*x))^4/(c*e+d*e*x),x,10,1/5*(a+b*arccosh(c+d*x))^5/(b*d*e)+(a+b*arccosh(c+d*x))^4*log(1+exp(-2*arccosh(c+d*x)))/(d*e)-2*b*(a+b*arccosh(c+d*x))^3*polylog(2,(-1)/exp(2*arccosh(c+d*x)))/(d*e)-3*b^2*(a+b*arccosh(c+d*x))^2*polylog(3,(-1)/exp(2*arccosh(c+d*x)))/(d*e)-3*b^3*(a+b*arccosh(c+d*x))*polylog(4,(-1)/exp(2*arccosh(c+d*x)))/(d*e)-3/2*b^4*polylog(5,(-1)/exp(2*arccosh(c+d*x)))/(d*e)],
[(a+b*arccosh(c+d*x))^4/(c*e+d*e*x)^2,x,13,-(a+b*arccosh(c+d*x))^4/(d*e^2*(c+d*x))+8*b*(a+b*arccosh(c+d*x))^3*arctan(exp(arccosh(c+d*x)))/(d*e^2)-12*I*b^2*(a+b*arccosh(c+d*x))^2*polylog(2,-I*exp(arccosh(c+d*x)))/(d*e^2)+12*I*b^2*(a+b*arccosh(c+d*x))^2*polylog(2,I*exp(arccosh(c+d*x)))/(d*e^2)+24*I*b^3*(a+b*arccosh(c+d*x))*polylog(3,-I*exp(arccosh(c+d*x)))/(d*e^2)-24*I*b^3*(a+b*arccosh(c+d*x))*polylog(3,I*exp(arccosh(c+d*x)))/(d*e^2)-24*I*b^4*polylog(4,-I*exp(arccosh(c+d*x)))/(d*e^2)+24*I*b^4*polylog(4,I*exp(arccosh(c+d*x)))/(d*e^2)],
[(a+b*arccosh(c+d*x))^4/(c*e+d*e*x)^3,x,10,-2*b*(a+b*arccosh(c+d*x))^3/(d*e^3)-1/2*(a+b*arccosh(c+d*x))^4/(d*e^3*(c+d*x)^2)-6*b^2*(a+b*arccosh(c+d*x))^2*log(1+exp(-2*arccosh(c+d*x)))/(d*e^3)+6*b^3*(a+b*arccosh(c+d*x))*polylog(2,(-1)/exp(2*arccosh(c+d*x)))/(d*e^3)+3*b^4*polylog(3,(-1)/exp(2*arccosh(c+d*x)))/(d*e^3)+2*b*(a+b*arccosh(c+d*x))^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^3*(c+d*x))],
[(a+b*arccosh(c+d*x))^4/(c*e+d*e*x)^4,x,21,2*b^2*(a+b*arccosh(c+d*x))^2/(d*e^4*(c+d*x))-1/3*(a+b*arccosh(c+d*x))^4/(d*e^4*(c+d*x)^3)-8*b^3*(a+b*arccosh(c+d*x))*arctan(exp(arccosh(c+d*x)))/(d*e^4)+4/3*b*(a+b*arccosh(c+d*x))^3*arctan(exp(arccosh(c+d*x)))/(d*e^4)+4*I*b^4*polylog(2,-I*exp(arccosh(c+d*x)))/(d*e^4)-2*I*b^2*(a+b*arccosh(c+d*x))^2*polylog(2,-I*exp(arccosh(c+d*x)))/(d*e^4)-4*I*b^4*polylog(2,I*exp(arccosh(c+d*x)))/(d*e^4)+2*I*b^2*(a+b*arccosh(c+d*x))^2*polylog(2,I*exp(arccosh(c+d*x)))/(d*e^4)+4*I*b^3*(a+b*arccosh(c+d*x))*polylog(3,-I*exp(arccosh(c+d*x)))/(d*e^4)-4*I*b^3*(a+b*arccosh(c+d*x))*polylog(3,I*exp(arccosh(c+d*x)))/(d*e^4)-4*I*b^4*polylog(4,-I*exp(arccosh(c+d*x)))/(d*e^4)+4*I*b^4*polylog(4,I*exp(arccosh(c+d*x)))/(d*e^4)+2/3*b*(a+b*arccosh(c+d*x))^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^4*(c+d*x)^2)],

# n<0
[(c*e+d*e*x)^4/(a+b*arccosh(c+d*x)),x,14,1/8*e^4*cosh(a/b)*Shi((a+b*arccosh(c+d*x))/b)/(b*d)+3/16*e^4*cosh(3*a/b)*Shi(3*(a+b*arccosh(c+d*x))/b)/(b*d)+1/16*e^4*cosh(5*a/b)*Shi(5*(a+b*arccosh(c+d*x))/b)/(b*d)-1/8*e^4*Chi((a+b*arccosh(c+d*x))/b)*sinh(a/b)/(b*d)-3/16*e^4*Chi(3*(a+b*arccosh(c+d*x))/b)*sinh(3*a/b)/(b*d)-1/16*e^4*Chi(5*(a+b*arccosh(c+d*x))/b)*sinh(5*a/b)/(b*d)],
[(c*e+d*e*x)^3/(a+b*arccosh(c+d*x)),x,11,1/4*e^3*cosh(2*a/b)*Shi(2*(a+b*arccosh(c+d*x))/b)/(b*d)+1/8*e^3*cosh(4*a/b)*Shi(4*(a+b*arccosh(c+d*x))/b)/(b*d)-1/4*e^3*Chi(2*(a+b*arccosh(c+d*x))/b)*sinh(2*a/b)/(b*d)-1/8*e^3*Chi(4*(a+b*arccosh(c+d*x))/b)*sinh(4*a/b)/(b*d)],
[(c*e+d*e*x)^2/(a+b*arccosh(c+d*x)),x,11,1/4*e^2*cosh(a/b)*Shi((a+b*arccosh(c+d*x))/b)/(b*d)+1/4*e^2*cosh(3*a/b)*Shi(3*(a+b*arccosh(c+d*x))/b)/(b*d)-1/4*e^2*Chi((a+b*arccosh(c+d*x))/b)*sinh(a/b)/(b*d)-1/4*e^2*Chi(3*(a+b*arccosh(c+d*x))/b)*sinh(3*a/b)/(b*d)],
[(c*e+d*e*x)/(a+b*arccosh(c+d*x)),x,8,1/2*e*cosh(2*a/b)*Shi(2*(a+b*arccosh(c+d*x))/b)/(b*d)-1/2*e*Chi(2*(a+b*arccosh(c+d*x))/b)*sinh(2*a/b)/(b*d)],
[1/(a+b*arccosh(c+d*x)),x,5,cosh(a/b)*Shi((a+b*arccosh(c+d*x))/b)/(b*d)-Chi((a+b*arccosh(c+d*x))/b)*sinh(a/b)/(b*d)],
[1/((c*e+d*e*x)*(a+b*arccosh(c+d*x))),x,2,Unintegrable(1/((c+d*x)*(a+b*arccosh(c+d*x))),x)/e],
[(c*e+d*e*x)^4/(a+b*arccosh(c+d*x))^2,x,13,1/8*e^4*Chi((a+b*arccosh(c+d*x))/b)*cosh(a/b)/(b^2*d)+9/16*e^4*Chi(3*(a+b*arccosh(c+d*x))/b)*cosh(3*a/b)/(b^2*d)+5/16*e^4*Chi(5*(a+b*arccosh(c+d*x))/b)*cosh(5*a/b)/(b^2*d)-1/8*e^4*Shi((a+b*arccosh(c+d*x))/b)*sinh(a/b)/(b^2*d)-9/16*e^4*Shi(3*(a+b*arccosh(c+d*x))/b)*sinh(3*a/b)/(b^2*d)-5/16*e^4*Shi(5*(a+b*arccosh(c+d*x))/b)*sinh(5*a/b)/(b^2*d)-e^4*(c+d*x)^4*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)^3/(a+b*arccosh(c+d*x))^2,x,10,1/2*e^3*Chi(2*(a+b*arccosh(c+d*x))/b)*cosh(2*a/b)/(b^2*d)+1/2*e^3*Chi(4*(a+b*arccosh(c+d*x))/b)*cosh(4*a/b)/(b^2*d)-1/2*e^3*Shi(2*(a+b*arccosh(c+d*x))/b)*sinh(2*a/b)/(b^2*d)-1/2*e^3*Shi(4*(a+b*arccosh(c+d*x))/b)*sinh(4*a/b)/(b^2*d)-e^3*(c+d*x)^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)^2/(a+b*arccosh(c+d*x))^2,x,10,1/4*e^2*Chi((a+b*arccosh(c+d*x))/b)*cosh(a/b)/(b^2*d)+3/4*e^2*Chi(3*(a+b*arccosh(c+d*x))/b)*cosh(3*a/b)/(b^2*d)-1/4*e^2*Shi((a+b*arccosh(c+d*x))/b)*sinh(a/b)/(b^2*d)-3/4*e^2*Shi(3*(a+b*arccosh(c+d*x))/b)*sinh(3*a/b)/(b^2*d)-e^2*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)/(a+b*arccosh(c+d*x))^2,x,6,e*Chi(2*(a+b*arccosh(c+d*x))/b)*cosh(2*a/b)/(b^2*d)-e*Shi(2*(a+b*arccosh(c+d*x))/b)*sinh(2*a/b)/(b^2*d)-e*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x)))],
[1/(a+b*arccosh(c+d*x))^2,x,6,Chi((a+b*arccosh(c+d*x))/b)*cosh(a/b)/(b^2*d)-Shi((a+b*arccosh(c+d*x))/b)*sinh(a/b)/(b^2*d)-sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x)))],
[1/((c*e+d*e*x)*(a+b*arccosh(c+d*x))^2),x,2,Unintegrable(1/((c+d*x)*(a+b*arccosh(c+d*x))^2),x)/e],
[(c*e+d*e*x)^4/(a+b*arccosh(c+d*x))^3,x,26,2*e^4*(c+d*x)^3/(b^2*d*(a+b*arccosh(c+d*x)))-5/2*e^4*(c+d*x)^5/(b^2*d*(a+b*arccosh(c+d*x)))+1/16*e^4*cosh(a/b)*Shi((a+b*arccosh(c+d*x))/b)/(b^3*d)+27/32*e^4*cosh(3*a/b)*Shi(3*(a+b*arccosh(c+d*x))/b)/(b^3*d)+25/32*e^4*cosh(5*a/b)*Shi(5*(a+b*arccosh(c+d*x))/b)/(b^3*d)-1/16*e^4*Chi((a+b*arccosh(c+d*x))/b)*sinh(a/b)/(b^3*d)-27/32*e^4*Chi(3*(a+b*arccosh(c+d*x))/b)*sinh(3*a/b)/(b^3*d)-25/32*e^4*Chi(5*(a+b*arccosh(c+d*x))/b)*sinh(5*a/b)/(b^3*d)-1/2*e^4*(c+d*x)^4*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^2)],
[(c*e+d*e*x)^3/(a+b*arccosh(c+d*x))^3,x,20,3/2*e^3*(c+d*x)^2/(b^2*d*(a+b*arccosh(c+d*x)))-2*e^3*(c+d*x)^4/(b^2*d*(a+b*arccosh(c+d*x)))+1/2*e^3*cosh(2*a/b)*Shi(2*(a+b*arccosh(c+d*x))/b)/(b^3*d)+e^3*cosh(4*a/b)*Shi(4*(a+b*arccosh(c+d*x))/b)/(b^3*d)-1/2*e^3*Chi(2*(a+b*arccosh(c+d*x))/b)*sinh(2*a/b)/(b^3*d)-e^3*Chi(4*(a+b*arccosh(c+d*x))/b)*sinh(4*a/b)/(b^3*d)-1/2*e^3*(c+d*x)^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^2)],
[(c*e+d*e*x)^2/(a+b*arccosh(c+d*x))^3,x,18,e^2*(c+d*x)/(b^2*d*(a+b*arccosh(c+d*x)))-3/2*e^2*(c+d*x)^3/(b^2*d*(a+b*arccosh(c+d*x)))+1/8*e^2*cosh(a/b)*Shi((a+b*arccosh(c+d*x))/b)/(b^3*d)+9/8*e^2*cosh(3*a/b)*Shi(3*(a+b*arccosh(c+d*x))/b)/(b^3*d)-1/8*e^2*Chi((a+b*arccosh(c+d*x))/b)*sinh(a/b)/(b^3*d)-9/8*e^2*Chi(3*(a+b*arccosh(c+d*x))/b)*sinh(3*a/b)/(b^3*d)-1/2*e^2*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^2)],
[(c*e+d*e*x)/(a+b*arccosh(c+d*x))^3,x,11,1/2*e/(b^2*d*(a+b*arccosh(c+d*x)))-e*(c+d*x)^2/(b^2*d*(a+b*arccosh(c+d*x)))+e*cosh(2*a/b)*Shi(2*(a+b*arccosh(c+d*x))/b)/(b^3*d)-e*Chi(2*(a+b*arccosh(c+d*x))/b)*sinh(2*a/b)/(b^3*d)-1/2*e*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^2)],
[1/(a+b*arccosh(c+d*x))^3,x,7,1/2*(-c-d*x)/(b^2*d*(a+b*arccosh(c+d*x)))+1/2*cosh(a/b)*Shi((a+b*arccosh(c+d*x))/b)/(b^3*d)-1/2*Chi((a+b*arccosh(c+d*x))/b)*sinh(a/b)/(b^3*d)-1/2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^2)],
[1/((c*e+d*e*x)*(a+b*arccosh(c+d*x))^3),x,2,Unintegrable(1/((c+d*x)*(a+b*arccosh(c+d*x))^3),x)/e],
[(c*e+d*e*x)^4/(a+b*arccosh(c+d*x))^4,x,24,2/3*e^4*(c+d*x)^3/(b^2*d*(a+b*arccosh(c+d*x))^2)-5/6*e^4*(c+d*x)^5/(b^2*d*(a+b*arccosh(c+d*x))^2)+1/48*e^4*Chi((a+b*arccosh(c+d*x))/b)*cosh(a/b)/(b^4*d)+27/32*e^4*Chi(3*(a+b*arccosh(c+d*x))/b)*cosh(3*a/b)/(b^4*d)+125/96*e^4*Chi(5*(a+b*arccosh(c+d*x))/b)*cosh(5*a/b)/(b^4*d)-1/48*e^4*Shi((a+b*arccosh(c+d*x))/b)*sinh(a/b)/(b^4*d)-27/32*e^4*Shi(3*(a+b*arccosh(c+d*x))/b)*sinh(3*a/b)/(b^4*d)-125/96*e^4*Shi(5*(a+b*arccosh(c+d*x))/b)*sinh(5*a/b)/(b^4*d)-1/3*e^4*(c+d*x)^4*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^3)+2*e^4*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*(a+b*arccosh(c+d*x)))-25/6*e^4*(c+d*x)^4*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)^3/(a+b*arccosh(c+d*x))^4,x,17,1/2*e^3*(c+d*x)^2/(b^2*d*(a+b*arccosh(c+d*x))^2)-2/3*e^3*(c+d*x)^4/(b^2*d*(a+b*arccosh(c+d*x))^2)+1/3*e^3*Chi(2*(a+b*arccosh(c+d*x))/b)*cosh(2*a/b)/(b^4*d)+4/3*e^3*Chi(4*(a+b*arccosh(c+d*x))/b)*cosh(4*a/b)/(b^4*d)-1/3*e^3*Shi(2*(a+b*arccosh(c+d*x))/b)*sinh(2*a/b)/(b^4*d)-4/3*e^3*Shi(4*(a+b*arccosh(c+d*x))/b)*sinh(4*a/b)/(b^4*d)-1/3*e^3*(c+d*x)^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^3)+e^3*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*(a+b*arccosh(c+d*x)))-8/3*e^3*(c+d*x)^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)^2/(a+b*arccosh(c+d*x))^4,x,18,1/3*e^2*(c+d*x)/(b^2*d*(a+b*arccosh(c+d*x))^2)-1/2*e^2*(c+d*x)^3/(b^2*d*(a+b*arccosh(c+d*x))^2)+1/24*e^2*Chi((a+b*arccosh(c+d*x))/b)*cosh(a/b)/(b^4*d)+9/8*e^2*Chi(3*(a+b*arccosh(c+d*x))/b)*cosh(3*a/b)/(b^4*d)-1/24*e^2*Shi((a+b*arccosh(c+d*x))/b)*sinh(a/b)/(b^4*d)-9/8*e^2*Shi(3*(a+b*arccosh(c+d*x))/b)*sinh(3*a/b)/(b^4*d)-1/3*e^2*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^3)+1/3*e^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*(a+b*arccosh(c+d*x)))-3/2*e^2*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)/(a+b*arccosh(c+d*x))^4,x,9,1/6*e/(b^2*d*(a+b*arccosh(c+d*x))^2)-1/3*e*(c+d*x)^2/(b^2*d*(a+b*arccosh(c+d*x))^2)+2/3*e*Chi(2*(a+b*arccosh(c+d*x))/b)*cosh(2*a/b)/(b^4*d)-2/3*e*Shi(2*(a+b*arccosh(c+d*x))/b)*sinh(2*a/b)/(b^4*d)-1/3*e*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^3)-2/3*e*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*(a+b*arccosh(c+d*x)))],
[1/(a+b*arccosh(c+d*x))^4,x,8,1/6*(-c-d*x)/(b^2*d*(a+b*arccosh(c+d*x))^2)+1/6*Chi((a+b*arccosh(c+d*x))/b)*cosh(a/b)/(b^4*d)-1/6*Shi((a+b*arccosh(c+d*x))/b)*sinh(a/b)/(b^4*d)-1/3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^3)-1/6*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*(a+b*arccosh(c+d*x)))],
[1/((c*e+d*e*x)*(a+b*arccosh(c+d*x))^4),x,2,Unintegrable(1/((c+d*x)*(a+b*arccosh(c+d*x))^4),x)/e],

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

# n>0
[(c*e+d*e*x)^4*sqrt(a+b*arccosh(c+d*x)),x,21,-1/320*e^4*exp(5*a/b)*erf(sqrt(5)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(1/5*Pi)/d-1/320*e^4*erfi(sqrt(5)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(1/5*Pi)/(d*exp(5*a/b))-1/64*e^4*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(1/3*Pi)/d-1/64*e^4*erfi(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(1/3*Pi)/(d*exp(3*a/b))-1/32*e^4*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/d-1/32*e^4*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/(d*exp(a/b))+1/5*e^4*(c+d*x)^5*sqrt(a+b*arccosh(c+d*x))/d],
[(c*e+d*e*x)^3*sqrt(a+b*arccosh(c+d*x)),x,16,-1/32*e^3*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(1/2*Pi)/d-1/32*e^3*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(1/2*Pi)/(d*exp(2*a/b))-1/256*e^3*exp(4*a/b)*erf(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/d-1/256*e^3*erfi(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/(d*exp(4*a/b))-3/32*e^3*sqrt(a+b*arccosh(c+d*x))/d+1/4*e^3*(c+d*x)^4*sqrt(a+b*arccosh(c+d*x))/d],
[(c*e+d*e*x)^2*sqrt(a+b*arccosh(c+d*x)),x,16,-1/48*e^2*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(1/3*Pi)/d-1/48*e^2*erfi(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(1/3*Pi)/(d*exp(3*a/b))-1/16*e^2*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/d-1/16*e^2*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/(d*exp(a/b))+1/3*e^2*(c+d*x)^3*sqrt(a+b*arccosh(c+d*x))/d],
[(c*e+d*e*x)*sqrt(a+b*arccosh(c+d*x)),x,11,-1/16*e*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(1/2*Pi)/d-1/16*e*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(1/2*Pi)/(d*exp(2*a/b))-1/4*e*sqrt(a+b*arccosh(c+d*x))/d+1/2*e*(c+d*x)^2*sqrt(a+b*arccosh(c+d*x))/d],
[sqrt(a+b*arccosh(c+d*x)),x,8,-1/4*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/d-1/4*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/(d*exp(a/b))+(c+d*x)*sqrt(a+b*arccosh(c+d*x))/d],
[sqrt(a+b*arccosh(c+d*x))/(c*e+d*e*x),x,2,Unintegrable(sqrt(a+b*arccosh(c+d*x))/(c+d*x),x)/e],
[(c*e+d*e*x)^3*(a+b*arccosh(c+d*x))^(3/2),x,27,-3/32*e^3*(a+b*arccosh(c+d*x))^(3/2)/d+1/4*e^3*(c+d*x)^4*(a+b*arccosh(c+d*x))^(3/2)/d-3/128*b^(3/2)*e^3*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/d+3/128*b^(3/2)*e^3*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/(d*exp(2*a/b))-3/2048*b^(3/2)*e^3*exp(4*a/b)*erf(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/d+3/2048*b^(3/2)*e^3*erfi(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(4*a/b))-9/64*b*e^3*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)*sqrt(a+b*arccosh(c+d*x))/d-3/32*b*e^3*(c+d*x)^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)*sqrt(a+b*arccosh(c+d*x))/d],
[(c*e+d*e*x)^2*(a+b*arccosh(c+d*x))^(3/2),x,24,1/3*e^2*(c+d*x)^3*(a+b*arccosh(c+d*x))^(3/2)/d-1/96*b^(3/2)*e^2*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/3*Pi)/d+1/96*b^(3/2)*e^2*erfi(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/3*Pi)/(d*exp(3*a/b))-3/32*b^(3/2)*e^2*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/d+3/32*b^(3/2)*e^2*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(a/b))-1/3*b*e^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)*sqrt(a+b*arccosh(c+d*x))/d-1/6*b*e^2*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)*sqrt(a+b*arccosh(c+d*x))/d],
[(c*e+d*e*x)*(a+b*arccosh(c+d*x))^(3/2),x,13,-1/4*e*(a+b*arccosh(c+d*x))^(3/2)/d+1/2*e*(c+d*x)^2*(a+b*arccosh(c+d*x))^(3/2)/d-3/64*b^(3/2)*e*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/d+3/64*b^(3/2)*e*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/(d*exp(2*a/b))-3/8*b*e*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)*sqrt(a+b*arccosh(c+d*x))/d],
[(a+b*arccosh(c+d*x))^(3/2),x,9,(c+d*x)*(a+b*arccosh(c+d*x))^(3/2)/d-3/8*b^(3/2)*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/d+3/8*b^(3/2)*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(a/b))-3/2*b*sqrt(-1+c+d*x)*sqrt(1+c+d*x)*sqrt(a+b*arccosh(c+d*x))/d],
[(a+b*arccosh(c+d*x))^(3/2)/(c*e+d*e*x),x,2,Unintegrable((a+b*arccosh(c+d*x))^(3/2)/(c+d*x),x)/e],
[(c*e+d*e*x)^3*(a+b*arccosh(c+d*x))^(5/2),x,29,-3/32*e^3*(a+b*arccosh(c+d*x))^(5/2)/d+1/4*e^3*(c+d*x)^4*(a+b*arccosh(c+d*x))^(5/2)/d-15/512*b^(5/2)*e^3*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/d-15/512*b^(5/2)*e^3*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/(d*exp(2*a/b))-15/16384*b^(5/2)*e^3*exp(4*a/b)*erf(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/d-15/16384*b^(5/2)*e^3*erfi(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(4*a/b))-15/64*b*e^3*(c+d*x)*(a+b*arccosh(c+d*x))^(3/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-5/32*b*e^3*(c+d*x)^3*(a+b*arccosh(c+d*x))^(3/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-225/2048*b^2*e^3*sqrt(a+b*arccosh(c+d*x))/d+45/256*b^2*e^3*(c+d*x)^2*sqrt(a+b*arccosh(c+d*x))/d+15/256*b^2*e^3*(c+d*x)^4*sqrt(a+b*arccosh(c+d*x))/d],
[(c*e+d*e*x)^2*(a+b*arccosh(c+d*x))^(5/2),x,26,1/3*e^2*(c+d*x)^3*(a+b*arccosh(c+d*x))^(5/2)/d-5/576*b^(5/2)*e^2*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/3*Pi)/d-5/576*b^(5/2)*e^2*erfi(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/3*Pi)/(d*exp(3*a/b))-15/64*b^(5/2)*e^2*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/d-15/64*b^(5/2)*e^2*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(a/b))-5/9*b*e^2*(a+b*arccosh(c+d*x))^(3/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-5/18*b*e^2*(c+d*x)^2*(a+b*arccosh(c+d*x))^(3/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d+5/6*b^2*e^2*(c+d*x)*sqrt(a+b*arccosh(c+d*x))/d+5/36*b^2*e^2*(c+d*x)^3*sqrt(a+b*arccosh(c+d*x))/d],
[(c*e+d*e*x)*(a+b*arccosh(c+d*x))^(5/2),x,14,-1/4*e*(a+b*arccosh(c+d*x))^(5/2)/d+1/2*e*(c+d*x)^2*(a+b*arccosh(c+d*x))^(5/2)/d-15/256*b^(5/2)*e*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/d-15/256*b^(5/2)*e*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/(d*exp(2*a/b))-5/8*b*e*(c+d*x)*(a+b*arccosh(c+d*x))^(3/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-15/64*b^2*e*sqrt(a+b*arccosh(c+d*x))/d+15/32*b^2*e*(c+d*x)^2*sqrt(a+b*arccosh(c+d*x))/d],
[(a+b*arccosh(c+d*x))^(5/2),x,10,(c+d*x)*(a+b*arccosh(c+d*x))^(5/2)/d-15/16*b^(5/2)*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/d-15/16*b^(5/2)*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(a/b))-5/2*b*(a+b*arccosh(c+d*x))^(3/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d+15/4*b^2*(c+d*x)*sqrt(a+b*arccosh(c+d*x))/d],
[(a+b*arccosh(c+d*x))^(5/2)/(c*e+d*e*x),x,2,Unintegrable((a+b*arccosh(c+d*x))^(5/2)/(c+d*x),x)/e],
[(c*e+d*e*x)^2*(a+b*arccosh(c+d*x))^(7/2),x,35,35/18*b^2*e^2*(c+d*x)*(a+b*arccosh(c+d*x))^(3/2)/d+35/108*b^2*e^2*(c+d*x)^3*(a+b*arccosh(c+d*x))^(3/2)/d+1/3*e^2*(c+d*x)^3*(a+b*arccosh(c+d*x))^(7/2)/d-35/3456*b^(7/2)*e^2*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/3*Pi)/d+35/3456*b^(7/2)*e^2*erfi(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/3*Pi)/(d*exp(3*a/b))-105/128*b^(7/2)*e^2*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/d+105/128*b^(7/2)*e^2*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(a/b))-7/9*b*e^2*(a+b*arccosh(c+d*x))^(5/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-7/18*b*e^2*(c+d*x)^2*(a+b*arccosh(c+d*x))^(5/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-175/54*b^3*e^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)*sqrt(a+b*arccosh(c+d*x))/d-35/216*b^3*e^2*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)*sqrt(a+b*arccosh(c+d*x))/d],
[(c*e+d*e*x)*(a+b*arccosh(c+d*x))^(7/2),x,16,-35/64*b^2*e*(a+b*arccosh(c+d*x))^(3/2)/d+35/32*b^2*e*(c+d*x)^2*(a+b*arccosh(c+d*x))^(3/2)/d-1/4*e*(a+b*arccosh(c+d*x))^(7/2)/d+1/2*e*(c+d*x)^2*(a+b*arccosh(c+d*x))^(7/2)/d-105/1024*b^(7/2)*e*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/d+105/1024*b^(7/2)*e*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/(d*exp(2*a/b))-7/8*b*e*(c+d*x)*(a+b*arccosh(c+d*x))^(5/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-105/128*b^3*e*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)*sqrt(a+b*arccosh(c+d*x))/d],
[(a+b*arccosh(c+d*x))^(7/2),x,11,35/4*b^2*(c+d*x)*(a+b*arccosh(c+d*x))^(3/2)/d+(c+d*x)*(a+b*arccosh(c+d*x))^(7/2)/d-105/32*b^(7/2)*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/d+105/32*b^(7/2)*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(a/b))-7/2*b*(a+b*arccosh(c+d*x))^(5/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-105/8*b^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)*sqrt(a+b*arccosh(c+d*x))/d],
[(a+b*arccosh(c+d*x))^(7/2)/(c*e+d*e*x),x,2,Unintegrable((a+b*arccosh(c+d*x))^(7/2)/(c+d*x),x)/e],

# n<0
[(c*e+d*e*x)^4/sqrt(a+b*arccosh(c+d*x)),x,20,-1/32*e^4*exp(5*a/b)*erf(sqrt(5)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/5*Pi)/(d*sqrt(b))+1/32*e^4*erfi(sqrt(5)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/5*Pi)/(d*exp(5*a/b)*sqrt(b))-1/16*e^4*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*sqrt(b))+1/16*e^4*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(a/b)*sqrt(b))-1/32*e^4*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(d*sqrt(b))+1/32*e^4*erfi(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(d*exp(3*a/b)*sqrt(b))],
[(c*e+d*e*x)^3/sqrt(a+b*arccosh(c+d*x)),x,15,-1/8*e^3*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/(d*sqrt(b))+1/8*e^3*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/(d*exp(2*a/b)*sqrt(b))-1/32*e^3*exp(4*a/b)*erf(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*sqrt(b))+1/32*e^3*erfi(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(4*a/b)*sqrt(b))],
[(c*e+d*e*x)^2/sqrt(a+b*arccosh(c+d*x)),x,15,-1/8*e^2*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/3*Pi)/(d*sqrt(b))+1/8*e^2*erfi(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/3*Pi)/(d*exp(3*a/b)*sqrt(b))-1/8*e^2*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*sqrt(b))+1/8*e^2*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(a/b)*sqrt(b))],
[(c*e+d*e*x)/sqrt(a+b*arccosh(c+d*x)),x,10,-1/4*e*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/(d*sqrt(b))+1/4*e*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/(d*exp(2*a/b)*sqrt(b))],
[1/sqrt(a+b*arccosh(c+d*x)),x,7,-1/2*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*sqrt(b))+1/2*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(d*exp(a/b)*sqrt(b))],
[1/((c*e+d*e*x)*sqrt(a+b*arccosh(c+d*x))),x,2,Unintegrable(1/((c+d*x)*sqrt(a+b*arccosh(c+d*x))),x)/e],
[(c*e+d*e*x)^4/(a+b*arccosh(c+d*x))^(3/2),x,19,1/8*e^4*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*d)+1/8*e^4*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*d*exp(a/b))+3/16*e^4*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*d)+3/16*e^4*erfi(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*d*exp(3*a/b))+1/16*e^4*exp(5*a/b)*erf(sqrt(5)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(5*Pi)/(b^(3/2)*d)+1/16*e^4*erfi(sqrt(5)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(5*Pi)/(b^(3/2)*d*exp(5*a/b))-2*e^4*(c+d*x)^4*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*sqrt(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)^3/(a+b*arccosh(c+d*x))^(3/2),x,14,1/2*e^3*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*d)+1/2*e^3*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*d*exp(2*a/b))+1/4*e^3*exp(4*a/b)*erf(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*d)+1/4*e^3*erfi(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*d*exp(4*a/b))-2*e^3*(c+d*x)^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*sqrt(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)^2/(a+b*arccosh(c+d*x))^(3/2),x,14,1/4*e^2*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*d)+1/4*e^2*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*d*exp(a/b))+1/4*e^2*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*d)+1/4*e^2*erfi(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*d*exp(3*a/b))-2*e^2*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*sqrt(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)/(a+b*arccosh(c+d*x))^(3/2),x,8,e*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*d)+e*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*d*exp(2*a/b))-2*e*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*sqrt(a+b*arccosh(c+d*x)))],
[1/(a+b*arccosh(c+d*x))^(3/2),x,8,exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*d)+erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*d*exp(a/b))-2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*sqrt(a+b*arccosh(c+d*x)))],
[1/((c*e+d*e*x)*(a+b*arccosh(c+d*x))^(3/2)),x,2,Unintegrable(1/((c+d*x)*(a+b*arccosh(c+d*x))^(3/2)),x)/e],
[(c*e+d*e*x)^4/(a+b*arccosh(c+d*x))^(5/2),x,36,-1/12*e^4*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(5/2)*d)+1/12*e^4*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(5/2)*d*exp(a/b))-3/8*e^4*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(b^(5/2)*d)+3/8*e^4*erfi(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(b^(5/2)*d*exp(3*a/b))-5/24*e^4*exp(5*a/b)*erf(sqrt(5)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(5*Pi)/(b^(5/2)*d)+5/24*e^4*erfi(sqrt(5)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(5*Pi)/(b^(5/2)*d*exp(5*a/b))-2/3*e^4*(c+d*x)^4*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^(3/2))+16/3*e^4*(c+d*x)^3/(b^2*d*sqrt(a+b*arccosh(c+d*x)))-20/3*e^4*(c+d*x)^5/(b^2*d*sqrt(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)^3/(a+b*arccosh(c+d*x))^(5/2),x,26,-2/3*e^3*exp(4*a/b)*erf(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(5/2)*d)+2/3*e^3*erfi(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(5/2)*d*exp(4*a/b))-1/3*e^3*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(2*Pi)/(b^(5/2)*d)+1/3*e^3*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(2*Pi)/(b^(5/2)*d*exp(2*a/b))-2/3*e^3*(c+d*x)^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^(3/2))+4*e^3*(c+d*x)^2/(b^2*d*sqrt(a+b*arccosh(c+d*x)))-16/3*e^3*(c+d*x)^4/(b^2*d*sqrt(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)^2/(a+b*arccosh(c+d*x))^(5/2),x,24,-1/6*e^2*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(5/2)*d)+1/6*e^2*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(5/2)*d*exp(a/b))-1/2*e^2*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(b^(5/2)*d)+1/2*e^2*erfi(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(b^(5/2)*d*exp(3*a/b))-2/3*e^2*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^(3/2))+8/3*e^2*(c+d*x)/(b^2*d*sqrt(a+b*arccosh(c+d*x)))-4*e^2*(c+d*x)^3/(b^2*d*sqrt(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)/(a+b*arccosh(c+d*x))^(5/2),x,13,-2/3*e*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(2*Pi)/(b^(5/2)*d)+2/3*e*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(2*Pi)/(b^(5/2)*d*exp(2*a/b))-2/3*e*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^(3/2))+4/3*e/(b^2*d*sqrt(a+b*arccosh(c+d*x)))-8/3*e*(c+d*x)^2/(b^2*d*sqrt(a+b*arccosh(c+d*x)))],
[1/(a+b*arccosh(c+d*x))^(5/2),x,9,-2/3*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(5/2)*d)+2/3*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(5/2)*d*exp(a/b))-2/3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^(3/2))-4/3*(c+d*x)/(b^2*d*sqrt(a+b*arccosh(c+d*x)))],
[1/((c*e+d*e*x)*(a+b*arccosh(c+d*x))^(5/2)),x,2,Unintegrable(1/((c+d*x)*(a+b*arccosh(c+d*x))^(5/2)),x)/e],
[(c*e+d*e*x)^4/(a+b*arccosh(c+d*x))^(7/2),x,34,16/15*e^4*(c+d*x)^3/(b^2*d*(a+b*arccosh(c+d*x))^(3/2))-4/3*e^4*(c+d*x)^5/(b^2*d*(a+b*arccosh(c+d*x))^(3/2))+1/30*e^4*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(7/2)*d)+1/30*e^4*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(7/2)*d*exp(a/b))+9/20*e^4*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(b^(7/2)*d)+9/20*e^4*erfi(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(b^(7/2)*d*exp(3*a/b))+5/12*e^4*exp(5*a/b)*erf(sqrt(5)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(5*Pi)/(b^(7/2)*d)+5/12*e^4*erfi(sqrt(5)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(5*Pi)/(b^(7/2)*d*exp(5*a/b))-2/5*e^4*(c+d*x)^4*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^(5/2))+32/5*e^4*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*sqrt(a+b*arccosh(c+d*x)))-40/3*e^4*(c+d*x)^4*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*sqrt(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)^3/(a+b*arccosh(c+d*x))^(7/2),x,23,4/5*e^3*(c+d*x)^2/(b^2*d*(a+b*arccosh(c+d*x))^(3/2))-16/15*e^3*(c+d*x)^4/(b^2*d*(a+b*arccosh(c+d*x))^(3/2))+16/15*e^3*exp(4*a/b)*erf(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(7/2)*d)+16/15*e^3*erfi(2*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(7/2)*d*exp(4*a/b))+4/15*e^3*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(2*Pi)/(b^(7/2)*d)+4/15*e^3*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(2*Pi)/(b^(7/2)*d*exp(2*a/b))-2/5*e^3*(c+d*x)^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^(5/2))+16/5*e^3*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*sqrt(a+b*arccosh(c+d*x)))-128/15*e^3*(c+d*x)^3*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*sqrt(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)^2/(a+b*arccosh(c+d*x))^(7/2),x,24,8/15*e^2*(c+d*x)/(b^2*d*(a+b*arccosh(c+d*x))^(3/2))-4/5*e^2*(c+d*x)^3/(b^2*d*(a+b*arccosh(c+d*x))^(3/2))+1/15*e^2*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(7/2)*d)+1/15*e^2*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(7/2)*d*exp(a/b))+3/5*e^2*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(b^(7/2)*d)+3/5*e^2*erfi(sqrt(3)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(3*Pi)/(b^(7/2)*d*exp(3*a/b))-2/5*e^2*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^(5/2))+16/15*e^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*sqrt(a+b*arccosh(c+d*x)))-24/5*e^2*(c+d*x)^2*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*sqrt(a+b*arccosh(c+d*x)))],
[(c*e+d*e*x)/(a+b*arccosh(c+d*x))^(7/2),x,11,4/15*e/(b^2*d*(a+b*arccosh(c+d*x))^(3/2))-8/15*e*(c+d*x)^2/(b^2*d*(a+b*arccosh(c+d*x))^(3/2))+8/15*e*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(2*Pi)/(b^(7/2)*d)+8/15*e*erfi(sqrt(2)*sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(2*Pi)/(b^(7/2)*d*exp(2*a/b))-2/5*e*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^(5/2))-32/15*e*(c+d*x)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*sqrt(a+b*arccosh(c+d*x)))],
[1/(a+b*arccosh(c+d*x))^(7/2),x,10,-4/15*(c+d*x)/(b^2*d*(a+b*arccosh(c+d*x))^(3/2))+4/15*exp(a/b)*erf(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(7/2)*d)+4/15*erfi(sqrt(a+b*arccosh(c+d*x))/sqrt(b))*sqrt(Pi)/(b^(7/2)*d*exp(a/b))-2/5*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b*d*(a+b*arccosh(c+d*x))^(5/2))-8/15*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(b^3*d*sqrt(a+b*arccosh(c+d*x)))],
[1/((c*e+d*e*x)*(a+b*arccosh(c+d*x))^(7/2)),x,2,Unintegrable(1/((c+d*x)*(a+b*arccosh(c+d*x))^(7/2)),x)/e],

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

# n>0
[(c*e+d*e*x)^(7/2)*(a+b*arccosh(c+d*x)),x,8,2/9*(e*(c+d*x))^(9/2)*(a+b*arccosh(c+d*x))/(d*e)-28/135*b*e^3*EllipticE(sqrt(1+c+d*x)/sqrt(2),sqrt(2))*sqrt(1-c-d*x)*sqrt(e*(c+d*x))/(d*sqrt(-c-d*x)*sqrt(-1+c+d*x))-28/405*b*e^2*(e*(c+d*x))^(3/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-4/81*b*(e*(c+d*x))^(7/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(c*e+d*e*x)^(5/2)*(a+b*arccosh(c+d*x)),x,8,2/7*(e*(c+d*x))^(7/2)*(a+b*arccosh(c+d*x))/(d*e)-20/147*b*e^(5/2)*EllipticF(sqrt(e*(c+d*x))/sqrt(e),I)*sqrt(1-c-d*x)/(d*sqrt(-1+c+d*x))-4/49*b*(e*(c+d*x))^(5/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d-20/147*b*e^2*sqrt(-1+c+d*x)*sqrt(e*(c+d*x))*sqrt(1+c+d*x)/d],
[(c*e+d*e*x)^(3/2)*(a+b*arccosh(c+d*x)),x,6,2/5*(e*(c+d*x))^(5/2)*(a+b*arccosh(c+d*x))/(d*e)-12/25*b*e*EllipticE(sqrt(1+c+d*x)/sqrt(2),sqrt(2))*sqrt(1-c-d*x)*sqrt(e*(c+d*x))/(d*sqrt(-c-d*x)*sqrt(-1+c+d*x))-4/25*b*(e*(c+d*x))^(3/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/d],
[(a+b*arccosh(c+d*x))*sqrt(c*e+d*e*x),x,6,2/3*(e*(c+d*x))^(3/2)*(a+b*arccosh(c+d*x))/(d*e)-4/9*b*EllipticF(sqrt(e*(c+d*x))/sqrt(e),I)*sqrt(e)*sqrt(1-c-d*x)/(d*sqrt(-1+c+d*x))-4/9*b*sqrt(-1+c+d*x)*sqrt(e*(c+d*x))*sqrt(1+c+d*x)/d],
[(a+b*arccosh(c+d*x))/sqrt(c*e+d*e*x),x,4,2*(a+b*arccosh(c+d*x))*sqrt(e*(c+d*x))/(d*e)-4*b*EllipticE(sqrt(1+c+d*x)/sqrt(2),sqrt(2))*sqrt(1-c-d*x)*sqrt(e*(c+d*x))/(d*e*sqrt(-c-d*x)*sqrt(-1+c+d*x))],
[(a+b*arccosh(c+d*x))/(c*e+d*e*x)^(3/2),x,4,4*b*EllipticF(sqrt(e*(c+d*x))/sqrt(e),I)*sqrt(1-c-d*x)/(d*e^(3/2)*sqrt(-1+c+d*x))-2*(a+b*arccosh(c+d*x))/(d*e*sqrt(e*(c+d*x)))],
[(a+b*arccosh(c+d*x))/(c*e+d*e*x)^(5/2),x,7,-2/3*(a+b*arccosh(c+d*x))/(d*e*(e*(c+d*x))^(3/2))-4/3*b*EllipticE(sqrt(1+c+d*x)/sqrt(2),sqrt(2))*sqrt(1-c-d*x)*sqrt(e*(c+d*x))/(d*e^3*sqrt(-c-d*x)*sqrt(-1+c+d*x))+4/3*b*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^2*sqrt(e*(c+d*x)))],
[(a+b*arccosh(c+d*x))/(c*e+d*e*x)^(7/2),x,7,-2/5*(a+b*arccosh(c+d*x))/(d*e*(e*(c+d*x))^(5/2))+4/15*b*EllipticF(sqrt(e*(c+d*x))/sqrt(e),I)*sqrt(1-c-d*x)/(d*e^(7/2)*sqrt(-1+c+d*x))+4/15*b*sqrt(-1+c+d*x)*sqrt(1+c+d*x)/(d*e^2*(e*(c+d*x))^(3/2))],
[(c*e+d*e*x)^(7/2)*(a+b*arccosh(c+d*x))^2,x,3,2/9*(e*(c+d*x))^(9/2)*(a+b*arccosh(c+d*x))^2/(d*e)-16/1287*b^2*(e*(c+d*x))^(13/2)*HypergeometricPFQ([1,13/4,13/4],[15/4,17/4],(c+d*x)^2)/(d*e^3)-8/99*b*(e*(c+d*x))^(11/2)*(a+b*arccosh(c+d*x))*hypergeom([1/2,11/4],[15/4],(c+d*x)^2)*sqrt(1-c-d*x)/(d*e^2*sqrt(-1+c+d*x))],
[(c*e+d*e*x)^(5/2)*(a+b*arccosh(c+d*x))^2,x,3,2/7*(e*(c+d*x))^(7/2)*(a+b*arccosh(c+d*x))^2/(d*e)-16/693*b^2*(e*(c+d*x))^(11/2)*HypergeometricPFQ([1,11/4,11/4],[13/4,15/4],(c+d*x)^2)/(d*e^3)-8/63*b*(e*(c+d*x))^(9/2)*(a+b*arccosh(c+d*x))*hypergeom([1/2,9/4],[13/4],(c+d*x)^2)*sqrt(1-c-d*x)/(d*e^2*sqrt(-1+c+d*x))],
[(c*e+d*e*x)^(3/2)*(a+b*arccosh(c+d*x))^2,x,3,2/5*(e*(c+d*x))^(5/2)*(a+b*arccosh(c+d*x))^2/(d*e)-16/315*b^2*(e*(c+d*x))^(9/2)*HypergeometricPFQ([1,9/4,9/4],[11/4,13/4],(c+d*x)^2)/(d*e^3)-8/35*b*(e*(c+d*x))^(7/2)*(a+b*arccosh(c+d*x))*hypergeom([1/2,7/4],[11/4],(c+d*x)^2)*sqrt(1-c-d*x)/(d*e^2*sqrt(-1+c+d*x))],
[(a+b*arccosh(c+d*x))^2*sqrt(c*e+d*e*x),x,3,2/3*(e*(c+d*x))^(3/2)*(a+b*arccosh(c+d*x))^2/(d*e)-16/105*b^2*(e*(c+d*x))^(7/2)*HypergeometricPFQ([1,7/4,7/4],[9/4,11/4],(c+d*x)^2)/(d*e^3)-8/15*b*(e*(c+d*x))^(5/2)*(a+b*arccosh(c+d*x))*hypergeom([1/2,5/4],[9/4],(c+d*x)^2)*sqrt(1-c-d*x)/(d*e^2*sqrt(-1+c+d*x))],
[(a+b*arccosh(c+d*x))^2/sqrt(c*e+d*e*x),x,3,-16/15*b^2*(e*(c+d*x))^(5/2)*HypergeometricPFQ([1,5/4,5/4],[7/4,9/4],(c+d*x)^2)/(d*e^3)-8/3*b*(e*(c+d*x))^(3/2)*(a+b*arccosh(c+d*x))*hypergeom([1/2,3/4],[7/4],(c+d*x)^2)*sqrt(1-c-d*x)/(d*e^2*sqrt(-1+c+d*x))+2*(a+b*arccosh(c+d*x))^2*sqrt(e*(c+d*x))/(d*e)],
[(a+b*arccosh(c+d*x))^2/(c*e+d*e*x)^(3/2),x,3,16/3*b^2*(e*(c+d*x))^(3/2)*HypergeometricPFQ([3/4,3/4,1],[5/4,7/4],(c+d*x)^2)/(d*e^3)-2*(a+b*arccosh(c+d*x))^2/(d*e*sqrt(e*(c+d*x)))+8*b*(a+b*arccosh(c+d*x))*hypergeom([1/4,1/2],[5/4],(c+d*x)^2)*sqrt(1-c-d*x)*sqrt(e*(c+d*x))/(d*e^2*sqrt(-1+c+d*x))],
[(a+b*arccosh(c+d*x))^2/(c*e+d*e*x)^(5/2),x,3,-2/3*(a+b*arccosh(c+d*x))^2/(d*e*(e*(c+d*x))^(3/2))-8/3*b*(a+b*arccosh(c+d*x))*hypergeom([-1/4,1/2],[3/4],(c+d*x)^2)*sqrt(1-c-d*x)/(d*e^2*sqrt(-1+c+d*x)*sqrt(e*(c+d*x)))-16/3*b^2*HypergeometricPFQ([1/4,1/4,1],[3/4,5/4],(c+d*x)^2)*sqrt(e*(c+d*x))/(d*e^3)],
[(a+b*arccosh(c+d*x))^2/(c*e+d*e*x)^(7/2),x,3,-2/5*(a+b*arccosh(c+d*x))^2/(d*e*(e*(c+d*x))^(5/2))-8/15*b*(a+b*arccosh(c+d*x))*hypergeom([-3/4,1/2],[1/4],(c+d*x)^2)*sqrt(1-c-d*x)/(d*e^2*(e*(c+d*x))^(3/2)*sqrt(-1+c+d*x))+16/15*b^2*HypergeometricPFQ([-1/4,-1/4,1],[1/4,3/4],(c+d*x)^2)/(d*e^3*sqrt(e*(c+d*x)))],
[(c*e+d*e*x)^(3/2)*(a+b*arccosh(c+d*x))^3,x,2,2/5*(e*(c+d*x))^(5/2)*(a+b*arccosh(c+d*x))^3/(d*e)-6/5*b*Unintegrable((e*(c+d*x))^(5/2)*(a+b*arccosh(c+d*x))^2/(sqrt(-1+c+d*x)*sqrt(1+c+d*x)),x)/e],
[(a+b*arccosh(c+d*x))^3*sqrt(c*e+d*e*x),x,2,2/3*(e*(c+d*x))^(3/2)*(a+b*arccosh(c+d*x))^3/(d*e)-2*b*Unintegrable((e*(c+d*x))^(3/2)*(a+b*arccosh(c+d*x))^2/(sqrt(-1+c+d*x)*sqrt(1+c+d*x)),x)/e],
[(a+b*arccosh(c+d*x))^3/sqrt(c*e+d*e*x),x,2,2*(a+b*arccosh(c+d*x))^3*sqrt(e*(c+d*x))/(d*e)-6*b*Unintegrable((a+b*arccosh(c+d*x))^2*sqrt(e*(c+d*x))/(sqrt(-1+c+d*x)*sqrt(1+c+d*x)),x)/e],
[(a+b*arccosh(c+d*x))^3/(c*e+d*e*x)^(3/2),x,2,-2*(a+b*arccosh(c+d*x))^3/(d*e*sqrt(e*(c+d*x)))+6*b*Unintegrable((a+b*arccosh(c+d*x))^2/(sqrt(-1+c+d*x)*sqrt(e*(c+d*x))*sqrt(1+c+d*x)),x)/e],
[(a+b*arccosh(c+d*x))^3/(c*e+d*e*x)^(5/2),x,2,-2/3*(a+b*arccosh(c+d*x))^3/(d*e*(e*(c+d*x))^(3/2))+2*b*Unintegrable((a+b*arccosh(c+d*x))^2/((e*(c+d*x))^(3/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)),x)/e],
[(a+b*arccosh(c+d*x))^3/(c*e+d*e*x)^(7/2),x,2,-2/5*(a+b*arccosh(c+d*x))^3/(d*e*(e*(c+d*x))^(5/2))+6/5*b*Unintegrable((a+b*arccosh(c+d*x))^2/((e*(c+d*x))^(5/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)),x)/e],
[(c*e+d*e*x)^(3/2)*(a+b*arccosh(c+d*x))^4,x,2,2/5*(e*(c+d*x))^(5/2)*(a+b*arccosh(c+d*x))^4/(d*e)-8/5*b*Unintegrable((e*(c+d*x))^(5/2)*(a+b*arccosh(c+d*x))^3/(sqrt(-1+c+d*x)*sqrt(1+c+d*x)),x)/e],
[(a+b*arccosh(c+d*x))^4*sqrt(c*e+d*e*x),x,2,2/3*(e*(c+d*x))^(3/2)*(a+b*arccosh(c+d*x))^4/(d*e)-8/3*b*Unintegrable((e*(c+d*x))^(3/2)*(a+b*arccosh(c+d*x))^3/(sqrt(-1+c+d*x)*sqrt(1+c+d*x)),x)/e],
[(a+b*arccosh(c+d*x))^4/sqrt(c*e+d*e*x),x,2,2*(a+b*arccosh(c+d*x))^4*sqrt(e*(c+d*x))/(d*e)-8*b*Unintegrable((a+b*arccosh(c+d*x))^3*sqrt(e*(c+d*x))/(sqrt(-1+c+d*x)*sqrt(1+c+d*x)),x)/e],
[(a+b*arccosh(c+d*x))^4/(c*e+d*e*x)^(3/2),x,2,-2*(a+b*arccosh(c+d*x))^4/(d*e*sqrt(e*(c+d*x)))+8*b*Unintegrable((a+b*arccosh(c+d*x))^3/(sqrt(-1+c+d*x)*sqrt(e*(c+d*x))*sqrt(1+c+d*x)),x)/e],
[(a+b*arccosh(c+d*x))^4/(c*e+d*e*x)^(5/2),x,2,-2/3*(a+b*arccosh(c+d*x))^4/(d*e*(e*(c+d*x))^(3/2))+8/3*b*Unintegrable((a+b*arccosh(c+d*x))^3/((e*(c+d*x))^(3/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)),x)/e],
[(a+b*arccosh(c+d*x))^4/(c*e+d*e*x)^(7/2),x,2,-2/5*(a+b*arccosh(c+d*x))^4/(d*e*(e*(c+d*x))^(5/2))+8/5*b*Unintegrable((a+b*arccosh(c+d*x))^3/((e*(c+d*x))^(5/2)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)),x)/e],

# n<0

# Integrands of the form (e c+e d x)^m (a+b ArcCosh[c+d x])^n with m symbolic
[(c*e+d*e*x)^m*(a+b*arccosh(c+d*x))^4,x,2,(e*(c+d*x))^(1+m)*(a+b*arccosh(c+d*x))^4/(d*e*(1+m))-4*b*Unintegrable((e*(c+d*x))^(1+m)*(a+b*arccosh(c+d*x))^3/(sqrt(-1+c+d*x)*sqrt(1+c+d*x)),x)/(e*(1+m))],
[(c*e+d*e*x)^m*(a+b*arccosh(c+d*x))^3,x,2,(e*(c+d*x))^(1+m)*(a+b*arccosh(c+d*x))^3/(d*e*(1+m))-3*b*Unintegrable((e*(c+d*x))^(1+m)*(a+b*arccosh(c+d*x))^2/(sqrt(-1+c+d*x)*sqrt(1+c+d*x)),x)/(e*(1+m))],
[(c*e+d*e*x)^m*(a+b*arccosh(c+d*x))^2,x,3,(e*(c+d*x))^(1+m)*(a+b*arccosh(c+d*x))^2/(d*e*(1+m))-2*b^2*(e*(c+d*x))^(3+m)*HypergeometricPFQ([1,3/2+1/2*m,3/2+1/2*m],[2+1/2*m,5/2+1/2*m],(c+d*x)^2)/(d*e^3*(3+m)*(2+3*m+m^2))-2*b*(e*(c+d*x))^(2+m)*(a+b*arccosh(c+d*x))*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],(c+d*x)^2)*sqrt(1-c-d*x)/(d*e^2*(1+m)*(2+m)*sqrt(-1+c+d*x))],
[(c*e+d*e*x)^m*(a+b*arccosh(c+d*x)),x,5,(e*(c+d*x))^(1+m)*(a+b*arccosh(c+d*x))/(d*e*(1+m))-b*(e*(c+d*x))^(2+m)*(1-(c+d*x)^2)*hypergeom([1,1/2*(3+m)],[1/2*(4+m)],(c+d*x)^2)/(d*e^2*(1+m)*(2+m)*sqrt(-1+c+d*x)*sqrt(1+c+d*x)),(e*(c+d*x))^(1+m)*(a+b*arccosh(c+d*x))/(d*e*(1+m))-b*(e*(c+d*x))^(2+m)*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],(c+d*x)^2)*sqrt(1-(c+d*x)^2)/(d*e^2*(1+m)*(2+m)*sqrt(-1+c+d*x)*sqrt(1+c+d*x))],
[(c*e+d*e*x)^m/(a+b*arccosh(c+d*x)),x,1,Unintegrable((e*(c+d*x))^m/(a+b*arccosh(c+d*x)),x)],

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

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

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

# n>0
[arccosh(a*x^5)/x,x,5,-1/10*arccosh(a*x^5)^2+1/5*arccosh(a*x^5)*log(1+exp(2*arccosh(a*x^5)))+1/10*polylog(2,-exp(2*arccosh(a*x^5)))],
[x^2*arccosh(sqrt(x)),x,7,-5/48*arccosh(sqrt(x))+1/3*x^3*arccosh(sqrt(x))-5/72*x^(3/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))-1/18*x^(5/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))-5/48*sqrt(x)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))],
[x*arccosh(sqrt(x)),x,6,-3/16*arccosh(sqrt(x))+1/2*x^2*arccosh(sqrt(x))-1/8*x^(3/2)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))-3/16*sqrt(x)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))],
[arccosh(sqrt(x)),x,5,-1/2*arccosh(sqrt(x))+x*arccosh(sqrt(x))-1/2*sqrt(x)*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))],
[arccosh(sqrt(x))/x,x,5,-arccosh(sqrt(x))^2+2*arccosh(sqrt(x))*log(1+exp(2*arccosh(sqrt(x))))+polylog(2,-exp(2*arccosh(sqrt(x))))],
[arccosh(sqrt(x))/x^2,x,3,-arccosh(sqrt(x))/x+sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/sqrt(x)],
[arccosh(sqrt(x))/x^3,x,4,-1/2*arccosh(sqrt(x))/x^2+1/6*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/x^(3/2)+1/3*sqrt(-1+sqrt(x))*sqrt(1+sqrt(x))/sqrt(x)],

# n<0
[arccosh(1/x),x,3,x*arcsech(x)+arcsin(x)*sqrt(1/(1+x))*sqrt(1+x)],

# Integrands of the form x^m ArcCosh[a x^n] with n symbolic
[arccosh(a*x^n)/x,x,5,-1/2*arccosh(a*x^n)^2/n+arccosh(a*x^n)*log(1+exp(2*arccosh(a*x^n)))/n+1/2*polylog(2,-exp(2*arccosh(a*x^n)))/n],

# Integrands of the form (a+b ArcCosh[c+d x^2])^n

# Integrands of the form (a+b ArcCosh[c+d x^2])^n when c^2=1
[(a+b*arccosh(1+d*x^2))^4,x,3,384*b^4*x+48*b^2*x*(a+b*arccosh(1+d*x^2))^2+x*(a+b*arccosh(1+d*x^2))^4-192*b^3*(2*x^2+d*x^4)*(a+b*arccosh(1+d*x^2))/(x*sqrt(d*x^2)*sqrt(2+d*x^2))-8*b*(2*x^2+d*x^4)*(a+b*arccosh(1+d*x^2))^3/(x*sqrt(d*x^2)*sqrt(2+d*x^2))],
[(a+b*arccosh(1+d*x^2))^3,x,7,24*a*b^2*x+24*b^3*x*arccosh(1+d*x^2)+x*(a+b*arccosh(1+d*x^2))^3-48*b^3*(2+d*x^2)*sqrt(d*x^2/(2+d*x^2))/(d*x)-6*b*(2*x^2+d*x^4)*(a+b*arccosh(1+d*x^2))^2/(x*sqrt(d*x^2)*sqrt(2+d*x^2))],
[(a+b*arccosh(1+d*x^2))^2,x,2,8*b^2*x+x*(a+b*arccosh(1+d*x^2))^2-4*b*(2*x^2+d*x^4)*(a+b*arccosh(1+d*x^2))/(x*sqrt(d*x^2)*sqrt(2+d*x^2))],
[a+b*arccosh(1+d*x^2),x,6,a*x+b*x*arccosh(1+d*x^2)-2*b*(2+d*x^2)*sqrt(d*x^2/(2+d*x^2))/(d*x)],
[1/(a+b*arccosh(1+d*x^2)),x,1,x*Chi(1/2*(a+b*arccosh(1+d*x^2))/b)*cosh(1/2*a/b)/(b*sqrt(2)*sqrt(d*x^2))-x*Shi(1/2*(a+b*arccosh(1+d*x^2))/b)*sinh(1/2*a/b)/(b*sqrt(2)*sqrt(d*x^2))],
[1/(a+b*arccosh(1+d*x^2))^2,x,1,1/2*x*cosh(1/2*a/b)*Shi(1/2*(a+b*arccosh(1+d*x^2))/b)/(b^2*sqrt(2)*sqrt(d*x^2))-1/2*x*Chi(1/2*(a+b*arccosh(1+d*x^2))/b)*sinh(1/2*a/b)/(b^2*sqrt(2)*sqrt(d*x^2))-1/2*sqrt(d*x^2)*sqrt(2+d*x^2)/(b*d*x*(a+b*arccosh(1+d*x^2)))],
[1/(a+b*arccosh(1+d*x^2))^3,x,2,-1/8*x/(b^2*(a+b*arccosh(1+d*x^2)))+1/8*x*Chi(1/2*(a+b*arccosh(1+d*x^2))/b)*cosh(1/2*a/b)/(b^3*sqrt(2)*sqrt(d*x^2))-1/8*x*Shi(1/2*(a+b*arccosh(1+d*x^2))/b)*sinh(1/2*a/b)/(b^3*sqrt(2)*sqrt(d*x^2))+1/4*(-2*x^2-d*x^4)/(b*x*(a+b*arccosh(1+d*x^2))^2*sqrt(d*x^2)*sqrt(2+d*x^2))],
[(a+b*arccosh(-1+d*x^2))^4,x,3,384*b^4*x+48*b^2*x*(a+b*arccosh(-1+d*x^2))^2+x*(a+b*arccosh(-1+d*x^2))^4+192*b^3*(2*x^2-d*x^4)*(a+b*arccosh(-1+d*x^2))/(x*sqrt(d*x^2)*sqrt(-2+d*x^2))+8*b*(2*x^2-d*x^4)*(a+b*arccosh(-1+d*x^2))^3/(x*sqrt(d*x^2)*sqrt(-2+d*x^2))],
[(a+b*arccosh(-1+d*x^2))^3,x,5,24*a*b^2*x+24*b^3*x*arccosh(-1+d*x^2)+x*(a+b*arccosh(-1+d*x^2))^3-48*b^3*x*sqrt(1+(-2)/(d*x^2))+6*b*(2*x^2-d*x^4)*(a+b*arccosh(-1+d*x^2))^2/(x*sqrt(d*x^2)*sqrt(-2+d*x^2))],
[(a+b*arccosh(-1+d*x^2))^2,x,2,8*b^2*x+x*(a+b*arccosh(-1+d*x^2))^2+4*b*(2*x^2-d*x^4)*(a+b*arccosh(-1+d*x^2))/(x*sqrt(d*x^2)*sqrt(-2+d*x^2))],
[a+b*arccosh(-1+d*x^2),x,4,a*x+b*x*arccosh(-1+d*x^2)-2*b*x*sqrt(1+(-2)/(d*x^2))],
[1/(a+b*arccosh(-1+d*x^2)),x,1,x*cosh(1/2*a/b)*Shi(1/2*(a+b*arccosh(-1+d*x^2))/b)/(b*sqrt(2)*sqrt(d*x^2))-x*Chi(1/2*(a+b*arccosh(-1+d*x^2))/b)*sinh(1/2*a/b)/(b*sqrt(2)*sqrt(d*x^2))],
[1/(a+b*arccosh(-1+d*x^2))^2,x,1,1/2*x*Chi(1/2*(a+b*arccosh(-1+d*x^2))/b)*cosh(1/2*a/b)/(b^2*sqrt(2)*sqrt(d*x^2))-1/2*x*Shi(1/2*(a+b*arccosh(-1+d*x^2))/b)*sinh(1/2*a/b)/(b^2*sqrt(2)*sqrt(d*x^2))-1/2*sqrt(d*x^2)*sqrt(-2+d*x^2)/(b*d*x*(a+b*arccosh(-1+d*x^2)))],
[1/(a+b*arccosh(-1+d*x^2))^3,x,2,-1/8*x/(b^2*(a+b*arccosh(-1+d*x^2)))+1/8*x*cosh(1/2*a/b)*Shi(1/2*(a+b*arccosh(-1+d*x^2))/b)/(b^3*sqrt(2)*sqrt(d*x^2))-1/8*x*Chi(1/2*(a+b*arccosh(-1+d*x^2))/b)*sinh(1/2*a/b)/(b^3*sqrt(2)*sqrt(d*x^2))+1/4*(2*x^2-d*x^4)/(b*x*(a+b*arccosh(-1+d*x^2))^2*sqrt(d*x^2)*sqrt(-2+d*x^2))],

# Integrands of the form (a+b ArcCosh[c+d x^2])^(n/2) when c^2=1
[(a+b*arccosh(1+d*x^2))^(5/2),x,2,x*(a+b*arccosh(1+d*x^2))^(5/2)-15*b^(5/2)*erfi(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(1/2*Pi)/(d*x)+15*b^(5/2)*erf(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(1/2*Pi)/(d*x)-5*b*(2*x^2+d*x^4)*(a+b*arccosh(1+d*x^2))^(3/2)/(x*sqrt(d*x^2)*sqrt(2+d*x^2))+30*b^2*sinh(1/2*arccosh(1+d*x^2))^2*sqrt(a+b*arccosh(1+d*x^2))/(d*x)],
[(a+b*arccosh(1+d*x^2))^(3/2),x,2,x*(a+b*arccosh(1+d*x^2))^(3/2)+3*b^(3/2)*erfi(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(1/2*Pi)/(d*x)+3*b^(3/2)*erf(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(1/2*Pi)/(d*x)-3*b*(2*x^2+d*x^4)*sqrt(a+b*arccosh(1+d*x^2))/(x*sqrt(d*x^2)*sqrt(2+d*x^2))],
[(a+b*arccosh(1+d*x^2))^(1/2),x,1,-erfi(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(b)*sqrt(1/2*Pi)/(d*x)+erf(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(b)*sqrt(1/2*Pi)/(d*x)+2*sinh(1/2*arccosh(1+d*x^2))^2*sqrt(a+b*arccosh(1+d*x^2))/(d*x)],
[1/(a+b*arccosh(1+d*x^2))^(1/2),x,1,erfi(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(1/2*Pi)/(d*x*sqrt(b))+erf(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(1/2*Pi)/(d*x*sqrt(b))],
[1/(a+b*arccosh(1+d*x^2))^(3/2),x,1,erfi(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(1/2*Pi)/(b^(3/2)*d*x)-erf(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(1/2*Pi)/(b^(3/2)*d*x)-sqrt(d*x^2)*sqrt(2+d*x^2)/(b*d*x*sqrt(a+b*arccosh(1+d*x^2)))],
[1/(a+b*arccosh(1+d*x^2))^(5/2),x,2,1/3*erfi(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(1/2*Pi)/(b^(5/2)*d*x)+1/3*erf(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(1/2*Pi)/(b^(5/2)*d*x)+1/3*(-2*x^2-d*x^4)/(b*x*(a+b*arccosh(1+d*x^2))^(3/2)*sqrt(d*x^2)*sqrt(2+d*x^2))-1/3*x/(b^2*sqrt(a+b*arccosh(1+d*x^2)))],
[1/(a+b*arccosh(1+d*x^2))^(7/2),x,2,-1/15*x/(b^2*(a+b*arccosh(1+d*x^2))^(3/2))+1/15*erfi(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(1/2*Pi)/(b^(7/2)*d*x)-1/15*erf(sqrt(a+b*arccosh(1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sinh(1/2*arccosh(1+d*x^2))*sqrt(1/2*Pi)/(b^(7/2)*d*x)+1/5*(-2*x^2-d*x^4)/(b*x*(a+b*arccosh(1+d*x^2))^(5/2)*sqrt(d*x^2)*sqrt(2+d*x^2))-1/15*sqrt(d*x^2)*sqrt(2+d*x^2)/(b^3*d*x*sqrt(a+b*arccosh(1+d*x^2)))],
[(a+b*arccosh(-1+d*x^2))^(5/2),x,2,x*(a+b*arccosh(-1+d*x^2))^(5/2)-15*b^(5/2)*cosh(1/2*arccosh(-1+d*x^2))*erfi(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sqrt(1/2*Pi)/(d*x)-15*b^(5/2)*cosh(1/2*arccosh(-1+d*x^2))*erf(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sqrt(1/2*Pi)/(d*x)+5*b*(2*x^2-d*x^4)*(a+b*arccosh(-1+d*x^2))^(3/2)/(x*sqrt(d*x^2)*sqrt(-2+d*x^2))+30*b^2*cosh(1/2*arccosh(-1+d*x^2))^2*sqrt(a+b*arccosh(-1+d*x^2))/(d*x)],
[(a+b*arccosh(-1+d*x^2))^(3/2),x,2,x*(a+b*arccosh(-1+d*x^2))^(3/2)+3*b^(3/2)*cosh(1/2*arccosh(-1+d*x^2))*erfi(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sqrt(1/2*Pi)/(d*x)-3*b^(3/2)*cosh(1/2*arccosh(-1+d*x^2))*erf(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sqrt(1/2*Pi)/(d*x)+3*b*(2*x^2-d*x^4)*sqrt(a+b*arccosh(-1+d*x^2))/(x*sqrt(d*x^2)*sqrt(-2+d*x^2))],
[(a+b*arccosh(-1+d*x^2))^(1/2),x,1,-cosh(1/2*arccosh(-1+d*x^2))*erfi(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sqrt(b)*sqrt(1/2*Pi)/(d*x)-cosh(1/2*arccosh(-1+d*x^2))*erf(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sqrt(b)*sqrt(1/2*Pi)/(d*x)+2*cosh(1/2*arccosh(-1+d*x^2))^2*sqrt(a+b*arccosh(-1+d*x^2))/(d*x)],
[1/(a+b*arccosh(-1+d*x^2))^(1/2),x,1,cosh(1/2*arccosh(-1+d*x^2))*erfi(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sqrt(1/2*Pi)/(d*x*sqrt(b))-cosh(1/2*arccosh(-1+d*x^2))*erf(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sqrt(1/2*Pi)/(d*x*sqrt(b))],
[1/(a+b*arccosh(-1+d*x^2))^(3/2),x,1,cosh(1/2*arccosh(-1+d*x^2))*erfi(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sqrt(1/2*Pi)/(b^(3/2)*d*x)+cosh(1/2*arccosh(-1+d*x^2))*erf(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sqrt(1/2*Pi)/(b^(3/2)*d*x)-sqrt(d*x^2)*sqrt(-2+d*x^2)/(b*d*x*sqrt(a+b*arccosh(-1+d*x^2)))],
[1/(a+b*arccosh(-1+d*x^2))^(5/2),x,2,1/3*cosh(1/2*arccosh(-1+d*x^2))*erfi(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sqrt(1/2*Pi)/(b^(5/2)*d*x)-1/3*cosh(1/2*arccosh(-1+d*x^2))*erf(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sqrt(1/2*Pi)/(b^(5/2)*d*x)+1/3*(2*x^2-d*x^4)/(b*x*(a+b*arccosh(-1+d*x^2))^(3/2)*sqrt(d*x^2)*sqrt(-2+d*x^2))-1/3*x/(b^2*sqrt(a+b*arccosh(-1+d*x^2)))],
[1/(a+b*arccosh(-1+d*x^2))^(7/2),x,2,-1/15*x/(b^2*(a+b*arccosh(-1+d*x^2))^(3/2))+1/15*cosh(1/2*arccosh(-1+d*x^2))*erfi(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)-sinh(1/2*a/b))*sqrt(1/2*Pi)/(b^(7/2)*d*x)+1/15*cosh(1/2*arccosh(-1+d*x^2))*erf(sqrt(a+b*arccosh(-1+d*x^2))/(sqrt(2)*sqrt(b)))*(cosh(1/2*a/b)+sinh(1/2*a/b))*sqrt(1/2*Pi)/(b^(7/2)*d*x)+1/5*(2*x^2-d*x^4)/(b*x*(a+b*arccosh(-1+d*x^2))^(5/2)*sqrt(d*x^2)*sqrt(-2+d*x^2))-1/15*sqrt(d*x^2)*sqrt(-2+d*x^2)/(b^3*d*x*sqrt(a+b*arccosh(-1+d*x^2)))],

# Integrands of the form u (a+b ArcCosh[Sqrt[1-c x]/Sqrt[1+c x]])^n
[(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))^n/(1-c^2*x^2),x,0,Unintegrable((a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))^n/(1-c^2*x^2),x)],
[(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))^3/(1-c^2*x^2),x,8,-1/4*(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))^4/(b*c)-(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))^3*log(1+exp(-2*arccosh(sqrt(1-c*x)/sqrt(1+c*x))))/c+3/2*b*(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))^2*polylog(2,(-1)/exp(2*arccosh(sqrt(1-c*x)/sqrt(1+c*x))))/c+3/2*b^2*(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))*polylog(3,(-1)/exp(2*arccosh(sqrt(1-c*x)/sqrt(1+c*x))))/c+3/4*b^3*polylog(4,(-1)/exp(2*arccosh(sqrt(1-c*x)/sqrt(1+c*x))))/c],
[(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))^2/(1-c^2*x^2),x,7,-1/3*(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))^3/(b*c)-(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))^2*log(1+exp(-2*arccosh(sqrt(1-c*x)/sqrt(1+c*x))))/c+b*(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))*polylog(2,(-1)/exp(2*arccosh(sqrt(1-c*x)/sqrt(1+c*x))))/c+1/2*b^2*polylog(3,(-1)/exp(2*arccosh(sqrt(1-c*x)/sqrt(1+c*x))))/c],
[(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))/(1-c^2*x^2),x,6,-1/2*(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))^2/(b*c)-(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))*log(1+exp(-2*arccosh(sqrt(1-c*x)/sqrt(1+c*x))))/c+1/2*b*polylog(2,(-1)/exp(2*arccosh(sqrt(1-c*x)/sqrt(1+c*x))))/c],
[1/((1-c^2*x^2)*(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))),x,0,Unintegrable(1/((1-c^2*x^2)*(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))),x)],
[1/((1-c^2*x^2)*(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))^2),x,0,Unintegrable(1/((1-c^2*x^2)*(a+b*arccosh(sqrt(1-c*x)/sqrt(1+c*x)))^2),x)],

# Integrands involving inverse hyperbolic cosines of exponentials

# x^m ArcCosh[c E^(a+b x)]
[arccosh(c*exp(a+b*x)),x,6,-1/2*arccosh(c*exp(a+b*x))^2/b+arccosh(c*exp(a+b*x))*log(1+exp(2*arccosh(c*exp(a+b*x))))/b+1/2*polylog(2,-exp(2*arccosh(c*exp(a+b*x))))/b],

# Integrands involving exponentials of inverse hyperbolic cosines

# x^m E^(ArcCosh[a+b x]^n)
[exp(arccosh(a+b*x))*x^3,x,5,1/48/(b^4*exp(3*arccosh(a+b*x)))-3/16*a/(b^4*exp(2*arccosh(a+b*x)))+1/8*(1+6*a^2)/(b^4*exp(arccosh(a+b*x)))-1/16*a*(3+4*a^2)*exp(2*arccosh(a+b*x))/b^4+1/24*(1+6*a^2)*exp(3*arccosh(a+b*x))/b^4-3/32*a*exp(4*arccosh(a+b*x))/b^4+1/80*exp(5*arccosh(a+b*x))/b^4+1/8*a*(3+4*a^2)*arccosh(a+b*x)/b^4],
[exp(arccosh(a+b*x))*x^2,x,5,1/16/(b^3*exp(2*arccosh(a+b*x)))-1/2*a/(b^3*exp(arccosh(a+b*x)))+1/16*(1+4*a^2)*exp(2*arccosh(a+b*x))/b^3-1/6*a*exp(3*arccosh(a+b*x))/b^3+1/32*exp(4*arccosh(a+b*x))/b^3-1/8*(1+4*a^2)*arccosh(a+b*x)/b^3],
[exp(arccosh(a+b*x))*x,x,5,1/4/(b^2*exp(arccosh(a+b*x)))-1/4*a*exp(2*arccosh(a+b*x))/b^2+1/12*exp(3*arccosh(a+b*x))/b^2+1/2*a*arccosh(a+b*x)/b^2],
[exp(arccosh(a+b*x)),x,5,1/4*exp(2*arccosh(a+b*x))/b-1/2*arccosh(a+b*x)/b],
[exp(arccosh(a+b*x))/x,x,9,b*x+2*a*arcsinh(sqrt(-1+a+b*x)/sqrt(2))+a*log(x)+2*arctan(sqrt(1-a)*sqrt(1+a+b*x)/(sqrt(1+a)*sqrt(-1+a+b*x)))*sqrt(1-a^2)+sqrt(-1+a+b*x)*sqrt(1+a+b*x)],
[exp(arccosh(a+b*x))/x^2,x,9,-a/x+2*b*arcsinh(sqrt(-1+a+b*x)/sqrt(2))+b*log(x)-2*a*b*arctan(sqrt(1-a)*sqrt(1+a+b*x)/(sqrt(1+a)*sqrt(-1+a+b*x)))/sqrt(1-a^2)-sqrt(-1+a+b*x)*sqrt(1+a+b*x)/x],
[exp(arccosh(a+b*x))/x^3,x,7,-1/2*a/x^2-b/x-b^2*arctan(sqrt(1-a)*sqrt(1+a+b*x)/(sqrt(1+a)*sqrt(-1+a+b*x)))/(1-a^2)^(3/2)-1/2*(1+a+b*x)^(3/2)*sqrt(-1+a+b*x)/((1+a)*x^2)+1/2*b*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/((1-a^2)*x)],
[exp(arccosh(a+b*x))/x^4,x,8,-1/3*a/x^3-1/2*b/x^2+1/3*(-1+a+b*x)^(3/2)*(1+a+b*x)^(3/2)/((1-a^2)*x^3)-a*b^3*arctan(sqrt(1-a)*sqrt(1+a+b*x)/(sqrt(1+a)*sqrt(-1+a+b*x)))/(1-a^2)^(5/2)-1/2*a*b*(1+a+b*x)^(3/2)*sqrt(-1+a+b*x)/((1-a)*(1+a)^2*x^2)+1/2*a*b^2*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/((1-a^2)^2*x)],
[exp(arccosh(a+b*x))/x^5,x,10,-1/4*a/x^4-1/3*b/x^3-1/4*(1+4*a^2)*b^4*arctan(sqrt(1-a)*sqrt(1+a+b*x)/(sqrt(1+a)*sqrt(-1+a+b*x)))/(1-a^2)^(7/2)-1/4*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/x^4+1/12*a*b*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/((1-a^2)*x^3)+1/24*(3+2*a^2)*b^2*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/((1-a^2)^2*x^2)+1/24*a*(13+2*a^2)*b^3*sqrt(-1+a+b*x)*sqrt(1+a+b*x)/((1-a^2)^3*x)],
[exp(arccosh(a+b*x)^2)*x^3,x,37,-1/32*erfi(-2+arccosh(a+b*x))*sqrt(Pi)/(b^4*exp(4))-1/16*erfi(-1+arccosh(a+b*x))*sqrt(Pi)/(b^4*E)-3/8*a^2*erfi(-1+arccosh(a+b*x))*sqrt(Pi)/(b^4*E)+1/16*erfi(1+arccosh(a+b*x))*sqrt(Pi)/(b^4*E)+3/8*a^2*erfi(1+arccosh(a+b*x))*sqrt(Pi)/(b^4*E)+1/32*erfi(2+arccosh(a+b*x))*sqrt(Pi)/(b^4*exp(4))+3/16*a*erfi(1/2*(-3+2*arccosh(a+b*x)))*sqrt(Pi)/(b^4*exp(9/4))+3/16*a*erfi(1/2*(-1+2*arccosh(a+b*x)))*sqrt(Pi)/(b^4*exp(1/4))+1/4*a^3*erfi(1/2*(-1+2*arccosh(a+b*x)))*sqrt(Pi)/(b^4*exp(1/4))-3/16*a*erfi(1/2*(1+2*arccosh(a+b*x)))*sqrt(Pi)/(b^4*exp(1/4))-1/4*a^3*erfi(1/2*(1+2*arccosh(a+b*x)))*sqrt(Pi)/(b^4*exp(1/4))-3/16*a*erfi(1/2*(3+2*arccosh(a+b*x)))*sqrt(Pi)/(b^4*exp(9/4))],
[exp(arccosh(a+b*x)^2)*x^2,x,27,1/4*a*erfi(-1+arccosh(a+b*x))*sqrt(Pi)/(b^3*E)-1/4*a*erfi(1+arccosh(a+b*x))*sqrt(Pi)/(b^3*E)-1/16*erfi(1/2*(-3+2*arccosh(a+b*x)))*sqrt(Pi)/(b^3*exp(9/4))-1/16*erfi(1/2*(-1+2*arccosh(a+b*x)))*sqrt(Pi)/(b^3*exp(1/4))-1/4*a^2*erfi(1/2*(-1+2*arccosh(a+b*x)))*sqrt(Pi)/(b^3*exp(1/4))+1/16*erfi(1/2*(1+2*arccosh(a+b*x)))*sqrt(Pi)/(b^3*exp(1/4))+1/4*a^2*erfi(1/2*(1+2*arccosh(a+b*x)))*sqrt(Pi)/(b^3*exp(1/4))+1/16*erfi(1/2*(3+2*arccosh(a+b*x)))*sqrt(Pi)/(b^3*exp(9/4))],
[exp(arccosh(a+b*x)^2)*x,x,17,-1/8*erfi(-1+arccosh(a+b*x))*sqrt(Pi)/(b^2*E)+1/8*erfi(1+arccosh(a+b*x))*sqrt(Pi)/(b^2*E)+1/4*a*erfi(1/2*(-1+2*arccosh(a+b*x)))*sqrt(Pi)/(b^2*exp(1/4))-1/4*a*erfi(1/2*(1+2*arccosh(a+b*x)))*sqrt(Pi)/(b^2*exp(1/4))],
[exp(arccosh(a+b*x)^2),x,7,-1/4*erfi(1/2*(-1+2*arccosh(a+b*x)))*sqrt(Pi)/(b*exp(1/4))+1/4*erfi(1/2*(1+2*arccosh(a+b*x)))*sqrt(Pi)/(b*exp(1/4))],
[exp(arccosh(a+b*x)^2)/x,x,0,CannotIntegrate(exp(arccosh(a+b*x)^2)/x,x)],
[exp(arccosh(a+b*x)^2)/x^2,x,0,CannotIntegrate(exp(arccosh(a+b*x)^2)/x^2,x)],

# Miscellaneous integrands involving inverse hyperbolic cosines
[arccosh(a+b*x)/(a*d/b+d*x),x,7,-1/2*arccosh(a+b*x)^2/d+arccosh(a+b*x)*log(1+exp(2*arccosh(a+b*x)))/d+1/2*polylog(2,-exp(2*arccosh(a+b*x)))/d],
[x/(arccosh(x)*sqrt(-1+x)*sqrt(1+x)),x,2,Chi(arccosh(x))],
[x^3*arccosh(a+b*x^4),x,4,1/4*(a+b*x^4)*arccosh(a+b*x^4)/b-1/4*sqrt(-1+a+b*x^4)*sqrt(1+a+b*x^4)/b],
[x^(-1+n)*arccosh(a+b*x^n),x,4,(a+b*x^n)*arccosh(a+b*x^n)/(b*n)-sqrt(-1+a+b*x^n)*sqrt(1+a+b*x^n)/(b*n)],
[arccosh(c/(a+b*x)),x,5,(a+b*x)*arcsech(a/c+b*x/c)/b-2*c*arctan(sqrt(((1-a/c)*c-b*x)/(a+c+b*x)))/b],
[arccosh(sqrt(1+b*x^2))^n/sqrt(1+b*x^2),x,2,arccosh(sqrt(1+b*x^2))^(1+n)*sqrt(-1+sqrt(1+b*x^2))*sqrt(1+sqrt(1+b*x^2))/(b*(1+n)*x)],
[1/(arccosh(sqrt(1+b*x^2))*sqrt(1+b*x^2)),x,2,log(arccosh(sqrt(1+b*x^2)))*sqrt(-1+sqrt(1+b*x^2))*sqrt(1+sqrt(1+b*x^2))/(b*x)]]:
