# Maple integration test file: "7 Inverse hyperbolic functions\7.2 Inverse hyperbolic cosine\7.2.4 (f x)^m (d+e x^2)^p (a+b arccosh(c x))^n.txt"

lst:=[

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

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

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

# p>0
[x^4*(d-c^2*d*x^2)*(a+b*arccosh(c*x)),x,8,1/5*d*x^5*(a+b*arccosh(c*x))-1/7*c^2*d*x^7*(a+b*arccosh(c*x))-152/3675*b*d*sqrt(-1+c*x)*sqrt(1+c*x)/c^5-76/3675*b*d*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-19/1225*b*d*x^4*sqrt(-1+c*x)*sqrt(1+c*x)/c+1/49*b*c*d*x^6*sqrt(-1+c*x)*sqrt(1+c*x)],
[x^3*(d-c^2*d*x^2)*(a+b*arccosh(c*x)),x,7,-1/24*b*d*arccosh(c*x)/c^4+1/4*d*x^4*(a+b*arccosh(c*x))-1/6*c^2*d*x^6*(a+b*arccosh(c*x))-1/24*b*d*x*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-1/36*b*d*x^3*sqrt(-1+c*x)*sqrt(1+c*x)/c+1/36*b*c*d*x^5*sqrt(-1+c*x)*sqrt(1+c*x)],
[x^2*(d-c^2*d*x^2)*(a+b*arccosh(c*x)),x,6,1/3*d*x^3*(a+b*arccosh(c*x))-1/5*c^2*d*x^5*(a+b*arccosh(c*x))-26/225*b*d*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-13/225*b*d*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/c+1/25*b*c*d*x^4*sqrt(-1+c*x)*sqrt(1+c*x)],
[x*(d-c^2*d*x^2)*(a+b*arccosh(c*x)),x,4,1/16*b*d*x*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/c+3/32*b*d*arccosh(c*x)/c^2-1/4*d*(1-c^2*x^2)^2*(a+b*arccosh(c*x))/c^2-3/32*b*d*x*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(d-c^2*d*x^2)*(a+b*arccosh(c*x)),x,4,d*x*(a+b*arccosh(c*x))-1/3*c^2*d*x^3*(a+b*arccosh(c*x))-7/9*b*d*sqrt(-1+c*x)*sqrt(1+c*x)/c+1/9*b*c*d*x^2*sqrt(-1+c*x)*sqrt(1+c*x)],
[(d-c^2*d*x^2)*(a+b*arccosh(c*x))/x,x,8,-1/4*b*d*arccosh(c*x)+1/2*d*(1-c^2*x^2)*(a+b*arccosh(c*x))+1/2*d*(a+b*arccosh(c*x))^2/b+d*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))-1/2*b*d*polylog(2,(-1)/exp(2*arccosh(c*x)))+1/4*b*c*d*x*sqrt(-1+c*x)*sqrt(1+c*x)],
[(d-c^2*d*x^2)*(a+b*arccosh(c*x))/x^2,x,5,-d*(a+b*arccosh(c*x))/x-c^2*d*x*(a+b*arccosh(c*x))+b*c*d*arctan(sqrt(-1+c*x)*sqrt(1+c*x))+b*c*d*sqrt(-1+c*x)*sqrt(1+c*x)],
[(d-c^2*d*x^2)*(a+b*arccosh(c*x))/x^3,x,9,-1/2*b*c^2*d*arccosh(c*x)-1/2*d*(1-c^2*x^2)*(a+b*arccosh(c*x))/x^2-1/2*c^2*d*(a+b*arccosh(c*x))^2/b-c^2*d*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))+1/2*b*c^2*d*polylog(2,(-1)/exp(2*arccosh(c*x)))+1/2*b*c*d*sqrt(-1+c*x)*sqrt(1+c*x)/x],
[(d-c^2*d*x^2)*(a+b*arccosh(c*x))/x^4,x,5,-1/3*d*(a+b*arccosh(c*x))/x^3+c^2*d*(a+b*arccosh(c*x))/x-5/6*b*c^3*d*arctan(sqrt(-1+c*x)*sqrt(1+c*x))+1/6*b*c*d*sqrt(-1+c*x)*sqrt(1+c*x)/x^2],
[x^4*(d-c^2*d*x^2)^2*(a+b*arccosh(c*x)),x,7,4/945*b*d^2*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/c^5-1/525*b*d^2*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/c^5-10/441*b*d^2*(-1+c*x)^(7/2)*(1+c*x)^(7/2)/c^5-1/81*b*d^2*(-1+c*x)^(9/2)*(1+c*x)^(9/2)/c^5+1/5*d^2*x^5*(a+b*arccosh(c*x))-2/7*c^2*d^2*x^7*(a+b*arccosh(c*x))+1/9*c^4*d^2*x^9*(a+b*arccosh(c*x))-8/315*b*d^2*sqrt(-1+c*x)*sqrt(1+c*x)/c^5,1/5*d^2*x^5*(a+b*arccosh(c*x))-2/7*c^2*d^2*x^7*(a+b*arccosh(c*x))+1/9*c^4*d^2*x^9*(a+b*arccosh(c*x))+8/315*b*d^2*(1-c^2*x^2)/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+4/945*b*d^2*(1-c^2*x^2)^2/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+1/525*b*d^2*(1-c^2*x^2)^3/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))-10/441*b*d^2*(1-c^2*x^2)^4/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+1/81*b*d^2*(1-c^2*x^2)^5/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^3*(d-c^2*d*x^2)^2*(a+b*arccosh(c*x)),x,9,-73/3072*b*d^2*arccosh(c*x)/c^4+1/4*d^2*x^4*(a+b*arccosh(c*x))-1/3*c^2*d^2*x^6*(a+b*arccosh(c*x))+1/8*c^4*d^2*x^8*(a+b*arccosh(c*x))-73/3072*b*d^2*x*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-73/4608*b*d^2*x^3*sqrt(-1+c*x)*sqrt(1+c*x)/c+43/1152*b*c*d^2*x^5*sqrt(-1+c*x)*sqrt(1+c*x)-1/64*b*c^3*d^2*x^7*sqrt(-1+c*x)*sqrt(1+c*x),1/4*d^2*x^4*(a+b*arccosh(c*x))-1/3*c^2*d^2*x^6*(a+b*arccosh(c*x))+1/8*c^4*d^2*x^8*(a+b*arccosh(c*x))+73/3072*b*d^2*x*(1-c^2*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+73/4608*b*d^2*x^3*(1-c^2*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-43/1152*b*c*d^2*x^5*(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/64*b*c^3*d^2*x^7*(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-73/3072*b*d^2*arctanh(c*x/sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(c^4*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^2*(d-c^2*d*x^2)^2*(a+b*arccosh(c*x)),x,6,4/315*b*d^2*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/c^3-1/175*b*d^2*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/c^3-1/49*b*d^2*(-1+c*x)^(7/2)*(1+c*x)^(7/2)/c^3+1/3*d^2*x^3*(a+b*arccosh(c*x))-2/5*c^2*d^2*x^5*(a+b*arccosh(c*x))+1/7*c^4*d^2*x^7*(a+b*arccosh(c*x))-8/105*b*d^2*sqrt(-1+c*x)*sqrt(1+c*x)/c^3,1/3*d^2*x^3*(a+b*arccosh(c*x))-2/5*c^2*d^2*x^5*(a+b*arccosh(c*x))+1/7*c^4*d^2*x^7*(a+b*arccosh(c*x))+8/105*b*d^2*(1-c^2*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+4/315*b*d^2*(1-c^2*x^2)^2/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/175*b*d^2*(1-c^2*x^2)^3/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))-1/49*b*d^2*(1-c^2*x^2)^4/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(d-c^2*d*x^2)^2*(a+b*arccosh(c*x)),x,5,5/144*b*d^2*x*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/c-1/36*b*d^2*x*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/c+5/96*b*d^2*arccosh(c*x)/c^2-1/6*d^2*(1-c^2*x^2)^3*(a+b*arccosh(c*x))/c^2-5/96*b*d^2*x*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(d-c^2*d*x^2)^2*(a+b*arccosh(c*x)),x,6,4/45*b*d^2*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/c-1/25*b*d^2*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/c+d^2*x*(a+b*arccosh(c*x))-2/3*c^2*d^2*x^3*(a+b*arccosh(c*x))+1/5*c^4*d^2*x^5*(a+b*arccosh(c*x))-8/15*b*d^2*sqrt(-1+c*x)*sqrt(1+c*x)/c,d^2*x*(a+b*arccosh(c*x))-2/3*c^2*d^2*x^3*(a+b*arccosh(c*x))+1/5*c^4*d^2*x^5*(a+b*arccosh(c*x))+8/15*b*d^2*(1-c^2*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))+4/45*b*d^2*(1-c^2*x^2)^2/(c*sqrt(-1+c*x)*sqrt(1+c*x))+1/25*b*d^2*(1-c^2*x^2)^3/(c*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^2*(a+b*arccosh(c*x))/x,x,12,-1/16*b*c*d^2*x*(-1+c*x)^(3/2)*(1+c*x)^(3/2)-11/32*b*d^2*arccosh(c*x)+1/2*d^2*(1-c^2*x^2)*(a+b*arccosh(c*x))+1/4*d^2*(1-c^2*x^2)^2*(a+b*arccosh(c*x))+1/2*d^2*(a+b*arccosh(c*x))^2/b+d^2*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))-1/2*b*d^2*polylog(2,(-1)/exp(2*arccosh(c*x)))+11/32*b*c*d^2*x*sqrt(-1+c*x)*sqrt(1+c*x)],
[(d-c^2*d*x^2)^2*(a+b*arccosh(c*x))/x^2,x,8,-1/9*b*c*d^2*(-1+c*x)^(3/2)*(1+c*x)^(3/2)-d^2*(a+b*arccosh(c*x))/x-2*c^2*d^2*x*(a+b*arccosh(c*x))+1/3*c^4*d^2*x^3*(a+b*arccosh(c*x))+b*c*d^2*arctan(sqrt(-1+c*x)*sqrt(1+c*x))+5/3*b*c*d^2*sqrt(-1+c*x)*sqrt(1+c*x),-d^2*(a+b*arccosh(c*x))/x-2*c^2*d^2*x*(a+b*arccosh(c*x))+1/3*c^4*d^2*x^3*(a+b*arccosh(c*x))-5/3*b*c*d^2*(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/9*b*c*d^2*(1-c^2*x^2)^2/(sqrt(-1+c*x)*sqrt(1+c*x))+b*c*d^2*arctan(sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^2*(a+b*arccosh(c*x))/x^3,x,13,-1/2*b*c*d^2*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/x-1/4*b*c^2*d^2*arccosh(c*x)-c^2*d^2*(1-c^2*x^2)*(a+b*arccosh(c*x))-1/2*d^2*(1-c^2*x^2)^2*(a+b*arccosh(c*x))/x^2-c^2*d^2*(a+b*arccosh(c*x))^2/b-2*c^2*d^2*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))+b*c^2*d^2*polylog(2,(-1)/exp(2*arccosh(c*x)))+1/4*b*c^3*d^2*x*sqrt(-1+c*x)*sqrt(1+c*x)],
[(d-c^2*d*x^2)^2*(a+b*arccosh(c*x))/x^4,x,8,-1/3*d^2*(a+b*arccosh(c*x))/x^3+2*c^2*d^2*(a+b*arccosh(c*x))/x+c^4*d^2*x*(a+b*arccosh(c*x))-11/6*b*c^3*d^2*arctan(sqrt(-1+c*x)*sqrt(1+c*x))-b*c^3*d^2*sqrt(-1+c*x)*sqrt(1+c*x)+1/6*b*c*d^2*sqrt(-1+c*x)*sqrt(1+c*x)/x^2,-1/3*d^2*(a+b*arccosh(c*x))/x^3+2*c^2*d^2*(a+b*arccosh(c*x))/x+c^4*d^2*x*(a+b*arccosh(c*x))+b*c^3*d^2*(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/6*b*c*d^2*(1-c^2*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))-11/6*b*c^3*d^2*arctan(sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^4*(d-c^2*d*x^2)^3*(a+b*arccosh(c*x)),x,6,8/3465*b*d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/c^5-2/1925*b*d^3*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/c^5+1/1617*b*d^3*(-1+c*x)^(7/2)*(1+c*x)^(7/2)/c^5+4/297*b*d^3*(-1+c*x)^(9/2)*(1+c*x)^(9/2)/c^5+1/121*b*d^3*(-1+c*x)^(11/2)*(1+c*x)^(11/2)/c^5+1/5*d^3*x^5*(a+b*arccosh(c*x))-3/7*c^2*d^3*x^7*(a+b*arccosh(c*x))+1/3*c^4*d^3*x^9*(a+b*arccosh(c*x))-1/11*c^6*d^3*x^11*(a+b*arccosh(c*x))-16/1155*b*d^3*sqrt(-1+c*x)*sqrt(1+c*x)/c^5,1/5*d^3*x^5*(a+b*arccosh(c*x))-3/7*c^2*d^3*x^7*(a+b*arccosh(c*x))+1/3*c^4*d^3*x^9*(a+b*arccosh(c*x))-1/11*c^6*d^3*x^11*(a+b*arccosh(c*x))+16/1155*b*d^3*(1-c^2*x^2)/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+8/3465*b*d^3*(1-c^2*x^2)^2/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+2/1925*b*d^3*(1-c^2*x^2)^3/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+1/1617*b*d^3*(1-c^2*x^2)^4/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))-4/297*b*d^3*(1-c^2*x^2)^5/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+1/121*b*d^3*(1-c^2*x^2)^6/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^3*(d-c^2*d*x^2)^3*(a+b*arccosh(c*x)),x,11,49/7680*b*d^3*x*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/c^3-49/9600*b*d^3*x*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/c^3+7/1600*b*d^3*x*(-1+c*x)^(7/2)*(1+c*x)^(7/2)/c^3+1/100*b*d^3*x*(-1+c*x)^(9/2)*(1+c*x)^(9/2)/c^3+49/5120*b*d^3*arccosh(c*x)/c^4-1/8*d^3*(-1+c*x)^4*(1+c*x)^4*(a+b*arccosh(c*x))/c^4-1/10*d^3*(-1+c*x)^5*(1+c*x)^5*(a+b*arccosh(c*x))/c^4-49/5120*b*d^3*x*sqrt(-1+c*x)*sqrt(1+c*x)/c^3,-1/8*d^3*(1-c^2*x^2)^4*(a+b*arccosh(c*x))/c^4+1/10*d^3*(1-c^2*x^2)^5*(a+b*arccosh(c*x))/c^4+49/5120*b*d^3*x*(1-c^2*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+49/7680*b*d^3*x*(1-c^2*x^2)^2/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+49/9600*b*d^3*x*(1-c^2*x^2)^3/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+7/1600*b*d^3*x*(1-c^2*x^2)^4/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))-1/100*b*d^3*x*(1-c^2*x^2)^5/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+49/5120*b*d^3*arctanh(c*x/sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(c^4*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^2*(d-c^2*d*x^2)^3*(a+b*arccosh(c*x)),x,6,8/945*b*d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/c^3-2/525*b*d^3*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/c^3+1/441*b*d^3*(-1+c*x)^(7/2)*(1+c*x)^(7/2)/c^3+1/81*b*d^3*(-1+c*x)^(9/2)*(1+c*x)^(9/2)/c^3+1/3*d^3*x^3*(a+b*arccosh(c*x))-3/5*c^2*d^3*x^5*(a+b*arccosh(c*x))+3/7*c^4*d^3*x^7*(a+b*arccosh(c*x))-1/9*c^6*d^3*x^9*(a+b*arccosh(c*x))-16/315*b*d^3*sqrt(-1+c*x)*sqrt(1+c*x)/c^3,1/3*d^3*x^3*(a+b*arccosh(c*x))-3/5*c^2*d^3*x^5*(a+b*arccosh(c*x))+3/7*c^4*d^3*x^7*(a+b*arccosh(c*x))-1/9*c^6*d^3*x^9*(a+b*arccosh(c*x))+16/315*b*d^3*(1-c^2*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+8/945*b*d^3*(1-c^2*x^2)^2/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+2/525*b*d^3*(1-c^2*x^2)^3/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/441*b*d^3*(1-c^2*x^2)^4/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))-1/81*b*d^3*(1-c^2*x^2)^5/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(d-c^2*d*x^2)^3*(a+b*arccosh(c*x)),x,6,35/1536*b*d^3*x*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/c-7/384*b*d^3*x*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/c+1/64*b*d^3*x*(-1+c*x)^(7/2)*(1+c*x)^(7/2)/c+35/1024*b*d^3*arccosh(c*x)/c^2-1/8*d^3*(1-c^2*x^2)^4*(a+b*arccosh(c*x))/c^2-35/1024*b*d^3*x*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(d-c^2*d*x^2)^3*(a+b*arccosh(c*x)),x,6,8/105*b*d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/c-6/175*b*d^3*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/c+1/49*b*d^3*(-1+c*x)^(7/2)*(1+c*x)^(7/2)/c+d^3*x*(a+b*arccosh(c*x))-c^2*d^3*x^3*(a+b*arccosh(c*x))+3/5*c^4*d^3*x^5*(a+b*arccosh(c*x))-1/7*c^6*d^3*x^7*(a+b*arccosh(c*x))-16/35*b*d^3*sqrt(-1+c*x)*sqrt(1+c*x)/c,d^3*x*(a+b*arccosh(c*x))-c^2*d^3*x^3*(a+b*arccosh(c*x))+3/5*c^4*d^3*x^5*(a+b*arccosh(c*x))-1/7*c^6*d^3*x^7*(a+b*arccosh(c*x))+16/35*b*d^3*(1-c^2*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))+8/105*b*d^3*(1-c^2*x^2)^2/(c*sqrt(-1+c*x)*sqrt(1+c*x))+6/175*b*d^3*(1-c^2*x^2)^3/(c*sqrt(-1+c*x)*sqrt(1+c*x))+1/49*b*d^3*(1-c^2*x^2)^4/(c*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^3*(a+b*arccosh(c*x))/x,x,17,-7/72*b*c*d^3*x*(-1+c*x)^(3/2)*(1+c*x)^(3/2)+1/36*b*c*d^3*x*(-1+c*x)^(5/2)*(1+c*x)^(5/2)-19/48*b*d^3*arccosh(c*x)+1/2*d^3*(1-c^2*x^2)*(a+b*arccosh(c*x))+1/4*d^3*(1-c^2*x^2)^2*(a+b*arccosh(c*x))+1/6*d^3*(1-c^2*x^2)^3*(a+b*arccosh(c*x))+1/2*d^3*(a+b*arccosh(c*x))^2/b+d^3*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))-1/2*b*d^3*polylog(2,(-1)/exp(2*arccosh(c*x)))+19/48*b*c*d^3*x*sqrt(-1+c*x)*sqrt(1+c*x)],
[(d-c^2*d*x^2)^3*(a+b*arccosh(c*x))/x^2,x,8,-1/5*b*c*d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2)+1/25*b*c*d^3*(-1+c*x)^(5/2)*(1+c*x)^(5/2)-d^3*(a+b*arccosh(c*x))/x-3*c^2*d^3*x*(a+b*arccosh(c*x))+c^4*d^3*x^3*(a+b*arccosh(c*x))-1/5*c^6*d^3*x^5*(a+b*arccosh(c*x))+b*c*d^3*arctan(sqrt(-1+c*x)*sqrt(1+c*x))+11/5*b*c*d^3*sqrt(-1+c*x)*sqrt(1+c*x),-d^3*(a+b*arccosh(c*x))/x-3*c^2*d^3*x*(a+b*arccosh(c*x))+c^4*d^3*x^3*(a+b*arccosh(c*x))-1/5*c^6*d^3*x^5*(a+b*arccosh(c*x))-11/5*b*c*d^3*(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/5*b*c*d^3*(1-c^2*x^2)^2/(sqrt(-1+c*x)*sqrt(1+c*x))-1/25*b*c*d^3*(1-c^2*x^2)^3/(sqrt(-1+c*x)*sqrt(1+c*x))+b*c*d^3*arctan(sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^3*(a+b*arccosh(c*x))/x^3,x,18,-7/16*b*c^3*d^3*x*(-1+c*x)^(3/2)*(1+c*x)^(3/2)+1/2*b*c*d^3*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/x+3/32*b*c^2*d^3*arccosh(c*x)-3/2*c^2*d^3*(1-c^2*x^2)*(a+b*arccosh(c*x))-3/4*c^2*d^3*(1-c^2*x^2)^2*(a+b*arccosh(c*x))-1/2*d^3*(1-c^2*x^2)^3*(a+b*arccosh(c*x))/x^2-3/2*c^2*d^3*(a+b*arccosh(c*x))^2/b-3*c^2*d^3*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))+3/2*b*c^2*d^3*polylog(2,(-1)/exp(2*arccosh(c*x)))-3/32*b*c^3*d^3*x*sqrt(-1+c*x)*sqrt(1+c*x)],
[(d-c^2*d*x^2)^3*(a+b*arccosh(c*x))/x^4,x,9,1/9*b*c^3*d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2)-1/3*d^3*(a+b*arccosh(c*x))/x^3+3*c^2*d^3*(a+b*arccosh(c*x))/x+3*c^4*d^3*x*(a+b*arccosh(c*x))-1/3*c^6*d^3*x^3*(a+b*arccosh(c*x))-17/6*b*c^3*d^3*arctan(sqrt(-1+c*x)*sqrt(1+c*x))-8/3*b*c^3*d^3*sqrt(-1+c*x)*sqrt(1+c*x)+1/6*b*c*d^3*sqrt(-1+c*x)*sqrt(1+c*x)/x^2,-1/3*d^3*(a+b*arccosh(c*x))/x^3+3*c^2*d^3*(a+b*arccosh(c*x))/x+3*c^4*d^3*x*(a+b*arccosh(c*x))-1/3*c^6*d^3*x^3*(a+b*arccosh(c*x))+8/3*b*c^3*d^3*(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/6*b*c*d^3*(1-c^2*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))+1/9*b*c^3*d^3*(1-c^2*x^2)^2/(sqrt(-1+c*x)*sqrt(1+c*x))-17/6*b*c^3*d^3*arctan(sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],

# p<0
[x^4*(a+b*arccosh(c*x))/(d-c^2*d*x^2),x,12,-x*(a+b*arccosh(c*x))/(c^4*d)-1/3*x^3*(a+b*arccosh(c*x))/(c^2*d)+2*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/(c^5*d)+b*polylog(2,-exp(arccosh(c*x)))/(c^5*d)-b*polylog(2,exp(arccosh(c*x)))/(c^5*d)+11/9*b*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d)+1/9*b*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d)],
[x^3*(a+b*arccosh(c*x))/(d-c^2*d*x^2),x,8,1/4*b*arccosh(c*x)/(c^4*d)-1/2*x^2*(a+b*arccosh(c*x))/(c^2*d)+1/2*(a+b*arccosh(c*x))^2/(b*c^4*d)-(a+b*arccosh(c*x))*log(1-exp(2*arccosh(c*x)))/(c^4*d)-1/2*b*polylog(2,exp(2*arccosh(c*x)))/(c^4*d)+1/4*b*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d)],
[x^2*(a+b*arccosh(c*x))/(d-c^2*d*x^2),x,8,-x*(a+b*arccosh(c*x))/(c^2*d)+2*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/(c^3*d)+b*polylog(2,-exp(arccosh(c*x)))/(c^3*d)-b*polylog(2,exp(arccosh(c*x)))/(c^3*d)+b*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d)],
[x*(a+b*arccosh(c*x))/(d-c^2*d*x^2),x,5,1/2*(a+b*arccosh(c*x))^2/(b*c^2*d)-(a+b*arccosh(c*x))*log(1-exp(2*arccosh(c*x)))/(c^2*d)-1/2*b*polylog(2,exp(2*arccosh(c*x)))/(c^2*d)],
[(a+b*arccosh(c*x))/(d-c^2*d*x^2),x,6,2*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/(c*d)+b*polylog(2,-exp(arccosh(c*x)))/(c*d)-b*polylog(2,exp(arccosh(c*x)))/(c*d)],
[(a+b*arccosh(c*x))/(x*(d-c^2*d*x^2)),x,7,2*(a+b*arccosh(c*x))*arctanh(exp(2*arccosh(c*x)))/d+1/2*b*polylog(2,-exp(2*arccosh(c*x)))/d-1/2*b*polylog(2,exp(2*arccosh(c*x)))/d],
[(a+b*arccosh(c*x))/(x^2*(d-c^2*d*x^2)),x,9,(-a-b*arccosh(c*x))/(d*x)+b*c*arctan(sqrt(-1+c*x)*sqrt(1+c*x))/d+2*c*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/d+b*c*polylog(2,-exp(arccosh(c*x)))/d-b*c*polylog(2,exp(arccosh(c*x)))/d],
[(a+b*arccosh(c*x))/(x^3*(d-c^2*d*x^2)),x,9,1/2*(-a-b*arccosh(c*x))/(d*x^2)+2*c^2*(a+b*arccosh(c*x))*arctanh(exp(2*arccosh(c*x)))/d+1/2*b*c^2*polylog(2,-exp(2*arccosh(c*x)))/d-1/2*b*c^2*polylog(2,exp(2*arccosh(c*x)))/d+1/2*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/(d*x)],
[(a+b*arccosh(c*x))/(x^4*(d-c^2*d*x^2)),x,14,1/3*(-a-b*arccosh(c*x))/(d*x^3)-c^2*(a+b*arccosh(c*x))/(d*x)+7/6*b*c^3*arctan(sqrt(-1+c*x)*sqrt(1+c*x))/d+2*c^3*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/d+b*c^3*polylog(2,-exp(arccosh(c*x)))/d-b*c^3*polylog(2,exp(arccosh(c*x)))/d+1/6*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/(d*x^2)],
[x^4*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^2,x,12,3/2*x*(a+b*arccosh(c*x))/(c^4*d^2)+1/2*x^3*(a+b*arccosh(c*x))/(c^2*d^2*(1-c^2*x^2))-3*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/(c^5*d^2)-3/2*b*polylog(2,-exp(arccosh(c*x)))/(c^5*d^2)+3/2*b*polylog(2,exp(arccosh(c*x)))/(c^5*d^2)-1/2*b*x^2/(c^3*d^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/2*b*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d^2)],
[x^3*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^2,x,10,1/2*b*arccosh(c*x)/(c^4*d^2)+1/2*x^2*(a+b*arccosh(c*x))/(c^2*d^2*(1-c^2*x^2))-1/2*(a+b*arccosh(c*x))^2/(b*c^4*d^2)+(a+b*arccosh(c*x))*log(1-exp(2*arccosh(c*x)))/(c^4*d^2)+1/2*b*polylog(2,exp(2*arccosh(c*x)))/(c^4*d^2)-1/2*b/(c^4*d^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/2*b*sqrt(-1+c*x)/(c^4*d^2*sqrt(1+c*x))],
[x^2*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^2,x,8,1/2*x*(a+b*arccosh(c*x))/(c^2*d^2*(1-c^2*x^2))-(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/(c^3*d^2)-1/2*b*polylog(2,-exp(arccosh(c*x)))/(c^3*d^2)+1/2*b*polylog(2,exp(arccosh(c*x)))/(c^3*d^2)-1/2*b/(c^3*d^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^2,x,2,1/2*(a+b*arccosh(c*x))/(c^2*d^2*(1-c^2*x^2))-1/2*b*x/(c*d^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(d-c^2*d*x^2)^2,x,8,1/2*x*(a+b*arccosh(c*x))/(d^2*(1-c^2*x^2))+(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/(c*d^2)+1/2*b*polylog(2,-exp(arccosh(c*x)))/(c*d^2)-1/2*b*polylog(2,exp(arccosh(c*x)))/(c*d^2)-1/2*b/(c*d^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x*(d-c^2*d*x^2)^2),x,9,1/2*(a+b*arccosh(c*x))/(d^2*(1-c^2*x^2))+2*(a+b*arccosh(c*x))*arctanh(exp(2*arccosh(c*x)))/d^2+1/2*b*polylog(2,-exp(2*arccosh(c*x)))/d^2-1/2*b*polylog(2,exp(2*arccosh(c*x)))/d^2-1/2*b*c*x/(d^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x^2*(d-c^2*d*x^2)^2),x,13,(-a-b*arccosh(c*x))/(d^2*x*(1-c^2*x^2))+3/2*c^2*x*(a+b*arccosh(c*x))/(d^2*(1-c^2*x^2))+b*c*arctan(sqrt(-1+c*x)*sqrt(1+c*x))/d^2+3*c*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/d^2+3/2*b*c*polylog(2,-exp(arccosh(c*x)))/d^2-3/2*b*c*polylog(2,exp(arccosh(c*x)))/d^2-1/2*b*c/(d^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x^3*(d-c^2*d*x^2)^2),x,13,c^2*(a+b*arccosh(c*x))/(d^2*(1-c^2*x^2))+1/2*(-a-b*arccosh(c*x))/(d^2*x^2*(1-c^2*x^2))+4*c^2*(a+b*arccosh(c*x))*arctanh(exp(2*arccosh(c*x)))/d^2+b*c^2*polylog(2,-exp(2*arccosh(c*x)))/d^2-b*c^2*polylog(2,exp(2*arccosh(c*x)))/d^2-1/2*b*c/(d^2*x*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x^4*(d-c^2*d*x^2)^2),x,20,1/3*(-a-b*arccosh(c*x))/(d^2*x^3*(1-c^2*x^2))-5/3*c^2*(a+b*arccosh(c*x))/(d^2*x*(1-c^2*x^2))+5/2*c^4*x*(a+b*arccosh(c*x))/(d^2*(1-c^2*x^2))+13/6*b*c^3*arctan(sqrt(-1+c*x)*sqrt(1+c*x))/d^2+5*c^3*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/d^2+5/2*b*c^3*polylog(2,-exp(arccosh(c*x)))/d^2-5/2*b*c^3*polylog(2,exp(arccosh(c*x)))/d^2-1/3*b*c^3/(d^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/6*b*c/(d^2*x^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^4*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^3,x,13,1/12*b*x^3/(c^2*d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2))-1/12*b*(-1+c*x)^(3/2)/(c^5*d^3*(1+c*x)^(3/2))+1/4*x^3*(a+b*arccosh(c*x))/(c^2*d^3*(1-c^2*x^2)^2)-3/8*x*(a+b*arccosh(c*x))/(c^4*d^3*(1-c^2*x^2))+3/4*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/(c^5*d^3)+3/8*b*polylog(2,-exp(arccosh(c*x)))/(c^5*d^3)-3/8*b*polylog(2,exp(arccosh(c*x)))/(c^5*d^3)+1/4*b/(c^5*d^3*(1+c*x)^(3/2)*sqrt(-1+c*x))+3/8*b/(c^5*d^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^3*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^3,x,7,1/12*b*x^3/(c*d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2))-1/4*b*arccosh(c*x)/(c^4*d^3)+1/4*x^4*(a+b*arccosh(c*x))/(d^3*(1-c^2*x^2)^2)+1/4*b/(c^4*d^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/4*b*sqrt(-1+c*x)/(c^4*d^3*sqrt(1+c*x))],
[x^2*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^3,x,10,1/12*b/(c^3*d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2))+1/4*x*(a+b*arccosh(c*x))/(c^2*d^3*(1-c^2*x^2)^2)-1/8*x*(a+b*arccosh(c*x))/(c^2*d^3*(1-c^2*x^2))-1/4*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/(c^3*d^3)-1/8*b*polylog(2,-exp(arccosh(c*x)))/(c^3*d^3)+1/8*b*polylog(2,exp(arccosh(c*x)))/(c^3*d^3)+1/8*b/(c^3*d^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^3,x,3,1/12*b*x/(c*d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2))+1/4*(a+b*arccosh(c*x))/(c^2*d^3*(1-c^2*x^2)^2)-1/6*b*x/(c*d^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(d-c^2*d*x^2)^3,x,10,1/12*b/(c*d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2))+1/4*x*(a+b*arccosh(c*x))/(d^3*(1-c^2*x^2)^2)+3/8*x*(a+b*arccosh(c*x))/(d^3*(1-c^2*x^2))+3/4*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/(c*d^3)+3/8*b*polylog(2,-exp(arccosh(c*x)))/(c*d^3)-3/8*b*polylog(2,exp(arccosh(c*x)))/(c*d^3)-3/8*b/(c*d^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x*(d-c^2*d*x^2)^3),x,12,1/12*b*c*x/(d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2))+1/4*(a+b*arccosh(c*x))/(d^3*(1-c^2*x^2)^2)+1/2*(a+b*arccosh(c*x))/(d^3*(1-c^2*x^2))+2*(a+b*arccosh(c*x))*arctanh(exp(2*arccosh(c*x)))/d^3+1/2*b*polylog(2,-exp(2*arccosh(c*x)))/d^3-1/2*b*polylog(2,exp(2*arccosh(c*x)))/d^3-2/3*b*c*x/(d^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x^2*(d-c^2*d*x^2)^3),x,17,1/12*b*c/(d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2))+(-a-b*arccosh(c*x))/(d^3*x*(1-c^2*x^2)^2)+5/4*c^2*x*(a+b*arccosh(c*x))/(d^3*(1-c^2*x^2)^2)+15/8*c^2*x*(a+b*arccosh(c*x))/(d^3*(1-c^2*x^2))+b*c*arctan(sqrt(-1+c*x)*sqrt(1+c*x))/d^3+15/4*c*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/d^3+15/8*b*c*polylog(2,-exp(arccosh(c*x)))/d^3-15/8*b*c*polylog(2,exp(arccosh(c*x)))/d^3-7/8*b*c/(d^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x^3*(d-c^2*d*x^2)^3),x,17,1/2*b*c/(d^3*x*(-1+c*x)^(3/2)*(1+c*x)^(3/2))-5/12*b*c^3*x/(d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2))+3/4*c^2*(a+b*arccosh(c*x))/(d^3*(1-c^2*x^2)^2)+1/2*(-a-b*arccosh(c*x))/(d^3*x^2*(1-c^2*x^2)^2)+3/2*c^2*(a+b*arccosh(c*x))/(d^3*(1-c^2*x^2))+6*c^2*(a+b*arccosh(c*x))*arctanh(exp(2*arccosh(c*x)))/d^3+3/2*b*c^2*polylog(2,-exp(2*arccosh(c*x)))/d^3-3/2*b*c^2*polylog(2,exp(2*arccosh(c*x)))/d^3-2/3*b*c^3*x/(d^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x^4*(d-c^2*d*x^2)^3),x,26,-1/12*b*c^3/(d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2))+1/6*b*c/(d^3*x^2*(-1+c*x)^(3/2)*(1+c*x)^(3/2))+1/3*(-a-b*arccosh(c*x))/(d^3*x^3*(1-c^2*x^2)^2)-7/3*c^2*(a+b*arccosh(c*x))/(d^3*x*(1-c^2*x^2)^2)+35/12*c^4*x*(a+b*arccosh(c*x))/(d^3*(1-c^2*x^2)^2)+35/8*c^4*x*(a+b*arccosh(c*x))/(d^3*(1-c^2*x^2))+19/6*b*c^3*arctan(sqrt(-1+c*x)*sqrt(1+c*x))/d^3+35/4*c^3*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))/d^3+35/8*b*c^3*polylog(2,-exp(arccosh(c*x)))/d^3-35/8*b*c^3*polylog(2,exp(arccosh(c*x)))/d^3-29/24*b*c^3/(d^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[arccosh(a*x)/(c-a^2*c*x^2),x,6,2*arccosh(a*x)*arctanh(exp(arccosh(a*x)))/(a*c)+polylog(2,-exp(arccosh(a*x)))/(a*c)-polylog(2,exp(arccosh(a*x)))/(a*c)],
[arccosh(a*x)/(c-a^2*c*x^2)^2,x,8,1/2*x*arccosh(a*x)/(c^2*(1-a^2*x^2))+arccosh(a*x)*arctanh(exp(arccosh(a*x)))/(a*c^2)+1/2*polylog(2,-exp(arccosh(a*x)))/(a*c^2)-1/2*polylog(2,exp(arccosh(a*x)))/(a*c^2)+(-1/2)/(a*c^2*sqrt(-1+a*x)*sqrt(1+a*x))],
[arccosh(a*x)/(c-a^2*c*x^2)^3,x,10,1/12/(a*c^3*(-1+a*x)^(3/2)*(1+a*x)^(3/2))+1/4*x*arccosh(a*x)/(c^3*(1-a^2*x^2)^2)+3/8*x*arccosh(a*x)/(c^3*(1-a^2*x^2))+3/4*arccosh(a*x)*arctanh(exp(arccosh(a*x)))/(a*c^3)+3/8*polylog(2,-exp(arccosh(a*x)))/(a*c^3)-3/8*polylog(2,exp(arccosh(a*x)))/(a*c^3)+(-3/8)/(a*c^3*sqrt(-1+a*x)*sqrt(1+a*x))],

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

# p>0
[x^4*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2),x,7,-1/16*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^4-1/24*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+1/6*x^5*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+1/32*b*x^2*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/96*b*x^4*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/36*b*c*x^6*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/32*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c^5*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2),x,5,-1/8*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+1/4*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+1/16*b*x^2*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/16*b*c*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/16*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2),x,3,1/2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-1/4*b*c*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/4*(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)/x^2,x,3,-(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/x+1/2*c*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*sqrt(-1+c*x)*sqrt(1+c*x))+b*c*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/x^4,x,4,-1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/(d*x^3)-1/6*b*c*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/3*b*c^3*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/x^6,x,4,-1/5*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/(d*x^5)-2/15*c^2*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/(d*x^3)-1/20*b*c*sqrt(d-c^2*d*x^2)/(x^4*sqrt(-1+c*x)*sqrt(1+c*x))+1/30*b*c^3*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))-2/15*b*c^5*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/x^8,x,4,-1/7*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/(d*x^7)-4/35*c^2*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/(d*x^5)-8/105*c^4*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/(d*x^3)-1/42*b*c*sqrt(d-c^2*d*x^2)/(x^6*sqrt(-1+c*x)*sqrt(1+c*x))+1/140*b*c^3*sqrt(d-c^2*d*x^2)/(x^4*sqrt(-1+c*x)*sqrt(1+c*x))+2/105*b*c^5*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))-8/105*b*c^7*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^5*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2),x,3,-1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/(c^6*d)+2/5*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(c^6*d^2)-1/7*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(c^6*d^3)+8/105*b*x*sqrt(d-c^2*d*x^2)/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+4/315*b*x^3*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/175*b*x^5*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/49*b*c*x^7*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2),x,3,-1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/(c^4*d)+1/5*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(c^4*d^2)+2/15*b*x*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/45*b*x^3*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/25*b*c*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2),x,3,-1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/(c^2*d)+1/3*b*x*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/9*b*c*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/x,x,8,(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-b*c*x*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+I*b*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-I*b*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/x^3,x,8,-1/2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/x^2-1/2*b*c*sqrt(d-c^2*d*x^2)/(x*sqrt(-1+c*x)*sqrt(1+c*x))+c^2*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/2*I*b*c^2*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/2*I*b*c^2*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/x^5,x,10,-1/4*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/x^4+1/8*c^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/x^2-1/12*b*c*sqrt(d-c^2*d*x^2)/(x^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/8*b*c^3*sqrt(d-c^2*d*x^2)/(x*sqrt(-1+c*x)*sqrt(1+c*x))+1/4*c^4*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/8*I*b*c^4*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/8*I*b*c^4*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^4*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x)),x,11,1/8*x^5*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))-3/128*d*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^4-1/64*d*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+1/16*d*x^5*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+3/256*b*d*x^2*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/256*b*d*x^4*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/32*b*c*d*x^6*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/64*b*c^3*d*x^8*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3/256*d*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c^5*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^2*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x)),x,9,1/6*x^3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))-1/16*d*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+1/8*d*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+1/32*b*d*x^2*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-7/96*b*c*d*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/36*b*c^3*d*x^6*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/32*d*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x)),x,7,1/4*x*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))+3/8*d*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-5/16*b*c*d*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/16*b*c^3*d*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3/16*d*(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))/x^2,x,7,-(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x-3/2*c^2*d*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+1/4*b*c^3*d*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3/4*c*d*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*sqrt(-1+c*x)*sqrt(1+c*x))+b*c*d*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x^4,x,7,-1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x^3+c^2*d*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/x-1/6*b*c*d*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/2*c^3*d*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*sqrt(-1+c*x)*sqrt(1+c*x))-4/3*b*c^3*d*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x^6,x,5,-1/5*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(d*x^5)-1/20*b*c*d*sqrt(d-c^2*d*x^2)/(x^4*sqrt(-1+c*x)*sqrt(1+c*x))+1/5*b*c^3*d*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))+1/5*b*c^5*d*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x^8,x,5,-1/7*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(d*x^7)-2/35*c^2*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(d*x^5)-1/42*b*c*d*sqrt(d-c^2*d*x^2)/(x^6*sqrt(-1+c*x)*sqrt(1+c*x))+2/35*b*c^3*d*sqrt(d-c^2*d*x^2)/(x^4*sqrt(-1+c*x)*sqrt(1+c*x))-1/70*b*c^5*d*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))+2/35*b*c^7*d*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x^10,x,5,-1/9*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(d*x^9)-4/63*c^2*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(d*x^7)-8/315*c^4*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(d*x^5)-1/72*b*c*d*sqrt(d-c^2*d*x^2)/(x^8*sqrt(-1+c*x)*sqrt(1+c*x))+5/189*b*c^3*d*sqrt(d-c^2*d*x^2)/(x^6*sqrt(-1+c*x)*sqrt(1+c*x))-1/420*b*c^5*d*sqrt(d-c^2*d*x^2)/(x^4*sqrt(-1+c*x)*sqrt(1+c*x))-2/315*b*c^7*d*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))+8/315*b*c^9*d*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x^12,x,5,-1/11*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(d*x^11)-2/33*c^2*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(d*x^9)-8/231*c^4*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(d*x^7)-16/1155*c^6*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(d*x^5)-1/110*b*c*d*sqrt(d-c^2*d*x^2)/(x^10*sqrt(-1+c*x)*sqrt(1+c*x))+1/66*b*c^3*d*sqrt(d-c^2*d*x^2)/(x^8*sqrt(-1+c*x)*sqrt(1+c*x))-1/1386*b*c^5*d*sqrt(d-c^2*d*x^2)/(x^6*sqrt(-1+c*x)*sqrt(1+c*x))-1/770*b*c^7*d*sqrt(d-c^2*d*x^2)/(x^4*sqrt(-1+c*x)*sqrt(1+c*x))-4/1155*b*c^9*d*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))+16/1155*b*c^11*d*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^7*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x)),x,4,-1/5*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(c^8*d)+3/7*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(c^8*d^2)-1/3*(d-c^2*d*x^2)^(9/2)*(a+b*arccosh(c*x))/(c^8*d^3)+1/11*(d-c^2*d*x^2)^(11/2)*(a+b*arccosh(c*x))/(c^8*d^4)+16/1155*b*d*x*sqrt(d-c^2*d*x^2)/(c^7*sqrt(-1+c*x)*sqrt(1+c*x))+8/3465*b*d*x^3*sqrt(d-c^2*d*x^2)/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+2/1925*b*d*x^5*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/1617*b*d*x^7*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-4/297*b*c*d*x^9*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/121*b*c^3*d*x^11*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^5*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x)),x,4,-1/5*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(c^6*d)+2/7*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(c^6*d^2)-1/9*(d-c^2*d*x^2)^(9/2)*(a+b*arccosh(c*x))/(c^6*d^3)+8/315*b*d*x*sqrt(d-c^2*d*x^2)/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+4/945*b*d*x^3*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/525*b*d*x^5*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-10/441*b*c*d*x^7*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/81*b*c^3*d*x^9*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x)),x,4,-1/5*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(c^4*d)+1/7*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(c^4*d^2)+2/35*b*d*x*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/105*b*d*x^3*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-8/175*b*c*d*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/49*b*c^3*d*x^7*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x)),x,4,-1/5*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(c^2*d)+1/5*b*d*x*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-2/15*b*c*d*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/25*b*c^3*d*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x,x,11,1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))+d*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-4/3*b*c*d*x*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/9*b*c^3*d*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*d*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+I*b*d*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-I*b*d*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x^3,x,12,-1/2*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x^2-3/2*c^2*d*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-1/2*b*c*d*sqrt(d-c^2*d*x^2)/(x*sqrt(-1+c*x)*sqrt(1+c*x))+b*c^3*d*x*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3*c^2*d*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3/2*I*b*c^2*d*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3/2*I*b*c^2*d*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x^5,x,12,-1/4*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x^4+3/8*c^2*d*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/x^2-1/12*b*c*d*sqrt(d-c^2*d*x^2)/(x^3*sqrt(-1+c*x)*sqrt(1+c*x))+5/8*b*c^3*d*sqrt(d-c^2*d*x^2)/(x*sqrt(-1+c*x)*sqrt(1+c*x))-3/4*c^4*d*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3/8*I*b*c^4*d*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3/8*I*b*c^4*d*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^4*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x)),x,16,1/16*d*x^5*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))+1/10*x^5*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))-3/256*d^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^4-1/128*d^2*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+1/32*d^2*x^5*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+3/512*b*d^2*x^2*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/512*b*d^2*x^4*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-31/960*b*c*d^2*x^6*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+21/640*b*c^3*d^2*x^8*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/100*b*c^5*d^2*x^10*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3/512*d^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*c^5*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^2*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x)),x,14,5/48*d*x^3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))+1/8*x^3*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))-5/128*d^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/c^2+5/64*d^2*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+5/256*b*d^2*x^2*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-59/768*b*c*d^2*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+17/288*b*c^3*d^2*x^6*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/64*b*c^5*d^2*x^8*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-5/256*d^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))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x)),x,10,5/24*d*x*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))+1/6*x*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))+5/16*d^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-25/96*b*c*d^2*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+5/96*b*c^3*d^2*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/36*b*d^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*(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))/x^2,x,12,-5/4*c^2*d*x*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))-(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/x-15/8*c^2*d^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)+9/16*b*c^3*d^2*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/16*b*c^5*d^2*x^4*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+15/16*c*d^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*sqrt(-1+c*x)*sqrt(1+c*x))+b*c*d^2*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/x^4,x,12,5/3*c^2*d*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x-1/3*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/x^3+5/2*c^4*d^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-1/6*b*c*d^2*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/4*b*c^5*d^2*x^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-5/4*c^3*d^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*sqrt(-1+c*x)*sqrt(1+c*x))-7/3*b*c^3*d^2*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/x^6,x,12,1/3*c^2*d*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x^3-1/5*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/x^5-c^4*d^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/x-1/20*b*c*d^2*sqrt(d-c^2*d*x^2)/(x^4*sqrt(-1+c*x)*sqrt(1+c*x))+11/30*b*c^3*d^2*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))+1/2*c^5*d^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(b*sqrt(-1+c*x)*sqrt(1+c*x))+23/15*b*c^5*d^2*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/x^8,x,5,-1/7*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(d*x^7)-1/42*b*c*d^2*sqrt(d-c^2*d*x^2)/(x^6*sqrt(-1+c*x)*sqrt(1+c*x))+3/28*b*c^3*d^2*sqrt(d-c^2*d*x^2)/(x^4*sqrt(-1+c*x)*sqrt(1+c*x))-3/14*b*c^5*d^2*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/7*b*c^7*d^2*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/x^10,x,6,-1/9*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(d*x^9)-2/63*c^2*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(d*x^7)-1/189*b*c^3*d^2*sqrt(d-c^2*d*x^2)/(x^6*sqrt(-1+c*x)*sqrt(1+c*x))+1/42*b*c^5*d^2*sqrt(d-c^2*d*x^2)/(x^4*sqrt(-1+c*x)*sqrt(1+c*x))-1/21*b*c^7*d^2*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/72*b*c*d^2*(1-c^2*x^2)^4*sqrt(d-c^2*d*x^2)/(x^8*sqrt(-1+c*x)*sqrt(1+c*x))-2/63*b*c^9*d^2*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/x^12,x,5,-1/11*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(d*x^11)-4/99*c^2*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(d*x^9)-8/693*c^4*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(d*x^7)-1/110*b*c*d^2*sqrt(d-c^2*d*x^2)/(x^10*sqrt(-1+c*x)*sqrt(1+c*x))+23/792*b*c^3*d^2*sqrt(d-c^2*d*x^2)/(x^8*sqrt(-1+c*x)*sqrt(1+c*x))-113/4158*b*c^5*d^2*sqrt(d-c^2*d*x^2)/(x^6*sqrt(-1+c*x)*sqrt(1+c*x))+1/924*b*c^7*d^2*sqrt(d-c^2*d*x^2)/(x^4*sqrt(-1+c*x)*sqrt(1+c*x))+2/693*b*c^9*d^2*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))-8/693*b*c^11*d^2*log(x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^7*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x)),x,4,-1/7*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(c^8*d)+1/3*(d-c^2*d*x^2)^(9/2)*(a+b*arccosh(c*x))/(c^8*d^2)-3/11*(d-c^2*d*x^2)^(11/2)*(a+b*arccosh(c*x))/(c^8*d^3)+1/13*(d-c^2*d*x^2)^(13/2)*(a+b*arccosh(c*x))/(c^8*d^4)+16/3003*b*d^2*x*sqrt(d-c^2*d*x^2)/(c^7*sqrt(-1+c*x)*sqrt(1+c*x))+8/9009*b*d^2*x^3*sqrt(d-c^2*d*x^2)/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+2/5005*b*d^2*x^5*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+5/21021*b*d^2*x^7*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-53/3861*b*c*d^2*x^9*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+27/1573*b*c^3*d^2*x^11*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/169*b*c^5*d^2*x^13*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^5*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x)),x,4,-1/7*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(c^6*d)+2/9*(d-c^2*d*x^2)^(9/2)*(a+b*arccosh(c*x))/(c^6*d^2)-1/11*(d-c^2*d*x^2)^(11/2)*(a+b*arccosh(c*x))/(c^6*d^3)+8/693*b*d^2*x*sqrt(d-c^2*d*x^2)/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+4/2079*b*d^2*x^3*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/1155*b*d^2*x^5*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-113/4851*b*c*d^2*x^7*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+23/891*b*c^3*d^2*x^9*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/121*b*c^5*d^2*x^11*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^3*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x)),x,4,-1/7*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(c^4*d)+1/9*(d-c^2*d*x^2)^(9/2)*(a+b*arccosh(c*x))/(c^4*d^2)+2/63*b*d^2*x*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/189*b*d^2*x^3*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/21*b*c*d^2*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+19/441*b*c^3*d^2*x^7*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/81*b*c^5*d^2*x^9*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x)),x,4,-1/7*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))/(c^2*d)+1/7*b*d^2*x*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/7*b*c*d^2*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3/35*b*c^3*d^2*x^5*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/49*b*c^5*d^2*x^7*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/x,x,15,1/3*d*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))+1/5*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))+d^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-23/15*b*c*d^2*x*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+11/45*b*c^3*d^2*x^3*sqrt(d-c^2*d*x^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)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*d^2*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+I*b*d^2*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-I*b*d^2*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/x^3,x,15,-5/6*c^2*d*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))-1/2*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/x^2-5/2*c^2*d^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-1/2*b*c*d^2*sqrt(d-c^2*d*x^2)/(x*sqrt(-1+c*x)*sqrt(1+c*x))+7/3*b*c^3*d^2*x*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/9*b*c^5*d^2*x^3*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+5*c^2*d^2*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-5/2*I*b*c^2*d^2*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+5/2*I*b*c^2*d^2*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/x^5,x,16,5/8*c^2*d*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/x^2-1/4*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/x^4+15/8*c^4*d^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)-1/12*b*c*d^2*sqrt(d-c^2*d*x^2)/(x^3*sqrt(-1+c*x)*sqrt(1+c*x))+9/8*b*c^3*d^2*sqrt(d-c^2*d*x^2)/(x*sqrt(-1+c*x)*sqrt(1+c*x))-b*c^5*d^2*x*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-15/4*c^4*d^2*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+15/8*I*b*c^4*d^2*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-15/8*I*b*c^4*d^2*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[arccosh(x)*sqrt(1-x^2),x,3,-1/4*x^2*sqrt(1-x)/sqrt(-1+x)-1/4*arccosh(x)^2*sqrt(1-x)/sqrt(-1+x)+1/2*x*arccosh(x)*sqrt(1-x^2)],

# p<0
[x^5*(a+b*arccosh(c*x))/sqrt(d-c^2*d*x^2),x,6,-8/15*b*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*sqrt(d-c^2*d*x^2))-4/45*b*x^3*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*sqrt(d-c^2*d*x^2))-1/25*b*x^5*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))-8/15*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c^6*d)-4/15*x^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c^4*d)-1/5*x^4*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c^2*d)],
[x^4*(a+b*arccosh(c*x))/sqrt(d-c^2*d*x^2),x,5,-3/16*b*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*sqrt(d-c^2*d*x^2))-1/16*b*x^4*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))+3/16*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^5*sqrt(d-c^2*d*x^2))-3/8*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c^4*d)-1/4*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c^2*d)],
[x^3*(a+b*arccosh(c*x))/sqrt(d-c^2*d*x^2),x,4,-2/3*b*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*sqrt(d-c^2*d*x^2))-1/9*b*x^3*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))-2/3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c^4*d)-1/3*x^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c^2*d)],
[x^2*(a+b*arccosh(c*x))/sqrt(d-c^2*d*x^2),x,3,-1/4*b*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))+1/4*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^3*sqrt(d-c^2*d*x^2))-1/2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c^2*d)],
[x*(a+b*arccosh(c*x))/sqrt(d-c^2*d*x^2),x,2,-b*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))-(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c^2*d)],
[(a+b*arccosh(c*x))/sqrt(d-c^2*d*x^2),x,1,1/2*(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))/(x*sqrt(d-c^2*d*x^2)),x,6,2*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-I*b*polylog(2,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)+I*b*polylog(2,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)],
[(a+b*arccosh(c*x))/(x^2*sqrt(d-c^2*d*x^2)),x,2,-b*c*log(x)*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(d*x)],
[(a+b*arccosh(c*x))/(x^3*sqrt(d-c^2*d*x^2)),x,8,1/2*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/(x*sqrt(d-c^2*d*x^2))+c^2*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-1/2*I*b*c^2*polylog(2,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)+1/2*I*b*c^2*polylog(2,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-1/2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(d*x^2)],
[(a+b*arccosh(c*x))/(x^4*sqrt(d-c^2*d*x^2)),x,4,1/6*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/(x^2*sqrt(d-c^2*d*x^2))-2/3*b*c^3*log(x)*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-1/3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(d*x^3)-2/3*c^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(d*x)],
[x^5*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(3/2),x,5,-1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/(c^6*d^3)+(a+b*arccosh(c*x))/(c^6*d*sqrt(d-c^2*d*x^2))+2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c^6*d^2)-5/3*b*x*sqrt(d-c^2*d*x^2)/(c^5*d^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/9*b*x^3*sqrt(d-c^2*d*x^2)/(c^3*d^2*sqrt(-1+c*x)*sqrt(1+c*x))-b*arctanh(c*x)*sqrt(d-c^2*d*x^2)/(c^6*d^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^4*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(3/2),x,7,x^3*(a+b*arccosh(c*x))/(c^2*d*sqrt(d-c^2*d*x^2))+1/4*b*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d*sqrt(d-c^2*d*x^2))-3/4*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^5*d*sqrt(d-c^2*d*x^2))-1/2*b*log(1-c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d*sqrt(d-c^2*d*x^2))+3/2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c^4*d^2)],
[x^3*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(3/2),x,4,(a+b*arccosh(c*x))/(c^4*d*sqrt(d-c^2*d*x^2))+(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c^4*d^2)-b*x*sqrt(d-c^2*d*x^2)/(c^3*d^2*sqrt(-1+c*x)*sqrt(1+c*x))-b*arctanh(c*x)*sqrt(d-c^2*d*x^2)/(c^4*d^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^2*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(3/2),x,4,x*(a+b*arccosh(c*x))/(c^2*d*sqrt(d-c^2*d*x^2))-1/2*(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*log(1-c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d*sqrt(d-c^2*d*x^2))],
[x*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(3/2),x,3,(a+b*arccosh(c*x))/(c^2*d*sqrt(d-c^2*d*x^2))+b*arctanh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*d*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(3/2),x,2,x*(a+b*arccosh(c*x))/(d*sqrt(d-c^2*d*x^2))-1/2*b*log(1-c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))/(x*(d-c^2*d*x^2)^(3/2)),x,9,(a+b*arccosh(c*x))/(d*sqrt(d-c^2*d*x^2))+2*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))+b*arctanh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-I*b*polylog(2,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))+I*b*polylog(2,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))/(x^2*(d-c^2*d*x^2)^(3/2)),x,5,(-a-b*arccosh(c*x))/(d*x*sqrt(d-c^2*d*x^2))+2*c^2*x*(a+b*arccosh(c*x))/(d*sqrt(d-c^2*d*x^2))+b*c*log(x)*sqrt(d-c^2*d*x^2)/(d^2*sqrt(-1+c*x)*sqrt(1+c*x))+1/2*b*c*log(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(d^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x^3*(d-c^2*d*x^2)^(3/2)),x,13,3/2*c^2*(a+b*arccosh(c*x))/(d*sqrt(d-c^2*d*x^2))+1/2*(-a-b*arccosh(c*x))/(d*x^2*sqrt(d-c^2*d*x^2))+1/2*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/(d*x*sqrt(d-c^2*d*x^2))+3*c^2*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))+b*c^2*arctanh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-3/2*I*b*c^2*polylog(2,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))+3/2*I*b*c^2*polylog(2,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))/(x^4*(d-c^2*d*x^2)^(3/2)),x,5,1/3*(-a-b*arccosh(c*x))/(d*x^3*sqrt(d-c^2*d*x^2))-4/3*c^2*(a+b*arccosh(c*x))/(d*x*sqrt(d-c^2*d*x^2))+8/3*c^4*x*(a+b*arccosh(c*x))/(d*sqrt(d-c^2*d*x^2))-1/6*b*c*sqrt(d-c^2*d*x^2)/(d^2*x^2*sqrt(-1+c*x)*sqrt(1+c*x))+5/3*b*c^3*log(x)*sqrt(d-c^2*d*x^2)/(d^2*sqrt(-1+c*x)*sqrt(1+c*x))+1/2*b*c^3*log(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(d^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^5*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(5/2),x,5,1/3*(a+b*arccosh(c*x))/(c^6*d*(d-c^2*d*x^2)^(3/2))-2*(a+b*arccosh(c*x))/(c^6*d^2*sqrt(d-c^2*d*x^2))-(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c^6*d^3)+b*x*sqrt(d-c^2*d*x^2)/(c^5*d^3*sqrt(-1+c*x)*sqrt(1+c*x))-1/6*b*x*sqrt(d-c^2*d*x^2)/(c^5*d^3*(1-c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x))+11/6*b*arctanh(c*x)*sqrt(d-c^2*d*x^2)/(c^6*d^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^4*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(5/2),x,9,1/3*x^3*(a+b*arccosh(c*x))/(c^2*d*(d-c^2*d*x^2)^(3/2))+1/6*b*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d*(d-c^2*d*x^2)^(3/2))-x*(a+b*arccosh(c*x))/(c^4*d^2*sqrt(d-c^2*d*x^2))+1/2*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^5*d^2*sqrt(d-c^2*d*x^2))+2/3*b*log(1-c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d^2*sqrt(d-c^2*d*x^2)),1/3*x^3*(a+b*arccosh(c*x))/(c^2*d*(d-c^2*d*x^2)^(3/2))-x*(a+b*arccosh(c*x))/(c^4*d^2*sqrt(d-c^2*d*x^2))+1/6*b*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+1/2*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^5*d^2*sqrt(d-c^2*d*x^2))+2/3*b*log(1-c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d^2*sqrt(d-c^2*d*x^2))],
[x^3*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(5/2),x,4,1/3*(a+b*arccosh(c*x))/(c^4*d*(d-c^2*d*x^2)^(3/2))+(-a-b*arccosh(c*x))/(c^4*d^2*sqrt(d-c^2*d*x^2))+1/6*b*x*sqrt(d-c^2*d*x^2)/(c^3*d^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2))+5/6*b*arctanh(c*x)*sqrt(d-c^2*d*x^2)/(c^4*d^3*sqrt(-1+c*x)*sqrt(1+c*x)),1/3*(a+b*arccosh(c*x))/(c^4*d*(d-c^2*d*x^2)^(3/2))+(-a-b*arccosh(c*x))/(c^4*d^2*sqrt(d-c^2*d*x^2))-1/6*b*x*sqrt(d-c^2*d*x^2)/(c^3*d^3*(1-c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x))+5/6*b*arctanh(c*x)*sqrt(d-c^2*d*x^2)/(c^4*d^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^2*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(5/2),x,5,1/3*x^3*(a+b*arccosh(c*x))/(d*(d-c^2*d*x^2)^(3/2))+1/6*b*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d*(d-c^2*d*x^2)^(3/2))+1/6*b*log(1-c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d^2*sqrt(d-c^2*d*x^2)),1/3*x^3*(a+b*arccosh(c*x))/(d*(d-c^2*d*x^2)^(3/2))+1/6*b*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+1/6*b*log(1-c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d^2*sqrt(d-c^2*d*x^2))],
[x*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(5/2),x,4,1/3*(a+b*arccosh(c*x))/(c^2*d*(d-c^2*d*x^2)^(3/2))+1/6*b*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d*(d-c^2*d*x^2)^(3/2))+1/6*b*arctanh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*d^2*sqrt(d-c^2*d*x^2)),1/3*(a+b*arccosh(c*x))/(c^2*d*(d-c^2*d*x^2)^(3/2))+1/6*b*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+1/6*b*arctanh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(5/2),x,5,1/3*x*(a+b*arccosh(c*x))/(d*(d-c^2*d*x^2)^(3/2))+1/6*b*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d*(d-c^2*d*x^2)^(3/2))+2/3*x*(a+b*arccosh(c*x))/(d^2*sqrt(d-c^2*d*x^2))-1/3*b*log(1-c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d^2*sqrt(d-c^2*d*x^2)),1/3*x*(a+b*arccosh(c*x))/(d*(d-c^2*d*x^2)^(3/2))+2/3*x*(a+b*arccosh(c*x))/(d^2*sqrt(d-c^2*d*x^2))+1/6*b*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))-1/3*b*log(1-c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))/(x*(d-c^2*d*x^2)^(5/2)),x,13,1/3*(a+b*arccosh(c*x))/(d*(d-c^2*d*x^2)^(3/2))+(a+b*arccosh(c*x))/(d^2*sqrt(d-c^2*d*x^2))+1/6*b*c*x*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+2*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))+7/6*b*arctanh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-I*b*polylog(2,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))+I*b*polylog(2,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))/(x^2*(d-c^2*d*x^2)^(5/2)),x,5,(-a-b*arccosh(c*x))/(d*x*(d-c^2*d*x^2)^(3/2))+4/3*c^2*x*(a+b*arccosh(c*x))/(d*(d-c^2*d*x^2)^(3/2))+8/3*c^2*x*(a+b*arccosh(c*x))/(d^2*sqrt(d-c^2*d*x^2))-1/6*b*c*sqrt(d-c^2*d*x^2)/(d^3*(1-c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x))+b*c*log(x)*sqrt(d-c^2*d*x^2)/(d^3*sqrt(-1+c*x)*sqrt(1+c*x))+5/6*b*c*log(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(d^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x^3*(d-c^2*d*x^2)^(5/2)),x,18,5/6*c^2*(a+b*arccosh(c*x))/(d*(d-c^2*d*x^2)^(3/2))+1/2*(-a-b*arccosh(c*x))/(d*x^2*(d-c^2*d*x^2)^(3/2))+5/2*c^2*(a+b*arccosh(c*x))/(d^2*sqrt(d-c^2*d*x^2))+3/4*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*x*sqrt(d-c^2*d*x^2))-1/4*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*x*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+5/12*b*c^3*x*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+5*c^2*(a+b*arccosh(c*x))*arctan(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))+13/6*b*c^2*arctanh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-5/2*I*b*c^2*polylog(2,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))+5/2*I*b*c^2*polylog(2,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))/(x^4*(d-c^2*d*x^2)^(5/2)),x,5,1/3*(-a-b*arccosh(c*x))/(d*x^3*(d-c^2*d*x^2)^(3/2))-2*c^2*(a+b*arccosh(c*x))/(d*x*(d-c^2*d*x^2)^(3/2))+8/3*c^4*x*(a+b*arccosh(c*x))/(d*(d-c^2*d*x^2)^(3/2))+16/3*c^4*x*(a+b*arccosh(c*x))/(d^2*sqrt(d-c^2*d*x^2))-1/6*b*c*sqrt(d-c^2*d*x^2)/(d^3*x^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/6*b*c^3*sqrt(d-c^2*d*x^2)/(d^3*(1-c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x))+8/3*b*c^3*log(x)*sqrt(d-c^2*d*x^2)/(d^3*sqrt(-1+c*x)*sqrt(1+c*x))+4/3*b*c^3*log(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(d^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[arccosh(a*x)/(c-a^2*c*x^2)^(7/2),x,8,1/5*x*arccosh(a*x)/(c*(c-a^2*c*x^2)^(5/2))+4/15*x*arccosh(a*x)/(c^2*(c-a^2*c*x^2)^(3/2))+8/15*x*arccosh(a*x)/(c^3*sqrt(c-a^2*c*x^2))+1/20*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*(1-a^2*x^2)^2*sqrt(c-a^2*c*x^2))+2/15*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*(1-a^2*x^2)*sqrt(c-a^2*c*x^2))-4/15*log(1-a^2*x^2)*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*sqrt(c-a^2*c*x^2))],
[x^4*arccosh(a*x)/sqrt(1-a^2*x^2),x,5,-3/16*x^2*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))-1/16*x^4*sqrt(-1+a*x)/(a*sqrt(1-a*x))+3/16*arccosh(a*x)^2*sqrt(-1+a*x)/(a^5*sqrt(1-a*x))-3/8*x*arccosh(a*x)*sqrt(1-a^2*x^2)/a^4-1/4*x^3*arccosh(a*x)*sqrt(1-a^2*x^2)/a^2],
[x^3*arccosh(a*x)/sqrt(1-a^2*x^2),x,4,-2/3*x*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))-1/9*x^3*sqrt(-1+a*x)/(a*sqrt(1-a*x))-2/3*arccosh(a*x)*sqrt(1-a^2*x^2)/a^4-1/3*x^2*arccosh(a*x)*sqrt(1-a^2*x^2)/a^2],
[x^2*arccosh(a*x)/sqrt(1-a^2*x^2),x,3,-1/4*x^2*sqrt(-1+a*x)/(a*sqrt(1-a*x))+1/4*arccosh(a*x)^2*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))-1/2*x*arccosh(a*x)*sqrt(1-a^2*x^2)/a^2],
[x*arccosh(a*x)/sqrt(1-a^2*x^2),x,2,-x*sqrt(-1+a*x)/(a*sqrt(1-a*x))-arccosh(a*x)*sqrt(1-a^2*x^2)/a^2],
[arccosh(a*x)/sqrt(1-a^2*x^2),x,1,1/2*arccosh(a*x)^2*sqrt(-1+a*x)/(a*sqrt(1-a*x))],
[arccosh(a*x)/(x*sqrt(1-a^2*x^2)),x,6,2*arccosh(a*x)*arctan(exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-I*polylog(2,-I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+I*polylog(2,I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)],
[arccosh(a*x)/(x^2*sqrt(1-a^2*x^2)),x,2,-a*log(x)*sqrt(-1+a*x)/sqrt(1-a*x)-arccosh(a*x)*sqrt(1-a^2*x^2)/x],
[arccosh(a*x)/(x^3*sqrt(1-a^2*x^2)),x,8,1/2*a*sqrt(-1+a*x)/(x*sqrt(1-a*x))+a^2*arccosh(a*x)*arctan(exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-1/2*I*a^2*polylog(2,-I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+1/2*I*a^2*polylog(2,I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-1/2*arccosh(a*x)*sqrt(1-a^2*x^2)/x^2],

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

# p>0

# p<0
[(f*x)^(3/2)*(a+b*arccosh(c*x))/sqrt(1-c^2*x^2),x,1,2/5*(f*x)^(5/2)*(a+b*arccosh(c*x))*hypergeom([1/2,5/4],[9/4],c^2*x^2)/f+4/35*b*c*(f*x)^(7/2)*HypergeometricPFQ([1,7/4,7/4],[9/4,11/4],c^2*x^2)*sqrt(-1+c*x)/(f^2*sqrt(1-c*x))],
[(f*x)^(3/2)*(a+b*arccosh(c*x))/sqrt(d-c^2*d*x^2),x,1,4/35*b*c*(f*x)^(7/2)*HypergeometricPFQ([1,7/4,7/4],[9/4,11/4],c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(f^2*sqrt(d-c^2*d*x^2))+2/5*(f*x)^(5/2)*(a+b*arccosh(c*x))*hypergeom([1/2,5/4],[9/4],c^2*x^2)*sqrt(1-c^2*x^2)/(f*sqrt(d-c^2*d*x^2))],

# Integrands of the form (f x)^m (d-c^2 d x^2)^p (a+b ArcCosh[c x]) with m symbolic
[(f*x)^m*(d-c^2*d*x^2)^3*(a+b*arccosh(c*x)),x,8,d^3*(f*x)^(1+m)*(a+b*arccosh(c*x))/(f*(1+m))-3*c^2*d^3*(f*x)^(3+m)*(a+b*arccosh(c*x))/(f^3*(3+m))+3*c^4*d^3*(f*x)^(5+m)*(a+b*arccosh(c*x))/(f^5*(5+m))-c^6*d^3*(f*x)^(7+m)*(a+b*arccosh(c*x))/(f^7*(7+m))-b*c*d^3*(2271+1329*m+284*m^2+27*m^3+m^4)*(f*x)^(2+m)*(1-c^2*x^2)/(f^2*(7+m)^2*(15+8*m+m^2)^2*sqrt(-1+c*x)*sqrt(1+c*x))+b*c^3*d^3*(9+m)*(13+2*m)*(f*x)^(4+m)*(1-c^2*x^2)/(f^4*(5+m)^2*(7+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-b*c^5*d^3*(f*x)^(6+m)*(1-c^2*x^2)/(f^6*(7+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-3*b*c*d^3*(2161+1813*m+455*m^2+35*m^3)*(f*x)^(2+m)*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(f^2*(7+m)^2*(2+3*m+m^2)*(15+8*m+m^2)^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f*x)^m*(d-c^2*d*x^2)^2*(a+b*arccosh(c*x)),x,7,d^2*(f*x)^(1+m)*(a+b*arccosh(c*x))/(f*(1+m))-2*c^2*d^2*(f*x)^(3+m)*(a+b*arccosh(c*x))/(f^3*(3+m))+c^4*d^2*(f*x)^(5+m)*(a+b*arccosh(c*x))/(f^5*(5+m))-b*c*d^2*(38+13*m+m^2)*(f*x)^(2+m)*(1-c^2*x^2)/(f^2*(3+m)^2*(5+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))+b*c^3*d^2*(f*x)^(4+m)*(1-c^2*x^2)/(f^4*(5+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-b*c*d^2*(149+100*m+15*m^2)*(f*x)^(2+m)*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(f^2*(2+3*m+m^2)*(15+8*m+m^2)^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f*x)^m*(d-c^2*d*x^2)*(a+b*arccosh(c*x)),x,6,d*(f*x)^(1+m)*(a+b*arccosh(c*x))/(f*(1+m))-c^2*d*(f*x)^(3+m)*(a+b*arccosh(c*x))/(f^3*(3+m))+b*c*d*(f*x)^(2+m)*sqrt(-1+c*x)*sqrt(1+c*x)/(f^2*(3+m)^2)-b*c*d*(7+3*m)*(f*x)^(2+m)*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(f^2*(3+m)^2*(2+3*m+m^2)*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f*x)^m*(a+b*arccosh(c*x))/(d-c^2*d*x^2),x,0,Unintegrable((f*x)^m*(a+b*arccosh(c*x))/(d-c^2*d*x^2),x)],
[(f*x)^m*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^2,x,4,1/2*(f*x)^(1+m)*(a+b*arccosh(c*x))/(d^2*f*(1-c^2*x^2))-1/2*b*c*(f*x)^(2+m)*hypergeom([3/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(d^2*f^2*(2+m)*sqrt(-1+c*x)*sqrt(1+c*x))+1/2*(1-m)*Unintegrable((f*x)^m*(a+b*arccosh(c*x))/(d-c^2*d*x^2),x)/d],
[(f*x)^m*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^3,x,8,1/4*(f*x)^(1+m)*(a+b*arccosh(c*x))/(d^3*f*(1-c^2*x^2)^2)+1/8*(3-m)*(f*x)^(1+m)*(a+b*arccosh(c*x))/(d^3*f*(1-c^2*x^2))-1/8*b*c*(3-m)*(f*x)^(2+m)*hypergeom([3/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(d^3*f^2*(2+m)*sqrt(-1+c*x)*sqrt(1+c*x))-1/4*b*c*(f*x)^(2+m)*hypergeom([5/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(d^3*f^2*(2+m)*sqrt(-1+c*x)*sqrt(1+c*x))+1/8*(1-m)*(3-m)*Unintegrable((f*x)^m*(a+b*arccosh(c*x))/(d-c^2*d*x^2),x)/d^2],
[(f*x)^m*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x)),x,11,5*d*(f*x)^(1+m)*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/(f*(4+m)*(6+m))+(f*x)^(1+m)*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))/(f*(6+m))+15*d^2*(f*x)^(1+m)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f*(6+m)*(8+6*m+m^2))+15*d^2*(f*x)^(1+m)*(a+b*arccosh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],c^2*x^2)*sqrt(d-c^2*d*x^2)/(f*(6+m)*(8+14*m+7*m^2+m^3)*sqrt(1-c*x)*sqrt(1+c*x))-b*c*d^2*(f*x)^(2+m)*sqrt(d-c^2*d*x^2)/(f^2*(2+m)*(6+m)*sqrt(-1+c*x)*sqrt(1+c*x))-15*b*c*d^2*(f*x)^(2+m)*sqrt(d-c^2*d*x^2)/(f^2*(2+m)^2*(4+m)*(6+m)*sqrt(-1+c*x)*sqrt(1+c*x))-5*b*c*d^2*(f*x)^(2+m)*sqrt(d-c^2*d*x^2)/(f^2*(6+m)*(8+6*m+m^2)*sqrt(-1+c*x)*sqrt(1+c*x))+5*b*c^3*d^2*(f*x)^(4+m)*sqrt(d-c^2*d*x^2)/(f^4*(4+m)^2*(6+m)*sqrt(-1+c*x)*sqrt(1+c*x))+2*b*c^3*d^2*(f*x)^(4+m)*sqrt(d-c^2*d*x^2)/(f^4*(4+m)*(6+m)*sqrt(-1+c*x)*sqrt(1+c*x))-b*c^5*d^2*(f*x)^(6+m)*sqrt(d-c^2*d*x^2)/(f^6*(6+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-15*b*c*d^2*(f*x)^(2+m)*HypergeometricPFQ([1,1+1/2*m,1+1/2*m],[3/2+1/2*m,2+1/2*m],c^2*x^2)*sqrt(d-c^2*d*x^2)/(f^2*(2+m)^2*(6+m)*(4+5*m+m^2)*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f*x)^m*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x)),x,7,(f*x)^(1+m)*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))/(f*(4+m))+3*d*(f*x)^(1+m)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f*(8+6*m+m^2))+3*d*(f*x)^(1+m)*(a+b*arccosh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],c^2*x^2)*sqrt(d-c^2*d*x^2)/(f*(8+14*m+7*m^2+m^3)*sqrt(1-c*x)*sqrt(1+c*x))-3*b*c*d*(f*x)^(2+m)*sqrt(d-c^2*d*x^2)/(f^2*(2+m)^2*(4+m)*sqrt(-1+c*x)*sqrt(1+c*x))-b*c*d*(f*x)^(2+m)*sqrt(d-c^2*d*x^2)/(f^2*(2+m)*(4+m)*sqrt(-1+c*x)*sqrt(1+c*x))+b*c^3*d*(f*x)^(4+m)*sqrt(d-c^2*d*x^2)/(f^4*(4+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-3*b*c*d*(f*x)^(2+m)*HypergeometricPFQ([1,1+1/2*m,1+1/2*m],[3/2+1/2*m,2+1/2*m],c^2*x^2)*sqrt(d-c^2*d*x^2)/(f^2*(2+m)^2*(4+5*m+m^2)*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f*x)^m*(d-c^2*d*x^2)^(1/2)*(a+b*arccosh(c*x)),x,3,(f*x)^(1+m)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f*(2+m))+(f*x)^(1+m)*(a+b*arccosh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],c^2*x^2)*sqrt(d-c^2*d*x^2)/(f*(2+3*m+m^2)*sqrt(1-c*x)*sqrt(1+c*x))-b*c*(f*x)^(2+m)*sqrt(d-c^2*d*x^2)/(f^2*(2+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-b*c*(f*x)^(2+m)*HypergeometricPFQ([1,1+1/2*m,1+1/2*m],[3/2+1/2*m,2+1/2*m],c^2*x^2)*sqrt(d-c^2*d*x^2)/(f^2*(1+m)*(2+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f*x)^m*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(1/2),x,1,b*c*(f*x)^(2+m)*HypergeometricPFQ([1,1+1/2*m,1+1/2*m],[3/2+1/2*m,2+1/2*m],c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(f^2*(1+m)*(2+m)*sqrt(d-c^2*d*x^2))+(f*x)^(1+m)*(a+b*arccosh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(f*(1+m)*sqrt(d-c^2*d*x^2))],
[(f*x)^m*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(3/2),x,4,(f*x)^(1+m)*(a+b*arccosh(c*x))/(d*f*sqrt(d-c^2*d*x^2))+b*c*(f*x)^(2+m)*hypergeom([1,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(d*f^2*(2+m)*sqrt(d-c^2*d*x^2))-b*c*m*(f*x)^(2+m)*HypergeometricPFQ([1,1+1/2*m,1+1/2*m],[3/2+1/2*m,2+1/2*m],c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(d*f^2*(1+m)*(2+m)*sqrt(d-c^2*d*x^2))-m*(f*x)^(1+m)*(a+b*arccosh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(d*f*(1+m)*sqrt(d-c^2*d*x^2))],
[(f*x)^m*(a+b*arccosh(c*x))/(d-c^2*d*x^2)^(5/2),x,7,1/3*(f*x)^(1+m)*(a+b*arccosh(c*x))/(d*f*(d-c^2*d*x^2)^(3/2))+1/3*(2-m)*(f*x)^(1+m)*(a+b*arccosh(c*x))/(d^2*f*sqrt(d-c^2*d*x^2))+1/3*b*c*(2-m)*(f*x)^(2+m)*hypergeom([1,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*f^2*(2+m)*sqrt(d-c^2*d*x^2))+1/3*b*c*(f*x)^(2+m)*hypergeom([2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*f^2*(2+m)*sqrt(d-c^2*d*x^2))-1/3*b*c*(2-m)*m*(f*x)^(2+m)*HypergeometricPFQ([1,1+1/2*m,1+1/2*m],[3/2+1/2*m,2+1/2*m],c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*f^2*(1+m)*(2+m)*sqrt(d-c^2*d*x^2))-1/3*(2-m)*m*(f*x)^(1+m)*(a+b*arccosh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(d^2*f*(1+m)*sqrt(d-c^2*d*x^2))],
[(f*x)^m*(d1+c*d1*x)^(5/2)*(d2-c*d2*x)^(5/2)*(a+b*arccosh(c*x)),x,11,5*d1*d2*(f*x)^(1+m)*(d1+c*d1*x)^(3/2)*(d2-c*d2*x)^(3/2)*(a+b*arccosh(c*x))/(f*(4+m)*(6+m))+(f*x)^(1+m)*(d1+c*d1*x)^(5/2)*(d2-c*d2*x)^(5/2)*(a+b*arccosh(c*x))/(f*(6+m))+15*d1^2*d2^2*(f*x)^(1+m)*(a+b*arccosh(c*x))*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f*(6+m)*(8+6*m+m^2))+15*d1^2*d2^2*(f*x)^(1+m)*(a+b*arccosh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],c^2*x^2)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f*(6+m)*(8+14*m+7*m^2+m^3)*sqrt(1-c*x)*sqrt(1+c*x))-b*c*d1^2*d2^2*(f*x)^(2+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f^2*(2+m)*(6+m)*sqrt(-1+c*x)*sqrt(1+c*x))-15*b*c*d1^2*d2^2*(f*x)^(2+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f^2*(2+m)^2*(4+m)*(6+m)*sqrt(-1+c*x)*sqrt(1+c*x))-5*b*c*d1^2*d2^2*(f*x)^(2+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f^2*(6+m)*(8+6*m+m^2)*sqrt(-1+c*x)*sqrt(1+c*x))+5*b*c^3*d1^2*d2^2*(f*x)^(4+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f^4*(4+m)^2*(6+m)*sqrt(-1+c*x)*sqrt(1+c*x))+2*b*c^3*d1^2*d2^2*(f*x)^(4+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f^4*(4+m)*(6+m)*sqrt(-1+c*x)*sqrt(1+c*x))-b*c^5*d1^2*d2^2*(f*x)^(6+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f^6*(6+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-15*b*c*d1^2*d2^2*(f*x)^(2+m)*HypergeometricPFQ([1,1+1/2*m,1+1/2*m],[3/2+1/2*m,2+1/2*m],c^2*x^2)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f^2*(2+m)^2*(6+m)*(4+5*m+m^2)*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f*x)^m*(d1+c*d1*x)^(3/2)*(d2-c*d2*x)^(3/2)*(a+b*arccosh(c*x)),x,7,(f*x)^(1+m)*(d1+c*d1*x)^(3/2)*(d2-c*d2*x)^(3/2)*(a+b*arccosh(c*x))/(f*(4+m))+3*d1*d2*(f*x)^(1+m)*(a+b*arccosh(c*x))*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f*(8+6*m+m^2))+3*d1*d2*(f*x)^(1+m)*(a+b*arccosh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],c^2*x^2)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f*(8+14*m+7*m^2+m^3)*sqrt(1-c*x)*sqrt(1+c*x))-3*b*c*d1*d2*(f*x)^(2+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f^2*(2+m)^2*(4+m)*sqrt(-1+c*x)*sqrt(1+c*x))-b*c*d1*d2*(f*x)^(2+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f^2*(2+m)*(4+m)*sqrt(-1+c*x)*sqrt(1+c*x))+b*c^3*d1*d2*(f*x)^(4+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f^4*(4+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-3*b*c*d1*d2*(f*x)^(2+m)*HypergeometricPFQ([1,1+1/2*m,1+1/2*m],[3/2+1/2*m,2+1/2*m],c^2*x^2)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f^2*(2+m)^2*(4+5*m+m^2)*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f*x)^m*(d1+c*d1*x)^(1/2)*(d2-c*d2*x)^(1/2)*(a+b*arccosh(c*x)),x,3,(f*x)^(1+m)*(a+b*arccosh(c*x))*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f*(2+m))+(f*x)^(1+m)*(a+b*arccosh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],c^2*x^2)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f*(2+3*m+m^2)*sqrt(1-c*x)*sqrt(1+c*x))-b*c*(f*x)^(2+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f^2*(2+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-b*c*(f*x)^(2+m)*HypergeometricPFQ([1,1+1/2*m,1+1/2*m],[3/2+1/2*m,2+1/2*m],c^2*x^2)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x)/(f^2*(1+m)*(2+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f*x)^m*(a+b*arccosh(c*x))/((d1+c*d1*x)^(1/2)*(d2-c*d2*x)^(1/2)),x,1,b*c*(f*x)^(2+m)*HypergeometricPFQ([1,1+1/2*m,1+1/2*m],[3/2+1/2*m,2+1/2*m],c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(f^2*(1+m)*(2+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))+(f*x)^(1+m)*(a+b*arccosh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(f*(1+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))],
[(f*x)^m*(a+b*arccosh(c*x))/((d1+c*d1*x)^(3/2)*(d2-c*d2*x)^(3/2)),x,4,(f*x)^(1+m)*(a+b*arccosh(c*x))/(d1*d2*f*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))+b*c*(f*x)^(2+m)*hypergeom([1,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(d1*d2*f^2*(2+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))-b*c*m*(f*x)^(2+m)*HypergeometricPFQ([1,1+1/2*m,1+1/2*m],[3/2+1/2*m,2+1/2*m],c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(d1*d2*f^2*(1+m)*(2+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))-m*(f*x)^(1+m)*(a+b*arccosh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(d1*d2*f*(1+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))],
[(f*x)^m*(a+b*arccosh(c*x))/((d1+c*d1*x)^(5/2)*(d2-c*d2*x)^(5/2)),x,7,1/3*(f*x)^(1+m)*(a+b*arccosh(c*x))/(d1*d2*f*(d1+c*d1*x)^(3/2)*(d2-c*d2*x)^(3/2))+1/3*(2-m)*(f*x)^(1+m)*(a+b*arccosh(c*x))/(d1^2*d2^2*f*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))+1/3*b*c*(2-m)*(f*x)^(2+m)*hypergeom([1,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(d1^2*d2^2*f^2*(2+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))+1/3*b*c*(f*x)^(2+m)*hypergeom([2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(d1^2*d2^2*f^2*(2+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))-1/3*b*c*(2-m)*m*(f*x)^(2+m)*HypergeometricPFQ([1,1+1/2*m,1+1/2*m],[3/2+1/2*m,2+1/2*m],c^2*x^2)*sqrt(-1+c*x)*sqrt(1+c*x)/(d1^2*d2^2*f^2*(1+m)*(2+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))-1/3*(2-m)*m*(f*x)^(1+m)*(a+b*arccosh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(d1^2*d2^2*f*(1+m)*sqrt(d1+c*d1*x)*sqrt(d2-c*d2*x))],
[(f*x)^m*arccosh(a*x)/sqrt(1-a^2*x^2),x,1,(f*x)^(1+m)*arccosh(a*x)*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],a^2*x^2)/(f*(1+m))+a*(f*x)^(2+m)*HypergeometricPFQ([1,1+1/2*m,1+1/2*m],[3/2+1/2*m,2+1/2*m],a^2*x^2)*sqrt(-1+a*x)/(f^2*(1+m)*(2+m)*sqrt(1-a*x))],

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

# Integrands of the form x^m (d-c^2 d x^2)^p (a+b ArcCosh[c x])^2
[(c-a^2*c*x^2)^3*arccosh(a*x)^2,x,17,4322/3675*c^3*x-1514/11025*a^2*c^3*x^3+234/6125*a^4*c^3*x^5-2/343*a^6*c^3*x^7+16/105*c^3*(-1+a*x)^(3/2)*(1+a*x)^(3/2)*arccosh(a*x)/a-12/175*c^3*(-1+a*x)^(5/2)*(1+a*x)^(5/2)*arccosh(a*x)/a+2/49*c^3*(-1+a*x)^(7/2)*(1+a*x)^(7/2)*arccosh(a*x)/a+16/35*c^3*x*arccosh(a*x)^2+8/35*c^3*x*(1-a^2*x^2)*arccosh(a*x)^2+6/35*c^3*x*(1-a^2*x^2)^2*arccosh(a*x)^2+1/7*c^3*x*(1-a^2*x^2)^3*arccosh(a*x)^2-32/35*c^3*arccosh(a*x)*sqrt(-1+a*x)*sqrt(1+a*x)/a],
[(c-a^2*c*x^2)^2*arccosh(a*x)^2,x,12,298/225*c^2*x-76/675*a^2*c^2*x^3+2/125*a^4*c^2*x^5+8/45*c^2*(-1+a*x)^(3/2)*(1+a*x)^(3/2)*arccosh(a*x)/a-2/25*c^2*(-1+a*x)^(5/2)*(1+a*x)^(5/2)*arccosh(a*x)/a+8/15*c^2*x*arccosh(a*x)^2+4/15*c^2*x*(1-a^2*x^2)*arccosh(a*x)^2+1/5*c^2*x*(1-a^2*x^2)^2*arccosh(a*x)^2-16/15*c^2*arccosh(a*x)*sqrt(-1+a*x)*sqrt(1+a*x)/a],
[(c-a^2*c*x^2)*arccosh(a*x)^2,x,7,14/9*c*x-2/27*a^2*c*x^3+2/9*c*(-1+a*x)^(3/2)*(1+a*x)^(3/2)*arccosh(a*x)/a+2/3*c*x*arccosh(a*x)^2+1/3*c*x*(1-a^2*x^2)*arccosh(a*x)^2-4/3*c*arccosh(a*x)*sqrt(-1+a*x)*sqrt(1+a*x)/a],
[arccosh(a*x)^2/(c-a^2*c*x^2),x,8,2*arccosh(a*x)^2*arctanh(exp(arccosh(a*x)))/(a*c)+2*arccosh(a*x)*polylog(2,-exp(arccosh(a*x)))/(a*c)-2*arccosh(a*x)*polylog(2,exp(arccosh(a*x)))/(a*c)-2*polylog(3,-exp(arccosh(a*x)))/(a*c)+2*polylog(3,exp(arccosh(a*x)))/(a*c)],
[arccosh(a*x)^2/(c-a^2*c*x^2)^2,x,12,1/2*x*arccosh(a*x)^2/(c^2*(1-a^2*x^2))+arccosh(a*x)^2*arctanh(exp(arccosh(a*x)))/(a*c^2)-arctanh(a*x)/(a*c^2)+arccosh(a*x)*polylog(2,-exp(arccosh(a*x)))/(a*c^2)-arccosh(a*x)*polylog(2,exp(arccosh(a*x)))/(a*c^2)-polylog(3,-exp(arccosh(a*x)))/(a*c^2)+polylog(3,exp(arccosh(a*x)))/(a*c^2)-arccosh(a*x)/(a*c^2*sqrt(-1+a*x)*sqrt(1+a*x))],
[arccosh(a*x)^2/(c-a^2*c*x^2)^3,x,17,-1/12*x/(c^3*(1-a^2*x^2))+1/6*arccosh(a*x)/(a*c^3*(-1+a*x)^(3/2)*(1+a*x)^(3/2))+1/4*x*arccosh(a*x)^2/(c^3*(1-a^2*x^2)^2)+3/8*x*arccosh(a*x)^2/(c^3*(1-a^2*x^2))+3/4*arccosh(a*x)^2*arctanh(exp(arccosh(a*x)))/(a*c^3)-5/6*arctanh(a*x)/(a*c^3)+3/4*arccosh(a*x)*polylog(2,-exp(arccosh(a*x)))/(a*c^3)-3/4*arccosh(a*x)*polylog(2,exp(arccosh(a*x)))/(a*c^3)-3/4*polylog(3,-exp(arccosh(a*x)))/(a*c^3)+3/4*polylog(3,exp(arccosh(a*x)))/(a*c^3)-3/4*arccosh(a*x)/(a*c^3*sqrt(-1+a*x)*sqrt(1+a*x))],

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

# p>0
[x^3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2),x,16,-856/3375*b^2*sqrt(d-c^2*d*x^2)/c^4+22/3375*b^2*x^2*sqrt(d-c^2*d*x^2)/c^2+2/125*b^2*x^4*sqrt(d-c^2*d*x^2)-2/15*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/c^4-1/15*x^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/c^2+1/5*x^4*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)+4/15*a*b*x*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+4/15*b^2*x*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+2/45*b*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-2/25*b*c*x^5*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2),x,11,-1/64*b^2*x*sqrt(d-c^2*d*x^2)/c^2+1/32*b^2*x^3*sqrt(d-c^2*d*x^2)-1/8*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/c^2+1/4*x^3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)-1/64*b^2*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/8*b*x^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/8*b*c*x^4*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/24*(a+b*arccosh(c*x))^3*sqrt(d-c^2*d*x^2)/(b*c^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2),x,6,-1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2/(c^2*d)-14/27*b^2*sqrt(d-c^2*d*x^2)/c^2+2/27*b^2*x^2*sqrt(d-c^2*d*x^2)+2/3*b*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-2/9*b*c*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2),x,5,1/4*b^2*x*sqrt(d-c^2*d*x^2)+1/2*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)+1/4*b^2*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/2*b*c*x^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/6*(a+b*arccosh(c*x))^3*sqrt(d-c^2*d*x^2)/(b*c*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/x,x,12,2*b^2*sqrt(d-c^2*d*x^2)+(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)-2*a*b*c*x*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*b^2*c*x*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*(a+b*arccosh(c*x))^2*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+2*I*b*(a+b*arccosh(c*x))*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*I*b*(a+b*arccosh(c*x))*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*I*b^2*polylog(3,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+2*I*b^2*polylog(3,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/x^2,x,7,-(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/x+c*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/3*c*(a+b*arccosh(c*x))^3*sqrt(d-c^2*d*x^2)/(b*sqrt(-1+c*x)*sqrt(1+c*x))+2*b*c*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-b^2*c*polylog(2,(-1)/exp(2*arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/x^3,x,12,-1/2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/x^2-b*c*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(x*sqrt(-1+c*x)*sqrt(1+c*x))+c^2*(a+b*arccosh(c*x))^2*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+b^2*c^2*arctan(sqrt(-1+c*x)*sqrt(1+c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-I*b*c^2*(a+b*arccosh(c*x))*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+I*b*c^2*(a+b*arccosh(c*x))*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+I*b^2*c^2*polylog(3,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-I*b^2*c^2*polylog(3,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/x^4,x,11,-1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2/(d*x^3)+1/3*b^2*c^2*sqrt(d-c^2*d*x^2)/x-1/3*b^2*c^3*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/3*b*c*(1-c^2*x^2)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/3*c^3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2/3*b*c^3*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/3*b^2*c^3*polylog(2,(-1)/exp(2*arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2,x,26,1/7*x^4*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2-37384/385875*b^2*d*sqrt(d-c^2*d*x^2)/c^4+3358/385875*b^2*d*x^2*sqrt(d-c^2*d*x^2)/c^2+484/42875*b^2*d*x^4*sqrt(d-c^2*d*x^2)-2/343*b^2*c^2*d*x^6*sqrt(d-c^2*d*x^2)-2/35*d*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/c^4-1/35*d*x^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/c^2+3/35*d*x^4*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)+4/35*a*b*d*x*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+4/35*b^2*d*x*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+2/105*b*d*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-16/175*b*c*d*x^5*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+2/49*b*c^3*d*x^7*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^2*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2,x,20,1/6*x^3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2+7/1152*b^2*d*x*sqrt(d-c^2*d*x^2)/c^2+43/1728*b^2*d*x^3*sqrt(d-c^2*d*x^2)-1/108*b^2*c^2*d*x^5*sqrt(d-c^2*d*x^2)-1/16*d*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/c^2+1/8*d*x^3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)+7/1152*b^2*d*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/16*b*d*x^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-7/48*b*c*d*x^4*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/18*b*c^3*d*x^6*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/48*d*(a+b*arccosh(c*x))^3*sqrt(d-c^2*d*x^2)/(b*c^3*sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2,x,8,-1/5*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2/(c^2*d)-16/75*b^2*d*(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(c^2*(1-c*x)*(1+c*x))-8/225*b^2*d*(1-c^2*x^2)^2*sqrt(d-c^2*d*x^2)/(c^2*(1-c*x)*(1+c*x))-2/125*b^2*d*(1-c^2*x^2)^3*sqrt(d-c^2*d*x^2)/(c^2*(1-c*x)*(1+c*x))+2/5*b*d*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-4/15*b*c*d*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+2/25*b*c^3*d*x^5*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2,x,11,1/4*x*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2+15/64*b^2*d*x*sqrt(d-c^2*d*x^2)+1/32*b^2*d*x*(1-c*x)*(1+c*x)*sqrt(d-c^2*d*x^2)+3/8*d*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)+9/64*b^2*d*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-3/8*b*c*d*x^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/8*b*d*(1-c^2*x^2)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/8*d*(a+b*arccosh(c*x))^3*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))^2/x,x,18,1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2+68/27*b^2*d*sqrt(d-c^2*d*x^2)-2/27*b^2*c^2*d*x^2*sqrt(d-c^2*d*x^2)+d*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)-2*a*b*c*d*x*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*b^2*c*d*x*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2/3*b*c*d*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+2/9*b*c^3*d*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*d*(a+b*arccosh(c*x))^2*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+2*I*b*d*(a+b*arccosh(c*x))*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*I*b*d*(a+b*arccosh(c*x))*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*I*b^2*d*polylog(3,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+2*I*b^2*d*polylog(3,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2/x^2,x,15,-(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2/x-1/4*b^2*c^2*d*x*sqrt(d-c^2*d*x^2)-3/2*c^2*d*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)-5/4*b^2*c*d*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3/2*b*c^3*d*x^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+b*c*d*(1-c^2*x^2)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+c*d*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+1/2*c*d*(a+b*arccosh(c*x))^3*sqrt(d-c^2*d*x^2)/(b*sqrt(-1+c*x)*sqrt(1+c*x))+2*b*c*d*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-b^2*c*d*polylog(2,(-1)/exp(2*arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2/x^3,x,18,-1/2*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2/x^2-2*b^2*c^2*d*sqrt(d-c^2*d*x^2)-3/2*c^2*d*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)+3*a*b*c^3*d*x*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3*b^2*c^3*d*x*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-b*c*d*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(x*sqrt(-1+c*x)*sqrt(1+c*x))-b*c^3*d*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3*c^2*d*(a+b*arccosh(c*x))^2*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+b^2*c^2*d*arctan(sqrt(-1+c*x)*sqrt(1+c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3*I*b*c^2*d*(a+b*arccosh(c*x))*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3*I*b*c^2*d*(a+b*arccosh(c*x))*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3*I*b^2*c^2*d*polylog(3,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3*I*b^2*c^2*d*polylog(3,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2/x^4,x,18,-1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2/x^3+1/3*b^2*c^2*d*sqrt(d-c^2*d*x^2)/x+c^2*d*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/x-1/3*b^2*c^3*d*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/3*b*c*d*(1-c^2*x^2)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))-4/3*c^3*d*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/3*c^3*d*(a+b*arccosh(c*x))^3*sqrt(d-c^2*d*x^2)/(b*sqrt(-1+c*x)*sqrt(1+c*x))-8/3*b*c^3*d*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+4/3*b^2*c^3*d*polylog(2,(-1)/exp(2*arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^3*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2,x,35,5/63*d*x^4*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2+1/9*x^4*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2-37384/694575*b^2*d^2*sqrt(d-c^2*d*x^2)/c^4+3358/694575*b^2*d^2*x^2*sqrt(d-c^2*d*x^2)/c^2+484/77175*b^2*d^2*x^4*sqrt(d-c^2*d*x^2)-10/3087*b^2*c^2*d^2*x^6*sqrt(d-c^2*d*x^2)+16/2835*b^2*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(c^4*(1-c*x)*(1+c*x))+8/8505*b^2*d^2*(1-c^2*x^2)^2*sqrt(d-c^2*d*x^2)/(c^4*(1-c*x)*(1+c*x))+2/4725*b^2*d^2*(1-c^2*x^2)^3*sqrt(d-c^2*d*x^2)/(c^4*(1-c*x)*(1+c*x))-20/3969*b^2*d^2*(1-c^2*x^2)^4*sqrt(d-c^2*d*x^2)/(c^4*(1-c*x)*(1+c*x))+2/729*b^2*d^2*(1-c^2*x^2)^5*sqrt(d-c^2*d*x^2)/(c^4*(1-c*x)*(1+c*x))-2/63*d^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/c^4-1/63*d^2*x^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/c^2+1/21*d^2*x^4*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)+4/63*a*b*d^2*x*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+4/63*b^2*d^2*x*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+2/189*b*d^2*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-2/21*b*c*d^2*x^5*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+38/441*b*c^3*d^2*x^7*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2/81*b*c^5*d^2*x^9*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^2*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2,x,31,5/48*d*x^3*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2+1/8*x^3*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2+35/9216*b^2*d^2*x*sqrt(d-c^2*d*x^2)/c^2+215/13824*b^2*d^2*x^3*sqrt(d-c^2*d*x^2)-5/864*b^2*c^2*d^2*x^5*sqrt(d-c^2*d*x^2)+73/12288*b^2*d^2*x*(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(c^2*(1-c*x)*(1+c*x))+73/18432*b^2*d^2*x^3*(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/((1-c*x)*(1+c*x))-43/4608*b^2*c^2*d^2*x^5*(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/((1-c*x)*(1+c*x))+1/256*b^2*c^4*d^2*x^7*(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/((1-c*x)*(1+c*x))-5/128*d^2*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/c^2+5/64*d^2*x^3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)+35/9216*b^2*d^2*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+5/128*b*d^2*x^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-59/384*b*c*d^2*x^4*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+17/144*b*c^3*d^2*x^6*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/32*b*c^5*d^2*x^8*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-5/384*d^2*(a+b*arccosh(c*x))^3*sqrt(d-c^2*d*x^2)/(b*c^3*sqrt(-1+c*x)*sqrt(1+c*x))-73/12288*b^2*d^2*arctanh(c*x/sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)*sqrt(d-c^2*d*x^2)/(c^3*(1-c*x)*(1+c*x))],
[x*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2,x,8,-1/7*(d-c^2*d*x^2)^(7/2)*(a+b*arccosh(c*x))^2/(c^2*d)-32/245*b^2*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(c^2*(1-c*x)*(1+c*x))-16/735*b^2*d^2*(1-c^2*x^2)^2*sqrt(d-c^2*d*x^2)/(c^2*(1-c*x)*(1+c*x))-12/1225*b^2*d^2*(1-c^2*x^2)^3*sqrt(d-c^2*d*x^2)/(c^2*(1-c*x)*(1+c*x))-2/343*b^2*d^2*(1-c^2*x^2)^4*sqrt(d-c^2*d*x^2)/(c^2*(1-c*x)*(1+c*x))+2/7*b*d^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-2/7*b*c*d^2*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+6/35*b*c^3*d^2*x^5*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2/49*b*c^5*d^2*x^7*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2,x,18,5/24*d*x*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2+1/6*x*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2+245/1152*b^2*d^2*x*sqrt(d-c^2*d*x^2)+65/1728*b^2*d^2*x*(1-c*x)*(1+c*x)*sqrt(d-c^2*d*x^2)+1/108*b^2*d^2*x*(1-c*x)^2*(1+c*x)^2*sqrt(d-c^2*d*x^2)+5/16*d^2*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)+115/1152*b^2*d^2*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-5/16*b*c*d^2*x^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+5/48*b*d^2*(1-c^2*x^2)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))+1/18*b*d^2*(1-c^2*x^2)^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-5/48*d^2*(a+b*arccosh(c*x))^3*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))^2/x,x,26,1/3*d*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2+1/5*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2+68/27*b^2*d^2*sqrt(d-c^2*d*x^2)-2/27*b^2*c^2*d^2*x^2*sqrt(d-c^2*d*x^2)+16/75*b^2*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/((1-c*x)*(1+c*x))+8/225*b^2*d^2*(1-c^2*x^2)^2*sqrt(d-c^2*d*x^2)/((1-c*x)*(1+c*x))+2/125*b^2*d^2*(1-c^2*x^2)^3*sqrt(d-c^2*d*x^2)/((1-c*x)*(1+c*x))+d^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)-2*a*b*c*d^2*x*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*b^2*c*d^2*x*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-16/15*b*c*d^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+22/45*b*c^3*d^2*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2/25*b*c^5*d^2*x^5*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*d^2*(a+b*arccosh(c*x))^2*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+2*I*b*d^2*(a+b*arccosh(c*x))*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*I*b*d^2*(a+b*arccosh(c*x))*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*I*b^2*d^2*polylog(3,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+2*I*b^2*d^2*polylog(3,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2/x^2,x,25,-5/4*c^2*d*x*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2-(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2/x-31/64*b^2*c^2*d^2*x*sqrt(d-c^2*d*x^2)-1/32*b^2*c^2*d^2*x*(1-c*x)*(1+c*x)*sqrt(d-c^2*d*x^2)-15/8*c^2*d^2*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)-89/64*b^2*c*d^2*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+15/8*b*c^3*d^2*x^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+b*c*d^2*(1-c^2*x^2)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/8*b*c*d^2*(1-c^2*x^2)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+c*d^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+5/8*c*d^2*(a+b*arccosh(c*x))^3*sqrt(d-c^2*d*x^2)/(b*sqrt(-1+c*x)*sqrt(1+c*x))+2*b*c*d^2*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-b^2*c*d^2*polylog(2,(-1)/exp(2*arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2/x^3,x,28,-5/6*c^2*d*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2-1/2*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2/x^2-170/27*b^2*c^2*d^2*sqrt(d-c^2*d*x^2)+5/27*b^2*c^4*d^2*x^2*sqrt(d-c^2*d*x^2)+5/3*b^2*c^2*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/((1-c*x)*(1+c*x))+1/9*b^2*c^2*d^2*(1-c^2*x^2)^2*sqrt(d-c^2*d*x^2)/((1-c*x)*(1+c*x))-5/2*c^2*d^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)+5*a*b*c^3*d^2*x*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+5*b^2*c^3*d^2*x*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-b*c*d^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(x*sqrt(-1+c*x)*sqrt(1+c*x))-1/3*b*c^3*d^2*x*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2/9*b*c^5*d^2*x^3*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+5*c^2*d^2*(a+b*arccosh(c*x))^2*arctan(exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-5*I*b*c^2*d^2*(a+b*arccosh(c*x))*polylog(2,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+5*I*b*c^2*d^2*(a+b*arccosh(c*x))*polylog(2,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+5*I*b^2*c^2*d^2*polylog(3,-I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-5*I*b^2*c^2*d^2*polylog(3,I*exp(arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-b^2*c^2*d^2*arctan(sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)*sqrt(d-c^2*d*x^2)/((1-c*x)*(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2/x^4,x,30,5/3*c^2*d*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2/x-1/3*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2/x^3+7/12*b^2*c^4*d^2*x*sqrt(d-c^2*d*x^2)+1/3*b^2*c^2*d^2*(1-c*x)*(1+c*x)*sqrt(d-c^2*d*x^2)/x+5/2*c^4*d^2*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)+23/12*b^2*c^3*d^2*arccosh(c*x)*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-5/2*b*c^5*d^2*x^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-7/3*b*c^3*d^2*(1-c^2*x^2)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/3*b*c*d^2*(1-c^2*x^2)^2*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))-7/3*c^3*d^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-5/6*c^3*d^2*(a+b*arccosh(c*x))^3*sqrt(d-c^2*d*x^2)/(b*sqrt(-1+c*x)*sqrt(1+c*x))-14/3*b*c^3*d^2*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+7/3*b^2*c^3*d^2*polylog(2,(-1)/exp(2*arccosh(c*x)))*sqrt(d-c^2*d*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],

# p<0
[x^5*(a+b*arccosh(c*x))^2/sqrt(d-c^2*d*x^2),x,16,-4144/3375*b^2*(1-c*x)*(1+c*x)/(c^6*sqrt(d-c^2*d*x^2))-272/3375*b^2*x^2*(1-c*x)*(1+c*x)/(c^4*sqrt(d-c^2*d*x^2))-2/125*b^2*x^4*(1-c*x)*(1+c*x)/(c^2*sqrt(d-c^2*d*x^2))-16/15*a*b*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*sqrt(d-c^2*d*x^2))-16/15*b^2*x*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*sqrt(d-c^2*d*x^2))-8/45*b*x^3*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*sqrt(d-c^2*d*x^2))-2/25*b*x^5*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))-8/15*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^6*d)-4/15*x^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^4*d)-1/5*x^4*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^2*d)],
[x^4*(a+b*arccosh(c*x))^2/sqrt(d-c^2*d*x^2),x,11,-15/64*b^2*x*(1-c*x)*(1+c*x)/(c^4*sqrt(d-c^2*d*x^2))-1/32*b^2*x^3*(1-c*x)*(1+c*x)/(c^2*sqrt(d-c^2*d*x^2))+15/64*b^2*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*sqrt(d-c^2*d*x^2))-3/8*b*x^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*sqrt(d-c^2*d*x^2))-1/8*b*x^4*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))+1/8*(a+b*arccosh(c*x))^3*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^5*sqrt(d-c^2*d*x^2))-3/8*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^4*d)-1/4*x^3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^2*d)],
[x^3*(a+b*arccosh(c*x))^2/sqrt(d-c^2*d*x^2),x,9,-40/27*b^2*(1-c*x)*(1+c*x)/(c^4*sqrt(d-c^2*d*x^2))-2/27*b^2*x^2*(1-c*x)*(1+c*x)/(c^2*sqrt(d-c^2*d*x^2))-4/3*a*b*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*sqrt(d-c^2*d*x^2))-4/3*b^2*x*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*sqrt(d-c^2*d*x^2))-2/9*b*x^3*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))-2/3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^4*d)-1/3*x^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^2*d)],
[x^2*(a+b*arccosh(c*x))^2/sqrt(d-c^2*d*x^2),x,5,-1/4*b^2*x*(1-c*x)*(1+c*x)/(c^2*sqrt(d-c^2*d*x^2))+1/4*b^2*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*sqrt(d-c^2*d*x^2))-1/2*b*x^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))+1/6*(a+b*arccosh(c*x))^3*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^3*sqrt(d-c^2*d*x^2))-1/2*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^2*d)],
[x*(a+b*arccosh(c*x))^2/sqrt(d-c^2*d*x^2),x,4,-2*b^2*(1-c*x)*(1+c*x)/(c^2*sqrt(d-c^2*d*x^2))-2*a*b*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))-2*b^2*x*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c*sqrt(d-c^2*d*x^2))-(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^2*d)],
[(a+b*arccosh(c*x))^2/sqrt(d-c^2*d*x^2),x,1,1/3*(a+b*arccosh(c*x))^3*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))^2/(x*sqrt(d-c^2*d*x^2)),x,8,2*(a+b*arccosh(c*x))^2*arctan(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-2*I*b*(a+b*arccosh(c*x))*polylog(2,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)+2*I*b*(a+b*arccosh(c*x))*polylog(2,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)+2*I*b^2*polylog(3,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-2*I*b^2*polylog(3,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)],
[(a+b*arccosh(c*x))^2/(x^2*sqrt(d-c^2*d*x^2)),x,6,-c*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-2*b*c*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)+b^2*c*polylog(2,(-1)/exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(d*x)],
[(a+b*arccosh(c*x))^2/(x^3*sqrt(d-c^2*d*x^2)),x,12,b*c*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(x*sqrt(d-c^2*d*x^2))+c^2*(a+b*arccosh(c*x))^2*arctan(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-b^2*c^2*arctan(sqrt(-1+c*x)*sqrt(1+c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-I*b*c^2*(a+b*arccosh(c*x))*polylog(2,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)+I*b*c^2*(a+b*arccosh(c*x))*polylog(2,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)+I*b^2*c^2*polylog(3,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-I*b^2*c^2*polylog(3,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-1/2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(d*x^2)],
[(a+b*arccosh(c*x))^2/(x^4*sqrt(d-c^2*d*x^2)),x,9,1/3*b^2*c^2*(1-c*x)*(1+c*x)/(x*sqrt(d-c^2*d*x^2))+1/3*b*c*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(x^2*sqrt(d-c^2*d*x^2))-2/3*c^3*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-4/3*b*c^3*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)+2/3*b^2*c^3*polylog(2,(-1)/exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/sqrt(d-c^2*d*x^2)-1/3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(d*x^3)-2/3*c^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(d*x)],
[x^5*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(3/2),x,23,94/27*b^2*(1-c*x)*(1+c*x)/(c^6*d*sqrt(d-c^2*d*x^2))+2/27*b^2*x^2*(1-c*x)*(1+c*x)/(c^4*d*sqrt(d-c^2*d*x^2))+x^4*(a+b*arccosh(c*x))^2/(c^2*d*sqrt(d-c^2*d*x^2))+16/3*a*b*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d*sqrt(d-c^2*d*x^2))+16/3*b^2*x*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d*sqrt(d-c^2*d*x^2))-2*b*x*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d*sqrt(d-c^2*d*x^2))+2/9*b*x^3*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d*sqrt(d-c^2*d*x^2))+4*b*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^6*d*sqrt(d-c^2*d*x^2))+2*b^2*polylog(2,-exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^6*d*sqrt(d-c^2*d*x^2))-2*b^2*polylog(2,exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^6*d*sqrt(d-c^2*d*x^2))+8/3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^6*d^2)+4/3*x^2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^4*d^2)],
[x^4*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(3/2),x,15,1/4*b^2*x*(1-c*x)*(1+c*x)/(c^4*d*sqrt(d-c^2*d*x^2))+x^3*(a+b*arccosh(c*x))^2/(c^2*d*sqrt(d-c^2*d*x^2))-1/4*b^2*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d*sqrt(d-c^2*d*x^2))+1/2*b*x^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d*sqrt(d-c^2*d*x^2))+(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d*sqrt(d-c^2*d*x^2))-1/2*(a+b*arccosh(c*x))^3*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^5*d*sqrt(d-c^2*d*x^2))-2*b*(a+b*arccosh(c*x))*log(1-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d*sqrt(d-c^2*d*x^2))-b^2*polylog(2,exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d*sqrt(d-c^2*d*x^2))+3/2*x*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^4*d^2)],
[x^3*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(3/2),x,14,2*b^2*(1-c*x)*(1+c*x)/(c^4*d*sqrt(d-c^2*d*x^2))+x^2*(a+b*arccosh(c*x))^2/(c^2*d*sqrt(d-c^2*d*x^2))+4*a*b*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d*sqrt(d-c^2*d*x^2))+4*b^2*x*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d*sqrt(d-c^2*d*x^2))-2*b*x*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d*sqrt(d-c^2*d*x^2))+4*b*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^4*d*sqrt(d-c^2*d*x^2))+2*b^2*polylog(2,-exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^4*d*sqrt(d-c^2*d*x^2))-2*b^2*polylog(2,exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^4*d*sqrt(d-c^2*d*x^2))+2*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^4*d^2)],
[x^2*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(3/2),x,8,x*(a+b*arccosh(c*x))^2/(c^2*d*sqrt(d-c^2*d*x^2))+(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d*sqrt(d-c^2*d*x^2))-1/3*(a+b*arccosh(c*x))^3*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^3*d*sqrt(d-c^2*d*x^2))-2*b*(a+b*arccosh(c*x))*log(1-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d*sqrt(d-c^2*d*x^2))-b^2*polylog(2,exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d*sqrt(d-c^2*d*x^2))],
[x*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(3/2),x,8,(a+b*arccosh(c*x))^2/(c^2*d*sqrt(d-c^2*d*x^2))+4*b*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*d*sqrt(d-c^2*d*x^2))+2*b^2*polylog(2,-exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*d*sqrt(d-c^2*d*x^2))-2*b^2*polylog(2,exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*d*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(3/2),x,6,x*(a+b*arccosh(c*x))^2/(d*sqrt(d-c^2*d*x^2))+(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d*sqrt(d-c^2*d*x^2))-2*b*(a+b*arccosh(c*x))*log(1-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d*sqrt(d-c^2*d*x^2))-b^2*polylog(2,exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))^2/(x*(d-c^2*d*x^2)^(3/2)),x,16,(a+b*arccosh(c*x))^2/(d*sqrt(d-c^2*d*x^2))+2*(a+b*arccosh(c*x))^2*arctan(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))+4*b*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))+2*b^2*polylog(2,-exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-2*I*b*(a+b*arccosh(c*x))*polylog(2,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))+2*I*b*(a+b*arccosh(c*x))*polylog(2,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-2*b^2*polylog(2,exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))+2*I*b^2*polylog(3,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-2*I*b^2*polylog(3,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))^2/(x^2*(d-c^2*d*x^2)^(3/2)),x,15,-(a+b*arccosh(c*x))^2/(d*x*sqrt(d-c^2*d*x^2))+2*c^2*x*(a+b*arccosh(c*x))^2/(d*sqrt(d-c^2*d*x^2))+2*c*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-4*b*c*(a+b*arccosh(c*x))*arctanh(exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-4*b*c*(a+b*arccosh(c*x))*log(1-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-b^2*c*polylog(2,-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-b^2*c*polylog(2,exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))^2/(x^3*(d-c^2*d*x^2)^(3/2)),x,27,3/2*c^2*(a+b*arccosh(c*x))^2/(d*sqrt(d-c^2*d*x^2))-1/2*(a+b*arccosh(c*x))^2/(d*x^2*sqrt(d-c^2*d*x^2))+b*c*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*x*sqrt(d-c^2*d*x^2))+3*c^2*(a+b*arccosh(c*x))^2*arctan(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-b^2*c^2*arctan(sqrt(-1+c*x)*sqrt(1+c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))+4*b*c^2*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))+2*b^2*c^2*polylog(2,-exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-3*I*b*c^2*(a+b*arccosh(c*x))*polylog(2,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))+3*I*b*c^2*(a+b*arccosh(c*x))*polylog(2,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-2*b^2*c^2*polylog(2,exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))+3*I*b^2*c^2*polylog(3,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-3*I*b^2*c^2*polylog(3,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))^2/(x^4*(d-c^2*d*x^2)^(3/2)),x,26,1/3*b^2*c^2*(1-c*x)*(1+c*x)/(d*x*sqrt(d-c^2*d*x^2))-1/3*(a+b*arccosh(c*x))^2/(d*x^3*sqrt(d-c^2*d*x^2))-4/3*c^2*(a+b*arccosh(c*x))^2/(d*x*sqrt(d-c^2*d*x^2))+8/3*c^4*x*(a+b*arccosh(c*x))^2/(d*sqrt(d-c^2*d*x^2))+1/3*b*c*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*x^2*sqrt(d-c^2*d*x^2))+8/3*c^3*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-20/3*b*c^3*(a+b*arccosh(c*x))*arctanh(exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-16/3*b*c^3*(a+b*arccosh(c*x))*log(1-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-5/3*b^2*c^3*polylog(2,-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))-b^2*c^3*polylog(2,exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d*sqrt(d-c^2*d*x^2))],
[x^5*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(5/2),x,28,1/3*x^4*(a+b*arccosh(c*x))^2/(c^2*d*(d-c^2*d*x^2)^(3/2))-1/3*b^2*x^2/(c^4*d^2*sqrt(d-c^2*d*x^2))-7/3*b^2*(1-c*x)*(1+c*x)/(c^6*d^2*sqrt(d-c^2*d*x^2))-4/3*x^2*(a+b*arccosh(c*x))^2/(c^4*d^2*sqrt(d-c^2*d*x^2))-16/3*a*b*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d^2*sqrt(d-c^2*d*x^2))-16/3*b^2*x*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d^2*sqrt(d-c^2*d*x^2))+11/3*b*x*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d^2*sqrt(d-c^2*d*x^2))+1/3*b*x^3*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))-22/3*b*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^6*d^2*sqrt(d-c^2*d*x^2))-11/3*b^2*polylog(2,-exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^6*d^2*sqrt(d-c^2*d*x^2))+11/3*b^2*polylog(2,exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^6*d^2*sqrt(d-c^2*d*x^2))-8/3*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(c^6*d^3)],
[x^4*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(5/2),x,20,1/3*x^3*(a+b*arccosh(c*x))^2/(c^2*d*(d-c^2*d*x^2)^(3/2))-1/3*b^2/(c^5*d^2*sqrt(d-c^2*d*x^2))+1/3*b^2*(1-c*x)/(c^5*d^2*sqrt(d-c^2*d*x^2))-x*(a+b*arccosh(c*x))^2/(c^4*d^2*sqrt(d-c^2*d*x^2))+1/3*b^2*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d^2*sqrt(d-c^2*d*x^2))+1/3*b*x^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))-4/3*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d^2*sqrt(d-c^2*d*x^2))+1/3*(a+b*arccosh(c*x))^3*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^5*d^2*sqrt(d-c^2*d*x^2))+8/3*b*(a+b*arccosh(c*x))*log(1-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d^2*sqrt(d-c^2*d*x^2))+4/3*b^2*polylog(2,exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^5*d^2*sqrt(d-c^2*d*x^2))],
[x^3*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(5/2),x,18,1/3*x^2*(a+b*arccosh(c*x))^2/(c^2*d*(d-c^2*d*x^2)^(3/2))-1/3*b^2/(c^4*d^2*sqrt(d-c^2*d*x^2))-2/3*(a+b*arccosh(c*x))^2/(c^4*d^2*sqrt(d-c^2*d*x^2))+1/3*b*x*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))-10/3*b*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^4*d^2*sqrt(d-c^2*d*x^2))-5/3*b^2*polylog(2,-exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^4*d^2*sqrt(d-c^2*d*x^2))+5/3*b^2*polylog(2,exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^4*d^2*sqrt(d-c^2*d*x^2))],
[x^2*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(5/2),x,12,1/3*x^3*(a+b*arccosh(c*x))^2/(d*(d-c^2*d*x^2)^(3/2))-1/3*b^2/(c^3*d^2*sqrt(d-c^2*d*x^2))+1/3*b^2*(1-c*x)/(c^3*d^2*sqrt(d-c^2*d*x^2))+1/3*b^2*arccosh(c*x)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d^2*sqrt(d-c^2*d*x^2))+1/3*b*x^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))-1/3*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d^2*sqrt(d-c^2*d*x^2))+2/3*b*(a+b*arccosh(c*x))*log(1-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d^2*sqrt(d-c^2*d*x^2))+1/3*b^2*polylog(2,exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*d^2*sqrt(d-c^2*d*x^2))],
[x*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(5/2),x,10,1/3*(a+b*arccosh(c*x))^2/(c^2*d*(d-c^2*d*x^2)^(3/2))-1/3*b^2/(c^2*d^2*sqrt(d-c^2*d*x^2))+1/3*b*x*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+2/3*b*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*d^2*sqrt(d-c^2*d*x^2))+1/3*b^2*polylog(2,-exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*d^2*sqrt(d-c^2*d*x^2))-1/3*b^2*polylog(2,exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c^2*d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(5/2),x,10,1/3*x*(a+b*arccosh(c*x))^2/(d*(d-c^2*d*x^2)^(3/2))-1/3*b^2*x/(d^2*sqrt(d-c^2*d*x^2))+2/3*x*(a+b*arccosh(c*x))^2/(d^2*sqrt(d-c^2*d*x^2))+1/3*b*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+2/3*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d^2*sqrt(d-c^2*d*x^2))-4/3*b*(a+b*arccosh(c*x))*log(1-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d^2*sqrt(d-c^2*d*x^2))-2/3*b^2*polylog(2,exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(c*d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))^2/(x*(d-c^2*d*x^2)^(5/2)),x,26,1/3*(a+b*arccosh(c*x))^2/(d*(d-c^2*d*x^2)^(3/2))-1/3*b^2/(d^2*sqrt(d-c^2*d*x^2))+(a+b*arccosh(c*x))^2/(d^2*sqrt(d-c^2*d*x^2))+1/3*b*c*x*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+2*(a+b*arccosh(c*x))^2*arctan(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))+14/3*b*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))+7/3*b^2*polylog(2,-exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-2*I*b*(a+b*arccosh(c*x))*polylog(2,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))+2*I*b*(a+b*arccosh(c*x))*polylog(2,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-7/3*b^2*polylog(2,exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))+2*I*b^2*polylog(3,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-2*I*b^2*polylog(3,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))^2/(x^2*(d-c^2*d*x^2)^(5/2)),x,21,-(a+b*arccosh(c*x))^2/(d*x*(d-c^2*d*x^2)^(3/2))+4/3*c^2*x*(a+b*arccosh(c*x))^2/(d*(d-c^2*d*x^2)^(3/2))-1/3*b^2*c^2*x/(d^2*sqrt(d-c^2*d*x^2))+8/3*c^2*x*(a+b*arccosh(c*x))^2/(d^2*sqrt(d-c^2*d*x^2))+1/3*b*c*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+8/3*c*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-4*b*c*(a+b*arccosh(c*x))*arctanh(exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-16/3*b*c*(a+b*arccosh(c*x))*log(1-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-b^2*c*polylog(2,-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-5/3*b^2*c*polylog(2,exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))^2/(x^3*(d-c^2*d*x^2)^(5/2)),x,41,5/6*c^2*(a+b*arccosh(c*x))^2/(d*(d-c^2*d*x^2)^(3/2))-1/2*(a+b*arccosh(c*x))^2/(d*x^2*(d-c^2*d*x^2)^(3/2))-1/3*b^2*c^2/(d^2*sqrt(d-c^2*d*x^2))+5/2*c^2*(a+b*arccosh(c*x))^2/(d^2*sqrt(d-c^2*d*x^2))+b*c*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*x*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))-2/3*b*c^3*x*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+5*c^2*(a+b*arccosh(c*x))^2*arctan(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-b^2*c^2*arctan(sqrt(-1+c*x)*sqrt(1+c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))+26/3*b*c^2*(a+b*arccosh(c*x))*arctanh(exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))+13/3*b^2*c^2*polylog(2,-exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-5*I*b*c^2*(a+b*arccosh(c*x))*polylog(2,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))+5*I*b*c^2*(a+b*arccosh(c*x))*polylog(2,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-13/3*b^2*c^2*polylog(2,exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))+5*I*b^2*c^2*polylog(3,-I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-5*I*b^2*c^2*polylog(3,I*exp(arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))^2/(x^4*(d-c^2*d*x^2)^(5/2)),x,36,-1/3*(a+b*arccosh(c*x))^2/(d*x^3*(d-c^2*d*x^2)^(3/2))-2*c^2*(a+b*arccosh(c*x))^2/(d*x*(d-c^2*d*x^2)^(3/2))+8/3*c^4*x*(a+b*arccosh(c*x))^2/(d*(d-c^2*d*x^2)^(3/2))+1/3*b^2*c^2/(d^2*x*sqrt(d-c^2*d*x^2))-2/3*b^2*c^4*x/(d^2*sqrt(d-c^2*d*x^2))+16/3*c^4*x*(a+b*arccosh(c*x))^2/(d^2*sqrt(d-c^2*d*x^2))+1/3*b*c*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*x^2*(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+16/3*c^3*(a+b*arccosh(c*x))^2*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-32/3*b*c^3*(a+b*arccosh(c*x))*arctanh(exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-32/3*b*c^3*(a+b*arccosh(c*x))*log(1-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-8/3*b^2*c^3*polylog(2,-exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))-8/3*b^2*c^3*polylog(2,exp(2*arccosh(c*x)))*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*sqrt(d-c^2*d*x^2))],
[arccosh(a*x)^2/(c-a^2*c*x^2)^(7/2),x,15,1/5*x*arccosh(a*x)^2/(c*(c-a^2*c*x^2)^(5/2))+4/15*x*arccosh(a*x)^2/(c^2*(c-a^2*c*x^2)^(3/2))-1/3*x/(c^3*sqrt(c-a^2*c*x^2))-1/30*x/(c^3*(1-a*x)*(1+a*x)*sqrt(c-a^2*c*x^2))+8/15*x*arccosh(a*x)^2/(c^3*sqrt(c-a^2*c*x^2))+1/10*arccosh(a*x)*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*(1-a^2*x^2)^2*sqrt(c-a^2*c*x^2))+4/15*arccosh(a*x)*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*(1-a^2*x^2)*sqrt(c-a^2*c*x^2))+8/15*arccosh(a*x)^2*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*sqrt(c-a^2*c*x^2))-16/15*arccosh(a*x)*log(1-exp(2*arccosh(a*x)))*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*sqrt(c-a^2*c*x^2))-8/15*polylog(2,exp(2*arccosh(a*x)))*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*sqrt(c-a^2*c*x^2))],
[x^4*arccosh(a*x)^2/sqrt(1-a^2*x^2),x,11,15/64*arccosh(a*x)*sqrt(-1+a*x)/(a^5*sqrt(1-a*x))-3/8*x^2*arccosh(a*x)*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))-1/8*x^4*arccosh(a*x)*sqrt(-1+a*x)/(a*sqrt(1-a*x))+1/8*arccosh(a*x)^3*sqrt(-1+a*x)/(a^5*sqrt(1-a*x))-15/64*x*sqrt(1-a*x)*sqrt(1+a*x)/a^4-1/32*x^3*sqrt(1-a*x)*sqrt(1+a*x)/a^2-3/8*x*arccosh(a*x)^2*sqrt(1-a^2*x^2)/a^4-1/4*x^3*arccosh(a*x)^2*sqrt(1-a^2*x^2)/a^2],
[x^3*arccosh(a*x)^2/sqrt(1-a^2*x^2),x,8,-4/3*x*arccosh(a*x)*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))-2/9*x^3*arccosh(a*x)*sqrt(-1+a*x)/(a*sqrt(1-a*x))-40/27*sqrt(1-a*x)*sqrt(1+a*x)/a^4-2/27*x^2*sqrt(1-a*x)*sqrt(1+a*x)/a^2-2/3*arccosh(a*x)^2*sqrt(1-a^2*x^2)/a^4-1/3*x^2*arccosh(a*x)^2*sqrt(1-a^2*x^2)/a^2],
[x^2*arccosh(a*x)^2/sqrt(1-a^2*x^2),x,5,1/4*arccosh(a*x)*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))-1/2*x^2*arccosh(a*x)*sqrt(-1+a*x)/(a*sqrt(1-a*x))+1/6*arccosh(a*x)^3*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))-1/4*x*sqrt(1-a*x)*sqrt(1+a*x)/a^2-1/2*x*arccosh(a*x)^2*sqrt(1-a^2*x^2)/a^2],
[x*arccosh(a*x)^2/sqrt(1-a^2*x^2),x,3,-2*x*arccosh(a*x)*sqrt(-1+a*x)/(a*sqrt(1-a*x))-2*sqrt(1-a*x)*sqrt(1+a*x)/a^2-arccosh(a*x)^2*sqrt(1-a^2*x^2)/a^2],
[arccosh(a*x)^2/sqrt(1-a^2*x^2),x,1,1/3*arccosh(a*x)^3*sqrt(-1+a*x)/(a*sqrt(1-a*x))],
[arccosh(a*x)^2/(x*sqrt(1-a^2*x^2)),x,8,2*arccosh(a*x)^2*arctan(exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-2*I*arccosh(a*x)*polylog(2,-I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+2*I*arccosh(a*x)*polylog(2,I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+2*I*polylog(3,-I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-2*I*polylog(3,I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)],
[arccosh(a*x)^2/(x^2*sqrt(1-a^2*x^2)),x,6,a*arccosh(a*x)^2*sqrt(-1+a*x)/sqrt(1-a*x)-2*a*arccosh(a*x)*log(1+exp(2*arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-a*polylog(2,-exp(2*arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-arccosh(a*x)^2*sqrt(1-a^2*x^2)/x],
[arccosh(a*x)^2/(x^3*sqrt(1-a^2*x^2)),x,12,a*arccosh(a*x)*sqrt(-1+a*x)/(x*sqrt(1-a*x))+a^2*arccosh(a*x)^2*arctan(exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-a^2*arctan(sqrt(-1+a*x)*sqrt(1+a*x))*sqrt(-1+a*x)/sqrt(1-a*x)-I*a^2*arccosh(a*x)*polylog(2,-I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+I*a^2*arccosh(a*x)*polylog(2,I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+I*a^2*polylog(3,-I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-I*a^2*polylog(3,I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-1/2*arccosh(a*x)^2*sqrt(1-a^2*x^2)/x^2],

# Integrands of the form (f x)^m (d-c^2 d x^2)^p (a+b ArcCosh[c x])^2 with m symbolic
#  {(f*x)^m*(d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x])^2, x, 1, 0}
# {(f*x)^m*(d - c^2*d*x^2)^1*(a + b*ArcCosh[c*x])^2, x, 1, 0}
# {(f*x)^m/(d - c^2*d*x^2)^1*(a + b*ArcCosh[c*x])^2, x, 1, 0}

# {(f*x)^m/(d - c^2*d*x^2)^2*(a + b*ArcCosh[c*x])^2, x, 1, 0} 
[(f*x)^m*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2,x,22,5*d*(f*x)^(1+m)*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2/(f*(4+m)*(6+m))+(f*x)^(1+m)*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^2/(f*(6+m))-10*b^2*c^2*d^2*(f*x)^(3+m)*sqrt(d-c^2*d*x^2)/(f^3*(4+m)^3*(6+m))-2*b^2*c^2*d^2*(52+15*m+m^2)*(f*x)^(3+m)*(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(f^3*(4+m)^2*(6+m)^3*(1-c*x)*(1+c*x))+2*b^2*c^4*d^2*(f*x)^(5+m)*(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(f^5*(6+m)^3*(1-c*x)*(1+c*x))+15*d^2*(f*x)^(1+m)*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(f*(6+m)*(8+6*m+m^2))-2*b*c*d^2*(f*x)^(2+m)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f^2*(2+m)*(6+m)*sqrt(-1+c*x)*sqrt(1+c*x))-30*b*c*d^2*(f*x)^(2+m)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f^2*(2+m)^2*(4+m)*(6+m)*sqrt(-1+c*x)*sqrt(1+c*x))-10*b*c*d^2*(f*x)^(2+m)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f^2*(6+m)*(8+6*m+m^2)*sqrt(-1+c*x)*sqrt(1+c*x))+10*b*c^3*d^2*(f*x)^(4+m)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f^4*(4+m)^2*(6+m)*sqrt(-1+c*x)*sqrt(1+c*x))+4*b*c^3*d^2*(f*x)^(4+m)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f^4*(4+m)*(6+m)*sqrt(-1+c*x)*sqrt(1+c*x))-2*b*c^5*d^2*(f*x)^(6+m)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f^6*(6+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-30*b^2*c^2*d^2*(f*x)^(3+m)*hypergeom([1/2,1/2*(3+m)],[1/2*(5+m)],c^2*x^2)*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(f^3*(2+m)^2*(3+m)*(4+m)*(6+m)*(1-c*x)*(1+c*x))-10*b^2*c^2*d^2*(10+3*m)*(f*x)^(3+m)*hypergeom([1/2,1/2*(3+m)],[1/2*(5+m)],c^2*x^2)*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(f^3*(4+m)^3*(6+m)*(6+5*m+m^2)*(1-c*x)*(1+c*x))-2*b^2*c^2*d^2*(264+130*m+15*m^2)*(f*x)^(3+m)*hypergeom([1/2,1/2*(3+m)],[1/2*(5+m)],c^2*x^2)*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(f^3*(4+m)^2*(6+m)^3*(6+5*m+m^2)*(1-c*x)*(1+c*x))+15*d^3*Unintegrable((f*x)^m*(a+b*arccosh(c*x))^2/sqrt(d-c^2*d*x^2),x)/((6+m)*(8+6*m+m^2))],
[(f*x)^m*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2,x,13,(f*x)^(1+m)*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^2/(f*(4+m))-2*b^2*c^2*d*(f*x)^(3+m)*sqrt(d-c^2*d*x^2)/(f^3*(4+m)^3)+3*d*(f*x)^(1+m)*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(f*(8+6*m+m^2))-6*b*c*d*(f*x)^(2+m)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f^2*(2+m)^2*(4+m)*sqrt(-1+c*x)*sqrt(1+c*x))-2*b*c*d*(f*x)^(2+m)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f^2*(2+m)*(4+m)*sqrt(-1+c*x)*sqrt(1+c*x))+2*b*c^3*d*(f*x)^(4+m)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f^4*(4+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-6*b^2*c^2*d*(f*x)^(3+m)*hypergeom([1/2,1/2*(3+m)],[1/2*(5+m)],c^2*x^2)*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(f^3*(2+m)^2*(3+m)*(4+m)*(1-c*x)*(1+c*x))-2*b^2*c^2*d*(10+3*m)*(f*x)^(3+m)*hypergeom([1/2,1/2*(3+m)],[1/2*(5+m)],c^2*x^2)*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(f^3*(4+m)^3*(6+5*m+m^2)*(1-c*x)*(1+c*x))+3*d^2*Unintegrable((f*x)^m*(a+b*arccosh(c*x))^2/sqrt(d-c^2*d*x^2),x)/(8+6*m+m^2)],
[(f*x)^m*(d-c^2*d*x^2)^(1/2)*(a+b*arccosh(c*x))^2,x,5,(f*x)^(1+m)*(a+b*arccosh(c*x))^2*sqrt(d-c^2*d*x^2)/(f*(2+m))-2*b*c*(f*x)^(2+m)*(a+b*arccosh(c*x))*sqrt(d-c^2*d*x^2)/(f^2*(2+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-2*b^2*c^2*(f*x)^(3+m)*hypergeom([1/2,1/2*(3+m)],[1/2*(5+m)],c^2*x^2)*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2)/(f^3*(2+m)^2*(3+m)*(1-c*x)*(1+c*x))+d*Unintegrable((f*x)^m*(a+b*arccosh(c*x))^2/sqrt(d-c^2*d*x^2),x)/(2+m)],
[(f*x)^m*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(1/2),x,0,Unintegrable((f*x)^m*(a+b*arccosh(c*x))^2/sqrt(d-c^2*d*x^2),x)],
[(f*x)^m*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(3/2),x,0,Unintegrable((f*x)^m*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(3/2),x)],
[(f*x)^m*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(5/2),x,0,Unintegrable((f*x)^m*(a+b*arccosh(c*x))^2/(d-c^2*d*x^2)^(5/2),x)],
[(f*x)^m*arccosh(c*x)^2/sqrt(1-c^2*x^2),x,0,Unintegrable((f*x)^m*arccosh(c*x)^2/sqrt(1-c^2*x^2),x)],

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

# Integrands of the form x^m (d-c^2 d x^2)^p (a+b ArcCosh[c x])^3
[(c-a^2*c*x^2)^3*arccosh(a*x)^3,x,29,4322/1225*c^3*x*arccosh(a*x)-1514/3675*a^2*c^3*x^3*arccosh(a*x)+702/6125*a^4*c^3*x^5*arccosh(a*x)-6/343*a^6*c^3*x^7*arccosh(a*x)+8/35*c^3*(-1+a*x)^(3/2)*(1+a*x)^(3/2)*arccosh(a*x)^2/a-18/175*c^3*(-1+a*x)^(5/2)*(1+a*x)^(5/2)*arccosh(a*x)^2/a+3/49*c^3*(-1+a*x)^(7/2)*(1+a*x)^(7/2)*arccosh(a*x)^2/a+16/35*c^3*x*arccosh(a*x)^3+8/35*c^3*x*(1-a^2*x^2)*arccosh(a*x)^3+6/35*c^3*x*(1-a^2*x^2)^2*arccosh(a*x)^3+1/7*c^3*x*(1-a^2*x^2)^3*arccosh(a*x)^3+7104/42875*c^3*(1-a^2*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+1184/42875*c^3*(1-a^2*x^2)^2/(a*sqrt(-1+a*x)*sqrt(1+a*x))+2664/214375*c^3*(1-a^2*x^2)^3/(a*sqrt(-1+a*x)*sqrt(1+a*x))+6/2401*c^3*(1-a^2*x^2)^4/(a*sqrt(-1+a*x)*sqrt(1+a*x))-976/315*c^3*sqrt(-1+a*x)*sqrt(1+a*x)/a+16/315*a*c^3*x^2*sqrt(-1+a*x)*sqrt(1+a*x)-48/35*c^3*arccosh(a*x)^2*sqrt(-1+a*x)*sqrt(1+a*x)/a],
[(c-a^2*c*x^2)^2*arccosh(a*x)^3,x,20,298/75*c^2*x*arccosh(a*x)-76/225*a^2*c^2*x^3*arccosh(a*x)+6/125*a^4*c^2*x^5*arccosh(a*x)+4/15*c^2*(-1+a*x)^(3/2)*(1+a*x)^(3/2)*arccosh(a*x)^2/a-3/25*c^2*(-1+a*x)^(5/2)*(1+a*x)^(5/2)*arccosh(a*x)^2/a+8/15*c^2*x*arccosh(a*x)^3+4/15*c^2*x*(1-a^2*x^2)*arccosh(a*x)^3+1/5*c^2*x*(1-a^2*x^2)^2*arccosh(a*x)^3+16/125*c^2*(1-a^2*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+8/375*c^2*(1-a^2*x^2)^2/(a*sqrt(-1+a*x)*sqrt(1+a*x))+6/625*c^2*(1-a^2*x^2)^3/(a*sqrt(-1+a*x)*sqrt(1+a*x))-488/135*c^2*sqrt(-1+a*x)*sqrt(1+a*x)/a+8/135*a*c^2*x^2*sqrt(-1+a*x)*sqrt(1+a*x)-8/5*c^2*arccosh(a*x)^2*sqrt(-1+a*x)*sqrt(1+a*x)/a],
[(c-a^2*c*x^2)*arccosh(a*x)^3,x,11,14/3*c*x*arccosh(a*x)-2/9*a^2*c*x^3*arccosh(a*x)+1/3*c*(-1+a*x)^(3/2)*(1+a*x)^(3/2)*arccosh(a*x)^2/a+2/3*c*x*arccosh(a*x)^3+1/3*c*x*(1-a^2*x^2)*arccosh(a*x)^3-122/27*c*sqrt(-1+a*x)*sqrt(1+a*x)/a+2/27*a*c*x^2*sqrt(-1+a*x)*sqrt(1+a*x)-2*c*arccosh(a*x)^2*sqrt(-1+a*x)*sqrt(1+a*x)/a],
[arccosh(a*x)^3/(c-a^2*c*x^2),x,10,2*arccosh(a*x)^3*arctanh(exp(arccosh(a*x)))/(a*c)+3*arccosh(a*x)^2*polylog(2,-exp(arccosh(a*x)))/(a*c)-3*arccosh(a*x)^2*polylog(2,exp(arccosh(a*x)))/(a*c)-6*arccosh(a*x)*polylog(3,-exp(arccosh(a*x)))/(a*c)+6*arccosh(a*x)*polylog(3,exp(arccosh(a*x)))/(a*c)+6*polylog(4,-exp(arccosh(a*x)))/(a*c)-6*polylog(4,exp(arccosh(a*x)))/(a*c)],
[arccosh(a*x)^3/(c-a^2*c*x^2)^2,x,19,1/2*x*arccosh(a*x)^3/(c^2*(1-a^2*x^2))-6*arccosh(a*x)*arctanh(exp(arccosh(a*x)))/(a*c^2)+arccosh(a*x)^3*arctanh(exp(arccosh(a*x)))/(a*c^2)-3*polylog(2,-exp(arccosh(a*x)))/(a*c^2)+3/2*arccosh(a*x)^2*polylog(2,-exp(arccosh(a*x)))/(a*c^2)+3*polylog(2,exp(arccosh(a*x)))/(a*c^2)-3/2*arccosh(a*x)^2*polylog(2,exp(arccosh(a*x)))/(a*c^2)-3*arccosh(a*x)*polylog(3,-exp(arccosh(a*x)))/(a*c^2)+3*arccosh(a*x)*polylog(3,exp(arccosh(a*x)))/(a*c^2)+3*polylog(4,-exp(arccosh(a*x)))/(a*c^2)-3*polylog(4,exp(arccosh(a*x)))/(a*c^2)-3/2*arccosh(a*x)^2/(a*c^2*sqrt(-1+a*x)*sqrt(1+a*x))],
[arccosh(a*x)^3/(c-a^2*c*x^2)^3,x,30,-1/4*x*arccosh(a*x)/(c^3*(1-a^2*x^2))+1/4*arccosh(a*x)^2/(a*c^3*(-1+a*x)^(3/2)*(1+a*x)^(3/2))+1/4*x*arccosh(a*x)^3/(c^3*(1-a^2*x^2)^2)+3/8*x*arccosh(a*x)^3/(c^3*(1-a^2*x^2))-5*arccosh(a*x)*arctanh(exp(arccosh(a*x)))/(a*c^3)+3/4*arccosh(a*x)^3*arctanh(exp(arccosh(a*x)))/(a*c^3)-5/2*polylog(2,-exp(arccosh(a*x)))/(a*c^3)+9/8*arccosh(a*x)^2*polylog(2,-exp(arccosh(a*x)))/(a*c^3)+5/2*polylog(2,exp(arccosh(a*x)))/(a*c^3)-9/8*arccosh(a*x)^2*polylog(2,exp(arccosh(a*x)))/(a*c^3)-9/4*arccosh(a*x)*polylog(3,-exp(arccosh(a*x)))/(a*c^3)+9/4*arccosh(a*x)*polylog(3,exp(arccosh(a*x)))/(a*c^3)+9/4*polylog(4,-exp(arccosh(a*x)))/(a*c^3)-9/4*polylog(4,exp(arccosh(a*x)))/(a*c^3)+1/4/(a*c^3*sqrt(-1+a*x)*sqrt(1+a*x))-9/8*arccosh(a*x)^2/(a*c^3*sqrt(-1+a*x)*sqrt(1+a*x))],

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

# p>0
[(c-a^2*c*x^2)^(5/2)*arccosh(a*x)^3,x,29,5/24*c*x*(c-a^2*c*x^2)^(3/2)*arccosh(a*x)^3+1/6*x*(c-a^2*c*x^2)^(5/2)*arccosh(a*x)^3+245/384*c^2*x*arccosh(a*x)*sqrt(c-a^2*c*x^2)+65/576*c^2*x*(1-a*x)*(1+a*x)*arccosh(a*x)*sqrt(c-a^2*c*x^2)+1/36*c^2*x*(1-a*x)^2*(1+a*x)^2*arccosh(a*x)*sqrt(c-a^2*c*x^2)+5/16*c^2*x*arccosh(a*x)^3*sqrt(c-a^2*c*x^2)-865/2304*a*c^2*x^2*sqrt(c-a^2*c*x^2)/(sqrt(-1+a*x)*sqrt(1+a*x))+65/2304*a^3*c^2*x^4*sqrt(c-a^2*c*x^2)/(sqrt(-1+a*x)*sqrt(1+a*x))+1/216*c^2*(1-a^2*x^2)^3*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+115/768*c^2*arccosh(a*x)^2*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-15/32*a*c^2*x^2*arccosh(a*x)^2*sqrt(c-a^2*c*x^2)/(sqrt(-1+a*x)*sqrt(1+a*x))+5/32*c^2*(1-a^2*x^2)^2*arccosh(a*x)^2*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+1/12*c^2*(1-a^2*x^2)^3*arccosh(a*x)^2*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-5/64*c^2*arccosh(a*x)^4*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))],
[(c-a^2*c*x^2)^(3/2)*arccosh(a*x)^3,x,16,1/4*x*(c-a^2*c*x^2)^(3/2)*arccosh(a*x)^3+45/64*c*x*arccosh(a*x)*sqrt(c-a^2*c*x^2)+3/32*c*x*(1-a*x)*(1+a*x)*arccosh(a*x)*sqrt(c-a^2*c*x^2)+3/8*c*x*arccosh(a*x)^3*sqrt(c-a^2*c*x^2)-51/128*a*c*x^2*sqrt(c-a^2*c*x^2)/(sqrt(-1+a*x)*sqrt(1+a*x))+3/128*a^3*c*x^4*sqrt(c-a^2*c*x^2)/(sqrt(-1+a*x)*sqrt(1+a*x))+27/128*c*arccosh(a*x)^2*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-9/16*a*c*x^2*arccosh(a*x)^2*sqrt(c-a^2*c*x^2)/(sqrt(-1+a*x)*sqrt(1+a*x))+3/16*c*(1-a^2*x^2)^2*arccosh(a*x)^2*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-3/32*c*arccosh(a*x)^4*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))],
[arccosh(a*x)^3*sqrt(c-a^2*c*x^2),x,6,3/4*x*arccosh(a*x)*sqrt(c-a^2*c*x^2)+1/2*x*arccosh(a*x)^3*sqrt(c-a^2*c*x^2)-3/8*a*x^2*sqrt(c-a^2*c*x^2)/(sqrt(-1+a*x)*sqrt(1+a*x))+3/8*arccosh(a*x)^2*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-3/4*a*x^2*arccosh(a*x)^2*sqrt(c-a^2*c*x^2)/(sqrt(-1+a*x)*sqrt(1+a*x))-1/8*arccosh(a*x)^4*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))],

# p<0
[arccosh(a*x)^3/(c-a^2*c*x^2)^(1/2),x,1,1/4*arccosh(a*x)^4*sqrt(-1+a*x)*sqrt(1+a*x)/(a*sqrt(c-a^2*c*x^2))],
[arccosh(a*x)^3/(c-a^2*c*x^2)^(3/2),x,7,x*arccosh(a*x)^3/(c*sqrt(c-a^2*c*x^2))+arccosh(a*x)^3*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c*sqrt(c-a^2*c*x^2))-3*arccosh(a*x)^2*log(1-exp(2*arccosh(a*x)))*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c*sqrt(c-a^2*c*x^2))-3*arccosh(a*x)*polylog(2,exp(2*arccosh(a*x)))*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c*sqrt(c-a^2*c*x^2))+3/2*polylog(3,exp(2*arccosh(a*x)))*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c*sqrt(c-a^2*c*x^2))],
[arccosh(a*x)^3/(c-a^2*c*x^2)^(5/2),x,12,1/3*x*arccosh(a*x)^3/(c*(c-a^2*c*x^2)^(3/2))-x*arccosh(a*x)/(c^2*sqrt(c-a^2*c*x^2))+2/3*x*arccosh(a*x)^3/(c^2*sqrt(c-a^2*c*x^2))+1/2*arccosh(a*x)^2*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^2*(1-a^2*x^2)*sqrt(c-a^2*c*x^2))+2/3*arccosh(a*x)^3*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^2*sqrt(c-a^2*c*x^2))-2*arccosh(a*x)^2*log(1-exp(2*arccosh(a*x)))*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^2*sqrt(c-a^2*c*x^2))+1/2*log(1-a^2*x^2)*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^2*sqrt(c-a^2*c*x^2))-2*arccosh(a*x)*polylog(2,exp(2*arccosh(a*x)))*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^2*sqrt(c-a^2*c*x^2))+polylog(3,exp(2*arccosh(a*x)))*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^2*sqrt(c-a^2*c*x^2))],
[arccosh(a*x)^3/(c-a^2*c*x^2)^(7/2),x,20,1/5*x*arccosh(a*x)^3/(c*(c-a^2*c*x^2)^(5/2))+4/15*x*arccosh(a*x)^3/(c^2*(c-a^2*c*x^2)^(3/2))-x*arccosh(a*x)/(c^3*sqrt(c-a^2*c*x^2))-1/10*x*arccosh(a*x)/(c^3*(1-a*x)*(1+a*x)*sqrt(c-a^2*c*x^2))+8/15*x*arccosh(a*x)^3/(c^3*sqrt(c-a^2*c*x^2))-1/20*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*(1-a^2*x^2)*sqrt(c-a^2*c*x^2))+3/20*arccosh(a*x)^2*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*(1-a^2*x^2)^2*sqrt(c-a^2*c*x^2))+2/5*arccosh(a*x)^2*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*(1-a^2*x^2)*sqrt(c-a^2*c*x^2))+8/15*arccosh(a*x)^3*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*sqrt(c-a^2*c*x^2))-8/5*arccosh(a*x)^2*log(1-exp(2*arccosh(a*x)))*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*sqrt(c-a^2*c*x^2))+1/2*log(1-a^2*x^2)*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*sqrt(c-a^2*c*x^2))-8/5*arccosh(a*x)*polylog(2,exp(2*arccosh(a*x)))*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*sqrt(c-a^2*c*x^2))+4/5*polylog(3,exp(2*arccosh(a*x)))*sqrt(-1+a*x)*sqrt(1+a*x)/(a*c^3*sqrt(c-a^2*c*x^2))],
[x^4*arccosh(a*x)^3/sqrt(1-a^2*x^2),x,13,-45/128*x^2*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))-3/128*x^4*sqrt(-1+a*x)/(a*sqrt(1-a*x))+45/128*arccosh(a*x)^2*sqrt(-1+a*x)/(a^5*sqrt(1-a*x))-9/16*x^2*arccosh(a*x)^2*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))-3/16*x^4*arccosh(a*x)^2*sqrt(-1+a*x)/(a*sqrt(1-a*x))+3/32*arccosh(a*x)^4*sqrt(-1+a*x)/(a^5*sqrt(1-a*x))-45/64*x*arccosh(a*x)*sqrt(1-a*x)*sqrt(1+a*x)/a^4-3/32*x^3*arccosh(a*x)*sqrt(1-a*x)*sqrt(1+a*x)/a^2-3/8*x*arccosh(a*x)^3*sqrt(1-a^2*x^2)/a^4-1/4*x^3*arccosh(a*x)^3*sqrt(1-a^2*x^2)/a^2],
[x^3*arccosh(a*x)^3/sqrt(1-a^2*x^2),x,10,-40/9*x*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))-2/27*x^3*sqrt(-1+a*x)/(a*sqrt(1-a*x))-2*x*arccosh(a*x)^2*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))-1/3*x^3*arccosh(a*x)^2*sqrt(-1+a*x)/(a*sqrt(1-a*x))-40/9*arccosh(a*x)*sqrt(1-a*x)*sqrt(1+a*x)/a^4-2/9*x^2*arccosh(a*x)*sqrt(1-a*x)*sqrt(1+a*x)/a^2-2/3*arccosh(a*x)^3*sqrt(1-a^2*x^2)/a^4-1/3*x^2*arccosh(a*x)^3*sqrt(1-a^2*x^2)/a^2],
[x^2*arccosh(a*x)^3/sqrt(1-a^2*x^2),x,6,-3/8*x^2*sqrt(-1+a*x)/(a*sqrt(1-a*x))+3/8*arccosh(a*x)^2*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))-3/4*x^2*arccosh(a*x)^2*sqrt(-1+a*x)/(a*sqrt(1-a*x))+1/8*arccosh(a*x)^4*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))-3/4*x*arccosh(a*x)*sqrt(1-a*x)*sqrt(1+a*x)/a^2-1/2*x*arccosh(a*x)^3*sqrt(1-a^2*x^2)/a^2],
[x*arccosh(a*x)^3/sqrt(1-a^2*x^2),x,4,-6*x*sqrt(-1+a*x)/(a*sqrt(1-a*x))-3*x*arccosh(a*x)^2*sqrt(-1+a*x)/(a*sqrt(1-a*x))-6*arccosh(a*x)*sqrt(1-a*x)*sqrt(1+a*x)/a^2-arccosh(a*x)^3*sqrt(1-a^2*x^2)/a^2],
[arccosh(a*x)^3/sqrt(1-a^2*x^2),x,1,1/4*arccosh(a*x)^4*sqrt(-1+a*x)/(a*sqrt(1-a*x))],
[arccosh(a*x)^3/(x*sqrt(1-a^2*x^2)),x,10,2*arccosh(a*x)^3*arctan(exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-3*I*arccosh(a*x)^2*polylog(2,-I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+3*I*arccosh(a*x)^2*polylog(2,I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+6*I*arccosh(a*x)*polylog(3,-I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-6*I*arccosh(a*x)*polylog(3,I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-6*I*polylog(4,-I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+6*I*polylog(4,I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)],
[arccosh(a*x)^3/(x^2*sqrt(1-a^2*x^2)),x,7,a*arccosh(a*x)^3*sqrt(-1+a*x)/sqrt(1-a*x)-3*a*arccosh(a*x)^2*log(1+exp(2*arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-3*a*arccosh(a*x)*polylog(2,-exp(2*arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+3/2*a*polylog(3,-exp(2*arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-arccosh(a*x)^3*sqrt(1-a^2*x^2)/x],
[arccosh(a*x)^3/(x^3*sqrt(1-a^2*x^2)),x,18,3/2*a*arccosh(a*x)^2*sqrt(-1+a*x)/(x*sqrt(1-a*x))-6*a^2*arccosh(a*x)*arctan(exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+a^2*arccosh(a*x)^3*arctan(exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+3*I*a^2*polylog(2,-I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-3/2*I*a^2*arccosh(a*x)^2*polylog(2,-I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-3*I*a^2*polylog(2,I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+3/2*I*a^2*arccosh(a*x)^2*polylog(2,I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+3*I*a^2*arccosh(a*x)*polylog(3,-I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-3*I*a^2*arccosh(a*x)*polylog(3,I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-3*I*a^2*polylog(4,-I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)+3*I*a^2*polylog(4,I*exp(arccosh(a*x)))*sqrt(-1+a*x)/sqrt(1-a*x)-1/2*arccosh(a*x)^3*sqrt(1-a^2*x^2)/x^2],

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

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

# Integrands of the form x^m (d-c^2 d x^2)^p / (a+b ArcCosh[c x])
[(c-a^2*c*x^2)^3/arccosh(a*x),x,7,35/64*c^3*Shi(arccosh(a*x))/a-21/64*c^3*Shi(3*arccosh(a*x))/a+7/64*c^3*Shi(5*arccosh(a*x))/a-1/64*c^3*Shi(7*arccosh(a*x))/a],
[(c-a^2*c*x^2)^2/arccosh(a*x),x,6,5/8*c^2*Shi(arccosh(a*x))/a-5/16*c^2*Shi(3*arccosh(a*x))/a+1/16*c^2*Shi(5*arccosh(a*x))/a],
[(c-a^2*c*x^2)/arccosh(a*x),x,5,3/4*c*Shi(arccosh(a*x))/a-1/4*c*Shi(3*arccosh(a*x))/a],
[1/((c-a^2*c*x^2)*arccosh(a*x)),x,0,Unintegrable(1/((c-a^2*c*x^2)*arccosh(a*x)),x)],
[1/((c-a^2*c*x^2)^2*arccosh(a*x)),x,0,Unintegrable(1/((c-a^2*c*x^2)^2*arccosh(a*x)),x)],

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

# p>0
[x^4*sqrt(1-c^2*x^2)/(a+b*arccosh(c*x)),x,12,-1/32*Chi(2*(a+b*arccosh(c*x))/b)*cosh(2*a/b)*sqrt(1-c*x)/(b*c^5*sqrt(-1+c*x))+1/16*Chi(4*(a+b*arccosh(c*x))/b)*cosh(4*a/b)*sqrt(1-c*x)/(b*c^5*sqrt(-1+c*x))+1/32*Chi(6*(a+b*arccosh(c*x))/b)*cosh(6*a/b)*sqrt(1-c*x)/(b*c^5*sqrt(-1+c*x))-1/16*log(a+b*arccosh(c*x))*sqrt(1-c*x)/(b*c^5*sqrt(-1+c*x))+1/32*Shi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(1-c*x)/(b*c^5*sqrt(-1+c*x))-1/16*Shi(4*(a+b*arccosh(c*x))/b)*sinh(4*a/b)*sqrt(1-c*x)/(b*c^5*sqrt(-1+c*x))-1/32*Shi(6*(a+b*arccosh(c*x))/b)*sinh(6*a/b)*sqrt(1-c*x)/(b*c^5*sqrt(-1+c*x))],
[x^3*sqrt(1-c^2*x^2)/(a+b*arccosh(c*x)),x,12,-1/8*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))+1/16*Chi(3*(a+b*arccosh(c*x))/b)*cosh(3*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))+1/16*Chi(5*(a+b*arccosh(c*x))/b)*cosh(5*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))+1/8*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))-1/16*Shi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))-1/16*Shi(5*(a+b*arccosh(c*x))/b)*sinh(5*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))],
[x^2*sqrt(1-c^2*x^2)/(a+b*arccosh(c*x)),x,6,1/8*Chi(4*(a+b*arccosh(c*x))/b)*cosh(4*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))-1/8*log(a+b*arccosh(c*x))*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))-1/8*Shi(4*(a+b*arccosh(c*x))/b)*sinh(4*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))],
[x*sqrt(1-c^2*x^2)/(a+b*arccosh(c*x)),x,9,-1/4*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))+1/4*Chi(3*(a+b*arccosh(c*x))/b)*cosh(3*a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))+1/4*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))-1/4*Shi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))],
[sqrt(1-c^2*x^2)/(a+b*arccosh(c*x)),x,6,1/2*Chi(2*(a+b*arccosh(c*x))/b)*cosh(2*a/b)*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))-1/2*log(a+b*arccosh(c*x))*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))-1/2*Shi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))],
[sqrt(1-c^2*x^2)/(x*(a+b*arccosh(c*x))),x,6,-Chi((a+b*arccosh(c*x))/b)*cosh(a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))+Shi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))+Unintegrable(1/(x*(a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x)],
[sqrt(1-c^2*x^2)/(x^2*(a+b*arccosh(c*x))),x,3,-c*log(a+b*arccosh(c*x))*sqrt(-1+c*x)/(b*sqrt(1-c*x))+Unintegrable(1/(x^2*(a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x)],
[sqrt(1-c^2*x^2)/(x^3*(a+b*arccosh(c*x))),x,0,Unintegrable(sqrt(1-c^2*x^2)/(x^3*(a+b*arccosh(c*x))),x)],
[sqrt(1-c^2*x^2)/(x^4*(a+b*arccosh(c*x))),x,0,Unintegrable(sqrt(1-c^2*x^2)/(x^4*(a+b*arccosh(c*x))),x)],
[x^3*(1-c^2*x^2)^(3/2)/(a+b*arccosh(c*x)),x,15,-3/64*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))+3/64*Chi(3*(a+b*arccosh(c*x))/b)*cosh(3*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))+1/64*Chi(5*(a+b*arccosh(c*x))/b)*cosh(5*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))-1/64*Chi(7*(a+b*arccosh(c*x))/b)*cosh(7*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))+3/64*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))-3/64*Shi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))-1/64*Shi(5*(a+b*arccosh(c*x))/b)*sinh(5*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))+1/64*Shi(7*(a+b*arccosh(c*x))/b)*sinh(7*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))],
[x^2*(1-c^2*x^2)^(3/2)/(a+b*arccosh(c*x)),x,12,1/32*Chi(2*(a+b*arccosh(c*x))/b)*cosh(2*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))+1/16*Chi(4*(a+b*arccosh(c*x))/b)*cosh(4*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))-1/32*Chi(6*(a+b*arccosh(c*x))/b)*cosh(6*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))-1/16*log(a+b*arccosh(c*x))*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))-1/32*Shi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))-1/16*Shi(4*(a+b*arccosh(c*x))/b)*sinh(4*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))+1/32*Shi(6*(a+b*arccosh(c*x))/b)*sinh(6*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))],
[x*(1-c^2*x^2)^(3/2)/(a+b*arccosh(c*x)),x,12,-1/8*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))+3/16*Chi(3*(a+b*arccosh(c*x))/b)*cosh(3*a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))-1/16*Chi(5*(a+b*arccosh(c*x))/b)*cosh(5*a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))+1/8*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))-3/16*Shi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))+1/16*Shi(5*(a+b*arccosh(c*x))/b)*sinh(5*a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))],
[(1-c^2*x^2)^(3/2)/(a+b*arccosh(c*x)),x,9,1/2*Chi(2*(a+b*arccosh(c*x))/b)*cosh(2*a/b)*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))-1/8*Chi(4*(a+b*arccosh(c*x))/b)*cosh(4*a/b)*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))-3/8*log(a+b*arccosh(c*x))*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))-1/2*Shi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))+1/8*Shi(4*(a+b*arccosh(c*x))/b)*sinh(4*a/b)*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))],
[(1-c^2*x^2)^(3/2)/(x*(a+b*arccosh(c*x))),x,15,-5/4*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))+1/4*Chi(3*(a+b*arccosh(c*x))/b)*cosh(3*a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))+5/4*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))-1/4*Shi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))+Unintegrable(1/(x*(a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x)],
[(1-c^2*x^2)^(3/2)/(x^2*(a+b*arccosh(c*x))),x,9,1/2*c*Chi(2*(a+b*arccosh(c*x))/b)*cosh(2*a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))-3/2*c*log(a+b*arccosh(c*x))*sqrt(-1+c*x)/(b*sqrt(1-c*x))-1/2*c*Shi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))+Unintegrable(1/(x^2*(a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x)],
[(1-c^2*x^2)^(3/2)/(x^3*(a+b*arccosh(c*x))),x,0,Unintegrable((1-c^2*x^2)^(3/2)/(x^3*(a+b*arccosh(c*x))),x)],
[(1-c^2*x^2)^(3/2)/(x^4*(a+b*arccosh(c*x))),x,0,Unintegrable((1-c^2*x^2)^(3/2)/(x^4*(a+b*arccosh(c*x))),x)],
[x^3*(1-c^2*x^2)^(5/2)/(a+b*arccosh(c*x)),x,15,-3/128*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))+1/32*Chi(3*(a+b*arccosh(c*x))/b)*cosh(3*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))-3/256*Chi(7*(a+b*arccosh(c*x))/b)*cosh(7*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))+1/256*Chi(9*(a+b*arccosh(c*x))/b)*cosh(9*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))+3/128*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))-1/32*Shi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))+3/256*Shi(7*(a+b*arccosh(c*x))/b)*sinh(7*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))-1/256*Shi(9*(a+b*arccosh(c*x))/b)*sinh(9*a/b)*sqrt(1-c*x)/(b*c^4*sqrt(-1+c*x))],
[x^2*(1-c^2*x^2)^(5/2)/(a+b*arccosh(c*x)),x,15,1/32*Chi(2*(a+b*arccosh(c*x))/b)*cosh(2*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))+1/32*Chi(4*(a+b*arccosh(c*x))/b)*cosh(4*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))-1/32*Chi(6*(a+b*arccosh(c*x))/b)*cosh(6*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))+1/128*Chi(8*(a+b*arccosh(c*x))/b)*cosh(8*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))-5/128*log(a+b*arccosh(c*x))*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))-1/32*Shi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))-1/32*Shi(4*(a+b*arccosh(c*x))/b)*sinh(4*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))+1/32*Shi(6*(a+b*arccosh(c*x))/b)*sinh(6*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))-1/128*Shi(8*(a+b*arccosh(c*x))/b)*sinh(8*a/b)*sqrt(1-c*x)/(b*c^3*sqrt(-1+c*x))],
[x*(1-c^2*x^2)^(5/2)/(a+b*arccosh(c*x)),x,15,-5/64*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))+9/64*Chi(3*(a+b*arccosh(c*x))/b)*cosh(3*a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))-5/64*Chi(5*(a+b*arccosh(c*x))/b)*cosh(5*a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))+1/64*Chi(7*(a+b*arccosh(c*x))/b)*cosh(7*a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))+5/64*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))-9/64*Shi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))+5/64*Shi(5*(a+b*arccosh(c*x))/b)*sinh(5*a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))-1/64*Shi(7*(a+b*arccosh(c*x))/b)*sinh(7*a/b)*sqrt(1-c*x)/(b*c^2*sqrt(-1+c*x))],
[(1-c^2*x^2)^(5/2)/(a+b*arccosh(c*x)),x,12,15/32*Chi(2*(a+b*arccosh(c*x))/b)*cosh(2*a/b)*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))-3/16*Chi(4*(a+b*arccosh(c*x))/b)*cosh(4*a/b)*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))+1/32*Chi(6*(a+b*arccosh(c*x))/b)*cosh(6*a/b)*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))-5/16*log(a+b*arccosh(c*x))*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))-15/32*Shi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))+3/16*Shi(4*(a+b*arccosh(c*x))/b)*sinh(4*a/b)*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))-1/32*Shi(6*(a+b*arccosh(c*x))/b)*sinh(6*a/b)*sqrt(1-c*x)/(b*c*sqrt(-1+c*x))],
[(1-c^2*x^2)^(5/2)/(x*(a+b*arccosh(c*x))),x,27,-11/8*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))+7/16*Chi(3*(a+b*arccosh(c*x))/b)*cosh(3*a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))-1/16*Chi(5*(a+b*arccosh(c*x))/b)*cosh(5*a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))+11/8*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))-7/16*Shi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))+1/16*Shi(5*(a+b*arccosh(c*x))/b)*sinh(5*a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))+Unintegrable(1/(x*(a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x)],
[(1-c^2*x^2)^(5/2)/(x^2*(a+b*arccosh(c*x))),x,18,c*Chi(2*(a+b*arccosh(c*x))/b)*cosh(2*a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))-1/8*c*Chi(4*(a+b*arccosh(c*x))/b)*cosh(4*a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))-15/8*c*log(a+b*arccosh(c*x))*sqrt(-1+c*x)/(b*sqrt(1-c*x))-c*Shi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))+1/8*c*Shi(4*(a+b*arccosh(c*x))/b)*sinh(4*a/b)*sqrt(-1+c*x)/(b*sqrt(1-c*x))+Unintegrable(1/(x^2*(a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x)],
[(1-c^2*x^2)^(5/2)/(x^3*(a+b*arccosh(c*x))),x,0,Unintegrable((1-c^2*x^2)^(5/2)/(x^3*(a+b*arccosh(c*x))),x)],
[(1-c^2*x^2)^(5/2)/(x^4*(a+b*arccosh(c*x))),x,0,Unintegrable((1-c^2*x^2)^(5/2)/(x^4*(a+b*arccosh(c*x))),x)],

# p<0
[x^4/(arccosh(a*x)*sqrt(1-a^2*x^2)),x,5,1/2*Chi(2*arccosh(a*x))*sqrt(-1+a*x)/(a^5*sqrt(1-a*x))+1/8*Chi(4*arccosh(a*x))*sqrt(-1+a*x)/(a^5*sqrt(1-a*x))+3/8*log(arccosh(a*x))*sqrt(-1+a*x)/(a^5*sqrt(1-a*x))],
[x^3/(arccosh(a*x)*sqrt(1-a^2*x^2)),x,5,3/4*Chi(arccosh(a*x))*sqrt(-1+a*x)/(a^4*sqrt(1-a*x))+1/4*Chi(3*arccosh(a*x))*sqrt(-1+a*x)/(a^4*sqrt(1-a*x))],
[x^2/(arccosh(a*x)*sqrt(1-a^2*x^2)),x,4,1/2*Chi(2*arccosh(a*x))*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))+1/2*log(arccosh(a*x))*sqrt(-1+a*x)/(a^3*sqrt(1-a*x))],
[x/(arccosh(a*x)*sqrt(1-a^2*x^2)),x,2,Chi(arccosh(a*x))*sqrt(-1+a*x)/(a^2*sqrt(1-a*x))],
[1/(arccosh(a*x)*sqrt(1-a^2*x^2)),x,1,log(arccosh(a*x))*sqrt(-1+a*x)/(a*sqrt(1-a*x))],
[1/(x*arccosh(a*x)*sqrt(1-a^2*x^2)),x,0,Unintegrable(1/(x*arccosh(a*x)*sqrt(1-a^2*x^2)),x)],
[1/(x^2*arccosh(a*x)*sqrt(1-a^2*x^2)),x,0,Unintegrable(1/(x^2*arccosh(a*x)*sqrt(1-a^2*x^2)),x)],
[x^3/((a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x,9,3/4*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)*sqrt(-1+c*x)/(b*c^4*sqrt(1-c*x))+1/4*Chi(3*(a+b*arccosh(c*x))/b)*cosh(3*a/b)*sqrt(-1+c*x)/(b*c^4*sqrt(1-c*x))-3/4*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(-1+c*x)/(b*c^4*sqrt(1-c*x))-1/4*Shi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(-1+c*x)/(b*c^4*sqrt(1-c*x))],
[x^2/((a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x,6,1/2*Chi(2*(a+b*arccosh(c*x))/b)*cosh(2*a/b)*sqrt(-1+c*x)/(b*c^3*sqrt(1-c*x))+1/2*log(a+b*arccosh(c*x))*sqrt(-1+c*x)/(b*c^3*sqrt(1-c*x))-1/2*Shi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(-1+c*x)/(b*c^3*sqrt(1-c*x))],
[x/((a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x,4,Chi((a+b*arccosh(c*x))/b)*cosh(a/b)*sqrt(-1+c*x)/(b*c^2*sqrt(1-c*x))-Shi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(-1+c*x)/(b*c^2*sqrt(1-c*x))],
[1/((a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x,1,log(a+b*arccosh(c*x))*sqrt(-1+c*x)/(b*c*sqrt(1-c*x))],
[1/(x*(a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x,0,Unintegrable(1/(x*(a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x)],
[1/(x^2*(a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x,0,Unintegrable(1/(x^2*(a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x)],
[x^2/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))),x,0,Unintegrable(x^2/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))),x)],
[x/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))),x,0,Unintegrable(x/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))),x)],
[1/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))),x,0,Unintegrable(1/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))),x)],
[1/(x*(1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))),x,0,Unintegrable(1/(x*(1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))),x)],
[1/(x^2*(1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))),x,0,Unintegrable(1/(x^2*(1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))),x)],

# Integrands of the form (f x)^m (d-c^2 d x^2)^p / (a+b ArcCosh[c x]) with m symbolic
[x^m*(1-c^2*x^2)^(3/2)/(a+b*arccosh(c*x)),x,0,Unintegrable(x^m*(1-c^2*x^2)^(3/2)/(a+b*arccosh(c*x)),x)],
[x^m*(1-c^2*x^2)^(1/2)/(a+b*arccosh(c*x)),x,0,Unintegrable(x^m*sqrt(1-c^2*x^2)/(a+b*arccosh(c*x)),x)],
[x^m/((1-c^2*x^2)^(1/2)*(a+b*arccosh(c*x))),x,0,Unintegrable(x^m/((a+b*arccosh(c*x))*sqrt(1-c^2*x^2)),x)],
[x^m/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))),x,0,Unintegrable(x^m/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))),x)],
[x^m/((1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))),x,0,Unintegrable(x^m/((1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))),x)],

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

# Integrands of the form x^m (d-c^2 d x^2)^p / (a+b ArcCosh[c x])^2
[(c-a^2*c*x^2)^3/arccosh(a*x)^2,x,8,c^3*(-1+a*x)^(7/2)*(1+a*x)^(7/2)/(a*arccosh(a*x))+35/64*c^3*Chi(arccosh(a*x))/a-63/64*c^3*Chi(3*arccosh(a*x))/a+35/64*c^3*Chi(5*arccosh(a*x))/a-7/64*c^3*Chi(7*arccosh(a*x))/a],
[(c-a^2*c*x^2)^2/arccosh(a*x)^2,x,7,-c^2*(-1+a*x)^(5/2)*(1+a*x)^(5/2)/(a*arccosh(a*x))+5/8*c^2*Chi(arccosh(a*x))/a-15/16*c^2*Chi(3*arccosh(a*x))/a+5/16*c^2*Chi(5*arccosh(a*x))/a],
[(c-a^2*c*x^2)/arccosh(a*x)^2,x,6,c*(-1+a*x)^(3/2)*(1+a*x)^(3/2)/(a*arccosh(a*x))+3/4*c*Chi(arccosh(a*x))/a-3/4*c*Chi(3*arccosh(a*x))/a],
[1/((c-a^2*c*x^2)*arccosh(a*x)^2),x,1,1/(a*c*arccosh(a*x)*sqrt(-1+a*x)*sqrt(1+a*x))+a*Unintegrable(x/((-1+a*x)^(3/2)*(1+a*x)^(3/2)*arccosh(a*x)),x)/c],
[1/((c-a^2*c*x^2)^2*arccosh(a*x)^2),x,1,(-1)/(a*c^2*(-1+a*x)^(3/2)*(1+a*x)^(3/2)*arccosh(a*x))-3*a*Unintegrable(x/((-1+a*x)^(5/2)*(1+a*x)^(5/2)*arccosh(a*x)),x)/c^2],

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

# p>0
[x^3*sqrt(1-c^2*x^2)/(a+b*arccosh(c*x))^2,x,22,-1/8*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^4*sqrt(-1+c*x))+3/16*cosh(3*a/b)*Shi(3*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^4*sqrt(-1+c*x))+5/16*cosh(5*a/b)*Shi(5*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^4*sqrt(-1+c*x))+1/8*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(1-c*x)/(b^2*c^4*sqrt(-1+c*x))-3/16*Chi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(1-c*x)/(b^2*c^4*sqrt(-1+c*x))-5/16*Chi(5*(a+b*arccosh(c*x))/b)*sinh(5*a/b)*sqrt(1-c*x)/(b^2*c^4*sqrt(-1+c*x))-x^3*sqrt(-1+c*x)*sqrt(1+c*x)*sqrt(1-c^2*x^2)/(b*c*(a+b*arccosh(c*x)))],
[x^2*sqrt(1-c^2*x^2)/(a+b*arccosh(c*x))^2,x,16,1/2*cosh(4*a/b)*Shi(4*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))-1/2*Chi(4*(a+b*arccosh(c*x))/b)*sinh(4*a/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))-x^2*sqrt(-1+c*x)*sqrt(1+c*x)*sqrt(1-c^2*x^2)/(b*c*(a+b*arccosh(c*x)))],
[x*sqrt(1-c^2*x^2)/(a+b*arccosh(c*x))^2,x,14,-1/4*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))+3/4*cosh(3*a/b)*Shi(3*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))+1/4*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))-3/4*Chi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))-x*sqrt(-1+c*x)*sqrt(1+c*x)*sqrt(1-c^2*x^2)/(b*c*(a+b*arccosh(c*x)))],
[sqrt(1-c^2*x^2)/(a+b*arccosh(c*x))^2,x,7,cosh(2*a/b)*Shi(2*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c*sqrt(-1+c*x))-Chi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(1-c*x)/(b^2*c*sqrt(-1+c*x))-sqrt(-1+c*x)*sqrt(1+c*x)*sqrt(1-c^2*x^2)/(b*c*(a+b*arccosh(c*x)))],
[sqrt(1-c^2*x^2)/(x*(a+b*arccosh(c*x))^2),x,5,cosh(a/b)*Shi((a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*sqrt(-1+c*x))-Chi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(1-c*x)/(b^2*sqrt(-1+c*x))-sqrt(-1+c*x)*sqrt(1+c*x)*sqrt(1-c^2*x^2)/(b*c*x*(a+b*arccosh(c*x)))+sqrt(1-c*x)*Unintegrable(1/(x^2*(a+b*arccosh(c*x))),x)/(b*c*sqrt(-1+c*x))],
[sqrt(1-c^2*x^2)/(x^2*(a+b*arccosh(c*x))^2),x,1,-sqrt(-1+c*x)*sqrt(1+c*x)*sqrt(1-c^2*x^2)/(b*c*x^2*(a+b*arccosh(c*x)))+2*sqrt(1-c*x)*Unintegrable(1/(x^3*(a+b*arccosh(c*x))),x)/(b*c*sqrt(-1+c*x))],
[sqrt(1-c^2*x^2)/(x^3*(a+b*arccosh(c*x))^2),x,0,Unintegrable(sqrt(1-c^2*x^2)/(x^3*(a+b*arccosh(c*x))^2),x)],
[sqrt(1-c^2*x^2)/(x^4*(a+b*arccosh(c*x))^2),x,0,Unintegrable(sqrt(1-c^2*x^2)/(x^4*(a+b*arccosh(c*x))^2),x)],
[x^2*(1-c^2*x^2)^(3/2)/(a+b*arccosh(c*x))^2,x,21,1/16*cosh(2*a/b)*Shi(2*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))+1/4*cosh(4*a/b)*Shi(4*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))-3/16*cosh(6*a/b)*Shi(6*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))-1/16*Chi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))-1/4*Chi(4*(a+b*arccosh(c*x))/b)*sinh(4*a/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))+3/16*Chi(6*(a+b*arccosh(c*x))/b)*sinh(6*a/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))-x^2*(1-c^2*x^2)^(3/2)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))],
[x*(1-c^2*x^2)^(3/2)/(a+b*arccosh(c*x))^2,x,24,-1/8*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))+9/16*cosh(3*a/b)*Shi(3*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))-5/16*cosh(5*a/b)*Shi(5*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))+1/8*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))-9/16*Chi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))+5/16*Chi(5*(a+b*arccosh(c*x))/b)*sinh(5*a/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))-x*(1-c^2*x^2)^(3/2)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))],
[(1-c^2*x^2)^(3/2)/(a+b*arccosh(c*x))^2,x,11,cosh(2*a/b)*Shi(2*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c*sqrt(-1+c*x))-1/2*cosh(4*a/b)*Shi(4*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c*sqrt(-1+c*x))-Chi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(1-c*x)/(b^2*c*sqrt(-1+c*x))+1/2*Chi(4*(a+b*arccosh(c*x))/b)*sinh(4*a/b)*sqrt(1-c*x)/(b^2*c*sqrt(-1+c*x))-(1-c^2*x^2)^(3/2)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))],
[(1-c^2*x^2)^(3/2)/(x*(a+b*arccosh(c*x))^2),x,12,9/4*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*sqrt(-1+c*x))-3/4*cosh(3*a/b)*Shi(3*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*sqrt(-1+c*x))-9/4*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(1-c*x)/(b^2*sqrt(-1+c*x))+3/4*Chi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(1-c*x)/(b^2*sqrt(-1+c*x))-(1-c^2*x^2)^(3/2)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*x*(a+b*arccosh(c*x)))-sqrt(1-c*x)*Unintegrable((-1+c^2*x^2)/(x^2*(a+b*arccosh(c*x))),x)/(b*c*sqrt(-1+c*x))],
[(1-c^2*x^2)^(3/2)/(x^2*(a+b*arccosh(c*x))^2),x,3,-(1-c^2*x^2)^(3/2)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*x^2*(a+b*arccosh(c*x)))-2*sqrt(1-c*x)*Unintegrable((-1+c^2*x^2)/(x^3*(a+b*arccosh(c*x))),x)/(b*c*sqrt(-1+c*x))-2*c*sqrt(1-c*x)*Unintegrable((-1+c^2*x^2)/(x*(a+b*arccosh(c*x))),x)/(b*sqrt(-1+c*x))],
[(1-c^2*x^2)^(3/2)/(x^3*(a+b*arccosh(c*x))^2),x,0,Unintegrable((1-c^2*x^2)^(3/2)/(x^3*(a+b*arccosh(c*x))^2),x)],
[(1-c^2*x^2)^(3/2)/(x^4*(a+b*arccosh(c*x))^2),x,2,-(1-c^2*x^2)^(3/2)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*x^4*(a+b*arccosh(c*x)))-4*sqrt(1-c*x)*Unintegrable((-1+c^2*x^2)/(x^5*(a+b*arccosh(c*x))),x)/(b*c*sqrt(-1+c*x))],
[x^2*(1-c^2*x^2)^(5/2)/(a+b*arccosh(c*x))^2,x,30,1/16*cosh(2*a/b)*Shi(2*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))+1/8*cosh(4*a/b)*Shi(4*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))-3/16*cosh(6*a/b)*Shi(6*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))+1/16*cosh(8*a/b)*Shi(8*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))-1/16*Chi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))-1/8*Chi(4*(a+b*arccosh(c*x))/b)*sinh(4*a/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))+3/16*Chi(6*(a+b*arccosh(c*x))/b)*sinh(6*a/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))-1/16*Chi(8*(a+b*arccosh(c*x))/b)*sinh(8*a/b)*sqrt(1-c*x)/(b^2*c^3*sqrt(-1+c*x))-x^2*(1-c^2*x^2)^(5/2)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))],
[x*(1-c^2*x^2)^(5/2)/(a+b*arccosh(c*x))^2,x,30,-5/64*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))+27/64*cosh(3*a/b)*Shi(3*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))-25/64*cosh(5*a/b)*Shi(5*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))+7/64*cosh(7*a/b)*Shi(7*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))+5/64*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))-27/64*Chi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))+25/64*Chi(5*(a+b*arccosh(c*x))/b)*sinh(5*a/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))-7/64*Chi(7*(a+b*arccosh(c*x))/b)*sinh(7*a/b)*sqrt(1-c*x)/(b^2*c^2*sqrt(-1+c*x))-x*(1-c^2*x^2)^(5/2)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))],
[(1-c^2*x^2)^(5/2)/(a+b*arccosh(c*x))^2,x,14,15/16*cosh(2*a/b)*Shi(2*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c*sqrt(-1+c*x))-3/4*cosh(4*a/b)*Shi(4*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c*sqrt(-1+c*x))+3/16*cosh(6*a/b)*Shi(6*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*c*sqrt(-1+c*x))-15/16*Chi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(1-c*x)/(b^2*c*sqrt(-1+c*x))+3/4*Chi(4*(a+b*arccosh(c*x))/b)*sinh(4*a/b)*sqrt(1-c*x)/(b^2*c*sqrt(-1+c*x))-3/16*Chi(6*(a+b*arccosh(c*x))/b)*sinh(6*a/b)*sqrt(1-c*x)/(b^2*c*sqrt(-1+c*x))-(1-c^2*x^2)^(5/2)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))],
[(1-c^2*x^2)^(5/2)/(x*(a+b*arccosh(c*x))^2),x,15,25/8*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*sqrt(-1+c*x))-25/16*cosh(3*a/b)*Shi(3*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*sqrt(-1+c*x))+5/16*cosh(5*a/b)*Shi(5*(a+b*arccosh(c*x))/b)*sqrt(1-c*x)/(b^2*sqrt(-1+c*x))-25/8*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(1-c*x)/(b^2*sqrt(-1+c*x))+25/16*Chi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(1-c*x)/(b^2*sqrt(-1+c*x))-5/16*Chi(5*(a+b*arccosh(c*x))/b)*sinh(5*a/b)*sqrt(1-c*x)/(b^2*sqrt(-1+c*x))-(1-c^2*x^2)^(5/2)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*x*(a+b*arccosh(c*x)))+sqrt(1-c*x)*Unintegrable((-1+c^2*x^2)^2/(x^2*(a+b*arccosh(c*x))),x)/(b*c*sqrt(-1+c*x))],
[(1-c^2*x^2)^(5/2)/(x^2*(a+b*arccosh(c*x))^2),x,3,-(1-c^2*x^2)^(5/2)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*x^2*(a+b*arccosh(c*x)))+2*sqrt(1-c*x)*Unintegrable((-1+c^2*x^2)^2/(x^3*(a+b*arccosh(c*x))),x)/(b*c*sqrt(-1+c*x))+4*c*sqrt(1-c*x)*Unintegrable((-1+c^2*x^2)^2/(x*(a+b*arccosh(c*x))),x)/(b*sqrt(-1+c*x))],
[(1-c^2*x^2)^(5/2)/(x^3*(a+b*arccosh(c*x))^2),x,0,Unintegrable((1-c^2*x^2)^(5/2)/(x^3*(a+b*arccosh(c*x))^2),x)],
[(1-c^2*x^2)^(5/2)/(x^4*(a+b*arccosh(c*x))^2),x,0,Unintegrable((1-c^2*x^2)^(5/2)/(x^4*(a+b*arccosh(c*x))^2),x)],

# p<0
[x^5/((a+b*arccosh(c*x))^2*sqrt(1-c^2*x^2)),x,13,-x^5*sqrt(-1+c*x)/(b*c*(a+b*arccosh(c*x))*sqrt(1-c*x))+5/8*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(b^2*c^6*sqrt(1-c*x))+15/16*cosh(3*a/b)*Shi(3*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(b^2*c^6*sqrt(1-c*x))+5/16*cosh(5*a/b)*Shi(5*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(b^2*c^6*sqrt(1-c*x))-5/8*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(-1+c*x)/(b^2*c^6*sqrt(1-c*x))-15/16*Chi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(-1+c*x)/(b^2*c^6*sqrt(1-c*x))-5/16*Chi(5*(a+b*arccosh(c*x))/b)*sinh(5*a/b)*sqrt(-1+c*x)/(b^2*c^6*sqrt(1-c*x))],
[x^4/((a+b*arccosh(c*x))^2*sqrt(1-c^2*x^2)),x,10,-x^4*sqrt(-1+c*x)/(b*c*(a+b*arccosh(c*x))*sqrt(1-c*x))+cosh(2*a/b)*Shi(2*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(b^2*c^5*sqrt(1-c*x))+1/2*cosh(4*a/b)*Shi(4*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(b^2*c^5*sqrt(1-c*x))-Chi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(-1+c*x)/(b^2*c^5*sqrt(1-c*x))-1/2*Chi(4*(a+b*arccosh(c*x))/b)*sinh(4*a/b)*sqrt(-1+c*x)/(b^2*c^5*sqrt(1-c*x))],
[x^3/((a+b*arccosh(c*x))^2*sqrt(1-c^2*x^2)),x,10,-x^3*sqrt(-1+c*x)/(b*c*(a+b*arccosh(c*x))*sqrt(1-c*x))+3/4*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(b^2*c^4*sqrt(1-c*x))+3/4*cosh(3*a/b)*Shi(3*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(b^2*c^4*sqrt(1-c*x))-3/4*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(-1+c*x)/(b^2*c^4*sqrt(1-c*x))-3/4*Chi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)*sqrt(-1+c*x)/(b^2*c^4*sqrt(1-c*x))],
[x^2/((a+b*arccosh(c*x))^2*sqrt(1-c^2*x^2)),x,7,-x^2*sqrt(-1+c*x)/(b*c*(a+b*arccosh(c*x))*sqrt(1-c*x))+cosh(2*a/b)*Shi(2*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(b^2*c^3*sqrt(1-c*x))-Chi(2*(a+b*arccosh(c*x))/b)*sinh(2*a/b)*sqrt(-1+c*x)/(b^2*c^3*sqrt(1-c*x))],
[x/((a+b*arccosh(c*x))^2*sqrt(1-c^2*x^2)),x,5,-x*sqrt(-1+c*x)/(b*c*(a+b*arccosh(c*x))*sqrt(1-c*x))+cosh(a/b)*Shi((a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(b^2*c^2*sqrt(1-c*x))-Chi((a+b*arccosh(c*x))/b)*sinh(a/b)*sqrt(-1+c*x)/(b^2*c^2*sqrt(1-c*x))],
[1/((a+b*arccosh(c*x))^2*sqrt(1-c^2*x^2)),x,1,-sqrt(-1+c*x)/(b*c*(a+b*arccosh(c*x))*sqrt(1-c*x))],
[1/(x*(a+b*arccosh(c*x))^2*sqrt(1-c^2*x^2)),x,1,-sqrt(-1+c*x)/(b*c*x*(a+b*arccosh(c*x))*sqrt(1-c*x))-sqrt(-1+c*x)*Unintegrable(1/(x^2*(a+b*arccosh(c*x))),x)/(b*c*sqrt(1-c*x))],
[1/(x^2*(a+b*arccosh(c*x))^2*sqrt(1-c^2*x^2)),x,1,-sqrt(-1+c*x)/(b*c*x^2*(a+b*arccosh(c*x))*sqrt(1-c*x))-2*sqrt(-1+c*x)*Unintegrable(1/(x^3*(a+b*arccosh(c*x))),x)/(b*c*sqrt(1-c*x))],
[x^3/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x,0,Unintegrable(x^3/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x)],
[x^2/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x,2,-x^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x)))+2*sqrt(-1+c*x)*Unintegrable(x/((-1+c^2*x^2)^2*(a+b*arccosh(c*x))),x)/(b*c*sqrt(1-c*x))],
[x/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x,0,Unintegrable(x/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x)],
[1/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x,2,-sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x)))+2*c*sqrt(-1+c*x)*Unintegrable(x/((-1+c^2*x^2)^2*(a+b*arccosh(c*x))),x)/(b*sqrt(1-c*x))],
[1/(x*(1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x,0,Unintegrable(1/(x*(1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x)],
[1/(x^2*(1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x,0,Unintegrable(1/(x^2*(1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x)],
[x^4/((1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x,2,-x^4*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x)))-4*sqrt(-1+c*x)*Unintegrable(x^3/((-1+c^2*x^2)^3*(a+b*arccosh(c*x))),x)/(b*c*sqrt(1-c*x))],
[x^3/((1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x,0,Unintegrable(x^3/((1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x)],
[x^2/((1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x,0,Unintegrable(x^2/((1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x)],
[x/((1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x,0,Unintegrable(x/((1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x)],
[1/((1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x,2,-sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x)))-4*c*sqrt(-1+c*x)*Unintegrable(x/((-1+c^2*x^2)^3*(a+b*arccosh(c*x))),x)/(b*sqrt(1-c*x))],
[1/(x*(1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x,0,Unintegrable(1/(x*(1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x)],
[1/(x^2*(1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x,0,Unintegrable(1/(x^2*(1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x)],

# Integrands of the form (f x)^m (d-c^2 d x^2)^p / (a+b ArcCosh[c x])^2 with m symbolic
[(f*x)^m*(1-c^2*x^2)^(3/2)/(a+b*arccosh(c*x))^2,x,0,Unintegrable((f*x)^m*(1-c^2*x^2)^(3/2)/(a+b*arccosh(c*x))^2,x)],
[(f*x)^m*(1-c^2*x^2)^(1/2)/(a+b*arccosh(c*x))^2,x,0,Unintegrable((f*x)^m*sqrt(1-c^2*x^2)/(a+b*arccosh(c*x))^2,x)],
[(f*x)^m/((1-c^2*x^2)^(1/2)*(a+b*arccosh(c*x))^2),x,1,-(f*x)^m*sqrt(-1+c*x)/(b*c*(a+b*arccosh(c*x))*sqrt(1-c*x))+f*m*sqrt(-1+c*x)*Unintegrable((f*x)^(-1+m)/(a+b*arccosh(c*x)),x)/(b*c*sqrt(1-c*x))],
[(f*x)^m/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x,0,Unintegrable((f*x)^m/((1-c^2*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x)],
[(f*x)^m/((1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x,0,Unintegrable((f*x)^m/((1-c^2*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x)],

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

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

# Integrands of the form (f x)^m (d-c^2 d x^2)^(p/2) / (a+b ArcCosh[c x])^3
[1/(arccosh(a*x)^3*sqrt(1-a^2*x^2)),x,1,-1/2*sqrt(-1+a*x)/(a*arccosh(a*x)^2*sqrt(1-a*x))],

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

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

# n>0

# n<0
[x^3*(d-c^2*d*x^2)/(a+b*arccosh(c*x))^(3/2),x,27,3/16*d*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^4)+3/16*d*erfi(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^4*exp(2*a/b))-1/16*d*exp(6*a/b)*erf(sqrt(6)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3/2*Pi)/(b^(3/2)*c^4)-1/16*d*erfi(sqrt(6)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3/2*Pi)/(b^(3/2)*c^4*exp(6*a/b))+2*d*x^3*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/(b*c*sqrt(a+b*arccosh(c*x)))],
[x^2*(d-c^2*d*x^2)/(a+b*arccosh(c*x))^(3/2),x,32,1/8*d*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c^3)+1/8*d*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c^3*exp(a/b))+1/16*d*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*c^3)+1/16*d*erfi(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*c^3*exp(3*a/b))-1/16*d*exp(5*a/b)*erf(sqrt(5)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(5*Pi)/(b^(3/2)*c^3)-1/16*d*erfi(sqrt(5)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(5*Pi)/(b^(3/2)*c^3*exp(5*a/b))+2*d*x^2*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/(b*c*sqrt(a+b*arccosh(c*x)))],
[x*(d-c^2*d*x^2)/(a+b*arccosh(c*x))^(3/2),x,17,1/2*d*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^2)+1/2*d*erfi(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^2*exp(2*a/b))-1/4*d*exp(4*a/b)*erf(2*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c^2)-1/4*d*erfi(2*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c^2*exp(4*a/b))+2*d*x*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/(b*c*sqrt(a+b*arccosh(c*x)))],
[(d-c^2*d*x^2)/(a+b*arccosh(c*x))^(3/2),x,14,3/4*d*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c)+3/4*d*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c*exp(a/b))-1/4*d*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*c)-1/4*d*erfi(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*c*exp(3*a/b))+2*d*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/(b*c*sqrt(a+b*arccosh(c*x)))],
[(d-c^2*d*x^2)/(x*(a+b*arccosh(c*x))^(3/2)),x,12,-d*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/b^(3/2)-d*erfi(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*exp(2*a/b))+2*d*(-1+c*x)^(3/2)*(1+c*x)^(3/2)/(b*c*x*sqrt(a+b*arccosh(c*x)))+2*d*Unintegrable(1/(x^2*sqrt(-1+c*x)*sqrt(1+c*x)*sqrt(a+b*arccosh(c*x))),x)/(b*c)],
[x^3*(d-c^2*d*x^2)^2/(a+b*arccosh(c*x))^(3/2),x,32,3/32*d^2*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^4)+1/32*d^2*exp(8*a/b)*erf(2*sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^4)+3/32*d^2*erfi(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^4*exp(2*a/b))+1/32*d^2*erfi(2*sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^4*exp(8*a/b))-1/32*d^2*exp(4*a/b)*erf(2*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c^4)-1/32*d^2*erfi(2*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c^4*exp(4*a/b))-1/32*d^2*exp(6*a/b)*erf(sqrt(6)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3/2*Pi)/(b^(3/2)*c^4)-1/32*d^2*erfi(sqrt(6)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3/2*Pi)/(b^(3/2)*c^4*exp(6*a/b))-2*d^2*x^3*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/(b*c*sqrt(a+b*arccosh(c*x)))],
[x^2*(d-c^2*d*x^2)^2/(a+b*arccosh(c*x))^(3/2),x,42,5/64*d^2*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c^3)+5/64*d^2*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c^3*exp(a/b))+1/64*d^2*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*c^3)+1/64*d^2*erfi(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*c^3*exp(3*a/b))-3/64*d^2*exp(5*a/b)*erf(sqrt(5)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(5*Pi)/(b^(3/2)*c^3)-3/64*d^2*erfi(sqrt(5)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(5*Pi)/(b^(3/2)*c^3*exp(5*a/b))+1/64*d^2*exp(7*a/b)*erf(sqrt(7)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(7*Pi)/(b^(3/2)*c^3)+1/64*d^2*erfi(sqrt(7)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(7*Pi)/(b^(3/2)*c^3*exp(7*a/b))-2*d^2*x^2*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/(b*c*sqrt(a+b*arccosh(c*x)))],
[x*(d-c^2*d*x^2)^2/(a+b*arccosh(c*x))^(3/2),x,32,5/16*d^2*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^2)+5/16*d^2*erfi(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^2*exp(2*a/b))-1/4*d^2*exp(4*a/b)*erf(2*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c^2)-1/4*d^2*erfi(2*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c^2*exp(4*a/b))+1/16*d^2*exp(6*a/b)*erf(sqrt(6)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3/2*Pi)/(b^(3/2)*c^2)+1/16*d^2*erfi(sqrt(6)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3/2*Pi)/(b^(3/2)*c^2*exp(6*a/b))-2*d^2*x*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/(b*c*sqrt(a+b*arccosh(c*x)))],
[(d-c^2*d*x^2)^2/(a+b*arccosh(c*x))^(3/2),x,19,5/8*d^2*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c)+5/8*d^2*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c*exp(a/b))-5/16*d^2*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*c)-5/16*d^2*erfi(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*c*exp(3*a/b))+1/16*d^2*exp(5*a/b)*erf(sqrt(5)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(5*Pi)/(b^(3/2)*c)+1/16*d^2*erfi(sqrt(5)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(5*Pi)/(b^(3/2)*c*exp(5*a/b))-2*d^2*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/(b*c*sqrt(a+b*arccosh(c*x)))],
[(d-c^2*d*x^2)^2/(x*(a+b*arccosh(c*x))^(3/2)),x,25,-3/2*d^2*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/b^(3/2)-3/2*d^2*erfi(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*exp(2*a/b))+1/4*d^2*exp(4*a/b)*erf(2*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/b^(3/2)+1/4*d^2*erfi(2*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*exp(4*a/b))-2*d^2*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/(b*c*x*sqrt(a+b*arccosh(c*x)))+2*d^2*Unintegrable(1/(x^2*sqrt(-1+c*x)*sqrt(1+c*x)*sqrt(a+b*arccosh(c*x))),x)/(b*c),1/2*d^2*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/b^(3/2)+1/2*d^2*erfi(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*exp(2*a/b))+1/4*d^2*exp(4*a/b)*erf(2*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/b^(3/2)+1/4*d^2*erfi(2*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*exp(4*a/b))-d^2*exp(2*a/b)*erf(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(2*Pi)/b^(3/2)-d^2*erfi(sqrt(2)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(2*Pi)/(b^(3/2)*exp(2*a/b))-2*d^2*(-1+c*x)^(5/2)*(1+c*x)^(5/2)/(b*c*x*sqrt(a+b*arccosh(c*x)))+2*d^2*Unintegrable(1/(x^2*sqrt(-1+c*x)*sqrt(1+c*x)*sqrt(a+b*arccosh(c*x))),x)/(b*c)],

# Integrands of the form x^m (d-c^2 d x^2)^(p/2) ArcCosh[c x]^(n/2)

# n>0
[(c-a^2*c*x^2)^(3/2)*sqrt(arccosh(a*x)),x,25,-1/4*c*arccosh(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+1/16*c*erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-1/16*c*erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-1/256*c*erf(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+1/256*c*erfi(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+1/4*x*(c-a^2*c*x^2)^(3/2)*sqrt(arccosh(a*x))+3/8*c*x*sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x))],
[sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x)),x,10,-1/3*arccosh(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+1/16*erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-1/16*erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+1/2*x*sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x))],
[sqrt(arccosh(a*x))/sqrt(c-a^2*c*x^2),x,1,2/3*arccosh(a*x)^(3/2)*sqrt(-1+a*x)*sqrt(1+a*x)/(a*sqrt(c-a^2*c*x^2))],
[sqrt(arccosh(a*x))/(c-a^2*c*x^2)^(3/2),x,1,x*sqrt(arccosh(a*x))/(c*sqrt(c-a^2*c*x^2))+1/2*a*sqrt(-1+a*x)*sqrt(1+a*x)*Unintegrable(x/((1-a^2*x^2)*sqrt(arccosh(a*x))),x)/(c*sqrt(c-a^2*c*x^2))],
[sqrt(arccosh(a*x))/(c-a^2*c*x^2)^(5/2),x,3,1/3*x*sqrt(arccosh(a*x))/(c*(c-a^2*c*x^2)^(3/2))+2/3*x*sqrt(arccosh(a*x))/(c^2*sqrt(c-a^2*c*x^2))+1/3*a*sqrt(-1+a*x)*sqrt(1+a*x)*Unintegrable(x/((1-a^2*x^2)*sqrt(arccosh(a*x))),x)/(c^2*sqrt(c-a^2*c*x^2))+1/6*a*sqrt(-1+a*x)*sqrt(1+a*x)*Unintegrable(x/((-1+a^2*x^2)^2*sqrt(arccosh(a*x))),x)/(c^2*sqrt(c-a^2*c*x^2))],
[(c-a^2*c*x^2)^(3/2)*arccosh(a*x)^(3/2),x,27,1/4*x*(c-a^2*c*x^2)^(3/2)*arccosh(a*x)^(3/2)+3/8*c*x*arccosh(a*x)^(3/2)*sqrt(c-a^2*c*x^2)-3/20*c*arccosh(a*x)^(5/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+3/64*c*erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+3/64*c*erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-3/2048*c*erf(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-3/2048*c*erfi(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+27/256*c*sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x))/(a*sqrt(-1+a*x)*sqrt(1+a*x))-9/32*a*c*x^2*sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x))/(sqrt(-1+a*x)*sqrt(1+a*x))+3/32*c*(1-a^2*x^2)^2*sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x))/(a*sqrt(-1+a*x)*sqrt(1+a*x))],
[arccosh(a*x)^(3/2)*sqrt(c-a^2*c*x^2),x,11,1/2*x*arccosh(a*x)^(3/2)*sqrt(c-a^2*c*x^2)-1/5*arccosh(a*x)^(5/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+3/64*erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+3/64*erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+3/16*sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x))/(a*sqrt(-1+a*x)*sqrt(1+a*x))-3/8*a*x^2*sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x))/(sqrt(-1+a*x)*sqrt(1+a*x))],
[arccosh(a*x)^(3/2)/sqrt(c-a^2*c*x^2),x,1,2/5*arccosh(a*x)^(5/2)*sqrt(-1+a*x)*sqrt(1+a*x)/(a*sqrt(c-a^2*c*x^2))],
[arccosh(a*x)^(3/2)/(c-a^2*c*x^2)^(3/2),x,1,x*arccosh(a*x)^(3/2)/(c*sqrt(c-a^2*c*x^2))+3/2*a*sqrt(-1+a*x)*sqrt(1+a*x)*Unintegrable(x*sqrt(arccosh(a*x))/(1-a^2*x^2),x)/(c*sqrt(c-a^2*c*x^2))],
[(c-a^2*c*x^2)^(3/2)*arccosh(a*x)^(5/2),x,41,1/4*x*(c-a^2*c*x^2)^(3/2)*arccosh(a*x)^(5/2)+3/8*c*x*arccosh(a*x)^(5/2)*sqrt(c-a^2*c*x^2)+45/256*c*arccosh(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-15/32*a*c*x^2*arccosh(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/(sqrt(-1+a*x)*sqrt(1+a*x))+5/32*c*(1-a^2*x^2)^2*arccosh(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-3/28*c*arccosh(a*x)^(7/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+15/256*c*erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-15/256*c*erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-15/16384*c*erf(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+15/16384*c*erfi(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+225/512*c*x*sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x))+15/256*c*x*(1-a*x)*(1+a*x)*sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x))],
[arccosh(a*x)^(5/2)*sqrt(c-a^2*c*x^2),x,13,1/2*x*arccosh(a*x)^(5/2)*sqrt(c-a^2*c*x^2)+5/16*arccosh(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-5/8*a*x^2*arccosh(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/(sqrt(-1+a*x)*sqrt(1+a*x))-1/7*arccosh(a*x)^(7/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+15/256*erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-15/256*erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+15/32*x*sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x))],
[arccosh(a*x)^(5/2)/sqrt(c-a^2*c*x^2),x,1,2/7*arccosh(a*x)^(7/2)*sqrt(-1+a*x)*sqrt(1+a*x)/(a*sqrt(c-a^2*c*x^2))],
[arccosh(a*x)^(5/2)/(c-a^2*c*x^2)^(3/2),x,1,x*arccosh(a*x)^(5/2)/(c*sqrt(c-a^2*c*x^2))+5/2*a*sqrt(-1+a*x)*sqrt(1+a*x)*Unintegrable(x*arccosh(a*x)^(3/2)/(1-a^2*x^2),x)/(c*sqrt(c-a^2*c*x^2))],
[(a^2-x^2)^(3/2)*sqrt(arccosh(x/a)),x,25,-1/4*a^3*arccosh(x/a)^(3/2)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))+1/16*a^3*erf(sqrt(2)*sqrt(arccosh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))-1/16*a^3*erfi(sqrt(2)*sqrt(arccosh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))-1/256*a^3*erf(2*sqrt(arccosh(x/a)))*sqrt(Pi)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))+1/256*a^3*erfi(2*sqrt(arccosh(x/a)))*sqrt(Pi)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))+1/4*x*(a^2-x^2)^(3/2)*sqrt(arccosh(x/a))+3/8*a^2*x*sqrt(a^2-x^2)*sqrt(arccosh(x/a))],
[sqrt(a^2-x^2)*sqrt(arccosh(x/a)),x,10,-1/3*a*arccosh(x/a)^(3/2)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))+1/16*a*erf(sqrt(2)*sqrt(arccosh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))-1/16*a*erfi(sqrt(2)*sqrt(arccosh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))+1/2*x*sqrt(a^2-x^2)*sqrt(arccosh(x/a))],
[sqrt(arccosh(x/a))/sqrt(a^2-x^2),x,1,2/3*a*arccosh(x/a)^(3/2)*sqrt(-1+x/a)*sqrt(1+x/a)/sqrt(a^2-x^2)],
[sqrt(arccosh(x/a))/(a^2-x^2)^(3/2),x,1,x*sqrt(arccosh(x/a))/(a^2*sqrt(a^2-x^2))+1/2*sqrt(-1+x/a)*sqrt(1+x/a)*Unintegrable(x/((1-x^2/a^2)*sqrt(arccosh(x/a))),x)/(a^3*sqrt(a^2-x^2))],
[sqrt(arccosh(x/a))/(a^2-x^2)^(5/2),x,3,1/3*x*sqrt(arccosh(x/a))/(a^2*(a^2-x^2)^(3/2))+2/3*x*sqrt(arccosh(x/a))/(a^4*sqrt(a^2-x^2))+1/3*sqrt(-1+x/a)*sqrt(1+x/a)*Unintegrable(x/((1-x^2/a^2)*sqrt(arccosh(x/a))),x)/(a^5*sqrt(a^2-x^2))+1/6*sqrt(-1+x/a)*sqrt(1+x/a)*Unintegrable(x/((-1+x^2/a^2)^2*sqrt(arccosh(x/a))),x)/(a^5*sqrt(a^2-x^2))],
[(a^2-x^2)^(3/2)*arccosh(x/a)^(3/2),x,27,1/4*x*(a^2-x^2)^(3/2)*arccosh(x/a)^(3/2)+3/8*a^2*x*arccosh(x/a)^(3/2)*sqrt(a^2-x^2)-3/20*a^3*arccosh(x/a)^(5/2)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))+3/64*a^3*erf(sqrt(2)*sqrt(arccosh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))+3/64*a^3*erfi(sqrt(2)*sqrt(arccosh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))-3/2048*a^3*erf(2*sqrt(arccosh(x/a)))*sqrt(Pi)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))-3/2048*a^3*erfi(2*sqrt(arccosh(x/a)))*sqrt(Pi)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))+3/32*(a^2-x^2)^(5/2)*sqrt(arccosh(x/a))/(a*sqrt(-1+x/a)*sqrt(1+x/a))+27/256*a^3*sqrt(a^2-x^2)*sqrt(arccosh(x/a))/(sqrt(-1+x/a)*sqrt(1+x/a))-9/32*a*x^2*sqrt(a^2-x^2)*sqrt(arccosh(x/a))/(sqrt(-1+x/a)*sqrt(1+x/a))],
[arccosh(x/a)^(3/2)*sqrt(a^2-x^2),x,11,1/2*x*arccosh(x/a)^(3/2)*sqrt(a^2-x^2)-1/5*a*arccosh(x/a)^(5/2)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))+3/64*a*erf(sqrt(2)*sqrt(arccosh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))+3/64*a*erfi(sqrt(2)*sqrt(arccosh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2-x^2)/(sqrt(-1+x/a)*sqrt(1+x/a))+3/16*a*sqrt(a^2-x^2)*sqrt(arccosh(x/a))/(sqrt(-1+x/a)*sqrt(1+x/a))-3/8*x^2*sqrt(a^2-x^2)*sqrt(arccosh(x/a))/(a*sqrt(-1+x/a)*sqrt(1+x/a))],
[arccosh(x/a)^(3/2)/sqrt(a^2-x^2),x,1,2/5*a*arccosh(x/a)^(5/2)*sqrt(-1+x/a)*sqrt(1+x/a)/sqrt(a^2-x^2)],
[arccosh(x/a)^(3/2)/(a^2-x^2)^(3/2),x,1,x*arccosh(x/a)^(3/2)/(a^2*sqrt(a^2-x^2))+3/2*sqrt(-1+x/a)*sqrt(1+x/a)*Unintegrable(x*sqrt(arccosh(x/a))/(1-x^2/a^2),x)/(a^3*sqrt(a^2-x^2))],

# n<0
[x/(sqrt(1-x^2)*sqrt(arccosh(x))),x,6,1/2*erf(sqrt(arccosh(x)))*sqrt(Pi)*sqrt(-1+x)/sqrt(1-x)+1/2*erfi(sqrt(arccosh(x)))*sqrt(Pi)*sqrt(-1+x)/sqrt(1-x)],
[(c-a^2*c*x^2)^(5/2)/sqrt(arccosh(a*x)),x,18,1/64*c^2*erf(sqrt(6)*sqrt(arccosh(a*x)))*sqrt(1/6*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+1/64*c^2*erfi(sqrt(6)*sqrt(arccosh(a*x)))*sqrt(1/6*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+15/64*c^2*erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+15/64*c^2*erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-3/64*c^2*erf(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-3/64*c^2*erfi(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-5/8*c^2*sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x))/(a*sqrt(-1+a*x)*sqrt(1+a*x))],
[(c-a^2*c*x^2)^(3/2)/sqrt(arccosh(a*x)),x,13,1/4*c*erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+1/4*c*erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-1/32*c*erf(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-1/32*c*erfi(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-3/4*c*sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x))/(a*sqrt(-1+a*x)*sqrt(1+a*x))],
[(c-a^2*c*x^2)^(1/2)/sqrt(arccosh(a*x)),x,8,1/4*erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+1/4*erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x))/(a*sqrt(-1+a*x)*sqrt(1+a*x))],
[1/((c-a^2*c*x^2)^(1/2)*sqrt(arccosh(a*x))),x,1,2*sqrt(-1+a*x)*sqrt(1+a*x)*sqrt(arccosh(a*x))/(a*sqrt(c-a^2*c*x^2))],
[1/((c-a^2*c*x^2)^(3/2)*sqrt(arccosh(a*x))),x,0,Unintegrable(1/((c-a^2*c*x^2)^(3/2)*sqrt(arccosh(a*x))),x)],
[1/((c-a^2*c*x^2)^(5/2)*sqrt(arccosh(a*x))),x,0,Unintegrable(1/((c-a^2*c*x^2)^(5/2)*sqrt(arccosh(a*x))),x)],
[(c-a^2*c*x^2)^(5/2)/arccosh(a*x)^(3/2),x,20,-15/16*c^2*erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+15/16*c^2*erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+3/8*c^2*erf(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-3/8*c^2*erfi(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-1/16*c^2*erf(sqrt(6)*sqrt(arccosh(a*x)))*sqrt(3/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+1/16*c^2*erfi(sqrt(6)*sqrt(arccosh(a*x)))*sqrt(3/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-2*(c-a^2*c*x^2)^(5/2)*sqrt(-1+a*x)*sqrt(1+a*x)/(a*sqrt(arccosh(a*x)))],
[(c-a^2*c*x^2)^(3/2)/arccosh(a*x)^(3/2),x,15,-c*erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+c*erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+1/4*c*erf(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-1/4*c*erfi(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-2*(c-a^2*c*x^2)^(3/2)*sqrt(-1+a*x)*sqrt(1+a*x)/(a*sqrt(arccosh(a*x)))],
[(c-a^2*c*x^2)^(1/2)/arccosh(a*x)^(3/2),x,9,-erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-2*sqrt(-1+a*x)*sqrt(1+a*x)*sqrt(c-a^2*c*x^2)/(a*sqrt(arccosh(a*x)))],
[1/((c-a^2*c*x^2)^(1/2)*arccosh(a*x)^(3/2)),x,1,-2*sqrt(-1+a*x)*sqrt(1+a*x)/(a*sqrt(c-a^2*c*x^2)*sqrt(arccosh(a*x)))],
[1/((c-a^2*c*x^2)^(3/2)*arccosh(a*x)^(3/2)),x,2,-2*sqrt(-1+a*x)*sqrt(1+a*x)/(a*(c-a^2*c*x^2)^(3/2)*sqrt(arccosh(a*x)))+4*a*sqrt(-1+a*x)*sqrt(1+a*x)*Unintegrable(x/((-1+a^2*x^2)^2*sqrt(arccosh(a*x))),x)/(c*sqrt(c-a^2*c*x^2))],
[1/((c-a^2*c*x^2)^(5/2)*arccosh(a*x)^(3/2)),x,2,-2*sqrt(-1+a*x)*sqrt(1+a*x)/(a*(c-a^2*c*x^2)^(5/2)*sqrt(arccosh(a*x)))-8*a*sqrt(-1+a*x)*sqrt(1+a*x)*Unintegrable(x/((-1+a^2*x^2)^3*sqrt(arccosh(a*x))),x)/(c^2*sqrt(c-a^2*c*x^2))],
[(c-a^2*c*x^2)^(3/2)/arccosh(a*x)^(5/2),x,19,-2/3*(c-a^2*c*x^2)^(3/2)*sqrt(-1+a*x)*sqrt(1+a*x)/(a*arccosh(a*x)^(3/2))-2/3*c*erf(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-2/3*c*erfi(2*sqrt(arccosh(a*x)))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+2/3*c*erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+2/3*c*erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-16/3*c*x*(1-a*x)*(1+a*x)*sqrt(c-a^2*c*x^2)/sqrt(arccosh(a*x))],
[(c-a^2*c*x^2)^(1/2)/arccosh(a*x)^(5/2),x,7,2/3*erf(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))+2/3*erfi(sqrt(2)*sqrt(arccosh(a*x)))*sqrt(2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(-1+a*x)*sqrt(1+a*x))-2/3*sqrt(-1+a*x)*sqrt(1+a*x)*sqrt(c-a^2*c*x^2)/(a*arccosh(a*x)^(3/2))-8/3*x*sqrt(c-a^2*c*x^2)/sqrt(arccosh(a*x))],
[1/((c-a^2*c*x^2)^(1/2)*arccosh(a*x)^(5/2)),x,1,-2/3*sqrt(-1+a*x)*sqrt(1+a*x)/(a*arccosh(a*x)^(3/2)*sqrt(c-a^2*c*x^2))],
[1/((c-a^2*c*x^2)^(3/2)*arccosh(a*x)^(5/2)),x,2,-2/3*sqrt(-1+a*x)*sqrt(1+a*x)/(a*(c-a^2*c*x^2)^(3/2)*arccosh(a*x)^(3/2))+4/3*a*sqrt(-1+a*x)*sqrt(1+a*x)*Unintegrable(x/((-1+a^2*x^2)^2*arccosh(a*x)^(3/2)),x)/(c*sqrt(c-a^2*c*x^2))],
[1/((c-a^2*c*x^2)^(5/2)*arccosh(a*x)^(5/2)),x,2,-2/3*sqrt(-1+a*x)*sqrt(1+a*x)/(a*(c-a^2*c*x^2)^(5/2)*arccosh(a*x)^(3/2))-8/3*a*sqrt(-1+a*x)*sqrt(1+a*x)*Unintegrable(x/((-1+a^2*x^2)^3*arccosh(a*x)^(3/2)),x)/(c^2*sqrt(c-a^2*c*x^2))],

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

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

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

# p>0
[x^2*(a+b*arccosh(c*x))^n*sqrt(d-c^2*d*x^2),x,6,-1/8*(a+b*arccosh(c*x))^(1+n)*sqrt(d-c^2*d*x^2)/(b*c^3*(1+n)*sqrt(-1+c*x)*sqrt(1+c*x))+(a+b*arccosh(c*x))^n*GAMMA(1+n,-4*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(2^(2*(3+n))*c^3*exp(4*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-exp(4*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,4*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(2^(2*(3+n))*c^3*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(a+b*arccosh(c*x))^n*sqrt(d-c^2*d*x^2),x,9,1/8*3^(-1-n)*(a+b*arccosh(c*x))^n*GAMMA(1+n,-3*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*exp(3*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-1/8*(a+b*arccosh(c*x))^n*GAMMA(1+n,(-a-b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*exp(a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+1/8*exp(a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-1/8*3^(-1-n)*exp(3*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,3*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))^n*sqrt(d-c^2*d*x^2),x,6,-1/2*(a+b*arccosh(c*x))^(1+n)*sqrt(d-c^2*d*x^2)/(b*c*(1+n)*sqrt(-1+c*x)*sqrt(1+c*x))+2^(-3-n)*(a+b*arccosh(c*x))^n*GAMMA(1+n,-2*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c*exp(2*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-2^(-3-n)*exp(2*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,2*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))^n*sqrt(d-c^2*d*x^2)/x,x,6,-1/2*d*(a+b*arccosh(c*x))^n*GAMMA(1+n,(-a-b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(exp(a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+1/2*d*exp(a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(((a+b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+d*Unintegrable((a+b*arccosh(c*x))^n/(x*sqrt(d-c^2*d*x^2)),x)],
[(a+b*arccosh(c*x))^n*sqrt(d-c^2*d*x^2)/x^2,x,3,-c*d*(a+b*arccosh(c*x))^(1+n)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*(1+n)*sqrt(d-c^2*d*x^2))+d*Unintegrable((a+b*arccosh(c*x))^n/(x^2*sqrt(d-c^2*d*x^2)),x)],
[x^2*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^n,x,12,-1/16*d*(a+b*arccosh(c*x))^(1+n)*sqrt(d-c^2*d*x^2)/(b*c^3*(1+n)*sqrt(-1+c*x)*sqrt(1+c*x))-2^(-7-n)*3^(-1-n)*d*(a+b*arccosh(c*x))^n*GAMMA(1+n,-6*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^3*exp(6*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+2^(-7-2*n)*d*(a+b*arccosh(c*x))^n*GAMMA(1+n,-4*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^3*exp(4*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+2^(-7-n)*d*(a+b*arccosh(c*x))^n*GAMMA(1+n,-2*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^3*exp(2*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-2^(-7-n)*d*exp(2*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,2*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^3*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-2^(-7-2*n)*d*exp(4*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,4*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^3*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+2^(-7-n)*3^(-1-n)*d*exp(6*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,6*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^3*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^n,x,12,-1/32*5^(-1-n)*d*(a+b*arccosh(c*x))^n*GAMMA(1+n,-5*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*exp(5*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+1/32*d*(a+b*arccosh(c*x))^n*GAMMA(1+n,-3*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(3^n*c^2*exp(3*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-1/16*d*(a+b*arccosh(c*x))^n*GAMMA(1+n,(-a-b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*exp(a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+1/16*d*exp(a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-1/32*d*exp(3*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,3*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(3^n*c^2*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+1/32*5^(-1-n)*d*exp(5*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,5*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^n,x,9,-3/8*d*(a+b*arccosh(c*x))^(1+n)*sqrt(d-c^2*d*x^2)/(b*c*(1+n)*sqrt(-1+c*x)*sqrt(1+c*x))-d*(a+b*arccosh(c*x))^n*GAMMA(1+n,-4*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(2^(2*(3+n))*c*exp(4*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+2^(-3-n)*d*(a+b*arccosh(c*x))^n*GAMMA(1+n,-2*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c*exp(2*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-2^(-3-n)*d*exp(2*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,2*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+d*exp(4*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,4*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(2^(2*(3+n))*c*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^n/x,x,15,1/8*3^(-1-n)*d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,-3*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(exp(3*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))-5/8*d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,(-a-b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(exp(a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+5/8*d^2*exp(a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(((a+b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))-1/8*3^(-1-n)*d^2*exp(3*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,3*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(((a+b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+d^2*Unintegrable((a+b*arccosh(c*x))^n/(x*sqrt(d-c^2*d*x^2)),x)],
[(d-c^2*d*x^2)^(3/2)*(a+b*arccosh(c*x))^n/x^2,x,9,-3/2*c*d^2*(a+b*arccosh(c*x))^(1+n)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*(1+n)*sqrt(d-c^2*d*x^2))+2^(-3-n)*c*d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,-2*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(exp(2*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))-2^(-3-n)*c*d^2*exp(2*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,2*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(((a+b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+d^2*Unintegrable((a+b*arccosh(c*x))^n/(x^2*sqrt(d-c^2*d*x^2)),x)],
[x^2*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^n,x,15,-5/128*d^2*(a+b*arccosh(c*x))^(1+n)*sqrt(d-c^2*d*x^2)/(b*c^3*(1+n)*sqrt(-1+c*x)*sqrt(1+c*x))+2^(-11-3*n)*d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,-8*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^3*exp(8*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-2^(-7-n)*3^(-1-n)*d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,-6*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^3*exp(6*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,-4*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(2^(2*(4+n))*c^3*exp(4*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+2^(-7-n)*d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,-2*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^3*exp(2*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-2^(-7-n)*d^2*exp(2*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,2*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^3*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-d^2*exp(4*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,4*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(2^(2*(4+n))*c^3*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+2^(-7-n)*3^(-1-n)*d^2*exp(6*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,6*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^3*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-2^(-11-3*n)*d^2*exp(8*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,8*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^3*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^n,x,15,1/128*7^(-1-n)*d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,-7*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*exp(7*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-1/128*d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,-5*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(5^n*c^2*exp(5*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+1/128*3^(1-n)*d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,-3*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*exp(3*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-5/128*d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,(-a-b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*exp(a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+5/128*d^2*exp(a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-1/128*3^(1-n)*d^2*exp(3*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,3*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+1/128*d^2*exp(5*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,5*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(5^n*c^2*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-1/128*7^(-1-n)*d^2*exp(7*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,7*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c^2*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^n,x,12,-5/16*d^2*(a+b*arccosh(c*x))^(1+n)*sqrt(d-c^2*d*x^2)/(b*c*(1+n)*sqrt(-1+c*x)*sqrt(1+c*x))+2^(-7-n)*3^(-1-n)*d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,-6*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c*exp(6*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-3*2^(-7-2*n)*d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,-4*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c*exp(4*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+15*2^(-7-n)*d^2*(a+b*arccosh(c*x))^n*GAMMA(1+n,-2*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c*exp(2*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-15*2^(-7-n)*d^2*exp(2*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,2*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))+3*2^(-7-2*n)*d^2*exp(4*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,4*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))-2^(-7-n)*3^(-1-n)*d^2*exp(6*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,6*(a+b*arccosh(c*x))/b)*sqrt(d-c^2*d*x^2)/(c*((a+b*arccosh(c*x))/b)^n*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^n/x,x,27,-1/32*5^(-1-n)*d^3*(a+b*arccosh(c*x))^n*GAMMA(1+n,-5*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(exp(5*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))-5/32*3^(-1-n)*d^3*(a+b*arccosh(c*x))^n*GAMMA(1+n,-3*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(exp(3*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+1/8*d^3*(a+b*arccosh(c*x))^n*GAMMA(1+n,-3*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(3^n*exp(3*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))-11/16*d^3*(a+b*arccosh(c*x))^n*GAMMA(1+n,(-a-b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(exp(a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+11/16*d^3*exp(a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(((a+b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+5/32*3^(-1-n)*d^3*exp(3*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,3*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(((a+b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))-1/8*d^3*exp(3*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,3*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(3^n*((a+b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+1/32*5^(-1-n)*d^3*exp(5*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,5*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(((a+b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+d^3*Unintegrable((a+b*arccosh(c*x))^n/(x*sqrt(d-c^2*d*x^2)),x)],
[(d-c^2*d*x^2)^(5/2)*(a+b*arccosh(c*x))^n/x^2,x,18,-15/8*c*d^3*(a+b*arccosh(c*x))^(1+n)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*(1+n)*sqrt(d-c^2*d*x^2))-c*d^3*(a+b*arccosh(c*x))^n*GAMMA(1+n,-4*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(2^(2*(3+n))*exp(4*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+2^(-2-n)*c*d^3*(a+b*arccosh(c*x))^n*GAMMA(1+n,-2*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(exp(2*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))-2^(-2-n)*c*d^3*exp(2*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,2*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(((a+b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+c*d^3*exp(4*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,4*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(2^(2*(3+n))*((a+b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+d^3*Unintegrable((a+b*arccosh(c*x))^n/(x^2*sqrt(d-c^2*d*x^2)),x)],

# p<0
[x^3*(a+b*arccosh(c*x))^n/sqrt(1-c^2*x^2),x,9,1/8*3^(-1-n)*(a+b*arccosh(c*x))^n*GAMMA(1+n,-3*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(c^4*exp(3*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(1-c*x))+3/8*(a+b*arccosh(c*x))^n*GAMMA(1+n,(-a-b*arccosh(c*x))/b)*sqrt(-1+c*x)/(c^4*exp(a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(1-c*x))-3/8*exp(a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(c^4*((a+b*arccosh(c*x))/b)^n*sqrt(1-c*x))-1/8*3^(-1-n)*exp(3*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,3*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(c^4*((a+b*arccosh(c*x))/b)^n*sqrt(1-c*x))],
[x^2*(a+b*arccosh(c*x))^n/sqrt(1-c^2*x^2),x,6,1/2*(a+b*arccosh(c*x))^(1+n)*sqrt(-1+c*x)/(b*c^3*(1+n)*sqrt(1-c*x))+2^(-3-n)*(a+b*arccosh(c*x))^n*GAMMA(1+n,-2*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(c^3*exp(2*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(1-c*x))-2^(-3-n)*exp(2*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,2*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)/(c^3*((a+b*arccosh(c*x))/b)^n*sqrt(1-c*x))],
[x*(a+b*arccosh(c*x))^n/sqrt(1-c^2*x^2),x,4,1/2*(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)*(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))],
[(a+b*arccosh(c*x))^n/sqrt(1-c^2*x^2),x,1,(a+b*arccosh(c*x))^(1+n)*sqrt(-1+c*x)/(b*c*(1+n)*sqrt(1-c*x))],
[(a+b*arccosh(c*x))^n/(x*sqrt(1-c^2*x^2)),x,0,Unintegrable((a+b*arccosh(c*x))^n/(x*sqrt(1-c^2*x^2)),x)],
[(a+b*arccosh(c*x))^n/(x^2*sqrt(1-c^2*x^2)),x,0,Unintegrable((a+b*arccosh(c*x))^n/(x^2*sqrt(1-c^2*x^2)),x)],
[x^3*(a+b*arccosh(c*x))^n/sqrt(d-c^2*d*x^2),x,9,1/8*3^(-1-n)*(a+b*arccosh(c*x))^n*GAMMA(1+n,-3*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^4*exp(3*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))+3/8*(a+b*arccosh(c*x))^n*GAMMA(1+n,(-a-b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^4*exp(a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))-3/8*exp(a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^4*((a+b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))-1/8*3^(-1-n)*exp(3*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,3*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^4*((a+b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))],
[x^2*(a+b*arccosh(c*x))^n/sqrt(d-c^2*d*x^2),x,6,1/2*(a+b*arccosh(c*x))^(1+n)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c^3*(1+n)*sqrt(d-c^2*d*x^2))+2^(-3-n)*(a+b*arccosh(c*x))^n*GAMMA(1+n,-2*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*exp(2*a/b)*((-a-b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))-2^(-3-n)*exp(2*a/b)*(a+b*arccosh(c*x))^n*GAMMA(1+n,2*(a+b*arccosh(c*x))/b)*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*((a+b*arccosh(c*x))/b)^n*sqrt(d-c^2*d*x^2))],
[x*(a+b*arccosh(c*x))^n/sqrt(d-c^2*d*x^2),x,4,1/2*(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(d-c^2*d*x^2))-1/2*exp(a/b)*(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(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))^n/sqrt(d-c^2*d*x^2),x,1,(a+b*arccosh(c*x))^(1+n)*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(1+n)*sqrt(d-c^2*d*x^2))],
[(a+b*arccosh(c*x))^n/(x*sqrt(d-c^2*d*x^2)),x,0,Unintegrable((a+b*arccosh(c*x))^n/(x*sqrt(d-c^2*d*x^2)),x)],
[(a+b*arccosh(c*x))^n/(x^2*sqrt(d-c^2*d*x^2)),x,0,Unintegrable((a+b*arccosh(c*x))^n/(x^2*sqrt(d-c^2*d*x^2)),x)],
[x^2*(a+b*arccosh(c*x))^n/(d-c^2*d*x^2)^(3/2),x,0,Unintegrable(x^2*(a+b*arccosh(c*x))^n/(d-c^2*d*x^2)^(3/2),x)],
[x*(a+b*arccosh(c*x))^n/(d-c^2*d*x^2)^(3/2),x,0,Unintegrable(x*(a+b*arccosh(c*x))^n/(d-c^2*d*x^2)^(3/2),x)],
[(a+b*arccosh(c*x))^n/(d-c^2*d*x^2)^(3/2),x,0,Unintegrable((a+b*arccosh(c*x))^n/(d-c^2*d*x^2)^(3/2),x)],
[(a+b*arccosh(c*x))^n/(x*(d-c^2*d*x^2)^(3/2)),x,0,Unintegrable((a+b*arccosh(c*x))^n/(x*(d-c^2*d*x^2)^(3/2)),x)],
[(a+b*arccosh(c*x))^n/(x^2*(d-c^2*d*x^2)^(3/2)),x,0,Unintegrable((a+b*arccosh(c*x))^n/(x^2*(d-c^2*d*x^2)^(3/2)),x)],

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

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

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

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

# p>0
[x^4*(d+e*x^2)*(a+b*arccosh(c*x)),x,7,1/5*d*x^5*(a+b*arccosh(c*x))+1/7*e*x^7*(a+b*arccosh(c*x))-8/3675*b*(49*c^2*d+30*e)*sqrt(-1+c*x)*sqrt(1+c*x)/c^7-4/3675*b*(49*c^2*d+30*e)*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/c^5-1/1225*b*(49*c^2*d+30*e)*x^4*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-1/49*b*e*x^6*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[x^3*(d+e*x^2)*(a+b*arccosh(c*x)),x,6,-1/96*b*(9*c^2*d+5*e)*arccosh(c*x)/c^6+1/4*d*x^4*(a+b*arccosh(c*x))+1/6*e*x^6*(a+b*arccosh(c*x))-1/96*b*(9*c^2*d+5*e)*x*sqrt(-1+c*x)*sqrt(1+c*x)/c^5-1/144*b*(9*c^2*d+5*e)*x^3*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-1/36*b*e*x^5*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[x^2*(d+e*x^2)*(a+b*arccosh(c*x)),x,5,1/3*d*x^3*(a+b*arccosh(c*x))+1/5*e*x^5*(a+b*arccosh(c*x))-2/225*b*(25*c^2*d+12*e)*sqrt(-1+c*x)*sqrt(1+c*x)/c^5-1/225*b*(25*c^2*d+12*e)*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-1/25*b*e*x^4*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[x*(d+e*x^2)*(a+b*arccosh(c*x)),x,4,-1/32*b*(8*c^2*d+3*e)*arccosh(c*x)/c^4+1/2*d*x^2*(a+b*arccosh(c*x))+1/4*e*x^4*(a+b*arccosh(c*x))-1/32*b*(8*c^2*d+3*e)*x*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-1/16*b*e*x^3*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(d+e*x^2)*(a+b*arccosh(c*x)),x,3,d*x*(a+b*arccosh(c*x))+1/3*e*x^3*(a+b*arccosh(c*x))-1/9*b*(9*c^2*d+2*e)*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-1/9*b*e*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(d+e*x^2)*(a+b*arccosh(c*x))/x,x,13,-1/4*b*e*arccosh(c*x)/c^2+1/2*e*x^2*(a+b*arccosh(c*x))+d*(a+b*arccosh(c*x))*log(x)-1/4*b*e*x*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/2*I*b*d*arcsin(c*x)^2*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+b*d*arcsin(c*x)*log(1-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-b*d*arcsin(c*x)*log(x)*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/2*I*b*d*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d+e*x^2)*(a+b*arccosh(c*x))/x^2,x,4,-d*(a+b*arccosh(c*x))/x+e*x*(a+b*arccosh(c*x))+b*c*d*arctan(sqrt(-1+c*x)*sqrt(1+c*x))-b*e*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(d+e*x^2)*(a+b*arccosh(c*x))/x^3,x,11,-1/2*d*(a+b*arccosh(c*x))/x^2+e*(a+b*arccosh(c*x))*log(x)+1/2*b*c*d*sqrt(-1+c*x)*sqrt(1+c*x)/x-1/2*I*b*e*arcsin(c*x)^2*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+b*e*arcsin(c*x)*log(1-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-b*e*arcsin(c*x)*log(x)*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/2*I*b*e*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d+e*x^2)*(a+b*arccosh(c*x))/x^4,x,4,-1/3*d*(a+b*arccosh(c*x))/x^3-e*(a+b*arccosh(c*x))/x+1/6*b*c*(c^2*d+6*e)*arctan(sqrt(-1+c*x)*sqrt(1+c*x))+1/6*b*c*d*sqrt(-1+c*x)*sqrt(1+c*x)/x^2],
[x^4*(d+e*x^2)^2*(a+b*arccosh(c*x)),x,7,1/5*d^2*x^5*(a+b*arccosh(c*x))+2/7*d*e*x^7*(a+b*arccosh(c*x))+1/9*e^2*x^9*(a+b*arccosh(c*x))+1/315*b*(63*c^4*d^2+90*c^2*d*e+35*e^2)*(1-c^2*x^2)/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))-2/945*b*(63*c^4*d^2+135*c^2*d*e+70*e^2)*(1-c^2*x^2)^2/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))+1/525*b*(21*c^4*d^2+90*c^2*d*e+70*e^2)*(1-c^2*x^2)^3/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))-2/441*b*e*(9*c^2*d+14*e)*(1-c^2*x^2)^4/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))+1/81*b*e^2*(1-c^2*x^2)^5/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^3*(d+e*x^2)^2*(a+b*arccosh(c*x)),x,9,1/4*d^2*x^4*(a+b*arccosh(c*x))+1/3*d*e*x^6*(a+b*arccosh(c*x))+1/8*e^2*x^8*(a+b*arccosh(c*x))+1/3072*b*(288*c^4*d^2+320*c^2*d*e+105*e^2)*x*(1-c^2*x^2)/(c^7*sqrt(-1+c*x)*sqrt(1+c*x))+1/4608*b*(288*c^4*d^2+320*c^2*d*e+105*e^2)*x^3*(1-c^2*x^2)/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+1/1152*b*e*(64*c^2*d+21*e)*x^5*(1-c^2*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/64*b*e^2*x^7*(1-c^2*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/3072*b*(288*c^4*d^2+320*c^2*d*e+105*e^2)*arctanh(c*x/sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(c^8*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^2*(d+e*x^2)^2*(a+b*arccosh(c*x)),x,6,1/3*d^2*x^3*(a+b*arccosh(c*x))+2/5*d*e*x^5*(a+b*arccosh(c*x))+1/7*e^2*x^7*(a+b*arccosh(c*x))+1/105*b*(35*c^4*d^2+42*c^2*d*e+15*e^2)*(1-c^2*x^2)/(c^7*sqrt(-1+c*x)*sqrt(1+c*x))-1/315*b*(35*c^4*d^2+84*c^2*d*e+45*e^2)*(1-c^2*x^2)^2/(c^7*sqrt(-1+c*x)*sqrt(1+c*x))+1/175*b*e*(14*c^2*d+15*e)*(1-c^2*x^2)^3/(c^7*sqrt(-1+c*x)*sqrt(1+c*x))-1/49*b*e^2*(1-c^2*x^2)^4/(c^7*sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(d+e*x^2)^2*(a+b*arccosh(c*x)),x,7,1/6*(d+e*x^2)^3*(a+b*arccosh(c*x))/e+1/288*b*(44*c^4*d^2+44*c^2*d*e+15*e^2)*x*(1-c^2*x^2)/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+5/144*b*(2*c^2*d+e)*x*(1-c^2*x^2)*(d+e*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/36*b*x*(1-c^2*x^2)*(d+e*x^2)^2/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/96*b*(2*c^2*d+e)*(8*c^4*d^2+8*c^2*d*e+5*e^2)*arctanh(c*x/sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(c^6*e*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d+e*x^2)^2*(a+b*arccosh(c*x)),x,6,d^2*x*(a+b*arccosh(c*x))+2/3*d*e*x^3*(a+b*arccosh(c*x))+1/5*e^2*x^5*(a+b*arccosh(c*x))+1/15*b*(15*c^4*d^2+10*c^2*d*e+3*e^2)*(1-c^2*x^2)/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))-2/45*b*e*(5*c^2*d+3*e)*(1-c^2*x^2)^2/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+1/25*b*e^2*(1-c^2*x^2)^3/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d+e*x^2)^2*(a+b*arccosh(c*x))/x,x,16,-1/32*b*e*(16*c^2*d+3*e)*arccosh(c*x)/c^4+d*e*x^2*(a+b*arccosh(c*x))+1/4*e^2*x^4*(a+b*arccosh(c*x))+d^2*(a+b*arccosh(c*x))*log(x)-1/32*b*e*(16*c^2*d+3*e)*x*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-1/16*b*e^2*x^3*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/2*I*b*d^2*arcsin(c*x)^2*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+b*d^2*arcsin(c*x)*log(1-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-b*d^2*arcsin(c*x)*log(x)*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/2*I*b*d^2*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x)),-1/2*b*d*e*arccosh(c*x)/c^2-3/32*b*e^2*arccosh(c*x)/c^4+d*e*x^2*(a+b*arccosh(c*x))+1/4*e^2*x^4*(a+b*arccosh(c*x))+d^2*(a+b*arccosh(c*x))*log(x)-1/2*b*d*e*x*sqrt(-1+c*x)*sqrt(1+c*x)/c-3/32*b*e^2*x*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-1/16*b*e^2*x^3*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/2*I*b*d^2*arcsin(c*x)^2*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+b*d^2*arcsin(c*x)*log(1-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-b*d^2*arcsin(c*x)*log(x)*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/2*I*b*d^2*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d+e*x^2)^2*(a+b*arccosh(c*x))/x^2,x,7,-d^2*(a+b*arccosh(c*x))/x+2*d*e*x*(a+b*arccosh(c*x))+1/3*e^2*x^3*(a+b*arccosh(c*x))+b*c*d^2*arctan(sqrt(-1+c*x)*sqrt(1+c*x))+1/3*b*e*(6*c^2*d+e)*(1-c^2*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))-1/9*b*e^2*(1-c^2*x^2)^2/(c^3*sqrt(-1+c*x)*sqrt(1+c*x)),-d^2*(a+b*arccosh(c*x))/x+2*d*e*x*(a+b*arccosh(c*x))+1/3*e^2*x^3*(a+b*arccosh(c*x))+1/3*b*e*(6*c^2*d+e)*(1-c^2*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))-1/9*b*e^2*(1-c^2*x^2)^2/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+b*c*d^2*arctan(sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d+e*x^2)^2*(a+b*arccosh(c*x))/x^3,x,14,-1/4*b*e^2*arccosh(c*x)/c^2-1/2*d^2*(a+b*arccosh(c*x))/x^2+1/2*e^2*x^2*(a+b*arccosh(c*x))+2*d*e*(a+b*arccosh(c*x))*log(x)+1/2*b*c*d^2*sqrt(-1+c*x)*sqrt(1+c*x)/x-1/4*b*e^2*x*sqrt(-1+c*x)*sqrt(1+c*x)/c-I*b*d*e*arcsin(c*x)^2*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+2*b*d*e*arcsin(c*x)*log(1-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-2*b*d*e*arcsin(c*x)*log(x)*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-I*b*d*e*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d+e*x^2)^2*(a+b*arccosh(c*x))/x^4,x,7,-1/3*d^2*(a+b*arccosh(c*x))/x^3-2*d*e*(a+b*arccosh(c*x))/x+e^2*x*(a+b*arccosh(c*x))+b*e^2*(1-c^2*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/6*b*c*d^2*(1-c^2*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))+1/6*b*c*d*(c^2*d+12*e)*arctan(sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[x^4*(d+e*x^2)^3*(a+b*arccosh(c*x)),x,6,1/5*d^3*x^5*(a+b*arccosh(c*x))+3/7*d^2*e*x^7*(a+b*arccosh(c*x))+1/3*d*e^2*x^9*(a+b*arccosh(c*x))+1/11*e^3*x^11*(a+b*arccosh(c*x))+1/1155*b*(231*c^6*d^3+495*c^4*d^2*e+385*c^2*d*e^2+105*e^3)*(1-c^2*x^2)/(c^11*sqrt(-1+c*x)*sqrt(1+c*x))-1/3465*b*(462*c^6*d^3+1485*c^4*d^2*e+1540*c^2*d*e^2+525*e^3)*(1-c^2*x^2)^2/(c^11*sqrt(-1+c*x)*sqrt(1+c*x))+1/1925*b*(77*c^6*d^3+495*c^4*d^2*e+770*c^2*d*e^2+350*e^3)*(1-c^2*x^2)^3/(c^11*sqrt(-1+c*x)*sqrt(1+c*x))-1/1617*b*e*(99*c^4*d^2+308*c^2*d*e+210*e^2)*(1-c^2*x^2)^4/(c^11*sqrt(-1+c*x)*sqrt(1+c*x))+1/297*b*e^2*(11*c^2*d+15*e)*(1-c^2*x^2)^5/(c^11*sqrt(-1+c*x)*sqrt(1+c*x))-1/121*b*e^3*(1-c^2*x^2)^6/(c^11*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^3*(d+e*x^2)^3*(a+b*arccosh(c*x)),x,10,-1/8*d*(d+e*x^2)^4*(a+b*arccosh(c*x))/e^2+1/10*(d+e*x^2)^5*(a+b*arccosh(c*x))/e^2-1/76800*b*(1232*c^8*d^4-2536*c^6*d^3*e-7758*c^4*d^2*e^2-6615*c^2*d*e^3-1890*e^4)*x*(1-c^2*x^2)/(c^9*e*sqrt(-1+c*x)*sqrt(1+c*x))-1/38400*b*(136*c^6*d^3-1096*c^4*d^2*e-1617*c^2*d*e^2-630*e^3)*x*(1-c^2*x^2)*(d+e*x^2)/(c^7*e*sqrt(-1+c*x)*sqrt(1+c*x))+1/9600*b*(26*c^4*d^2+201*c^2*d*e+126*e^2)*x*(1-c^2*x^2)*(d+e*x^2)^2/(c^5*e*sqrt(-1+c*x)*sqrt(1+c*x))+1/1600*b*(11*c^2*d+18*e)*x*(1-c^2*x^2)*(d+e*x^2)^3/(c^3*e*sqrt(-1+c*x)*sqrt(1+c*x))+1/100*b*x*(1-c^2*x^2)*(d+e*x^2)^4/(c*e*sqrt(-1+c*x)*sqrt(1+c*x))+1/5120*b*(128*c^10*d^5-480*c^6*d^3*e^2-800*c^4*d^2*e^3-525*c^2*d*e^4-126*e^5)*arctanh(c*x/sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(c^10*e^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^2*(d+e*x^2)^3*(a+b*arccosh(c*x)),x,6,1/3*d^3*x^3*(a+b*arccosh(c*x))+3/5*d^2*e*x^5*(a+b*arccosh(c*x))+3/7*d*e^2*x^7*(a+b*arccosh(c*x))+1/9*e^3*x^9*(a+b*arccosh(c*x))+1/315*b*(105*c^6*d^3+189*c^4*d^2*e+135*c^2*d*e^2+35*e^3)*(1-c^2*x^2)/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))-1/945*b*(105*c^6*d^3+378*c^4*d^2*e+405*c^2*d*e^2+140*e^3)*(1-c^2*x^2)^2/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))+1/525*b*e*(63*c^4*d^2+135*c^2*d*e+70*e^2)*(1-c^2*x^2)^3/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))-1/441*b*e^2*(27*c^2*d+28*e)*(1-c^2*x^2)^4/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))+1/81*b*e^3*(1-c^2*x^2)^5/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(d+e*x^2)^3*(a+b*arccosh(c*x)),x,8,1/8*(d+e*x^2)^4*(a+b*arccosh(c*x))/e+5/3072*b*(2*c^2*d+e)*(40*c^4*d^2+40*c^2*d*e+21*e^2)*x*(1-c^2*x^2)/(c^7*sqrt(-1+c*x)*sqrt(1+c*x))+1/1536*b*(104*c^4*d^2+104*c^2*d*e+35*e^2)*x*(1-c^2*x^2)*(d+e*x^2)/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+7/384*b*(2*c^2*d+e)*x*(1-c^2*x^2)*(d+e*x^2)^2/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/64*b*x*(1-c^2*x^2)*(d+e*x^2)^3/(c*sqrt(-1+c*x)*sqrt(1+c*x))-1/1024*b*(128*c^8*d^4+256*c^6*d^3*e+288*c^4*d^2*e^2+160*c^2*d*e^3+35*e^4)*arctanh(c*x/sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(c^8*e*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d+e*x^2)^3*(a+b*arccosh(c*x)),x,6,d^3*x*(a+b*arccosh(c*x))+d^2*e*x^3*(a+b*arccosh(c*x))+3/5*d*e^2*x^5*(a+b*arccosh(c*x))+1/7*e^3*x^7*(a+b*arccosh(c*x))+1/35*b*(35*c^6*d^3+35*c^4*d^2*e+21*c^2*d*e^2+5*e^3)*(1-c^2*x^2)/(c^7*sqrt(-1+c*x)*sqrt(1+c*x))-1/105*b*e*(35*c^4*d^2+42*c^2*d*e+15*e^2)*(1-c^2*x^2)^2/(c^7*sqrt(-1+c*x)*sqrt(1+c*x))+3/175*b*e^2*(7*c^2*d+5*e)*(1-c^2*x^2)^3/(c^7*sqrt(-1+c*x)*sqrt(1+c*x))-1/49*b*e^3*(1-c^2*x^2)^4/(c^7*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d+e*x^2)^3*(a+b*arccosh(c*x))/x,x,23,-3/4*b*d^2*e*arccosh(c*x)/c^2-9/32*b*d*e^2*arccosh(c*x)/c^4-5/96*b*e^3*arccosh(c*x)/c^6+3/2*d^2*e*x^2*(a+b*arccosh(c*x))+3/4*d*e^2*x^4*(a+b*arccosh(c*x))+1/6*e^3*x^6*(a+b*arccosh(c*x))+d^3*(a+b*arccosh(c*x))*log(x)-3/4*b*d^2*e*x*sqrt(-1+c*x)*sqrt(1+c*x)/c-9/32*b*d*e^2*x*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-5/96*b*e^3*x*sqrt(-1+c*x)*sqrt(1+c*x)/c^5-3/16*b*d*e^2*x^3*sqrt(-1+c*x)*sqrt(1+c*x)/c-5/144*b*e^3*x^3*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-1/36*b*e^3*x^5*sqrt(-1+c*x)*sqrt(1+c*x)/c-1/2*I*b*d^3*arcsin(c*x)^2*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+b*d^3*arcsin(c*x)*log(1-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-b*d^3*arcsin(c*x)*log(x)*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-1/2*I*b*d^3*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d+e*x^2)^3*(a+b*arccosh(c*x))/x^2,x,7,-d^3*(a+b*arccosh(c*x))/x+3*d^2*e*x*(a+b*arccosh(c*x))+d*e^2*x^3*(a+b*arccosh(c*x))+1/5*e^3*x^5*(a+b*arccosh(c*x))+1/5*b*e*(15*c^4*d^2+5*c^2*d*e+e^2)*(1-c^2*x^2)/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))-1/15*b*e^2*(5*c^2*d+2*e)*(1-c^2*x^2)^2/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+1/25*b*e^3*(1-c^2*x^2)^3/(c^5*sqrt(-1+c*x)*sqrt(1+c*x))+b*c*d^3*arctan(sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d+e*x^2)^3*(a+b*arccosh(c*x))/x^3,x,18,-1/2*d^3*(a+b*arccosh(c*x))/x^2+3/2*d*e^2*x^2*(a+b*arccosh(c*x))+1/4*e^3*x^4*(a+b*arccosh(c*x))+3*d^2*e*(a+b*arccosh(c*x))*log(x)-1/2*b*c*d^3*(1-c^2*x^2)/(x*sqrt(-1+c*x)*sqrt(1+c*x))+3/32*b*e^2*(8*c^2*d+e)*x*(1-c^2*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/16*b*e^3*x^3*(1-c^2*x^2)/(c*sqrt(-1+c*x)*sqrt(1+c*x))-3/2*I*b*d^2*e*arcsin(c*x)^2*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))+3*b*d^2*e*arcsin(c*x)*log(1-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3*b*d^2*e*arcsin(c*x)*log(x)*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3/2*I*b*d^2*e*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))-3/32*b*e^2*(8*c^2*d+e)*arctanh(c*x/sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(c^4*sqrt(-1+c*x)*sqrt(1+c*x))],
[(d+e*x^2)^3*(a+b*arccosh(c*x))/x^4,x,9,-1/3*d^3*(a+b*arccosh(c*x))/x^3-3*d^2*e*(a+b*arccosh(c*x))/x+3*d*e^2*x*(a+b*arccosh(c*x))+1/3*e^3*x^3*(a+b*arccosh(c*x))+1/3*b*e^2*(9*c^2*d+e)*(1-c^2*x^2)/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))-1/6*b*c*d^3*(1-c^2*x^2)/(x^2*sqrt(-1+c*x)*sqrt(1+c*x))-1/9*b*e^3*(1-c^2*x^2)^2/(c^3*sqrt(-1+c*x)*sqrt(1+c*x))+1/6*b*c*d^2*(c^2*d+18*e)*arctan(sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(sqrt(-1+c*x)*sqrt(1+c*x))],
[(d+e*x^2)^4*(a+b*arccosh(c*x)),x,6,d^4*x*(a+b*arccosh(c*x))+4/3*d^3*e*x^3*(a+b*arccosh(c*x))+6/5*d^2*e^2*x^5*(a+b*arccosh(c*x))+4/7*d*e^3*x^7*(a+b*arccosh(c*x))+1/9*e^4*x^9*(a+b*arccosh(c*x))+1/315*b*(315*c^8*d^4+420*c^6*d^3*e+378*c^4*d^2*e^2+180*c^2*d*e^3+35*e^4)*(1-c^2*x^2)/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))-4/945*b*e*(105*c^6*d^3+189*c^4*d^2*e+135*c^2*d*e^2+35*e^3)*(1-c^2*x^2)^2/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))+2/525*b*e^2*(63*c^4*d^2+90*c^2*d*e+35*e^2)*(1-c^2*x^2)^3/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))-4/441*b*e^3*(9*c^2*d+7*e)*(1-c^2*x^2)^4/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))+1/81*b*e^4*(1-c^2*x^2)^5/(c^9*sqrt(-1+c*x)*sqrt(1+c*x))],

# p<0
[x^4*(a+b*arccosh(c*x))/(d+e*x^2),x,27,-a*d*x/e^2-b*d*x*arccosh(c*x)/e^2+1/3*x^3*(a+b*arccosh(c*x))/e+1/2*(-d)^(3/2)*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^(5/2)-1/2*(-d)^(3/2)*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^(5/2)+1/2*(-d)^(3/2)*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^(5/2)-1/2*(-d)^(3/2)*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^(5/2)-1/2*b*(-d)^(3/2)*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^(5/2)+1/2*b*(-d)^(3/2)*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^(5/2)-1/2*b*(-d)^(3/2)*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^(5/2)+1/2*b*(-d)^(3/2)*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^(5/2)+b*d*sqrt(-1+c*x)*sqrt(1+c*x)/(c*e^2)-2/9*b*sqrt(-1+c*x)*sqrt(1+c*x)/(c^3*e)-1/9*b*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/(c*e)],
[x^3*(a+b*arccosh(c*x))/(d+e*x^2),x,23,-1/4*b*arccosh(c*x)/(c^2*e)+1/2*x^2*(a+b*arccosh(c*x))/e+1/2*d*(a+b*arccosh(c*x))^2/(b*e^2)-1/2*d*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^2-1/2*d*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^2-1/2*d*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^2-1/2*d*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^2-1/2*b*d*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^2-1/2*b*d*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^2-1/2*b*d*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^2-1/2*b*d*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^2-1/4*b*x*sqrt(-1+c*x)*sqrt(1+c*x)/(c*e)],
[x^2*(a+b*arccosh(c*x))/(d+e*x^2),x,23,a*x/e+b*x*arccosh(c*x)/e+1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(-d)/e^(3/2)-1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(-d)/e^(3/2)+1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(-d)/e^(3/2)-1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(-d)/e^(3/2)-1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(-d)/e^(3/2)+1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(-d)/e^(3/2)-1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(-d)/e^(3/2)+1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(-d)/e^(3/2)-b*sqrt(-1+c*x)*sqrt(1+c*x)/(c*e)],
[x*(a+b*arccosh(c*x))/(d+e*x^2),x,18,-1/2*(a+b*arccosh(c*x))^2/(b*e)+1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e+1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e+1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e+1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e+1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e+1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e+1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e+1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e],
[(a+b*arccosh(c*x))/(d+e*x^2),x,18,1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))-1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))+1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))-1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))-1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))+1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))-1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))+1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))],
[(a+b*arccosh(c*x))/(x*(d+e*x^2)),x,25,(a+b*arccosh(c*x))^2/(b*d)+(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))/d-1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d-1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d-1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d-1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d-1/2*b*polylog(2,(-1)/exp(2*arccosh(c*x)))/d-1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d-1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d-1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d-1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d],
[(a+b*arccosh(c*x))/(x^2*(d+e*x^2)),x,23,(-a-b*arccosh(c*x))/(d*x)+b*c*arctan(sqrt(-1+c*x)*sqrt(1+c*x))/d+1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(3/2)-1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(3/2)+1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(3/2)-1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(3/2)-1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(3/2)+1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(3/2)-1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(3/2)+1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(3/2)],
[(a+b*arccosh(c*x))/(x^3*(d+e*x^2)),x,27,1/2*(-a-b*arccosh(c*x))/(d*x^2)-e*(a+b*arccosh(c*x))^2/(b*d^2)-e*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))/d^2+1/2*e*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^2+1/2*e*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^2+1/2*e*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^2+1/2*e*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^2+1/2*b*e*polylog(2,(-1)/exp(2*arccosh(c*x)))/d^2+1/2*b*e*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^2+1/2*b*e*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^2+1/2*b*e*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^2+1/2*b*e*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^2+1/2*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/(d*x)],
[(a+b*arccosh(c*x))/(x^4*(d+e*x^2)),x,28,1/3*(-a-b*arccosh(c*x))/(d*x^3)+e*(a+b*arccosh(c*x))/(d^2*x)+1/6*b*c^3*arctan(sqrt(-1+c*x)*sqrt(1+c*x))/d-b*c*e*arctan(sqrt(-1+c*x)*sqrt(1+c*x))/d^2+1/2*e^(3/2)*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(-d)^(5/2)-1/2*e^(3/2)*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(-d)^(5/2)+1/2*e^(3/2)*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(-d)^(5/2)-1/2*e^(3/2)*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(-d)^(5/2)-1/2*b*e^(3/2)*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(-d)^(5/2)+1/2*b*e^(3/2)*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(-d)^(5/2)-1/2*b*e^(3/2)*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(-d)^(5/2)+1/2*b*e^(3/2)*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(-d)^(5/2)+1/6*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/(d*x^2)],
[x^3*(a+b*arccosh(c*x))/(d+e*x^2)^2,x,24,1/2*d*(a+b*arccosh(c*x))/(e^2*(d+e*x^2))-1/2*(a+b*arccosh(c*x))^2/(b*e^2)+1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^2+1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^2+1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^2+1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^2+1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^2+1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^2+1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^2+1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^2-1/2*b*c*arctanh(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(-1+c^2*x^2)))*sqrt(d)*sqrt(-1+c^2*x^2)/(e^2*sqrt(c^2*d+e)*sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(a+b*arccosh(c*x))/(d+e*x^2)^2,x,4,1/2*(-a-b*arccosh(c*x))/(e*(d+e*x^2))+1/2*b*c*arctanh(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(-1+c^2*x^2)))*sqrt(-1+c^2*x^2)/(e*sqrt(d)*sqrt(c^2*d+e)*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x*(d+e*x^2)^2),x,29,1/2*(a+b*arccosh(c*x))/(d*(d+e*x^2))+(a+b*arccosh(c*x))^2/(b*d^2)+(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))/d^2-1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^2-1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^2-1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^2-1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^2-1/2*b*polylog(2,(-1)/exp(2*arccosh(c*x)))/d^2-1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^2-1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^2-1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^2-1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^2-1/2*b*c*arctanh(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(-1+c^2*x^2)))*sqrt(-1+c^2*x^2)/(d^(3/2)*sqrt(c^2*d+e)*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x^3*(d+e*x^2)^2),x,31,1/2*(-a-b*arccosh(c*x))/(d^2*x^2)-1/2*e*(a+b*arccosh(c*x))/(d^2*(d+e*x^2))-2*e*(a+b*arccosh(c*x))^2/(b*d^3)-2*e*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))/d^3+e*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^3+e*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^3+e*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^3+e*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^3+b*e*polylog(2,(-1)/exp(2*arccosh(c*x)))/d^3+b*e*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^3+b*e*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^3+b*e*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^3+b*e*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^3+1/2*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/(d^2*x)+1/2*b*c*e*arctanh(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(-1+c^2*x^2)))*sqrt(-1+c^2*x^2)/(d^(5/2)*sqrt(c^2*d+e)*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^4*(a+b*arccosh(c*x))/(d+e*x^2)^2,x,49,a*x/e^2+b*x*arccosh(c*x)/e^2+3/4*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(-d)/e^(5/2)-3/4*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(-d)/e^(5/2)+3/4*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(-d)/e^(5/2)-3/4*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(-d)/e^(5/2)-3/4*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(-d)/e^(5/2)+3/4*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(-d)/e^(5/2)-3/4*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(-d)/e^(5/2)+3/4*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(-d)/e^(5/2)-1/4*d*(a+b*arccosh(c*x))/(e^(5/2)*(sqrt(-d)-x*sqrt(e)))+1/4*d*(a+b*arccosh(c*x))/(e^(5/2)*(sqrt(-d)+x*sqrt(e)))-b*sqrt(-1+c*x)*sqrt(1+c*x)/(c*e^2)+1/2*b*c*d*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))))/(e^(5/2)*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))-1/2*b*c*d*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))))/(e^(5/2)*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))],
[x^2*(a+b*arccosh(c*x))/(d+e*x^2)^2,x,46,1/4*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(e^(3/2)*sqrt(-d))-1/4*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(e^(3/2)*sqrt(-d))+1/4*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(e^(3/2)*sqrt(-d))-1/4*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(e^(3/2)*sqrt(-d))-1/4*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(e^(3/2)*sqrt(-d))+1/4*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(e^(3/2)*sqrt(-d))-1/4*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(e^(3/2)*sqrt(-d))+1/4*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(e^(3/2)*sqrt(-d))+1/4*(a+b*arccosh(c*x))/(e^(3/2)*(sqrt(-d)-x*sqrt(e)))+1/4*(-a-b*arccosh(c*x))/(e^(3/2)*(sqrt(-d)+x*sqrt(e)))-1/2*b*c*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))))/(e^(3/2)*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))+1/2*b*c*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))))/(e^(3/2)*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))],
[(a+b*arccosh(c*x))/(d+e*x^2)^2,x,26,-1/4*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/((-d)^(3/2)*sqrt(e))+1/4*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/((-d)^(3/2)*sqrt(e))-1/4*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/((-d)^(3/2)*sqrt(e))+1/4*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/((-d)^(3/2)*sqrt(e))+1/4*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/((-d)^(3/2)*sqrt(e))-1/4*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/((-d)^(3/2)*sqrt(e))+1/4*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/((-d)^(3/2)*sqrt(e))-1/4*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/((-d)^(3/2)*sqrt(e))+1/4*(-a-b*arccosh(c*x))/(d*sqrt(e)*(sqrt(-d)-x*sqrt(e)))+1/4*(a+b*arccosh(c*x))/(d*sqrt(e)*(sqrt(-d)+x*sqrt(e)))+1/2*b*c*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))))/(d*sqrt(e)*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))-1/2*b*c*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))))/(d*sqrt(e)*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))],
[(a+b*arccosh(c*x))/(x^2*(d+e*x^2)^2),x,49,(-a-b*arccosh(c*x))/(d^2*x)+b*c*arctan(sqrt(-1+c*x)*sqrt(1+c*x))/d^2-3/4*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(5/2)+3/4*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(5/2)-3/4*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(5/2)+3/4*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(5/2)+3/4*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(5/2)-3/4*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(5/2)+3/4*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(5/2)-3/4*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))*sqrt(e)/(-d)^(5/2)+1/4*(a+b*arccosh(c*x))*sqrt(e)/(d^2*(sqrt(-d)-x*sqrt(e)))-1/4*(a+b*arccosh(c*x))*sqrt(e)/(d^2*(sqrt(-d)+x*sqrt(e)))-1/2*b*c*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))))*sqrt(e)/(d^2*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))+1/2*b*c*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))))*sqrt(e)/(d^2*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))],
[x^5*(a+b*arccosh(c*x))/(d+e*x^2)^3,x,29,-1/4*d^2*(a+b*arccosh(c*x))/(e^3*(d+e*x^2)^2)+d*(a+b*arccosh(c*x))/(e^3*(d+e*x^2))-1/2*(a+b*arccosh(c*x))^2/(b*e^3)+1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^3+1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^3+1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^3+1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^3+1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^3+1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/e^3+1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^3+1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/e^3+1/8*b*c*d*x*(1-c^2*x^2)/(e^2*(c^2*d+e)*(d+e*x^2)*sqrt(-1+c*x)*sqrt(1+c*x))+1/8*b*c*(2*c^2*d+e)*arctanh(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(-1+c^2*x^2)))*sqrt(d)*sqrt(-1+c^2*x^2)/(e^3*(c^2*d+e)^(3/2)*sqrt(-1+c*x)*sqrt(1+c*x))-b*c*arctanh(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(-1+c^2*x^2)))*sqrt(d)*sqrt(-1+c^2*x^2)/(e^3*sqrt(c^2*d+e)*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^3*(a+b*arccosh(c*x))/(d+e*x^2)^3,x,9,1/4*x^4*(a+b*arccosh(c*x))/(d*(d+e*x^2)^2)-1/8*b*c*x*(1-c^2*x^2)/(e*(c^2*d+e)*(d+e*x^2)*sqrt(-1+c*x)*sqrt(1+c*x))-1/4*b*arcsin(c*x)*sqrt(1-c^2*x^2)/(d*e^2*sqrt(-1+c*x)*sqrt(1+c*x))+1/8*b*c*(2*c^2*d+3*e)*arctan(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(1-c^2*x^2)))*sqrt(1-c^2*x^2)/(e^2*(c^2*d+e)^(3/2)*sqrt(d)*sqrt(-1+c*x)*sqrt(1+c*x)),1/4*x^4*(a+b*arccosh(c*x))/(d*(d+e*x^2)^2)-1/8*b*c*x*(1-c^2*x^2)/(e*(c^2*d+e)*(d+e*x^2)*sqrt(-1+c*x)*sqrt(1+c*x))-1/4*b*arctanh(c*x/sqrt(-1+c^2*x^2))*sqrt(-1+c^2*x^2)/(d*e^2*sqrt(-1+c*x)*sqrt(1+c*x))+1/8*b*c*(2*c^2*d+3*e)*arctanh(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(-1+c^2*x^2)))*sqrt(-1+c^2*x^2)/(e^2*(c^2*d+e)^(3/2)*sqrt(d)*sqrt(-1+c*x)*sqrt(1+c*x))],
[x*(a+b*arccosh(c*x))/(d+e*x^2)^3,x,5,1/4*(-a-b*arccosh(c*x))/(e*(d+e*x^2)^2)+1/8*b*c*x*(1-c^2*x^2)/(d*(c^2*d+e)*(d+e*x^2)*sqrt(-1+c*x)*sqrt(1+c*x))+1/8*b*c*(2*c^2*d+e)*arctanh(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(-1+c^2*x^2)))*sqrt(-1+c^2*x^2)/(d^(3/2)*e*(c^2*d+e)^(3/2)*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x*(d+e*x^2)^3),x,34,1/4*(a+b*arccosh(c*x))/(d*(d+e*x^2)^2)+1/2*(a+b*arccosh(c*x))/(d^2*(d+e*x^2))+(a+b*arccosh(c*x))^2/(b*d^3)+(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))/d^3-1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^3-1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^3-1/2*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^3-1/2*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^3-1/2*b*polylog(2,(-1)/exp(2*arccosh(c*x)))/d^3-1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^3-1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^3-1/2*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^3-1/2*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^3-1/8*b*c*e*x*(1-c^2*x^2)/(d^2*(c^2*d+e)*(d+e*x^2)*sqrt(-1+c*x)*sqrt(1+c*x))-1/8*b*c*(2*c^2*d+e)*arctanh(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(-1+c^2*x^2)))*sqrt(-1+c^2*x^2)/(d^(5/2)*(c^2*d+e)^(3/2)*sqrt(-1+c*x)*sqrt(1+c*x))-1/2*b*c*arctanh(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(-1+c^2*x^2)))*sqrt(-1+c^2*x^2)/(d^(5/2)*sqrt(c^2*d+e)*sqrt(-1+c*x)*sqrt(1+c*x))],
[(a+b*arccosh(c*x))/(x^3*(d+e*x^2)^3),x,36,1/2*(-a-b*arccosh(c*x))/(d^3*x^2)-1/4*e*(a+b*arccosh(c*x))/(d^2*(d+e*x^2)^2)-e*(a+b*arccosh(c*x))/(d^3*(d+e*x^2))-3*e*(a+b*arccosh(c*x))^2/(b*d^4)-3*e*(a+b*arccosh(c*x))*log(1+exp(-2*arccosh(c*x)))/d^4+3/2*e*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^4+3/2*e*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^4+3/2*e*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^4+3/2*e*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^4+3/2*b*e*polylog(2,(-1)/exp(2*arccosh(c*x)))/d^4+3/2*b*e*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^4+3/2*b*e*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/d^4+3/2*b*e*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^4+3/2*b*e*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/d^4+1/8*b*c*e^2*x*(1-c^2*x^2)/(d^3*(c^2*d+e)*(d+e*x^2)*sqrt(-1+c*x)*sqrt(1+c*x))+1/2*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/(d^3*x)+1/8*b*c*e*(2*c^2*d+e)*arctanh(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(-1+c^2*x^2)))*sqrt(-1+c^2*x^2)/(d^(7/2)*(c^2*d+e)^(3/2)*sqrt(-1+c*x)*sqrt(1+c*x))+b*c*e*arctanh(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(-1+c^2*x^2)))*sqrt(-1+c^2*x^2)/(d^(7/2)*sqrt(c^2*d+e)*sqrt(-1+c*x)*sqrt(1+c*x))],
[x^4*(a+b*arccosh(c*x))/(d+e*x^2)^3,x,80,3/16*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(e^(5/2)*sqrt(-d))-3/16*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(e^(5/2)*sqrt(-d))+3/16*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(e^(5/2)*sqrt(-d))-3/16*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(e^(5/2)*sqrt(-d))-3/16*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(e^(5/2)*sqrt(-d))+3/16*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(e^(5/2)*sqrt(-d))-3/16*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(e^(5/2)*sqrt(-d))+3/16*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(e^(5/2)*sqrt(-d))-1/8*b*c^3*d*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))))/(e^(5/2)*(c*sqrt(-d)-sqrt(e))^(3/2)*(c*sqrt(-d)+sqrt(e))^(3/2))+1/8*b*c^3*d*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))))/(e^(5/2)*(c*sqrt(-d)-sqrt(e))^(3/2)*(c*sqrt(-d)+sqrt(e))^(3/2))-1/16*(a+b*arccosh(c*x))*sqrt(-d)/(e^(5/2)*(sqrt(-d)-x*sqrt(e))^2)+5/16*(a+b*arccosh(c*x))/(e^(5/2)*(sqrt(-d)-x*sqrt(e)))+1/16*(a+b*arccosh(c*x))*sqrt(-d)/(e^(5/2)*(sqrt(-d)+x*sqrt(e))^2)-5/16*(a+b*arccosh(c*x))/(e^(5/2)*(sqrt(-d)+x*sqrt(e)))-1/16*b*c*sqrt(-d)*sqrt(-1+c*x)*sqrt(1+c*x)/(e^2*(c^2*d+e)*(sqrt(-d)-x*sqrt(e)))-1/16*b*c*sqrt(-d)*sqrt(-1+c*x)*sqrt(1+c*x)/(e^2*(c^2*d+e)*(sqrt(-d)+x*sqrt(e)))-5/8*b*c*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))))/(e^(5/2)*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))+5/8*b*c*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))))/(e^(5/2)*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))],
[x^2*(a+b*arccosh(c*x))/(d+e*x^2)^3,x,62,-1/16*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/((-d)^(3/2)*e^(3/2))+1/16*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/((-d)^(3/2)*e^(3/2))-1/16*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/((-d)^(3/2)*e^(3/2))+1/16*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/((-d)^(3/2)*e^(3/2))+1/16*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/((-d)^(3/2)*e^(3/2))-1/16*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/((-d)^(3/2)*e^(3/2))+1/16*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/((-d)^(3/2)*e^(3/2))-1/16*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/((-d)^(3/2)*e^(3/2))+1/8*b*c^3*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))))/(e^(3/2)*(c*sqrt(-d)-sqrt(e))^(3/2)*(c*sqrt(-d)+sqrt(e))^(3/2))-1/8*b*c^3*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))))/(e^(3/2)*(c*sqrt(-d)-sqrt(e))^(3/2)*(c*sqrt(-d)+sqrt(e))^(3/2))+1/16*(-a-b*arccosh(c*x))/(e^(3/2)*sqrt(-d)*(sqrt(-d)-x*sqrt(e))^2)+1/16*(-a-b*arccosh(c*x))/(d*e^(3/2)*(sqrt(-d)-x*sqrt(e)))+1/16*(a+b*arccosh(c*x))/(e^(3/2)*sqrt(-d)*(sqrt(-d)+x*sqrt(e))^2)+1/16*(a+b*arccosh(c*x))/(d*e^(3/2)*(sqrt(-d)+x*sqrt(e)))-1/16*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/(e*(c^2*d+e)*sqrt(-d)*(sqrt(-d)-x*sqrt(e)))-1/16*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/(e*(c^2*d+e)*sqrt(-d)*(sqrt(-d)+x*sqrt(e)))+1/8*b*c*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))))/(d*e^(3/2)*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))-1/8*b*c*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))))/(d*e^(3/2)*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))],
[(a+b*arccosh(c*x))/(d+e*x^2)^3,x,34,3/16*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/((-d)^(5/2)*sqrt(e))-3/16*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/((-d)^(5/2)*sqrt(e))+3/16*(a+b*arccosh(c*x))*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/((-d)^(5/2)*sqrt(e))-3/16*(a+b*arccosh(c*x))*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/((-d)^(5/2)*sqrt(e))-3/16*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/((-d)^(5/2)*sqrt(e))+3/16*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/((-d)^(5/2)*sqrt(e))-3/16*b*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/((-d)^(5/2)*sqrt(e))+3/16*b*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/((-d)^(5/2)*sqrt(e))-1/8*b*c^3*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))))/(d*(c*sqrt(-d)-sqrt(e))^(3/2)*sqrt(e)*(c*sqrt(-d)+sqrt(e))^(3/2))+1/8*b*c^3*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))))/(d*(c*sqrt(-d)-sqrt(e))^(3/2)*sqrt(e)*(c*sqrt(-d)+sqrt(e))^(3/2))+1/16*(-a-b*arccosh(c*x))/((-d)^(3/2)*sqrt(e)*(sqrt(-d)-x*sqrt(e))^2)-3/16*(a+b*arccosh(c*x))/(d^2*sqrt(e)*(sqrt(-d)-x*sqrt(e)))+1/16*(a+b*arccosh(c*x))/((-d)^(3/2)*sqrt(e)*(sqrt(-d)+x*sqrt(e))^2)+3/16*(a+b*arccosh(c*x))/(d^2*sqrt(e)*(sqrt(-d)+x*sqrt(e)))-1/16*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/((-d)^(3/2)*(c^2*d+e)*(sqrt(-d)-x*sqrt(e)))-1/16*b*c*sqrt(-1+c*x)*sqrt(1+c*x)/((-d)^(3/2)*(c^2*d+e)*(sqrt(-d)+x*sqrt(e)))+3/8*b*c*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))))/(d^2*sqrt(e)*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))-3/8*b*c*arctanh(sqrt(1+c*x)*sqrt(c*sqrt(-d)+sqrt(e))/(sqrt(-1+c*x)*sqrt(c*sqrt(-d)-sqrt(e))))/(d^2*sqrt(e)*sqrt(c*sqrt(-d)-sqrt(e))*sqrt(c*sqrt(-d)+sqrt(e)))],

#  {(a + b*ArcCosh[c*x])/(x^2*(d + e*x^2)^3), x, 102, (b*c*e*Sqrt[1 - c^2*x^2])/(16*(-d)^(5/2)*(c^2*d + e)*(Sqrt[-d] - Sqrt[e]*x)) + (b*c*e*Sqrt[1 - c^2*x^2])/(16*(-d)^(5/2)*(c^2*d + e)*(Sqrt[-d] + Sqrt[e]*x)) - (a + b*ArcCosh[c*x])/(d^3*x) - (Sqrt[e]*(a + b*ArcCosh[c*x]))/(16*(-d)^(5/2)*(Sqrt[-d] - Sqrt[e]*x)^2) + (7*Sqrt[e]*(a + b*ArcCosh[c*x]))/(16*d^3*(Sqrt[-d] - Sqrt[e]*x)) + (Sqrt[e]*(a + b*ArcCosh[c*x]))/(16*(-d)^(5/2)*(Sqrt[-d] + Sqrt[e]*x)^2) - (7*Sqrt[e]*(a + b*ArcCosh[c*x]))/(16*d^3*(Sqrt[-d] + Sqrt[e]*x)) - (b*c^3*Sqrt[e]*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d^2*(c^2*d + e)^(3/2)) - (7*b*c*Sqrt[e]*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d^3*Sqrt[c^2*d + e]) - (b*c^3*Sqrt[e]*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d^2*(c^2*d + e)^(3/2)) - (7*b*c*Sqrt[e]*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d^3*Sqrt[c^2*d + e]) - (b*c*ArcTanh[Sqrt[1 - c^2*x^2]])/d^3 + (15*Sqrt[e]*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcCosh[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(16*(-d)^(7/2)) - (15*Sqrt[e]*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcCosh[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(16*(-d)^(7/2)) + (15*Sqrt[e]*(a + b*ArcCosh[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcCosh[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(16*(-d)^(7/2)) - (15*Sqrt[e]*(a + b*ArcCosh[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcCosh[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(16*(-d)^(7/2)) + (15*I*b*Sqrt[e]*PolyLog[2, -((Sqrt[e]*E^(I*ArcCosh[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/(16*(-d)^(7/2)) - (15*I*b*Sqrt[e]*PolyLog[2, (Sqrt[e]*E^(I*ArcCosh[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(16*(-d)^(7/2)) + (15*I*b*Sqrt[e]*PolyLog[2, -((Sqrt[e]*E^(I*ArcCosh[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/(16*(-d)^(7/2)) - (15*I*b*Sqrt[e]*PolyLog[2, (Sqrt[e]*E^(I*ArcCosh[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(16*(-d)^(7/2))} 

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

# Integrands of the form (f x)^m (d+e x^2)^p (a+b ArcCosh[c x]) with m symbolic
[(f*x)^m*(d+e*x^2)^3*(a+b*arccosh(c*x)),x,8,d^3*(f*x)^(1+m)*(a+b*arccosh(c*x))/(f*(1+m))+3*d^2*e*(f*x)^(3+m)*(a+b*arccosh(c*x))/(f^3*(3+m))+3*d*e^2*(f*x)^(5+m)*(a+b*arccosh(c*x))/(f^5*(5+m))+e^3*(f*x)^(7+m)*(a+b*arccosh(c*x))/(f^7*(7+m))+b*e*(3*c^2*d*e*(7+m)^2*(12+7*m+m^2)+3*c^4*d^2*(35+12*m+m^2)^2+e^2*(360+342*m+119*m^2+18*m^3+m^4))*(f*x)^(2+m)*(1-c^2*x^2)/(c^5*f^2*(3+m)^2*(5+m)^2*(7+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))+b*e^2*(3*c^2*d*(7+m)^2+e*(30+11*m+m^2))*(f*x)^(4+m)*(1-c^2*x^2)/(c^3*f^4*(5+m)^2*(7+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))+b*e^3*(f*x)^(6+m)*(1-c^2*x^2)/(c*f^6*(7+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-b*(c^6*d^3*(3+m)*(5+m)*(7+m)/(1+m)+e*(2+m)*(3*c^2*d*e*(7+m)^2*(12+7*m+m^2)+3*c^4*d^2*(35+12*m+m^2)^2+e^2*(360+342*m+119*m^2+18*m^3+m^4))/(105+71*m+15*m^2+m^3))*(f*x)^(2+m)*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(c^5*f^2*(2+m)*(3+m)*(5+m)*(7+m)*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f*x)^m*(d+e*x^2)^2*(a+b*arccosh(c*x)),x,7,d^2*(f*x)^(1+m)*(a+b*arccosh(c*x))/(f*(1+m))+2*d*e*(f*x)^(3+m)*(a+b*arccosh(c*x))/(f^3*(3+m))+e^2*(f*x)^(5+m)*(a+b*arccosh(c*x))/(f^5*(5+m))+b*e*(2*c^2*d*(5+m)^2+e*(12+7*m+m^2))*(f*x)^(2+m)*(1-c^2*x^2)/(c^3*f^2*(3+m)^2*(5+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))+b*e^2*(f*x)^(4+m)*(1-c^2*x^2)/(c*f^4*(5+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))-b*(c^4*d^2*(3+m)*(5+m)/(1+m)+e*(2+m)*(2*c^2*d*(5+m)^2+e*(12+7*m+m^2))/((3+m)*(5+m)))*(f*x)^(2+m)*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(c^3*f^2*(2+m)*(3+m)*(5+m)*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f*x)^m*(d+e*x^2)*(a+b*arccosh(c*x)),x,5,d*(f*x)^(1+m)*(a+b*arccosh(c*x))/(f*(1+m))+e*(f*x)^(3+m)*(a+b*arccosh(c*x))/(f^3*(3+m))-b*e*(f*x)^(2+m)*sqrt(-1+c*x)*sqrt(1+c*x)/(c*f^2*(3+m)^2)-b*(e*(1+m)*(2+m)+c^2*d*(3+m)^2)*(f*x)^(2+m)*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)*sqrt(1-c^2*x^2)/(c*f^2*(1+m)*(2+m)*(3+m)^2*sqrt(-1+c*x)*sqrt(1+c*x))],
[(f*x)^m*(a+b*arccosh(c*x))/(d+e*x^2),x,0,Unintegrable((f*x)^m*(a+b*arccosh(c*x))/(d+e*x^2),x)],
[(f*x)^m*(a+b*arccosh(c*x))/(d+e*x^2)^2,x,0,Unintegrable((f*x)^m*(a+b*arccosh(c*x))/(d+e*x^2)^2,x)],
[(f*x)^m*(a+b*arccosh(c*x))/(d+e*x^2)^3,x,0,Unintegrable((f*x)^m*(a+b*arccosh(c*x))/(d+e*x^2)^3,x)],

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

# Integrands of the form x^m (d+e x^2)^p (a+b ArcCosh[c x])^2
[(d+e*x^2)^3*(a+b*arccosh(c*x))^2,x,26,2*b^2*d^3*x+4/3*b^2*d^2*e*x/c^2+16/25*b^2*d*e^2*x/c^4+32/245*b^2*e^3*x/c^6+2/9*b^2*d^2*e*x^3+8/75*b^2*d*e^2*x^3/c^2+16/735*b^2*e^3*x^3/c^4+6/125*b^2*d*e^2*x^5+12/1225*b^2*e^3*x^5/c^2+2/343*b^2*e^3*x^7+d^3*x*(a+b*arccosh(c*x))^2+d^2*e*x^3*(a+b*arccosh(c*x))^2+3/5*d*e^2*x^5*(a+b*arccosh(c*x))^2+1/7*e^3*x^7*(a+b*arccosh(c*x))^2-2*b*d^3*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c-4/3*b*d^2*e*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-16/25*b*d*e^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c^5-32/245*b*e^3*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c^7-2/3*b*d^2*e*x^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c-8/25*b*d*e^2*x^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-16/245*b*e^3*x^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c^5-6/25*b*d*e^2*x^4*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c-12/245*b*e^3*x^4*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-2/49*b*e^3*x^6*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(d+e*x^2)^2*(a+b*arccosh(c*x))^2,x,17,2*b^2*d^2*x+8/9*b^2*d*e*x/c^2+16/75*b^2*e^2*x/c^4+4/27*b^2*d*e*x^3+8/225*b^2*e^2*x^3/c^2+2/125*b^2*e^2*x^5+d^2*x*(a+b*arccosh(c*x))^2+2/3*d*e*x^3*(a+b*arccosh(c*x))^2+1/5*e^2*x^5*(a+b*arccosh(c*x))^2-2*b*d^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c-8/9*b*d*e*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-16/75*b*e^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c^5-4/9*b*d*e*x^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c-8/75*b*e^2*x^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-2/25*b*e^2*x^4*(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,10,2*b^2*d*x+4/9*b^2*e*x/c^2+2/27*b^2*e*x^3+d*x*(a+b*arccosh(c*x))^2+1/3*e*x^3*(a+b*arccosh(c*x))^2-2*b*d*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c-4/9*b*e*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c^3-2/9*b*e*x^2*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(a+b*arccosh(c*x))^2,x,3,2*b^2*x+x*(a+b*arccosh(c*x))^2-2*b*(a+b*arccosh(c*x))*sqrt(-1+c*x)*sqrt(1+c*x)/c],
[(a+b*arccosh(c*x))^2/(d+e*x^2),x,22,1/2*(a+b*arccosh(c*x))^2*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))-1/2*(a+b*arccosh(c*x))^2*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))+1/2*(a+b*arccosh(c*x))^2*log(1-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))-1/2*(a+b*arccosh(c*x))^2*log(1+exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))-b*(a+b*arccosh(c*x))*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))+b*(a+b*arccosh(c*x))*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))-b*(a+b*arccosh(c*x))*polylog(2,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))+b*(a+b*arccosh(c*x))*polylog(2,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))+b^2*polylog(3,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))-b^2*polylog(3,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))+b^2*polylog(3,-exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))-b^2*polylog(3,exp(arccosh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d-e)))/(sqrt(-d)*sqrt(e))],

# Integrands of the form x^m (d+e x^2)^(p/2) (a+b ArcCosh[c x])^2
[(a+b*arccosh(c*x))^2*sqrt(d+e*x^2),x,0,Unintegrable((a+b*arccosh(c*x))^2*sqrt(d+e*x^2),x)],
[(a+b*arccosh(c*x))^2/sqrt(d+e*x^2),x,0,Unintegrable((a+b*arccosh(c*x))^2/sqrt(d+e*x^2),x)],
[(a+b*arccosh(c*x))^2/(d+e*x^2)^(3/2),x,0,Unintegrable((a+b*arccosh(c*x))^2/(d+e*x^2)^(3/2),x)],
[(a+b*arccosh(c*x))^2/(d+e*x^2)^(5/2),x,0,Unintegrable((a+b*arccosh(c*x))^2/(d+e*x^2)^(5/2),x)],

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

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

# Integrands of the form x^m (d+e x^2)^p / (a+b ArcCosh[c x])
[(d+e*x^2)^2/(a+b*arccosh(c*x)),x,27,d^2*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)/(b*c)+1/2*d*e*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)/(b*c^3)+1/8*e^2*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)/(b*c^5)+1/2*d*e*cosh(3*a/b)*Shi(3*(a+b*arccosh(c*x))/b)/(b*c^3)+3/16*e^2*cosh(3*a/b)*Shi(3*(a+b*arccosh(c*x))/b)/(b*c^5)+1/16*e^2*cosh(5*a/b)*Shi(5*(a+b*arccosh(c*x))/b)/(b*c^5)-d^2*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b*c)-1/2*d*e*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b*c^3)-1/8*e^2*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b*c^5)-1/2*d*e*Chi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)/(b*c^3)-3/16*e^2*Chi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)/(b*c^5)-1/16*e^2*Chi(5*(a+b*arccosh(c*x))/b)*sinh(5*a/b)/(b*c^5)],
[(d+e*x^2)/(a+b*arccosh(c*x)),x,15,1/4*(4*c^2*d+e)*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)/(b*c^3)+1/4*e*cosh(3*a/b)*Shi(3*(a+b*arccosh(c*x))/b)/(b*c^3)-1/4*(4*c^2*d+e)*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b*c^3)-1/4*e*Chi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)/(b*c^3),d*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)/(b*c)+1/4*e*cosh(a/b)*Shi((a+b*arccosh(c*x))/b)/(b*c^3)+1/4*e*cosh(3*a/b)*Shi(3*(a+b*arccosh(c*x))/b)/(b*c^3)-d*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b*c)-1/4*e*Chi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b*c^3)-1/4*e*Chi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)/(b*c^3)],
[1/(a+b*arccosh(c*x)),x,4,cosh(a/b)*Shi((a+b*arccosh(c*x))/b)/(b*c)-Chi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b*c)],
[1/((d+e*x^2)*(a+b*arccosh(c*x))),x,0,Unintegrable(1/((d+e*x^2)*(a+b*arccosh(c*x))),x)],
[1/((d+e*x^2)^2*(a+b*arccosh(c*x))),x,0,Unintegrable(1/((d+e*x^2)^2*(a+b*arccosh(c*x))),x)],

# Integrands of the form x^m (d+e x^2)^(p/2) / (a+b ArcCosh[c x])
[sqrt(d+e*x^2)/(a+b*arccosh(c*x)),x,0,Unintegrable(sqrt(d+e*x^2)/(a+b*arccosh(c*x)),x)],
[1/((a+b*arccosh(c*x))*sqrt(d+e*x^2)),x,0,Unintegrable(1/((a+b*arccosh(c*x))*sqrt(d+e*x^2)),x)],
[1/((d+e*x^2)^(3/2)*(a+b*arccosh(c*x))),x,0,Unintegrable(1/((d+e*x^2)^(3/2)*(a+b*arccosh(c*x))),x)],
[1/((d+e*x^2)^(5/2)*(a+b*arccosh(c*x))),x,0,Unintegrable(1/((d+e*x^2)^(5/2)*(a+b*arccosh(c*x))),x)],

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

# Integrands of the form x^m (d+e x^2)^p / (a+b ArcCosh[c x])^2
[(d+e*x^2)^2/(a+b*arccosh(c*x))^2,x,26,d^2*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)/(b^2*c)+1/2*d*e*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)/(b^2*c^3)+1/8*e^2*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)/(b^2*c^5)+3/2*d*e*Chi(3*(a+b*arccosh(c*x))/b)*cosh(3*a/b)/(b^2*c^3)+9/16*e^2*Chi(3*(a+b*arccosh(c*x))/b)*cosh(3*a/b)/(b^2*c^5)+5/16*e^2*Chi(5*(a+b*arccosh(c*x))/b)*cosh(5*a/b)/(b^2*c^5)-d^2*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b^2*c)-1/2*d*e*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b^2*c^3)-1/8*e^2*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b^2*c^5)-3/2*d*e*Shi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)/(b^2*c^3)-9/16*e^2*Shi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)/(b^2*c^5)-5/16*e^2*Shi(5*(a+b*arccosh(c*x))/b)*sinh(5*a/b)/(b^2*c^5)-d^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))-2*d*e*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))-e^2*x^4*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))],
[(d+e*x^2)/(a+b*arccosh(c*x))^2,x,15,d*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)/(b^2*c)+1/4*e*Chi((a+b*arccosh(c*x))/b)*cosh(a/b)/(b^2*c^3)+3/4*e*Chi(3*(a+b*arccosh(c*x))/b)*cosh(3*a/b)/(b^2*c^3)-d*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b^2*c)-1/4*e*Shi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b^2*c^3)-3/4*e*Shi(3*(a+b*arccosh(c*x))/b)*sinh(3*a/b)/(b^2*c^3)-d*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))-e*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*x)))],
[1/(a+b*arccosh(c*x))^2,x,5,Chi((a+b*arccosh(c*x))/b)*cosh(a/b)/(b^2*c)-Shi((a+b*arccosh(c*x))/b)*sinh(a/b)/(b^2*c)-sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*(a+b*arccosh(c*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)],
[1/((d+e*x^2)^2*(a+b*arccosh(c*x))^2),x,0,Unintegrable(1/((d+e*x^2)^2*(a+b*arccosh(c*x))^2),x)],

# Integrands of the form x^m (d+e x^2)^(p/2) / (a+b ArcCosh[c x])^2
[sqrt(d+e*x^2)/(a+b*arccosh(c*x))^2,x,0,Unintegrable(sqrt(d+e*x^2)/(a+b*arccosh(c*x))^2,x)],
[1/((a+b*arccosh(c*x))^2*sqrt(d+e*x^2)),x,0,Unintegrable(1/((a+b*arccosh(c*x))^2*sqrt(d+e*x^2)),x)],
[1/((d+e*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x,0,Unintegrable(1/((d+e*x^2)^(3/2)*(a+b*arccosh(c*x))^2),x)],
[1/((d+e*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x,0,Unintegrable(1/((d+e*x^2)^(5/2)*(a+b*arccosh(c*x))^2),x)],

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

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

# n>0
[(d+e*x^2)^2*sqrt(a+b*arccosh(c*x)),x,42,-1/320*e^2*exp(5*a/b)*erf(sqrt(5)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(1/5*Pi)/c^5-1/320*e^2*erfi(sqrt(5)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(1/5*Pi)/(c^5*exp(5*a/b))-1/24*d*e*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(1/3*Pi)/c^3-1/64*e^2*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(1/3*Pi)/c^5-1/24*d*e*erfi(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(1/3*Pi)/(c^3*exp(3*a/b))-1/64*e^2*erfi(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(1/3*Pi)/(c^5*exp(3*a/b))-1/4*d^2*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/c-1/8*d*e*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/c^3-1/32*e^2*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/c^5-1/4*d^2*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/(c*exp(a/b))-1/8*d*e*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/(c^3*exp(a/b))-1/32*e^2*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/(c^5*exp(a/b))+d^2*x*sqrt(a+b*arccosh(c*x))+2/3*d*e*x^3*sqrt(a+b*arccosh(c*x))+1/5*e^2*x^5*sqrt(a+b*arccosh(c*x))],
[(d+e*x^2)*sqrt(a+b*arccosh(c*x)),x,23,-1/48*e*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(1/3*Pi)/c^3-1/48*e*erfi(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(1/3*Pi)/(c^3*exp(3*a/b))-1/4*d*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/c-1/16*e*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/c^3-1/4*d*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/(c*exp(a/b))-1/16*e*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/(c^3*exp(a/b))+d*x*sqrt(a+b*arccosh(c*x))+1/3*e*x^3*sqrt(a+b*arccosh(c*x))],
[sqrt(a+b*arccosh(c*x)),x,7,-1/4*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/c-1/4*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(b)*sqrt(Pi)/(c*exp(a/b))+x*sqrt(a+b*arccosh(c*x))],
[sqrt(a+b*arccosh(c*x))/(d+e*x^2),x,0,Unintegrable(sqrt(a+b*arccosh(c*x))/(d+e*x^2),x)],
[sqrt(a+b*arccosh(c*x))/(d+e*x^2)^2,x,0,Unintegrable(sqrt(a+b*arccosh(c*x))/(d+e*x^2)^2,x)],
[(d+e*x^2)*(a+b*arccosh(c*x))^(3/2),x,32,d*x*(a+b*arccosh(c*x))^(3/2)+1/3*e*x^3*(a+b*arccosh(c*x))^(3/2)-1/96*b^(3/2)*e*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/3*Pi)/c^3+1/96*b^(3/2)*e*erfi(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/3*Pi)/(c^3*exp(3*a/b))-3/8*b^(3/2)*d*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/c-3/32*b^(3/2)*e*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/c^3+3/8*b^(3/2)*d*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c*exp(a/b))+3/32*b^(3/2)*e*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c^3*exp(a/b))-3/2*b*d*sqrt(-1+c*x)*sqrt(1+c*x)*sqrt(a+b*arccosh(c*x))/c-1/3*b*e*sqrt(-1+c*x)*sqrt(1+c*x)*sqrt(a+b*arccosh(c*x))/c^3-1/6*b*e*x^2*sqrt(-1+c*x)*sqrt(1+c*x)*sqrt(a+b*arccosh(c*x))/c],
[(a+b*arccosh(c*x))^(3/2),x,8,x*(a+b*arccosh(c*x))^(3/2)-3/8*b^(3/2)*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/c+3/8*b^(3/2)*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c*exp(a/b))-3/2*b*sqrt(-1+c*x)*sqrt(1+c*x)*sqrt(a+b*arccosh(c*x))/c],
[(a+b*arccosh(c*x))^(3/2)/(d+e*x^2),x,0,Unintegrable((a+b*arccosh(c*x))^(3/2)/(d+e*x^2),x)],
[(a+b*arccosh(c*x))^(3/2)/(d+e*x^2)^2,x,0,Unintegrable((a+b*arccosh(c*x))^(3/2)/(d+e*x^2)^2,x)],

# n<0
[(d+e*x^2)^2/sqrt(a+b*arccosh(c*x)),x,39,-1/32*e^2*exp(5*a/b)*erf(sqrt(5)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/5*Pi)/(c^5*sqrt(b))+1/32*e^2*erfi(sqrt(5)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/5*Pi)/(c^5*exp(5*a/b)*sqrt(b))-1/4*d*e*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/3*Pi)/(c^3*sqrt(b))+1/4*d*e*erfi(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/3*Pi)/(c^3*exp(3*a/b)*sqrt(b))-1/2*d^2*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c*sqrt(b))-1/4*d*e*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c^3*sqrt(b))-1/16*e^2*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c^5*sqrt(b))+1/2*d^2*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c*exp(a/b)*sqrt(b))+1/4*d*e*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c^3*exp(a/b)*sqrt(b))+1/16*e^2*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c^5*exp(a/b)*sqrt(b))-1/32*e^2*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3*Pi)/(c^5*sqrt(b))+1/32*e^2*erfi(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3*Pi)/(c^5*exp(3*a/b)*sqrt(b))],
[(d+e*x^2)/sqrt(a+b*arccosh(c*x)),x,21,-1/8*e*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/3*Pi)/(c^3*sqrt(b))+1/8*e*erfi(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(1/3*Pi)/(c^3*exp(3*a/b)*sqrt(b))-1/2*d*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c*sqrt(b))-1/8*e*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c^3*sqrt(b))+1/2*d*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c*exp(a/b)*sqrt(b))+1/8*e*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c^3*exp(a/b)*sqrt(b))],
[1/sqrt(a+b*arccosh(c*x)),x,6,-1/2*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c*sqrt(b))+1/2*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(c*exp(a/b)*sqrt(b))],
[1/((d+e*x^2)*sqrt(a+b*arccosh(c*x))),x,0,Unintegrable(1/((d+e*x^2)*sqrt(a+b*arccosh(c*x))),x)],
[1/((d+e*x^2)^2*sqrt(a+b*arccosh(c*x))),x,0,Unintegrable(1/((d+e*x^2)^2*sqrt(a+b*arccosh(c*x))),x)],
[(d+e*x^2)/(a+b*arccosh(c*x))^(3/2),x,21,d*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c)+1/4*e*exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c^3)+d*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c*exp(a/b))+1/4*e*erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c^3*exp(a/b))+1/4*e*exp(3*a/b)*erf(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*c^3)+1/4*e*erfi(sqrt(3)*sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*c^3*exp(3*a/b))-2*d*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*sqrt(a+b*arccosh(c*x)))-2*e*x^2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*sqrt(a+b*arccosh(c*x)))],
[1/(a+b*arccosh(c*x))^(3/2),x,7,exp(a/b)*erf(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c)+erfi(sqrt(a+b*arccosh(c*x))/sqrt(b))*sqrt(Pi)/(b^(3/2)*c*exp(a/b))-2*sqrt(-1+c*x)*sqrt(1+c*x)/(b*c*sqrt(a+b*arccosh(c*x)))],
[1/((d+e*x^2)*(a+b*arccosh(c*x))^(3/2)),x,0,Unintegrable(1/((d+e*x^2)*(a+b*arccosh(c*x))^(3/2)),x)],
[1/((d+e*x^2)^2*(a+b*arccosh(c*x))^(3/2)),x,0,Unintegrable(1/((d+e*x^2)^2*(a+b*arccosh(c*x))^(3/2)),x)]]:
