# Maple integration test file: "7 Inverse hyperbolic functions\7.1 Inverse hyperbolic sine\7.1.4 (f x)^m (d+e x^2)^p (a+b arcsinh(c x))^n.txt"

lst:=[

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

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

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

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

# p<0
[x^4*(a+b*arcsinh(c*x))/(d+c^2*d*x^2),x,12,-1/9*b*(1+c^2*x^2)^(3/2)/(c^5*d)-x*(a+b*arcsinh(c*x))/(c^4*d)+1/3*x^3*(a+b*arcsinh(c*x))/(c^2*d)+2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c^5*d)-I*b*polylog(2,-I*exp(arcsinh(c*x)))/(c^5*d)+I*b*polylog(2,I*exp(arcsinh(c*x)))/(c^5*d)+4/3*b*sqrt(1+c^2*x^2)/(c^5*d)],
[x^3*(a+b*arcsinh(c*x))/(d+c^2*d*x^2),x,8,1/4*b*arcsinh(c*x)/(c^4*d)+1/2*x^2*(a+b*arcsinh(c*x))/(c^2*d)+1/2*(a+b*arcsinh(c*x))^2/(b*c^4*d)-(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c^4*d)-1/2*b*polylog(2,-exp(2*arcsinh(c*x)))/(c^4*d)-1/4*b*x*sqrt(1+c^2*x^2)/(c^3*d)],
[x^2*(a+b*arcsinh(c*x))/(d+c^2*d*x^2),x,8,x*(a+b*arcsinh(c*x))/(c^2*d)-2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c^3*d)+I*b*polylog(2,-I*exp(arcsinh(c*x)))/(c^3*d)-I*b*polylog(2,I*exp(arcsinh(c*x)))/(c^3*d)-b*sqrt(1+c^2*x^2)/(c^3*d)],
[x*(a+b*arcsinh(c*x))/(d+c^2*d*x^2),x,5,-1/2*(a+b*arcsinh(c*x))^2/(b*c^2*d)+(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c^2*d)+1/2*b*polylog(2,-exp(2*arcsinh(c*x)))/(c^2*d)],
[(a+b*arcsinh(c*x))/(d+c^2*d*x^2),x,6,2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*d)-I*b*polylog(2,-I*exp(arcsinh(c*x)))/(c*d)+I*b*polylog(2,I*exp(arcsinh(c*x)))/(c*d)],
[(a+b*arcsinh(c*x))/(x*(d+c^2*d*x^2)),x,7,-2*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))/d-1/2*b*polylog(2,-exp(2*arcsinh(c*x)))/d+1/2*b*polylog(2,exp(2*arcsinh(c*x)))/d],
[(a+b*arcsinh(c*x))/(x^2*(d+c^2*d*x^2)),x,10,(-a-b*arcsinh(c*x))/(d*x)-2*c*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/d-b*c*arctanh(sqrt(1+c^2*x^2))/d+I*b*c*polylog(2,-I*exp(arcsinh(c*x)))/d-I*b*c*polylog(2,I*exp(arcsinh(c*x)))/d],
[(a+b*arcsinh(c*x))/(x^3*(d+c^2*d*x^2)),x,9,1/2*(-a-b*arcsinh(c*x))/(d*x^2)+2*c^2*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))/d+1/2*b*c^2*polylog(2,-exp(2*arcsinh(c*x)))/d-1/2*b*c^2*polylog(2,exp(2*arcsinh(c*x)))/d-1/2*b*c*sqrt(1+c^2*x^2)/(d*x)],
[(a+b*arcsinh(c*x))/(x^4*(d+c^2*d*x^2)),x,15,1/3*(-a-b*arcsinh(c*x))/(d*x^3)+c^2*(a+b*arcsinh(c*x))/(d*x)+2*c^3*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/d+7/6*b*c^3*arctanh(sqrt(1+c^2*x^2))/d-I*b*c^3*polylog(2,-I*exp(arcsinh(c*x)))/d+I*b*c^3*polylog(2,I*exp(arcsinh(c*x)))/d-1/6*b*c*sqrt(1+c^2*x^2)/(d*x^2)],
[x^4*(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^2,x,12,3/2*x*(a+b*arcsinh(c*x))/(c^4*d^2)-1/2*x^3*(a+b*arcsinh(c*x))/(c^2*d^2*(1+c^2*x^2))-3*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c^5*d^2)+3/2*I*b*polylog(2,-I*exp(arcsinh(c*x)))/(c^5*d^2)-3/2*I*b*polylog(2,I*exp(arcsinh(c*x)))/(c^5*d^2)+1/2*b/(c^5*d^2*sqrt(1+c^2*x^2))-b*sqrt(1+c^2*x^2)/(c^5*d^2)],
[x^3*(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^2,x,8,1/2*b*arcsinh(c*x)/(c^4*d^2)-1/2*x^2*(a+b*arcsinh(c*x))/(c^2*d^2*(1+c^2*x^2))-1/2*(a+b*arcsinh(c*x))^2/(b*c^4*d^2)+(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c^4*d^2)+1/2*b*polylog(2,-exp(2*arcsinh(c*x)))/(c^4*d^2)-1/2*b*x/(c^3*d^2*sqrt(1+c^2*x^2))],
[x^2*(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^2,x,8,-1/2*x*(a+b*arcsinh(c*x))/(c^2*d^2*(1+c^2*x^2))+(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c^3*d^2)-1/2*I*b*polylog(2,-I*exp(arcsinh(c*x)))/(c^3*d^2)+1/2*I*b*polylog(2,I*exp(arcsinh(c*x)))/(c^3*d^2)-1/2*b/(c^3*d^2*sqrt(1+c^2*x^2))],
[x*(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^2,x,2,1/2*(-a-b*arcsinh(c*x))/(c^2*d^2*(1+c^2*x^2))+1/2*b*x/(c*d^2*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^2,x,8,1/2*x*(a+b*arcsinh(c*x))/(d^2*(1+c^2*x^2))+(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*d^2)-1/2*I*b*polylog(2,-I*exp(arcsinh(c*x)))/(c*d^2)+1/2*I*b*polylog(2,I*exp(arcsinh(c*x)))/(c*d^2)+1/2*b/(c*d^2*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))/(x*(d+c^2*d*x^2)^2),x,9,1/2*(a+b*arcsinh(c*x))/(d^2*(1+c^2*x^2))-2*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))/d^2-1/2*b*polylog(2,-exp(2*arcsinh(c*x)))/d^2+1/2*b*polylog(2,exp(2*arcsinh(c*x)))/d^2-1/2*b*c*x/(d^2*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))/(x^2*(d+c^2*d*x^2)^2),x,13,(-a-b*arcsinh(c*x))/(d^2*x*(1+c^2*x^2))-3/2*c^2*x*(a+b*arcsinh(c*x))/(d^2*(1+c^2*x^2))-3*c*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/d^2-b*c*arctanh(sqrt(1+c^2*x^2))/d^2+3/2*I*b*c*polylog(2,-I*exp(arcsinh(c*x)))/d^2-3/2*I*b*c*polylog(2,I*exp(arcsinh(c*x)))/d^2-1/2*b*c/(d^2*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))/(x^3*(d+c^2*d*x^2)^2),x,12,-c^2*(a+b*arcsinh(c*x))/(d^2*(1+c^2*x^2))+1/2*(-a-b*arcsinh(c*x))/(d^2*x^2*(1+c^2*x^2))+4*c^2*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))/d^2+b*c^2*polylog(2,-exp(2*arcsinh(c*x)))/d^2-b*c^2*polylog(2,exp(2*arcsinh(c*x)))/d^2-1/2*b*c/(d^2*x*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))/(x^4*(d+c^2*d*x^2)^2),x,19,1/3*(-a-b*arcsinh(c*x))/(d^2*x^3*(1+c^2*x^2))+5/3*c^2*(a+b*arcsinh(c*x))/(d^2*x*(1+c^2*x^2))+5/2*c^4*x*(a+b*arcsinh(c*x))/(d^2*(1+c^2*x^2))+5*c^3*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/d^2+13/6*b*c^3*arctanh(sqrt(1+c^2*x^2))/d^2-5/2*I*b*c^3*polylog(2,-I*exp(arcsinh(c*x)))/d^2+5/2*I*b*c^3*polylog(2,I*exp(arcsinh(c*x)))/d^2+1/3*b*c^3/(d^2*sqrt(1+c^2*x^2))-1/6*b*c/(d^2*x^2*sqrt(1+c^2*x^2))],
[x^4*(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^3,x,12,1/12*b/(c^5*d^3*(1+c^2*x^2)^(3/2))-1/4*x^3*(a+b*arcsinh(c*x))/(c^2*d^3*(1+c^2*x^2)^2)-3/8*x*(a+b*arcsinh(c*x))/(c^4*d^3*(1+c^2*x^2))+3/4*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c^5*d^3)-3/8*I*b*polylog(2,-I*exp(arcsinh(c*x)))/(c^5*d^3)+3/8*I*b*polylog(2,I*exp(arcsinh(c*x)))/(c^5*d^3)-5/8*b/(c^5*d^3*sqrt(1+c^2*x^2))],
[x^3*(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^3,x,4,1/12*b*x^3/(c*d^3*(1+c^2*x^2)^(3/2))-1/4*b*arcsinh(c*x)/(c^4*d^3)+1/4*x^4*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2)^2)+1/4*b*x/(c^3*d^3*sqrt(1+c^2*x^2))],
[x^2*(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^3,x,10,-1/12*b/(c^3*d^3*(1+c^2*x^2)^(3/2))-1/4*x*(a+b*arcsinh(c*x))/(c^2*d^3*(1+c^2*x^2)^2)+1/8*x*(a+b*arcsinh(c*x))/(c^2*d^3*(1+c^2*x^2))+1/4*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c^3*d^3)-1/8*I*b*polylog(2,-I*exp(arcsinh(c*x)))/(c^3*d^3)+1/8*I*b*polylog(2,I*exp(arcsinh(c*x)))/(c^3*d^3)+1/8*b/(c^3*d^3*sqrt(1+c^2*x^2))],
[x*(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^3,x,3,1/12*b*x/(c*d^3*(1+c^2*x^2)^(3/2))+1/4*(-a-b*arcsinh(c*x))/(c^2*d^3*(1+c^2*x^2)^2)+1/6*b*x/(c*d^3*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^3,x,10,1/12*b/(c*d^3*(1+c^2*x^2)^(3/2))+1/4*x*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2)^2)+3/8*x*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2))+3/4*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*d^3)-3/8*I*b*polylog(2,-I*exp(arcsinh(c*x)))/(c*d^3)+3/8*I*b*polylog(2,I*exp(arcsinh(c*x)))/(c*d^3)+3/8*b/(c*d^3*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))/(x*(d+c^2*d*x^2)^3),x,12,-1/12*b*c*x/(d^3*(1+c^2*x^2)^(3/2))+1/4*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2)^2)+1/2*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2))-2*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))/d^3-1/2*b*polylog(2,-exp(2*arcsinh(c*x)))/d^3+1/2*b*polylog(2,exp(2*arcsinh(c*x)))/d^3-2/3*b*c*x/(d^3*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))/(x^2*(d+c^2*d*x^2)^3),x,16,-1/12*b*c/(d^3*(1+c^2*x^2)^(3/2))+(-a-b*arcsinh(c*x))/(d^3*x*(1+c^2*x^2)^2)-5/4*c^2*x*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2)^2)-15/8*c^2*x*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2))-15/4*c*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/d^3-b*c*arctanh(sqrt(1+c^2*x^2))/d^3+15/8*I*b*c*polylog(2,-I*exp(arcsinh(c*x)))/d^3-15/8*I*b*c*polylog(2,I*exp(arcsinh(c*x)))/d^3-7/8*b*c/(d^3*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))/(x^3*(d+c^2*d*x^2)^3),x,16,-1/2*b*c/(d^3*x*(1+c^2*x^2)^(3/2))-5/12*b*c^3*x/(d^3*(1+c^2*x^2)^(3/2))-3/4*c^2*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2)^2)+1/2*(-a-b*arcsinh(c*x))/(d^3*x^2*(1+c^2*x^2)^2)-3/2*c^2*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2))+6*c^2*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))/d^3+3/2*b*c^2*polylog(2,-exp(2*arcsinh(c*x)))/d^3-3/2*b*c^2*polylog(2,exp(2*arcsinh(c*x)))/d^3+2/3*b*c^3*x/(d^3*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))/(x^4*(d+c^2*d*x^2)^3),x,23,-1/12*b*c^3/(d^3*(1+c^2*x^2)^(3/2))-1/6*b*c/(d^3*x^2*(1+c^2*x^2)^(3/2))+1/3*(-a-b*arcsinh(c*x))/(d^3*x^3*(1+c^2*x^2)^2)+7/3*c^2*(a+b*arcsinh(c*x))/(d^3*x*(1+c^2*x^2)^2)+35/12*c^4*x*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2)^2)+35/8*c^4*x*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2))+35/4*c^3*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/d^3+19/6*b*c^3*arctanh(sqrt(1+c^2*x^2))/d^3-35/8*I*b*c^3*polylog(2,-I*exp(arcsinh(c*x)))/d^3+35/8*I*b*c^3*polylog(2,I*exp(arcsinh(c*x)))/d^3+29/24*b*c^3/(d^3*sqrt(1+c^2*x^2))],

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

# p>0
[x^3*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2),x,3,-1/3*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))/(c^4*Pi)+1/5*(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))/(c^4*Pi^2)+2/15*b*x*sqrt(Pi)/c^3-1/45*b*x^3*sqrt(Pi)/c-1/25*b*c*x^5*sqrt(Pi)],
[x^2*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2),x,5,-1/16*b*x^2*sqrt(Pi)/c-1/16*b*c*x^4*sqrt(Pi)-1/16*(a+b*arcsinh(c*x))^2*sqrt(Pi)/(b*c^3)+1/8*x*(a+b*arcsinh(c*x))*sqrt(Pi)*sqrt(1+c^2*x^2)/c^2+1/4*x^3*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[x*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2),x,2,1/3*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))/(c^2*Pi)-1/3*b*x*sqrt(Pi)/c-1/9*b*c*x^3*sqrt(Pi)],
[(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2),x,3,-1/4*b*c*x^2*sqrt(Pi)+1/4*(a+b*arcsinh(c*x))^2*sqrt(Pi)/(b*c)+1/2*x*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)/x,x,8,-b*c*x*sqrt(Pi)-2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))*sqrt(Pi)-b*polylog(2,-exp(arcsinh(c*x)))*sqrt(Pi)+b*polylog(2,exp(arcsinh(c*x)))*sqrt(Pi)+(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)/x^2,x,3,1/2*c*(a+b*arcsinh(c*x))^2*sqrt(Pi)/b+b*c*log(x)*sqrt(Pi)-(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)/x],
[(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)/x^3,x,8,-1/2*b*c*sqrt(Pi)/x-c^2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))*sqrt(Pi)-1/2*b*c^2*polylog(2,-exp(arcsinh(c*x)))*sqrt(Pi)+1/2*b*c^2*polylog(2,exp(arcsinh(c*x)))*sqrt(Pi)-1/2*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)/x^2],
[(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)/x^4,x,3,-1/3*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))/(Pi*x^3)-1/6*b*c*sqrt(Pi)/x^2+1/3*b*c^3*log(x)*sqrt(Pi)],
[x^3*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x)),x,4,2/35*b*Pi^(3/2)*x/c^3-1/105*b*Pi^(3/2)*x^3/c-8/175*b*c*Pi^(3/2)*x^5-1/49*b*c^3*Pi^(3/2)*x^7-1/5*(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))/(c^4*Pi)+1/7*(Pi+c^2*Pi*x^2)^(7/2)*(a+b*arcsinh(c*x))/(c^4*Pi^2)],
[x^2*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x)),x,8,-1/32*b*Pi^(3/2)*x^2/c-7/96*b*c*Pi^(3/2)*x^4-1/36*b*c^3*Pi^(3/2)*x^6+1/6*x^3*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))-1/32*Pi^(3/2)*(a+b*arcsinh(c*x))^2/(b*c^3)+1/16*Pi^(3/2)*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^2+1/8*Pi*x^3*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[x*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x)),x,3,-1/5*b*Pi^(3/2)*x/c-2/15*b*c*Pi^(3/2)*x^3-1/25*b*c^3*Pi^(3/2)*x^5+1/5*(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))/(c^2*Pi)],
[(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x)),x,6,-5/16*b*c*Pi^(3/2)*x^2-1/16*b*c^3*Pi^(3/2)*x^4+1/4*x*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))+3/16*Pi^(3/2)*(a+b*arcsinh(c*x))^2/(b*c)+3/8*Pi*x*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))/x,x,10,-4/3*b*c*Pi^(3/2)*x-1/9*b*c^3*Pi^(3/2)*x^3+1/3*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))-2*Pi^(3/2)*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))-b*Pi^(3/2)*polylog(2,-exp(arcsinh(c*x)))+b*Pi^(3/2)*polylog(2,exp(arcsinh(c*x)))+Pi*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))/x^2,x,6,-1/4*b*c^3*Pi^(3/2)*x^2-(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))/x+3/4*c*Pi^(3/2)*(a+b*arcsinh(c*x))^2/b+b*c*Pi^(3/2)*log(x)+3/2*c^2*Pi*x*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))/x^3,x,11,-1/2*b*c*Pi^(3/2)/x-b*c^3*Pi^(3/2)*x-1/2*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))/x^2-3*c^2*Pi^(3/2)*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))-3/2*b*c^2*Pi^(3/2)*polylog(2,-exp(arcsinh(c*x)))+3/2*b*c^2*Pi^(3/2)*polylog(2,exp(arcsinh(c*x)))+3/2*c^2*Pi*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))/x^4,x,6,-1/6*b*c*Pi^(3/2)/x^2-1/3*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))/x^3+1/2*c^3*Pi^(3/2)*(a+b*arcsinh(c*x))^2/b+4/3*b*c^3*Pi^(3/2)*log(x)-c^2*Pi*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)/x],
[x^3*(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x)),x,4,2/63*b*Pi^(5/2)*x/c^3-1/189*b*Pi^(5/2)*x^3/c-1/21*b*c*Pi^(5/2)*x^5-19/441*b*c^3*Pi^(5/2)*x^7-1/81*b*c^5*Pi^(5/2)*x^9-1/7*(Pi+c^2*Pi*x^2)^(7/2)*(a+b*arcsinh(c*x))/(c^4*Pi)+1/9*(Pi+c^2*Pi*x^2)^(9/2)*(a+b*arcsinh(c*x))/(c^4*Pi^2)],
[x^2*(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x)),x,12,-5/256*b*Pi^(5/2)*x^2/c-59/768*b*c*Pi^(5/2)*x^4-17/288*b*c^3*Pi^(5/2)*x^6-1/64*b*c^5*Pi^(5/2)*x^8+5/48*Pi*x^3*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))+1/8*x^3*(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))-5/256*Pi^(5/2)*(a+b*arcsinh(c*x))^2/(b*c^3)+5/128*Pi^(5/2)*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^2+5/64*Pi^2*x^3*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[x*(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x)),x,3,-1/7*b*Pi^(5/2)*x/c-1/7*b*c*Pi^(5/2)*x^3-3/35*b*c^3*Pi^(5/2)*x^5-1/49*b*c^5*Pi^(5/2)*x^7+1/7*(Pi+c^2*Pi*x^2)^(7/2)*(a+b*arcsinh(c*x))/(c^2*Pi)],
[(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x)),x,8,-25/96*b*c*Pi^(5/2)*x^2-5/96*b*c^3*Pi^(5/2)*x^4-1/36*b*Pi^(5/2)*(1+c^2*x^2)^3/c+5/24*Pi*x*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))+1/6*x*(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))+5/32*Pi^(5/2)*(a+b*arcsinh(c*x))^2/(b*c)+5/16*Pi^2*x*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))/x,x,13,-23/15*b*c*Pi^(5/2)*x-11/45*b*c^3*Pi^(5/2)*x^3-1/25*b*c^5*Pi^(5/2)*x^5+1/3*Pi*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))+1/5*(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))-2*Pi^(5/2)*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))-b*Pi^(5/2)*polylog(2,-exp(arcsinh(c*x)))+b*Pi^(5/2)*polylog(2,exp(arcsinh(c*x)))+Pi^2*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))/x^2,x,10,-9/16*b*c^3*Pi^(5/2)*x^2-1/16*b*c^5*Pi^(5/2)*x^4+5/4*c^2*Pi*x*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))-(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))/x+15/16*c*Pi^(5/2)*(a+b*arcsinh(c*x))^2/b+b*c*Pi^(5/2)*log(x)+15/8*c^2*Pi^2*x*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))/x^3,x,13,-1/2*b*c*Pi^(5/2)/x-7/3*b*c^3*Pi^(5/2)*x-1/9*b*c^5*Pi^(5/2)*x^3+5/6*c^2*Pi*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))-1/2*(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))/x^2-5*c^2*Pi^(5/2)*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))-5/2*b*c^2*Pi^(5/2)*polylog(2,-exp(arcsinh(c*x)))+5/2*b*c^2*Pi^(5/2)*polylog(2,exp(arcsinh(c*x)))+5/2*c^2*Pi^2*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))/x^4,x,10,-1/6*b*c*Pi^(5/2)/x^2-1/4*b*c^5*Pi^(5/2)*x^2-5/3*c^2*Pi*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))/x-1/3*(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))/x^3+5/4*c^3*Pi^(5/2)*(a+b*arcsinh(c*x))^2/b+7/3*b*c^3*Pi^(5/2)*log(x)+5/2*c^4*Pi^2*x*(a+b*arcsinh(c*x))*sqrt(Pi+c^2*Pi*x^2)],
[arcsinh(x)*sqrt(1+x^2),x,3,-1/4*x^2+1/4*arcsinh(x)^2+1/2*x*arcsinh(x)*sqrt(1+x^2)],

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

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

# p>0
[x^3*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2),x,3,-1/3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))/(c^4*d)+1/5*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))/(c^4*d^2)+2/15*b*x*sqrt(d+c^2*d*x^2)/(c^3*sqrt(1+c^2*x^2))-1/45*b*x^3*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-1/25*b*c*x^5*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[x^2*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2),x,5,1/8*x*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/c^2+1/4*x^3*(a+b*arcsinh(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^2*x^2))-1/16*b*c*x^4*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/16*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(b*c^3*sqrt(1+c^2*x^2))],
[x*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2),x,2,1/3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))/(c^2*d)-1/3*b*x*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-1/9*b*c*x^3*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2),x,3,1/2*x*(a+b*arcsinh(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^2*x^2)+1/4*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(b*c*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/x,x,8,(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)-b*c*x*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-b*polylog(2,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+b*polylog(2,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/x^2,x,3,-(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/x+1/2*c*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(b*sqrt(1+c^2*x^2))+b*c*log(x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/x^3,x,8,-1/2*(a+b*arcsinh(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^2*x^2))-c^2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/2*b*c^2*polylog(2,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+1/2*b*c^2*polylog(2,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/x^4,x,3,-1/3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))/(d*x^3)-1/6*b*c*sqrt(d+c^2*d*x^2)/(x^2*sqrt(1+c^2*x^2))+1/3*b*c^3*log(x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[x^3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x)),x,4,-1/5*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))/(c^4*d)+1/7*(d+c^2*d*x^2)^(7/2)*(a+b*arcsinh(c*x))/(c^4*d^2)+2/35*b*d*x*sqrt(d+c^2*d*x^2)/(c^3*sqrt(1+c^2*x^2))-1/105*b*d*x^3*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-8/175*b*c*d*x^5*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/49*b*c^3*d*x^7*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[x^2*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x)),x,8,1/6*x^3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))+1/16*d*x*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/c^2+1/8*d*x^3*(a+b*arcsinh(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^2*x^2))-7/96*b*c*d*x^4*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/36*b*c^3*d*x^6*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/32*d*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(b*c^3*sqrt(1+c^2*x^2))],
[x*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x)),x,3,1/5*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))/(c^2*d)-1/5*b*d*x*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-2/15*b*c*d*x^3*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/25*b*c^3*d*x^5*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x)),x,6,1/4*x*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))+3/8*d*x*(a+b*arcsinh(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^2*x^2)-1/16*b*c^3*d*x^4*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+3/16*d*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(b*c*sqrt(1+c^2*x^2))],
[(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))/x,x,10,1/3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))+d*(a+b*arcsinh(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^2*x^2)-1/9*b*c^3*d*x^3*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2*d*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-b*d*polylog(2,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+b*d*polylog(2,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))/x^2,x,6,-(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))/x+3/2*c^2*d*x*(a+b*arcsinh(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^2*x^2)+3/4*c*d*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(b*sqrt(1+c^2*x^2))+b*c*d*log(x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))/x^3,x,11,-1/2*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))/x^2+3/2*c^2*d*(a+b*arcsinh(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^2*x^2))-b*c^3*d*x*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-3*c^2*d*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-3/2*b*c^2*d*polylog(2,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+3/2*b*c^2*d*polylog(2,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))/x^4,x,6,-1/3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))/x^3-c^2*d*(a+b*arcsinh(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^2*x^2))+1/2*c^3*d*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(b*sqrt(1+c^2*x^2))+4/3*b*c^3*d*log(x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[x^3*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x)),x,4,-1/7*(d+c^2*d*x^2)^(7/2)*(a+b*arcsinh(c*x))/(c^4*d)+1/9*(d+c^2*d*x^2)^(9/2)*(a+b*arcsinh(c*x))/(c^4*d^2)+2/63*b*d^2*x*sqrt(d+c^2*d*x^2)/(c^3*sqrt(1+c^2*x^2))-1/189*b*d^2*x^3*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-1/21*b*c*d^2*x^5*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-19/441*b*c^3*d^2*x^7*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/81*b*c^5*d^2*x^9*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[x^2*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x)),x,12,5/48*d*x^3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))+1/8*x^3*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))+5/128*d^2*x*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/c^2+5/64*d^2*x^3*(a+b*arcsinh(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^2*x^2))-59/768*b*c*d^2*x^4*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-17/288*b*c^3*d^2*x^6*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/64*b*c^5*d^2*x^8*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-5/256*d^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(b*c^3*sqrt(1+c^2*x^2))],
[x*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x)),x,3,1/7*(d+c^2*d*x^2)^(7/2)*(a+b*arcsinh(c*x))/(c^2*d)-1/7*b*d^2*x*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-1/7*b*c*d^2*x^3*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-3/35*b*c^3*d^2*x^5*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/49*b*c^5*d^2*x^7*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x)),x,8,5/24*d*x*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))+1/6*x*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))-1/36*b*d^2*(1+c^2*x^2)^(5/2)*sqrt(d+c^2*d*x^2)/c+5/16*d^2*x*(a+b*arcsinh(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^2*x^2)-5/96*b*c^3*d^2*x^4*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+5/32*d^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(b*c*sqrt(1+c^2*x^2))],
[(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))/x,x,13,1/3*d*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))+1/5*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))+d^2*(a+b*arcsinh(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^2*x^2)-11/45*b*c^3*d^2*x^3*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/25*b*c^5*d^2*x^5*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2*d^2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-b*d^2*polylog(2,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+b*d^2*polylog(2,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))/x^2,x,10,5/4*c^2*d*x*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))-(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))/x+15/8*c^2*d^2*x*(a+b*arcsinh(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^2*x^2)-1/16*b*c^5*d^2*x^4*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+15/16*c*d^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(b*sqrt(1+c^2*x^2))+b*c*d^2*log(x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))/x^3,x,13,5/6*c^2*d*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))-1/2*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))/x^2+5/2*c^2*d^2*(a+b*arcsinh(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^2*x^2))-7/3*b*c^3*d^2*x*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/9*b*c^5*d^2*x^3*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-5*c^2*d^2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-5/2*b*c^2*d^2*polylog(2,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+5/2*b*c^2*d^2*polylog(2,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))/x^4,x,10,-5/3*c^2*d*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))/x-1/3*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))/x^3+5/2*c^4*d^2*x*(a+b*arcsinh(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^2*x^2))-1/4*b*c^5*d^2*x^2*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+5/4*c^3*d^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(b*sqrt(1+c^2*x^2))+7/3*b*c^3*d^2*log(x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[arcsinh(x)*sqrt(1+x^2),x,3,-1/4*x^2+1/4*arcsinh(x)^2+1/2*x*arcsinh(x)*sqrt(1+x^2)],

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

# Integrands of the form (f x)^m (d+c^2 d x^2)^p (a+b ArcSinh[c x]) and m symbolic
[x^m*(d+c^2*d*x^2)^3*(a+b*arcsinh(c*x)),x,6,d^3*x^(1+m)*(a+b*arcsinh(c*x))/(1+m)+3*c^2*d^3*x^(3+m)*(a+b*arcsinh(c*x))/(3+m)+3*c^4*d^3*x^(5+m)*(a+b*arcsinh(c*x))/(5+m)+c^6*d^3*x^(7+m)*(a+b*arcsinh(c*x))/(7+m)-3*b*c*d^3*(2161+1813*m+455*m^2+35*m^3)*x^(2+m)*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],-c^2*x^2)/((2+3*m+m^2)*(105+71*m+15*m^2+m^3)^2)-b*c*d^3*(2271+1329*m+284*m^2+27*m^3+m^4)*x^(2+m)*sqrt(1+c^2*x^2)/((7+m)^2*(15+8*m+m^2)^2)-b*c^3*d^3*(9+m)*(13+2*m)*x^(4+m)*sqrt(1+c^2*x^2)/((5+m)^2*(7+m)^2)-b*c^5*d^3*x^(6+m)*sqrt(1+c^2*x^2)/(7+m)^2],
[x^m*(d+c^2*d*x^2)^2*(a+b*arcsinh(c*x)),x,5,d^2*x^(1+m)*(a+b*arcsinh(c*x))/(1+m)+2*c^2*d^2*x^(3+m)*(a+b*arcsinh(c*x))/(3+m)+c^4*d^2*x^(5+m)*(a+b*arcsinh(c*x))/(5+m)-b*c*d^2*(149+100*m+15*m^2)*x^(2+m)*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],-c^2*x^2)/((2+3*m+m^2)*(15+8*m+m^2)^2)-b*c*d^2*(38+13*m+m^2)*x^(2+m)*sqrt(1+c^2*x^2)/((3+m)^2*(5+m)^2)-b*c^3*d^2*x^(4+m)*sqrt(1+c^2*x^2)/(5+m)^2],
[x^m*(d+c^2*d*x^2)*(a+b*arcsinh(c*x)),x,4,d*x^(1+m)*(a+b*arcsinh(c*x))/(1+m)+c^2*d*x^(3+m)*(a+b*arcsinh(c*x))/(3+m)-b*c*d*(7+3*m)*x^(2+m)*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],-c^2*x^2)/((3+m)^2*(2+3*m+m^2))-b*c*d*x^(2+m)*sqrt(1+c^2*x^2)/(3+m)^2],
[x^m*(a+b*arcsinh(c*x))/(d+c^2*d*x^2),x,0,Unintegrable(x^m*(a+b*arcsinh(c*x))/(d+c^2*d*x^2),x)],
[x^m*(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^2,x,2,1/2*x^(1+m)*(a+b*arcsinh(c*x))/(d^2*(1+c^2*x^2))-1/2*b*c*x^(2+m)*hypergeom([3/2,1/2*(2+m)],[1/2*(4+m)],-c^2*x^2)/(d^2*(2+m))+1/2*(1-m)*Unintegrable(x^m*(a+b*arcsinh(c*x))/(d+c^2*d*x^2),x)/d],
[x^m*(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^3,x,4,1/4*x^(1+m)*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2)^2)+1/8*(3-m)*x^(1+m)*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2))-1/8*b*c*(3-m)*x^(2+m)*hypergeom([3/2,1/2*(2+m)],[1/2*(4+m)],-c^2*x^2)/(d^3*(2+m))-1/4*b*c*x^(2+m)*hypergeom([5/2,1/2*(2+m)],[1/2*(4+m)],-c^2*x^2)/(d^3*(2+m))+1/8*(1-m)*(3-m)*Unintegrable(x^m*(a+b*arcsinh(c*x))/(d+c^2*d*x^2),x)/d^2],
[x^m*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x)),x,9,5*d*x^(1+m)*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))/((4+m)*(6+m))+x^(1+m)*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))/(6+m)+15*d^2*x^(1+m)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/((6+m)*(8+6*m+m^2))-15*b*c*d^2*x^(2+m)*sqrt(d+c^2*d*x^2)/((2+m)^2*(4+m)*(6+m)*sqrt(1+c^2*x^2))-5*b*c*d^2*x^(2+m)*sqrt(d+c^2*d*x^2)/((6+m)*(8+6*m+m^2)*sqrt(1+c^2*x^2))-b*c*d^2*x^(2+m)*sqrt(d+c^2*d*x^2)/((12+8*m+m^2)*sqrt(1+c^2*x^2))-5*b*c^3*d^2*x^(4+m)*sqrt(d+c^2*d*x^2)/((4+m)^2*(6+m)*sqrt(1+c^2*x^2))-2*b*c^3*d^2*x^(4+m)*sqrt(d+c^2*d*x^2)/((4+m)*(6+m)*sqrt(1+c^2*x^2))-b*c^5*d^2*x^(6+m)*sqrt(d+c^2*d*x^2)/((6+m)^2*sqrt(1+c^2*x^2))+15*d^2*x^(1+m)*(a+b*arcsinh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],-c^2*x^2)*sqrt(d+c^2*d*x^2)/((6+m)*(8+14*m+7*m^2+m^3)*sqrt(1+c^2*x^2))-15*b*c*d^2*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)/((2+m)^2*(6+m)*(4+5*m+m^2)*sqrt(1+c^2*x^2))],
[x^m*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x)),x,6,x^(1+m)*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))/(4+m)+3*d*x^(1+m)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(8+6*m+m^2)-3*b*c*d*x^(2+m)*sqrt(d+c^2*d*x^2)/((2+m)^2*(4+m)*sqrt(1+c^2*x^2))-b*c*d*x^(2+m)*sqrt(d+c^2*d*x^2)/((8+6*m+m^2)*sqrt(1+c^2*x^2))-b*c^3*d*x^(4+m)*sqrt(d+c^2*d*x^2)/((4+m)^2*sqrt(1+c^2*x^2))+3*d*x^(1+m)*(a+b*arcsinh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],-c^2*x^2)*sqrt(d+c^2*d*x^2)/((8+14*m+7*m^2+m^3)*sqrt(1+c^2*x^2))-3*b*c*d*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)/((2+m)^2*(4+5*m+m^2)*sqrt(1+c^2*x^2))],
[x^m*(d+c^2*d*x^2)^(1/2)*(a+b*arcsinh(c*x)),x,3,x^(1+m)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(2+m)-b*c*x^(2+m)*sqrt(d+c^2*d*x^2)/((2+m)^2*sqrt(1+c^2*x^2))+x^(1+m)*(a+b*arcsinh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],-c^2*x^2)*sqrt(d+c^2*d*x^2)/((2+3*m+m^2)*sqrt(1+c^2*x^2))-b*c*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)/((1+m)*(2+m)^2*sqrt(1+c^2*x^2))],
[x^m*(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^(1/2),x,1,x^(1+m)*(a+b*arcsinh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],-c^2*x^2)*sqrt(1+c^2*x^2)/((1+m)*sqrt(d+c^2*d*x^2))-b*c*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^2*x^2)/((2+3*m+m^2)*sqrt(d+c^2*d*x^2))],
[x^m*(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^(3/2),x,3,x^(1+m)*(a+b*arcsinh(c*x))/(d*sqrt(d+c^2*d*x^2))-m*x^(1+m)*(a+b*arcsinh(c*x))*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],-c^2*x^2)*sqrt(1+c^2*x^2)/(d*(1+m)*sqrt(d+c^2*d*x^2))-b*c*x^(2+m)*hypergeom([1,1/2*(2+m)],[1/2*(4+m)],-c^2*x^2)*sqrt(1+c^2*x^2)/(d*(2+m)*sqrt(d+c^2*d*x^2))+b*c*m*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^2*x^2)/(d*(2+3*m+m^2)*sqrt(d+c^2*d*x^2))],
[x^m*(a+b*arcsinh(c*x))/(d+c^2*d*x^2)^(5/2),x,5,1/3*x^(1+m)*(a+b*arcsinh(c*x))/(d*(d+c^2*d*x^2)^(3/2))+1/3*(2-m)*x^(1+m)*(a+b*arcsinh(c*x))/(d^2*sqrt(d+c^2*d*x^2))-1/3*(2-m)*m*x^(1+m)*(a+b*arcsinh(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*(1+m)*sqrt(d+c^2*d*x^2))-1/3*b*c*(2-m)*x^(2+m)*hypergeom([1,1/2*(2+m)],[1/2*(4+m)],-c^2*x^2)*sqrt(1+c^2*x^2)/(d^2*(2+m)*sqrt(d+c^2*d*x^2))-1/3*b*c*x^(2+m)*hypergeom([2,1/2*(2+m)],[1/2*(4+m)],-c^2*x^2)*sqrt(1+c^2*x^2)/(d^2*(2+m)*sqrt(d+c^2*d*x^2))+1/3*b*c*(2-m)*m*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^2*x^2)/(d^2*(2+3*m+m^2)*sqrt(d+c^2*d*x^2))],
[x^m*arcsinh(a*x)/sqrt(1+a^2*x^2),x,1,x^(1+m)*arcsinh(a*x)*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],-a^2*x^2)/(1+m)-a*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)/(2+3*m+m^2)],

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

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

# p>0
[x^4*(d+c^2*d*x^2)*(a+b*arcsinh(c*x))^2,x,11,304/3675*b^2*d*x/c^4-152/11025*b^2*d*x^3/c^2+38/6125*b^2*d*x^5+2/343*b^2*c^2*d*x^7-2/21*b*d*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/c^5+4/35*b*d*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))/c^5-2/49*b*d*(1+c^2*x^2)^(7/2)*(a+b*arcsinh(c*x))/c^5+2/35*d*x^5*(a+b*arcsinh(c*x))^2+1/7*d*x^5*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2-32/525*b*d*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^5+16/525*b*d*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-4/175*b*d*x^4*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[x^3*(d+c^2*d*x^2)*(a+b*arcsinh(c*x))^2,x,14,-1/24*b^2*d*x^2/c^2+1/72*b^2*d*x^4+1/108*b^2*c^2*d*x^6-1/24*d*(a+b*arcsinh(c*x))^2/c^4+1/12*d*x^4*(a+b*arcsinh(c*x))^2+1/6*d*x^4*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+1/12*b*d*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-1/18*b*d*x^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c-1/18*b*c*d*x^5*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)],
[x^2*(d+c^2*d*x^2)*(a+b*arcsinh(c*x))^2,x,9,-52/225*b^2*d*x/c^2+26/675*b^2*d*x^3+2/125*b^2*c^2*d*x^5+2/15*b*d*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/c^3-2/25*b*d*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))/c^3+2/15*d*x^3*(a+b*arcsinh(c*x))^2+1/5*d*x^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+8/45*b*d*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-4/45*b*d*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[x*(d+c^2*d*x^2)*(a+b*arcsinh(c*x))^2,x,7,5/32*b^2*d*x^2+1/32*b^2*c^2*d*x^4-1/8*b*d*x*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/c-3/32*d*(a+b*arcsinh(c*x))^2/c^2+1/4*d*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/c^2-3/16*b*d*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(d+c^2*d*x^2)*(a+b*arcsinh(c*x))^2,x,6,14/9*b^2*d*x+2/27*b^2*c^2*d*x^3-2/9*b*d*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/c+2/3*d*x*(a+b*arcsinh(c*x))^2+1/3*d*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2-4/3*b*d*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(d+c^2*d*x^2)*(a+b*arcsinh(c*x))^2/x,x,10,1/4*b^2*c^2*d*x^2-1/4*d*(a+b*arcsinh(c*x))^2+1/2*d*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+1/3*d*(a+b*arcsinh(c*x))^3/b+d*(a+b*arcsinh(c*x))^2*log(1+(-1)/exp(2*arcsinh(c*x)))-b*d*(a+b*arcsinh(c*x))*polylog(2,exp(-2*arcsinh(c*x)))-1/2*b^2*d*polylog(3,exp(-2*arcsinh(c*x)))-1/2*b*c*d*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)*(a+b*arcsinh(c*x))^2/x^2,x,12,2*b^2*c^2*d*x+2*c^2*d*x*(a+b*arcsinh(c*x))^2-d*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/x-4*b*c*d*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))-2*b^2*c*d*polylog(2,-exp(arcsinh(c*x)))+2*b^2*c*d*polylog(2,exp(arcsinh(c*x)))-2*b*c*d*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)*(a+b*arcsinh(c*x))^2/x^3,x,10,1/2*c^2*d*(a+b*arcsinh(c*x))^2-1/2*d*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/x^2+1/3*c^2*d*(a+b*arcsinh(c*x))^3/b+c^2*d*(a+b*arcsinh(c*x))^2*log(1+(-1)/exp(2*arcsinh(c*x)))+b^2*c^2*d*log(x)-b*c^2*d*(a+b*arcsinh(c*x))*polylog(2,exp(-2*arcsinh(c*x)))-1/2*b^2*c^2*d*polylog(3,exp(-2*arcsinh(c*x)))-b*c*d*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/x],
[(d+c^2*d*x^2)*(a+b*arcsinh(c*x))^2/x^4,x,16,-1/3*b^2*c^2*d/x-2/3*c^2*d*(a+b*arcsinh(c*x))^2/x-1/3*d*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/x^3-10/3*b*c^3*d*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))-5/3*b^2*c^3*d*polylog(2,-exp(arcsinh(c*x)))+5/3*b^2*c^3*d*polylog(2,exp(arcsinh(c*x)))-1/3*b*c*d*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/x^2],
[x^4*(d+c^2*d*x^2)^2*(a+b*arcsinh(c*x))^2,x,16,4208/99225*b^2*d^2*x/c^4-2104/297675*b^2*d^2*x^3/c^2+526/165375*b^2*d^2*x^5+212/27783*b^2*c^2*d^2*x^7+2/729*b^2*c^4*d^2*x^9-8/189*b*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/c^5+2/315*b*d^2*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))/c^5+20/441*b*d^2*(1+c^2*x^2)^(7/2)*(a+b*arcsinh(c*x))/c^5-2/81*b*d^2*(1+c^2*x^2)^(9/2)*(a+b*arcsinh(c*x))/c^5+8/315*d^2*x^5*(a+b*arcsinh(c*x))^2+4/63*d^2*x^5*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+1/9*d^2*x^5*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2-128/4725*b*d^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^5+64/4725*b*d^2*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-16/1575*b*d^2*x^4*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[x^3*(d+c^2*d*x^2)^2*(a+b*arcsinh(c*x))^2,x,25,-73/3072*b^2*d^2*x^2/c^2+73/9216*b^2*d^2*x^4+43/3456*b^2*c^2*d^2*x^6+1/256*b^2*c^4*d^2*x^8-1/32*b*c*d^2*x^5*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))-73/3072*d^2*(a+b*arcsinh(c*x))^2/c^4+1/24*d^2*x^4*(a+b*arcsinh(c*x))^2+1/12*d^2*x^4*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+1/8*d^2*x^4*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+73/1536*b*d^2*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-73/2304*b*d^2*x^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c-25/576*b*c*d^2*x^5*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)],
[x^2*(d+c^2*d*x^2)^2*(a+b*arcsinh(c*x))^2,x,14,-1636/11025*b^2*d^2*x/c^2+818/33075*b^2*d^2*x^3+136/6125*b^2*c^2*d^2*x^5+2/343*b^2*c^4*d^2*x^7+8/105*b*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/c^3+2/175*b*d^2*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))/c^3-2/49*b*d^2*(1+c^2*x^2)^(7/2)*(a+b*arcsinh(c*x))/c^3+8/105*d^2*x^3*(a+b*arcsinh(c*x))^2+4/35*d^2*x^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+1/7*d^2*x^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+32/315*b*d^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-16/315*b*d^2*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[x*(d+c^2*d*x^2)^2*(a+b*arcsinh(c*x))^2,x,9,25/288*b^2*d^2*x^2+5/288*b^2*c^2*d^2*x^4+1/108*b^2*d^2*(1+c^2*x^2)^3/c^2-5/72*b*d^2*x*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/c-1/18*b*d^2*x*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))/c-5/96*d^2*(a+b*arcsinh(c*x))^2/c^2+1/6*d^2*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2/c^2-5/48*b*d^2*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(d+c^2*d*x^2)^2*(a+b*arcsinh(c*x))^2,x,10,298/225*b^2*d^2*x+76/675*b^2*c^2*d^2*x^3+2/125*b^2*c^4*d^2*x^5-8/45*b*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/c-2/25*b*d^2*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))/c+8/15*d^2*x*(a+b*arcsinh(c*x))^2+4/15*d^2*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+1/5*d^2*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2-16/15*b*d^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(d+c^2*d*x^2)^2*(a+b*arcsinh(c*x))^2/x,x,17,13/32*b^2*c^2*d^2*x^2+1/32*b^2*c^4*d^2*x^4-1/8*b*c*d^2*x*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))-11/32*d^2*(a+b*arcsinh(c*x))^2+1/2*d^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+1/4*d^2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+1/3*d^2*(a+b*arcsinh(c*x))^3/b+d^2*(a+b*arcsinh(c*x))^2*log(1+(-1)/exp(2*arcsinh(c*x)))-b*d^2*(a+b*arcsinh(c*x))*polylog(2,exp(-2*arcsinh(c*x)))-1/2*b^2*d^2*polylog(3,exp(-2*arcsinh(c*x)))-11/16*b*c*d^2*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^2*(a+b*arcsinh(c*x))^2/x^2,x,17,32/9*b^2*c^2*d^2*x+2/27*b^2*c^4*d^2*x^3-2/9*b*c*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))+8/3*c^2*d^2*x*(a+b*arcsinh(c*x))^2+4/3*c^2*d^2*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2-d^2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/x-4*b*c*d^2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))-2*b^2*c*d^2*polylog(2,-exp(arcsinh(c*x)))+2*b^2*c*d^2*polylog(2,exp(arcsinh(c*x)))-10/3*b*c*d^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^2*(a+b*arcsinh(c*x))^2/x^3,x,17,1/4*b^2*c^4*d^2*x^2-b*c*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/x+1/4*c^2*d^2*(a+b*arcsinh(c*x))^2+c^2*d^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2-1/2*d^2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/x^2+2/3*c^2*d^2*(a+b*arcsinh(c*x))^3/b+2*c^2*d^2*(a+b*arcsinh(c*x))^2*log(1+(-1)/exp(2*arcsinh(c*x)))+b^2*c^2*d^2*log(x)-2*b*c^2*d^2*(a+b*arcsinh(c*x))*polylog(2,exp(-2*arcsinh(c*x)))-b^2*c^2*d^2*polylog(3,exp(-2*arcsinh(c*x)))+1/2*b*c^3*d^2*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^2*(a+b*arcsinh(c*x))^2/x^4,x,24,-1/3*b^2*c^2*d^2/x+2*b^2*c^4*d^2*x-1/3*b*c*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/x^2+8/3*c^4*d^2*x*(a+b*arcsinh(c*x))^2-4/3*c^2*d^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/x-1/3*d^2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/x^3-22/3*b*c^3*d^2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))-11/3*b^2*c^3*d^2*polylog(2,-exp(arcsinh(c*x)))+11/3*b^2*c^3*d^2*polylog(2,exp(arcsinh(c*x)))-5/3*b*c^3*d^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)],
[x^4*(d+c^2*d*x^2)^3*(a+b*arcsinh(c*x))^2,x,21,100976/4002075*b^2*d^3*x/c^4-50488/12006225*b^2*d^3*x^3/c^2+12622/6670125*b^2*d^3*x^5+9410/1120581*b^2*c^2*d^3*x^7+182/29403*b^2*c^4*d^3*x^9+2/1331*b^2*c^6*d^3*x^11-16/693*b*d^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/c^5+4/1155*b*d^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))/c^5-2/1617*b*d^3*(1+c^2*x^2)^(7/2)*(a+b*arcsinh(c*x))/c^5+8/297*b*d^3*(1+c^2*x^2)^(9/2)*(a+b*arcsinh(c*x))/c^5-2/121*b*d^3*(1+c^2*x^2)^(11/2)*(a+b*arcsinh(c*x))/c^5+16/1155*d^3*x^5*(a+b*arcsinh(c*x))^2+8/231*d^3*x^5*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+2/33*d^3*x^5*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+1/11*d^3*x^5*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2-256/17325*b*d^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^5+128/17325*b*d^3*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-32/5775*b*d^3*x^4*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[x^3*(d+c^2*d*x^2)^3*(a+b*arcsinh(c*x))^2,x,40,-79/5120*b^2*d^3*x^2/c^2+79/15360*b^2*d^3*x^4+401/28800*b^2*c^2*d^3*x^6+57/6400*b^2*c^4*d^3*x^8+1/500*b^2*c^6*d^3*x^10-1/32*b*c*d^3*x^5*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))-1/50*b*c*d^3*x^5*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))-79/5120*d^3*(a+b*arcsinh(c*x))^2/c^4+1/40*d^3*x^4*(a+b*arcsinh(c*x))^2+1/20*d^3*x^4*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+3/40*d^3*x^4*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+1/10*d^3*x^4*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2+79/2560*b*d^3*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-79/3840*b*d^3*x^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c-31/960*b*c*d^3*x^5*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)],
[x^2*(d+c^2*d*x^2)^3*(a+b*arcsinh(c*x))^2,x,19,-10516/99225*b^2*d^3*x/c^2+5258/297675*b^2*d^3*x^3+4198/165375*b^2*c^2*d^3*x^5+374/27783*b^2*c^4*d^3*x^7+2/729*b^2*c^6*d^3*x^9+16/315*b*d^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/c^3+4/525*b*d^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))/c^3+2/441*b*d^3*(1+c^2*x^2)^(7/2)*(a+b*arcsinh(c*x))/c^3-2/81*b*d^3*(1+c^2*x^2)^(9/2)*(a+b*arcsinh(c*x))/c^3+16/315*d^3*x^3*(a+b*arcsinh(c*x))^2+8/105*d^3*x^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+2/21*d^3*x^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+1/9*d^3*x^3*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2+64/945*b*d^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-32/945*b*d^3*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[x*(d+c^2*d*x^2)^3*(a+b*arcsinh(c*x))^2,x,11,175/3072*b^2*d^3*x^2+35/3072*b^2*c^2*d^3*x^4+7/1152*b^2*d^3*(1+c^2*x^2)^3/c^2+1/256*b^2*d^3*(1+c^2*x^2)^4/c^2-35/768*b*d^3*x*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/c-7/192*b*d^3*x*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))/c-1/32*b*d^3*x*(1+c^2*x^2)^(7/2)*(a+b*arcsinh(c*x))/c-35/1024*d^3*(a+b*arcsinh(c*x))^2/c^2+1/8*d^3*(1+c^2*x^2)^4*(a+b*arcsinh(c*x))^2/c^2-35/512*b*d^3*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(d+c^2*d*x^2)^3*(a+b*arcsinh(c*x))^2,x,14,4322/3675*b^2*d^3*x+1514/11025*b^2*c^2*d^3*x^3+234/6125*b^2*c^4*d^3*x^5+2/343*b^2*c^6*d^3*x^7-16/105*b*d^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/c-12/175*b*d^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))/c-2/49*b*d^3*(1+c^2*x^2)^(7/2)*(a+b*arcsinh(c*x))/c+16/35*d^3*x*(a+b*arcsinh(c*x))^2+8/35*d^3*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+6/35*d^3*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+1/7*d^3*x*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2-32/35*b*d^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(d+c^2*d*x^2)^3*(a+b*arcsinh(c*x))^2/x,x,26,71/144*b^2*c^2*d^3*x^2+7/144*b^2*c^4*d^3*x^4+1/108*b^2*d^3*(1+c^2*x^2)^3-7/36*b*c*d^3*x*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))-1/18*b*c*d^3*x*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))-19/48*d^3*(a+b*arcsinh(c*x))^2+1/2*d^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+1/4*d^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+1/6*d^3*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2+1/3*d^3*(a+b*arcsinh(c*x))^3/b+d^3*(a+b*arcsinh(c*x))^2*log(1+(-1)/exp(2*arcsinh(c*x)))-b*d^3*(a+b*arcsinh(c*x))*polylog(2,exp(-2*arcsinh(c*x)))-1/2*b^2*d^3*polylog(3,exp(-2*arcsinh(c*x)))-19/24*b*c*d^3*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^3*(a+b*arcsinh(c*x))^2/x^2,x,24,122/25*b^2*c^2*d^3*x+14/75*b^2*c^4*d^3*x^3+2/125*b^2*c^6*d^3*x^5-2/5*b*c*d^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))-2/25*b*c*d^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))+16/5*c^2*d^3*x*(a+b*arcsinh(c*x))^2+8/5*c^2*d^3*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+6/5*c^2*d^3*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2-d^3*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2/x-4*b*c*d^3*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))-2*b^2*c*d^3*polylog(2,-exp(arcsinh(c*x)))+2*b^2*c*d^3*polylog(2,exp(arcsinh(c*x)))-22/5*b*c*d^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^3*(a+b*arcsinh(c*x))^2/x^3,x,28,21/32*b^2*c^4*d^3*x^2+1/32*b^2*c^6*d^3*x^4+7/8*b*c^3*d^3*x*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))-b*c*d^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))/x-3/32*c^2*d^3*(a+b*arcsinh(c*x))^2+3/2*c^2*d^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2+3/4*c^2*d^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2-1/2*d^3*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2/x^2+c^2*d^3*(a+b*arcsinh(c*x))^3/b+3*c^2*d^3*(a+b*arcsinh(c*x))^2*log(1+(-1)/exp(2*arcsinh(c*x)))+b^2*c^2*d^3*log(x)-3*b*c^2*d^3*(a+b*arcsinh(c*x))*polylog(2,exp(-2*arcsinh(c*x)))-3/2*b^2*c^2*d^3*polylog(3,exp(-2*arcsinh(c*x)))-3/16*b*c^3*d^3*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^3*(a+b*arcsinh(c*x))^2/x^4,x,31,-1/3*b^2*c^2*d^3/x+50/9*b^2*c^4*d^3*x+2/27*b^2*c^6*d^3*x^3+1/9*b*c^3*d^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))-1/3*b*c*d^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))/x^2+16/3*c^4*d^3*x*(a+b*arcsinh(c*x))^2+8/3*c^4*d^3*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2-2*c^2*d^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/x-1/3*d^3*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2/x^3-34/3*b*c^3*d^3*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))-17/3*b^2*c^3*d^3*polylog(2,-exp(arcsinh(c*x)))+17/3*b^2*c^3*d^3*polylog(2,exp(arcsinh(c*x)))-5*b*c^3*d^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)],

# p<0
[x^4*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2),x,16,-22/9*b^2*x/(c^4*d)+2/27*b^2*x^3/(c^2*d)-x*(a+b*arcsinh(c*x))^2/(c^4*d)+1/3*x^3*(a+b*arcsinh(c*x))^2/(c^2*d)+2*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/(c^5*d)-2*I*b*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/(c^5*d)+2*I*b*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/(c^5*d)+2*I*b^2*polylog(3,-I*exp(arcsinh(c*x)))/(c^5*d)-2*I*b^2*polylog(3,I*exp(arcsinh(c*x)))/(c^5*d)+22/9*b*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c^5*d)-2/9*b*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c^3*d)],
[x^3*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2),x,10,1/4*b^2*x^2/(c^2*d)+1/4*(a+b*arcsinh(c*x))^2/(c^4*d)+1/2*x^2*(a+b*arcsinh(c*x))^2/(c^2*d)+1/3*(a+b*arcsinh(c*x))^3/(b*c^4*d)-(a+b*arcsinh(c*x))^2*log(1+exp(2*arcsinh(c*x)))/(c^4*d)-b*(a+b*arcsinh(c*x))*polylog(2,-exp(2*arcsinh(c*x)))/(c^4*d)+1/2*b^2*polylog(3,-exp(2*arcsinh(c*x)))/(c^4*d)-1/2*b*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c^3*d)],
[x^2*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2),x,11,2*b^2*x/(c^2*d)+x*(a+b*arcsinh(c*x))^2/(c^2*d)-2*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/(c^3*d)+2*I*b*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/(c^3*d)-2*I*b*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/(c^3*d)-2*I*b^2*polylog(3,-I*exp(arcsinh(c*x)))/(c^3*d)+2*I*b^2*polylog(3,I*exp(arcsinh(c*x)))/(c^3*d)-2*b*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c^3*d)],
[x*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2),x,6,-1/3*(a+b*arcsinh(c*x))^3/(b*c^2*d)+(a+b*arcsinh(c*x))^2*log(1+exp(2*arcsinh(c*x)))/(c^2*d)+b*(a+b*arcsinh(c*x))*polylog(2,-exp(2*arcsinh(c*x)))/(c^2*d)-1/2*b^2*polylog(3,-exp(2*arcsinh(c*x)))/(c^2*d)],
[(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2),x,8,2*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/(c*d)-2*I*b*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/(c*d)+2*I*b*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/(c*d)+2*I*b^2*polylog(3,-I*exp(arcsinh(c*x)))/(c*d)-2*I*b^2*polylog(3,I*exp(arcsinh(c*x)))/(c*d)],
[(a+b*arcsinh(c*x))^2/(x*(d+c^2*d*x^2)),x,9,-2*(a+b*arcsinh(c*x))^2*arctanh(exp(2*arcsinh(c*x)))/d-b*(a+b*arcsinh(c*x))*polylog(2,-exp(2*arcsinh(c*x)))/d+b*(a+b*arcsinh(c*x))*polylog(2,exp(2*arcsinh(c*x)))/d+1/2*b^2*polylog(3,-exp(2*arcsinh(c*x)))/d-1/2*b^2*polylog(3,exp(2*arcsinh(c*x)))/d],
[(a+b*arcsinh(c*x))^2/(x^2*(d+c^2*d*x^2)),x,15,-(a+b*arcsinh(c*x))^2/(d*x)-2*c*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/d-4*b*c*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))/d-2*b^2*c*polylog(2,-exp(arcsinh(c*x)))/d+2*I*b*c*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/d-2*I*b*c*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/d+2*b^2*c*polylog(2,exp(arcsinh(c*x)))/d-2*I*b^2*c*polylog(3,-I*exp(arcsinh(c*x)))/d+2*I*b^2*c*polylog(3,I*exp(arcsinh(c*x)))/d],
[(a+b*arcsinh(c*x))^2/(x^3*(d+c^2*d*x^2)),x,12,-1/2*(a+b*arcsinh(c*x))^2/(d*x^2)+2*c^2*(a+b*arcsinh(c*x))^2*arctanh(exp(2*arcsinh(c*x)))/d+b^2*c^2*log(x)/d+b*c^2*(a+b*arcsinh(c*x))*polylog(2,-exp(2*arcsinh(c*x)))/d-b*c^2*(a+b*arcsinh(c*x))*polylog(2,exp(2*arcsinh(c*x)))/d-1/2*b^2*c^2*polylog(3,-exp(2*arcsinh(c*x)))/d+1/2*b^2*c^2*polylog(3,exp(2*arcsinh(c*x)))/d-b*c*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(d*x)],
[(a+b*arcsinh(c*x))^2/(x^4*(d+c^2*d*x^2)),x,24,-1/3*b^2*c^2/(d*x)-1/3*(a+b*arcsinh(c*x))^2/(d*x^3)+c^2*(a+b*arcsinh(c*x))^2/(d*x)+2*c^3*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/d+14/3*b*c^3*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))/d+7/3*b^2*c^3*polylog(2,-exp(arcsinh(c*x)))/d-2*I*b*c^3*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/d+2*I*b*c^3*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/d-7/3*b^2*c^3*polylog(2,exp(arcsinh(c*x)))/d+2*I*b^2*c^3*polylog(3,-I*exp(arcsinh(c*x)))/d-2*I*b^2*c^3*polylog(3,I*exp(arcsinh(c*x)))/d-1/3*b*c*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(d*x^2)],
[x^4*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^2,x,15,2*b^2*x/(c^4*d^2)+3/2*x*(a+b*arcsinh(c*x))^2/(c^4*d^2)-1/2*x^3*(a+b*arcsinh(c*x))^2/(c^2*d^2*(1+c^2*x^2))-3*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/(c^5*d^2)-b^2*arctan(c*x)/(c^5*d^2)+3*I*b*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/(c^5*d^2)-3*I*b*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/(c^5*d^2)-3*I*b^2*polylog(3,-I*exp(arcsinh(c*x)))/(c^5*d^2)+3*I*b^2*polylog(3,I*exp(arcsinh(c*x)))/(c^5*d^2)+b*(a+b*arcsinh(c*x))/(c^5*d^2*sqrt(1+c^2*x^2))-2*b*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c^5*d^2)],
[x^3*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^2,x,10,1/2*(a+b*arcsinh(c*x))^2/(c^4*d^2)-1/2*x^2*(a+b*arcsinh(c*x))^2/(c^2*d^2*(1+c^2*x^2))-1/3*(a+b*arcsinh(c*x))^3/(b*c^4*d^2)+(a+b*arcsinh(c*x))^2*log(1+exp(2*arcsinh(c*x)))/(c^4*d^2)+1/2*b^2*log(1+c^2*x^2)/(c^4*d^2)+b*(a+b*arcsinh(c*x))*polylog(2,-exp(2*arcsinh(c*x)))/(c^4*d^2)-1/2*b^2*polylog(3,-exp(2*arcsinh(c*x)))/(c^4*d^2)-b*x*(a+b*arcsinh(c*x))/(c^3*d^2*sqrt(1+c^2*x^2))],
[x^2*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^2,x,11,-1/2*x*(a+b*arcsinh(c*x))^2/(c^2*d^2*(1+c^2*x^2))+(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/(c^3*d^2)+b^2*arctan(c*x)/(c^3*d^2)-I*b*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/(c^3*d^2)+I*b*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/(c^3*d^2)+I*b^2*polylog(3,-I*exp(arcsinh(c*x)))/(c^3*d^2)-I*b^2*polylog(3,I*exp(arcsinh(c*x)))/(c^3*d^2)-b*(a+b*arcsinh(c*x))/(c^3*d^2*sqrt(1+c^2*x^2))],
[x*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^2,x,3,-1/2*(a+b*arcsinh(c*x))^2/(c^2*d^2*(1+c^2*x^2))-1/2*b^2*log(1+c^2*x^2)/(c^2*d^2)+b*x*(a+b*arcsinh(c*x))/(c*d^2*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^2,x,11,1/2*x*(a+b*arcsinh(c*x))^2/(d^2*(1+c^2*x^2))+(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/(c*d^2)-b^2*arctan(c*x)/(c*d^2)-I*b*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/(c*d^2)+I*b*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/(c*d^2)+I*b^2*polylog(3,-I*exp(arcsinh(c*x)))/(c*d^2)-I*b^2*polylog(3,I*exp(arcsinh(c*x)))/(c*d^2)+b*(a+b*arcsinh(c*x))/(c*d^2*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))^2/(x*(d+c^2*d*x^2)^2),x,12,1/2*(a+b*arcsinh(c*x))^2/(d^2*(1+c^2*x^2))-2*(a+b*arcsinh(c*x))^2*arctanh(exp(2*arcsinh(c*x)))/d^2+1/2*b^2*log(1+c^2*x^2)/d^2-b*(a+b*arcsinh(c*x))*polylog(2,-exp(2*arcsinh(c*x)))/d^2+b*(a+b*arcsinh(c*x))*polylog(2,exp(2*arcsinh(c*x)))/d^2+1/2*b^2*polylog(3,-exp(2*arcsinh(c*x)))/d^2-1/2*b^2*polylog(3,exp(2*arcsinh(c*x)))/d^2-b*c*x*(a+b*arcsinh(c*x))/(d^2*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))^2/(x^2*(d+c^2*d*x^2)^2),x,20,-(a+b*arcsinh(c*x))^2/(d^2*x*(1+c^2*x^2))-3/2*c^2*x*(a+b*arcsinh(c*x))^2/(d^2*(1+c^2*x^2))-3*c*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/d^2+b^2*c*arctan(c*x)/d^2-4*b*c*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))/d^2-2*b^2*c*polylog(2,-exp(arcsinh(c*x)))/d^2+3*I*b*c*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/d^2-3*I*b*c*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/d^2+2*b^2*c*polylog(2,exp(arcsinh(c*x)))/d^2-3*I*b^2*c*polylog(3,-I*exp(arcsinh(c*x)))/d^2+3*I*b^2*c*polylog(3,I*exp(arcsinh(c*x)))/d^2-b*c*(a+b*arcsinh(c*x))/(d^2*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))^2/(x^3*(d+c^2*d*x^2)^2),x,17,-c^2*(a+b*arcsinh(c*x))^2/(d^2*(1+c^2*x^2))-1/2*(a+b*arcsinh(c*x))^2/(d^2*x^2*(1+c^2*x^2))+4*c^2*(a+b*arcsinh(c*x))^2*arctanh(exp(2*arcsinh(c*x)))/d^2+b^2*c^2*log(x)/d^2-1/2*b^2*c^2*log(1+c^2*x^2)/d^2+2*b*c^2*(a+b*arcsinh(c*x))*polylog(2,-exp(2*arcsinh(c*x)))/d^2-2*b*c^2*(a+b*arcsinh(c*x))*polylog(2,exp(2*arcsinh(c*x)))/d^2-b^2*c^2*polylog(3,-exp(2*arcsinh(c*x)))/d^2+b^2*c^2*polylog(3,exp(2*arcsinh(c*x)))/d^2-b*c*(a+b*arcsinh(c*x))/(d^2*x*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))^2/(x^4*(d+c^2*d*x^2)^2),x,32,-1/3*b^2*c^2/(d^2*x)-1/3*(a+b*arcsinh(c*x))^2/(d^2*x^3*(1+c^2*x^2))+5/3*c^2*(a+b*arcsinh(c*x))^2/(d^2*x*(1+c^2*x^2))+5/2*c^4*x*(a+b*arcsinh(c*x))^2/(d^2*(1+c^2*x^2))+5*c^3*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/d^2-b^2*c^3*arctan(c*x)/d^2+26/3*b*c^3*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))/d^2+13/3*b^2*c^3*polylog(2,-exp(arcsinh(c*x)))/d^2-5*I*b*c^3*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/d^2+5*I*b*c^3*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/d^2-13/3*b^2*c^3*polylog(2,exp(arcsinh(c*x)))/d^2+5*I*b^2*c^3*polylog(3,-I*exp(arcsinh(c*x)))/d^2-5*I*b^2*c^3*polylog(3,I*exp(arcsinh(c*x)))/d^2+2/3*b*c^3*(a+b*arcsinh(c*x))/(d^2*sqrt(1+c^2*x^2))-1/3*b*c*(a+b*arcsinh(c*x))/(d^2*x^2*sqrt(1+c^2*x^2))],
[x^4*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^3,x,16,-1/12*b^2*x/(c^4*d^3*(1+c^2*x^2))+1/6*b*(a+b*arcsinh(c*x))/(c^5*d^3*(1+c^2*x^2)^(3/2))-1/4*x^3*(a+b*arcsinh(c*x))^2/(c^2*d^3*(1+c^2*x^2)^2)-3/8*x*(a+b*arcsinh(c*x))^2/(c^4*d^3*(1+c^2*x^2))+3/4*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/(c^5*d^3)+7/6*b^2*arctan(c*x)/(c^5*d^3)-3/4*I*b*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/(c^5*d^3)+3/4*I*b*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/(c^5*d^3)+3/4*I*b^2*polylog(3,-I*exp(arcsinh(c*x)))/(c^5*d^3)-3/4*I*b^2*polylog(3,I*exp(arcsinh(c*x)))/(c^5*d^3)-5/4*b*(a+b*arcsinh(c*x))/(c^5*d^3*sqrt(1+c^2*x^2))],
[x^3*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^3,x,8,-1/12*b^2/(c^4*d^3*(1+c^2*x^2))+1/6*b*x^3*(a+b*arcsinh(c*x))/(c*d^3*(1+c^2*x^2)^(3/2))-1/4*(a+b*arcsinh(c*x))^2/(c^4*d^3)+1/4*x^4*(a+b*arcsinh(c*x))^2/(d^3*(1+c^2*x^2)^2)-1/3*b^2*log(1+c^2*x^2)/(c^4*d^3)+1/2*b*x*(a+b*arcsinh(c*x))/(c^3*d^3*sqrt(1+c^2*x^2))],
[x^2*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^3,x,15,1/12*b^2*x/(c^2*d^3*(1+c^2*x^2))-1/6*b*(a+b*arcsinh(c*x))/(c^3*d^3*(1+c^2*x^2)^(3/2))-1/4*x*(a+b*arcsinh(c*x))^2/(c^2*d^3*(1+c^2*x^2)^2)+1/8*x*(a+b*arcsinh(c*x))^2/(c^2*d^3*(1+c^2*x^2))+1/4*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/(c^3*d^3)-1/6*b^2*arctan(c*x)/(c^3*d^3)-1/4*I*b*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/(c^3*d^3)+1/4*I*b*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/(c^3*d^3)+1/4*I*b^2*polylog(3,-I*exp(arcsinh(c*x)))/(c^3*d^3)-1/4*I*b^2*polylog(3,I*exp(arcsinh(c*x)))/(c^3*d^3)+1/4*b*(a+b*arcsinh(c*x))/(c^3*d^3*sqrt(1+c^2*x^2))],
[x*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^3,x,5,1/12*b^2/(c^2*d^3*(1+c^2*x^2))+1/6*b*x*(a+b*arcsinh(c*x))/(c*d^3*(1+c^2*x^2)^(3/2))-1/4*(a+b*arcsinh(c*x))^2/(c^2*d^3*(1+c^2*x^2)^2)-1/6*b^2*log(1+c^2*x^2)/(c^2*d^3)+1/3*b*x*(a+b*arcsinh(c*x))/(c*d^3*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^3,x,15,-1/12*b^2*x/(d^3*(1+c^2*x^2))+1/6*b*(a+b*arcsinh(c*x))/(c*d^3*(1+c^2*x^2)^(3/2))+1/4*x*(a+b*arcsinh(c*x))^2/(d^3*(1+c^2*x^2)^2)+3/8*x*(a+b*arcsinh(c*x))^2/(d^3*(1+c^2*x^2))+3/4*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/(c*d^3)-5/6*b^2*arctan(c*x)/(c*d^3)-3/4*I*b*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/(c*d^3)+3/4*I*b*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/(c*d^3)+3/4*I*b^2*polylog(3,-I*exp(arcsinh(c*x)))/(c*d^3)-3/4*I*b^2*polylog(3,I*exp(arcsinh(c*x)))/(c*d^3)+3/4*b*(a+b*arcsinh(c*x))/(c*d^3*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))^2/(x*(d+c^2*d*x^2)^3),x,17,-1/12*b^2/(d^3*(1+c^2*x^2))-1/6*b*c*x*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2)^(3/2))+1/4*(a+b*arcsinh(c*x))^2/(d^3*(1+c^2*x^2)^2)+1/2*(a+b*arcsinh(c*x))^2/(d^3*(1+c^2*x^2))-2*(a+b*arcsinh(c*x))^2*arctanh(exp(2*arcsinh(c*x)))/d^3+2/3*b^2*log(1+c^2*x^2)/d^3-b*(a+b*arcsinh(c*x))*polylog(2,-exp(2*arcsinh(c*x)))/d^3+b*(a+b*arcsinh(c*x))*polylog(2,exp(2*arcsinh(c*x)))/d^3+1/2*b^2*polylog(3,-exp(2*arcsinh(c*x)))/d^3-1/2*b^2*polylog(3,exp(2*arcsinh(c*x)))/d^3-4/3*b*c*x*(a+b*arcsinh(c*x))/(d^3*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))^2/(x^2*(d+c^2*d*x^2)^3),x,27,1/12*b^2*c^2*x/(d^3*(1+c^2*x^2))-1/6*b*c*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2)^(3/2))-(a+b*arcsinh(c*x))^2/(d^3*x*(1+c^2*x^2)^2)-5/4*c^2*x*(a+b*arcsinh(c*x))^2/(d^3*(1+c^2*x^2)^2)-15/8*c^2*x*(a+b*arcsinh(c*x))^2/(d^3*(1+c^2*x^2))-15/4*c*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/d^3+11/6*b^2*c*arctan(c*x)/d^3-4*b*c*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))/d^3-2*b^2*c*polylog(2,-exp(arcsinh(c*x)))/d^3+15/4*I*b*c*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/d^3-15/4*I*b*c*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/d^3+2*b^2*c*polylog(2,exp(arcsinh(c*x)))/d^3-15/4*I*b^2*c*polylog(3,-I*exp(arcsinh(c*x)))/d^3+15/4*I*b^2*c*polylog(3,I*exp(arcsinh(c*x)))/d^3-7/4*b*c*(a+b*arcsinh(c*x))/(d^3*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))^2/(x^3*(d+c^2*d*x^2)^3),x,23,1/12*b^2*c^2/(d^3*(1+c^2*x^2))-b*c*(a+b*arcsinh(c*x))/(d^3*x*(1+c^2*x^2)^(3/2))-5/6*b*c^3*x*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2)^(3/2))-3/4*c^2*(a+b*arcsinh(c*x))^2/(d^3*(1+c^2*x^2)^2)-1/2*(a+b*arcsinh(c*x))^2/(d^3*x^2*(1+c^2*x^2)^2)-3/2*c^2*(a+b*arcsinh(c*x))^2/(d^3*(1+c^2*x^2))+6*c^2*(a+b*arcsinh(c*x))^2*arctanh(exp(2*arcsinh(c*x)))/d^3+b^2*c^2*log(x)/d^3-7/6*b^2*c^2*log(1+c^2*x^2)/d^3+3*b*c^2*(a+b*arcsinh(c*x))*polylog(2,-exp(2*arcsinh(c*x)))/d^3-3*b*c^2*(a+b*arcsinh(c*x))*polylog(2,exp(2*arcsinh(c*x)))/d^3-3/2*b^2*c^2*polylog(3,-exp(2*arcsinh(c*x)))/d^3+3/2*b^2*c^2*polylog(3,exp(2*arcsinh(c*x)))/d^3+4/3*b*c^3*x*(a+b*arcsinh(c*x))/(d^3*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))^2/(x^4*(d+c^2*d*x^2)^3),x,43,-1/2*b^2*c^2/(d^3*x)+1/6*b^2*c^2/(d^3*x*(1+c^2*x^2))+1/12*b^2*c^4*x/(d^3*(1+c^2*x^2))-1/6*b*c^3*(a+b*arcsinh(c*x))/(d^3*(1+c^2*x^2)^(3/2))-1/3*b*c*(a+b*arcsinh(c*x))/(d^3*x^2*(1+c^2*x^2)^(3/2))-1/3*(a+b*arcsinh(c*x))^2/(d^3*x^3*(1+c^2*x^2)^2)+7/3*c^2*(a+b*arcsinh(c*x))^2/(d^3*x*(1+c^2*x^2)^2)+35/12*c^4*x*(a+b*arcsinh(c*x))^2/(d^3*(1+c^2*x^2)^2)+35/8*c^4*x*(a+b*arcsinh(c*x))^2/(d^3*(1+c^2*x^2))+35/4*c^3*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))/d^3-17/6*b^2*c^3*arctan(c*x)/d^3+38/3*b*c^3*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))/d^3+19/3*b^2*c^3*polylog(2,-exp(arcsinh(c*x)))/d^3-35/4*I*b*c^3*(a+b*arcsinh(c*x))*polylog(2,-I*exp(arcsinh(c*x)))/d^3+35/4*I*b*c^3*(a+b*arcsinh(c*x))*polylog(2,I*exp(arcsinh(c*x)))/d^3-19/3*b^2*c^3*polylog(2,exp(arcsinh(c*x)))/d^3+35/4*I*b^2*c^3*polylog(3,-I*exp(arcsinh(c*x)))/d^3-35/4*I*b^2*c^3*polylog(3,I*exp(arcsinh(c*x)))/d^3+29/12*b*c^3*(a+b*arcsinh(c*x))/(d^3*sqrt(1+c^2*x^2))],

# Integrands of the form x^m (Pi+Pi c^2 x^2)^(p/2) (a+b ArcSinh[c x])^2
[(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))^2,x,16,65/1728*b^2*Pi^(5/2)*x*(1+c^2*x^2)^(3/2)+1/108*b^2*Pi^(5/2)*x*(1+c^2*x^2)^(5/2)-115/1152*b^2*Pi^(5/2)*arcsinh(c*x)/c-5/16*b*c*Pi^(5/2)*x^2*(a+b*arcsinh(c*x))-5/48*b*Pi^(5/2)*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/c-1/18*b*Pi^(5/2)*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))/c+5/24*Pi*x*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))^2+1/6*x*(Pi+c^2*Pi*x^2)^(5/2)*(a+b*arcsinh(c*x))^2+5/48*Pi^(5/2)*(a+b*arcsinh(c*x))^3/(b*c)+245/1152*b^2*Pi^(5/2)*x*sqrt(1+c^2*x^2)+5/16*Pi^2*x*(a+b*arcsinh(c*x))^2*sqrt(Pi+c^2*Pi*x^2)],
[(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))^2,x,10,1/32*b^2*Pi^(3/2)*x*(1+c^2*x^2)^(3/2)-9/64*b^2*Pi^(3/2)*arcsinh(c*x)/c-3/8*b*c*Pi^(3/2)*x^2*(a+b*arcsinh(c*x))-1/8*b*Pi^(3/2)*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/c+1/4*x*(Pi+c^2*Pi*x^2)^(3/2)*(a+b*arcsinh(c*x))^2+1/8*Pi^(3/2)*(a+b*arcsinh(c*x))^3/(b*c)+15/64*b^2*Pi^(3/2)*x*sqrt(1+c^2*x^2)+3/8*Pi*x*(a+b*arcsinh(c*x))^2*sqrt(Pi+c^2*Pi*x^2)],
[(Pi+c^2*Pi*x^2)^(1/2)*(a+b*arcsinh(c*x))^2,x,5,-1/4*b^2*arcsinh(c*x)*sqrt(Pi)/c-1/2*b*c*x^2*(a+b*arcsinh(c*x))*sqrt(Pi)+1/6*(a+b*arcsinh(c*x))^3*sqrt(Pi)/(b*c)+1/4*b^2*x*sqrt(Pi)*sqrt(1+c^2*x^2)+1/2*x*(a+b*arcsinh(c*x))^2*sqrt(Pi+c^2*Pi*x^2)],
[(a+b*arcsinh(c*x))^2/(Pi+c^2*Pi*x^2)^(1/2),x,1,1/3*(a+b*arcsinh(c*x))^3/(b*c*sqrt(Pi))],
[(a+b*arcsinh(c*x))^2/(Pi+c^2*Pi*x^2)^(3/2),x,6,(a+b*arcsinh(c*x))^2/(c*Pi^(3/2))-2*b*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*Pi^(3/2))-b^2*polylog(2,-exp(2*arcsinh(c*x)))/(c*Pi^(3/2))+x*(a+b*arcsinh(c*x))^2/(Pi*sqrt(Pi+c^2*Pi*x^2))],
[(a+b*arcsinh(c*x))^2/(Pi+c^2*Pi*x^2)^(5/2),x,9,1/3*b*(a+b*arcsinh(c*x))/(c*Pi^(5/2)*(1+c^2*x^2))+2/3*(a+b*arcsinh(c*x))^2/(c*Pi^(5/2))+1/3*x*(a+b*arcsinh(c*x))^2/(Pi*(Pi+c^2*Pi*x^2)^(3/2))-4/3*b*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*Pi^(5/2))-2/3*b^2*polylog(2,-exp(2*arcsinh(c*x)))/(c*Pi^(5/2))-1/3*b^2*x/(Pi^(5/2)*sqrt(1+c^2*x^2))+2/3*x*(a+b*arcsinh(c*x))^2/(Pi^2*sqrt(Pi+c^2*Pi*x^2))],

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

# p>0
[x^3*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2),x,14,-52/225*b^2*sqrt(d+c^2*d*x^2)/c^4-26/675*b^2*(1+c^2*x^2)*sqrt(d+c^2*d*x^2)/c^4+2/125*b^2*(1+c^2*x^2)^2*sqrt(d+c^2*d*x^2)/c^4-2/15*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/c^4+1/15*x^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/c^2+1/5*x^4*(a+b*arcsinh(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^2*x^2))+4/15*b^2*x*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/(c^3*sqrt(1+c^2*x^2))-2/45*b*x^3*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-2/25*b*c*x^5*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[x^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2),x,10,1/64*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*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/c^2+1/4*x^3*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)-1/64*b^2*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/(c^3*sqrt(1+c^2*x^2))-1/8*b*x^2*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-1/8*b*c*x^4*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/24*(a+b*arcsinh(c*x))^3*sqrt(d+c^2*d*x^2)/(b*c^3*sqrt(1+c^2*x^2))],
[x*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2),x,5,1/3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(c^2*d)+4/9*b^2*sqrt(d+c^2*d*x^2)/c^2+2/27*b^2*(1+c^2*x^2)*sqrt(d+c^2*d*x^2)/c^2-2/3*b*x*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-2/9*b*c*x^3*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(a+b*arcsinh(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*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)-1/4*b^2*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-1/2*b*c*x^2*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+1/6*(a+b*arcsinh(c*x))^3*sqrt(d+c^2*d*x^2)/(b*c*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(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*arcsinh(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^2*x^2)-2*b^2*c*x*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2*(a+b*arcsinh(c*x))^2*arctanh(exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2*b*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+2*b*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+2*b^2*polylog(3,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2*b^2*polylog(3,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/x^2,x,7,-(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/x+c*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+1/3*c*(a+b*arcsinh(c*x))^3*sqrt(d+c^2*d*x^2)/(b*sqrt(1+c^2*x^2))+2*b*c*(a+b*arcsinh(c*x))*log(1+(-1)/exp(2*arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-b^2*c*polylog(2,exp(-2*arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/x^3,x,13,-1/2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/x^2-b*c*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(x*sqrt(1+c^2*x^2))-c^2*(a+b*arcsinh(c*x))^2*arctanh(exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-b^2*c^2*arctanh(sqrt(1+c^2*x^2))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-b*c^2*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+b*c^2*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+b^2*c^2*polylog(3,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-b^2*c^2*polylog(3,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/x^4,x,9,-1/3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(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*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+1/3*c^3*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+2/3*b*c^3*(a+b*arcsinh(c*x))*log(1+(-1)/exp(2*arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/3*b^2*c^3*polylog(2,exp(-2*arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/3*b*c*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2)/x^2],
[x^3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2,x,20,1/7*x^4*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2-304/3675*b^2*d*sqrt(d+c^2*d*x^2)/c^4-152/11025*b^2*d*(1+c^2*x^2)*sqrt(d+c^2*d*x^2)/c^4-38/6125*b^2*d*(1+c^2*x^2)^2*sqrt(d+c^2*d*x^2)/c^4+2/343*b^2*d*(1+c^2*x^2)^3*sqrt(d+c^2*d*x^2)/c^4-2/35*d*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/c^4+1/35*d*x^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/c^2+3/35*d*x^4*(a+b*arcsinh(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^2*x^2))+4/35*b^2*d*x*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/(c^3*sqrt(1+c^2*x^2))-2/105*b*d*x^3*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-16/175*b*c*d*x^5*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2/49*b*c^3*d*x^7*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[x^2*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2,x,17,1/6*x^3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(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*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/c^2+1/8*d*x^3*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)+7/1152*b^2*d*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/(c^3*sqrt(1+c^2*x^2))-1/16*b*d*x^2*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-7/48*b*c*d*x^4*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/18*b*c^3*d*x^6*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/48*d*(a+b*arcsinh(c*x))^3*sqrt(d+c^2*d*x^2)/(b*c^3*sqrt(1+c^2*x^2))],
[x*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2,x,6,1/5*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/(c^2*d)+16/75*b^2*d*sqrt(d+c^2*d*x^2)/c^2+8/225*b^2*d*(1+c^2*x^2)*sqrt(d+c^2*d*x^2)/c^2+2/125*b^2*d*(1+c^2*x^2)^2*sqrt(d+c^2*d*x^2)/c^2-2/5*b*d*x*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-4/15*b*c*d*x^3*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2/25*b*c^3*d*x^5*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2,x,10,1/4*x*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2+15/64*b^2*d*x*sqrt(d+c^2*d*x^2)+1/32*b^2*d*x*(1+c^2*x^2)*sqrt(d+c^2*d*x^2)-1/8*b*d*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/c+3/8*d*x*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)-9/64*b^2*d*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-3/8*b*c*d*x^2*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+1/8*d*(a+b*arcsinh(c*x))^3*sqrt(d+c^2*d*x^2)/(b*c*sqrt(1+c^2*x^2))],
[(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/x,x,17,1/3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2+22/9*b^2*d*sqrt(d+c^2*d*x^2)+2/27*b^2*d*(1+c^2*x^2)*sqrt(d+c^2*d*x^2)+d*(a+b*arcsinh(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^2*x^2)-2*b^2*c*d*x*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2/3*b*c*d*x*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2/9*b*c^3*d*x^3*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2*d*(a+b*arcsinh(c*x))^2*arctanh(exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2*b*d*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+2*b*d*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+2*b^2*d*polylog(3,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2*b^2*d*polylog(3,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/x^2,x,14,-(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(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*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)-5/4*b^2*c*d*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-3/2*b*c^3*d*x^2*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+c*d*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+1/2*c*d*(a+b*arcsinh(c*x))^3*sqrt(d+c^2*d*x^2)/(b*sqrt(1+c^2*x^2))+2*b*c*d*(a+b*arcsinh(c*x))*log(1+(-1)/exp(2*arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-b^2*c*d*polylog(2,exp(-2*arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+b*c*d*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2)],
[(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/x^3,x,18,-1/2*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(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*arcsinh(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^2*x^2)-3*b^2*c^3*d*x*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-b*c*d*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(x*sqrt(1+c^2*x^2))+b*c^3*d*x*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-3*c^2*d*(a+b*arcsinh(c*x))^2*arctanh(exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-b^2*c^2*d*arctanh(sqrt(1+c^2*x^2))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-3*b*c^2*d*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+3*b*c^2*d*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+3*b^2*c^2*d*polylog(3,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-3*b^2*c^2*d*polylog(3,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/x^4,x,16,-1/3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(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*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/x+1/3*b^2*c^3*d*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+4/3*c^3*d*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+1/3*c^3*d*(a+b*arcsinh(c*x))^3*sqrt(d+c^2*d*x^2)/(b*sqrt(1+c^2*x^2))+8/3*b*c^3*d*(a+b*arcsinh(c*x))*log(1+(-1)/exp(2*arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-4/3*b^2*c^3*d*polylog(2,exp(-2*arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/3*b*c*d*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2)/x^2],
[x^3*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2,x,27,5/63*d*x^4*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2+1/9*x^4*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2-160/3969*b^2*d^2*sqrt(d+c^2*d*x^2)/c^4-80/11907*b^2*d^2*(1+c^2*x^2)*sqrt(d+c^2*d*x^2)/c^4-4/1323*b^2*d^2*(1+c^2*x^2)^2*sqrt(d+c^2*d*x^2)/c^4-50/27783*b^2*d^2*(1+c^2*x^2)^3*sqrt(d+c^2*d*x^2)/c^4+2/729*b^2*d^2*(1+c^2*x^2)^4*sqrt(d+c^2*d*x^2)/c^4-2/63*d^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/c^4+1/63*d^2*x^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/c^2+1/21*d^2*x^4*(a+b*arcsinh(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^2*x^2))+4/63*b^2*d^2*x*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/(c^3*sqrt(1+c^2*x^2))-2/189*b*d^2*x^3*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-2/21*b*c*d^2*x^5*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-38/441*b*c^3*d^2*x^7*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2/81*b*c^5*d^2*x^9*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[x^2*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2,x,25,5/48*d*x^3*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2+1/8*x^3*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2-359/36864*b^2*d^2*x*sqrt(d+c^2*d*x^2)/c^2+1079/55296*b^2*d^2*x^3*sqrt(d+c^2*d*x^2)+209/13824*b^2*c^2*d^2*x^5*sqrt(d+c^2*d*x^2)+1/256*b^2*c^4*d^2*x^7*sqrt(d+c^2*d*x^2)+5/128*d^2*x*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/c^2+5/64*d^2*x^3*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)+359/36864*b^2*d^2*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/(c^3*sqrt(1+c^2*x^2))-5/128*b*d^2*x^2*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-59/384*b*c*d^2*x^4*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-17/144*b*c^3*d^2*x^6*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-1/32*b*c^5*d^2*x^8*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-5/384*d^2*(a+b*arcsinh(c*x))^3*sqrt(d+c^2*d*x^2)/(b*c^3*sqrt(1+c^2*x^2))],
[x*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2,x,6,1/7*(d+c^2*d*x^2)^(7/2)*(a+b*arcsinh(c*x))^2/(c^2*d)+32/245*b^2*d^2*sqrt(d+c^2*d*x^2)/c^2+16/735*b^2*d^2*(1+c^2*x^2)*sqrt(d+c^2*d*x^2)/c^2+12/1225*b^2*d^2*(1+c^2*x^2)^2*sqrt(d+c^2*d*x^2)/c^2+2/343*b^2*d^2*(1+c^2*x^2)^3*sqrt(d+c^2*d*x^2)/c^2-2/7*b*d^2*x*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-2/7*b*c*d^2*x^3*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-6/35*b*c^3*d^2*x^5*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2/49*b*c^5*d^2*x^7*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2,x,16,5/24*d*x*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2+1/6*x*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(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^2*x^2)*sqrt(d+c^2*d*x^2)+1/108*b^2*d^2*x*(1+c^2*x^2)^2*sqrt(d+c^2*d*x^2)-5/48*b*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/c-1/18*b*d^2*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/c+5/16*d^2*x*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)-115/1152*b^2*d^2*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/(c*sqrt(1+c^2*x^2))-5/16*b*c*d^2*x^2*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+5/48*d^2*(a+b*arcsinh(c*x))^3*sqrt(d+c^2*d*x^2)/(b*c*sqrt(1+c^2*x^2))],
[(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/x,x,23,1/3*d*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2+1/5*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2+598/225*b^2*d^2*sqrt(d+c^2*d*x^2)+74/675*b^2*d^2*(1+c^2*x^2)*sqrt(d+c^2*d*x^2)+2/125*b^2*d^2*(1+c^2*x^2)^2*sqrt(d+c^2*d*x^2)+d^2*(a+b*arcsinh(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^2*x^2)-2*b^2*c*d^2*x*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-16/15*b*c*d^2*x*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-22/45*b*c^3*d^2*x^3*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2/25*b*c^5*d^2*x^5*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2*d^2*(a+b*arcsinh(c*x))^2*arctanh(exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2*b*d^2*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+2*b*d^2*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+2*b^2*d^2*polylog(3,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2*b^2*d^2*polylog(3,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/x^2,x,23,5/4*c^2*d*x*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2-(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(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^2*x^2)*sqrt(d+c^2*d*x^2)-1/8*b*c*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)+15/8*c^2*d^2*x*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)-89/64*b^2*c*d^2*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-15/8*b*c^3*d^2*x^2*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+c*d^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+5/8*c*d^2*(a+b*arcsinh(c*x))^3*sqrt(d+c^2*d*x^2)/(b*sqrt(1+c^2*x^2))+2*b*c*d^2*(a+b*arcsinh(c*x))*log(1+(-1)/exp(2*arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-b^2*c*d^2*polylog(2,exp(-2*arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+b*c*d^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2)],
[(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/x^3,x,25,5/6*c^2*d*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2-1/2*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/x^2+40/9*b^2*c^2*d^2*sqrt(d+c^2*d*x^2)+2/27*b^2*c^2*d^2*(1+c^2*x^2)*sqrt(d+c^2*d*x^2)+5/2*c^2*d^2*(a+b*arcsinh(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^2*x^2)-5*b^2*c^3*d^2*x*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-b*c*d^2*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/(x*sqrt(1+c^2*x^2))+1/3*b*c^3*d^2*x*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-2/9*b*c^5*d^2*x^3*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-5*c^2*d^2*(a+b*arcsinh(c*x))^2*arctanh(exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-b^2*c^2*d^2*arctanh(sqrt(1+c^2*x^2))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-5*b*c^2*d^2*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+5*b*c^2*d^2*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+5*b^2*c^2*d^2*polylog(3,-exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-5*b^2*c^2*d^2*polylog(3,exp(arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)],
[(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/x^4,x,27,-5/3*c^2*d*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/x-1/3*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(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^2*x^2)*sqrt(d+c^2*d*x^2)/x-1/3*b*c*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/x^2+5/2*c^4*d^2*x*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)-23/12*b^2*c^3*d^2*arcsinh(c*x)*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-5/2*b*c^5*d^2*x^2*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+7/3*c^3*d^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+5/6*c^3*d^2*(a+b*arcsinh(c*x))^3*sqrt(d+c^2*d*x^2)/(b*sqrt(1+c^2*x^2))+14/3*b*c^3*d^2*(a+b*arcsinh(c*x))*log(1+(-1)/exp(2*arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)-7/3*b^2*c^3*d^2*polylog(2,exp(-2*arcsinh(c*x)))*sqrt(d+c^2*d*x^2)/sqrt(1+c^2*x^2)+7/3*b*c^3*d^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2)],

# p<0
[x^4*arcsinh(a*x)^2/sqrt(1+a^2*x^2),x,10,15/64*arcsinh(a*x)/a^5+3/8*x^2*arcsinh(a*x)/a^3-1/8*x^4*arcsinh(a*x)/a+1/8*arcsinh(a*x)^3/a^5-15/64*x*sqrt(1+a^2*x^2)/a^4+1/32*x^3*sqrt(1+a^2*x^2)/a^2-3/8*x*arcsinh(a*x)^2*sqrt(1+a^2*x^2)/a^4+1/4*x^3*arcsinh(a*x)^2*sqrt(1+a^2*x^2)/a^2],
[x^3*arcsinh(a*x)^2/sqrt(1+a^2*x^2),x,8,2/27*(1+a^2*x^2)^(3/2)/a^4+4/3*x*arcsinh(a*x)/a^3-2/9*x^3*arcsinh(a*x)/a-14/9*sqrt(1+a^2*x^2)/a^4-2/3*arcsinh(a*x)^2*sqrt(1+a^2*x^2)/a^4+1/3*x^2*arcsinh(a*x)^2*sqrt(1+a^2*x^2)/a^2],
[x^2*arcsinh(a*x)^2/sqrt(1+a^2*x^2),x,5,-1/4*arcsinh(a*x)/a^3-1/2*x^2*arcsinh(a*x)/a-1/6*arcsinh(a*x)^3/a^3+1/4*x*sqrt(1+a^2*x^2)/a^2+1/2*x*arcsinh(a*x)^2*sqrt(1+a^2*x^2)/a^2],
[x*arcsinh(a*x)^2/sqrt(1+a^2*x^2),x,3,-2*x*arcsinh(a*x)/a+2*sqrt(1+a^2*x^2)/a^2+arcsinh(a*x)^2*sqrt(1+a^2*x^2)/a^2],
[arcsinh(a*x)^2/sqrt(1+a^2*x^2),x,1,1/3*arcsinh(a*x)^3/a],
[arcsinh(a*x)^2/(x*sqrt(1+a^2*x^2)),x,8,-2*arcsinh(a*x)^2*arctanh(exp(arcsinh(a*x)))-2*arcsinh(a*x)*polylog(2,-exp(arcsinh(a*x)))+2*arcsinh(a*x)*polylog(2,exp(arcsinh(a*x)))+2*polylog(3,-exp(arcsinh(a*x)))-2*polylog(3,exp(arcsinh(a*x)))],
[arcsinh(a*x)^2/(x^2*sqrt(1+a^2*x^2)),x,6,-a*arcsinh(a*x)^2+2*a*arcsinh(a*x)*log(1-exp(2*arcsinh(a*x)))+a*polylog(2,exp(2*arcsinh(a*x)))-arcsinh(a*x)^2*sqrt(1+a^2*x^2)/x],
[arcsinh(a*x)^2/(x^3*sqrt(1+a^2*x^2)),x,13,-a*arcsinh(a*x)/x+a^2*arcsinh(a*x)^2*arctanh(exp(arcsinh(a*x)))-a^2*arctanh(sqrt(1+a^2*x^2))+a^2*arcsinh(a*x)*polylog(2,-exp(arcsinh(a*x)))-a^2*arcsinh(a*x)*polylog(2,exp(arcsinh(a*x)))-a^2*polylog(3,-exp(arcsinh(a*x)))+a^2*polylog(3,exp(arcsinh(a*x)))-1/2*arcsinh(a*x)^2*sqrt(1+a^2*x^2)/x^2],
[x^5*(a+b*arcsinh(c*x))^2/sqrt(d+c^2*d*x^2),x,14,298/225*b^2*(1+c^2*x^2)/(c^6*sqrt(d+c^2*d*x^2))-76/675*b^2*(1+c^2*x^2)^2/(c^6*sqrt(d+c^2*d*x^2))+2/125*b^2*(1+c^2*x^2)^3/(c^6*sqrt(d+c^2*d*x^2))-16/15*a*b*x*sqrt(1+c^2*x^2)/(c^5*sqrt(d+c^2*d*x^2))-16/15*b^2*x*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c^5*sqrt(d+c^2*d*x^2))+8/45*b*x^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c^3*sqrt(d+c^2*d*x^2))-2/25*b*x^5*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c*sqrt(d+c^2*d*x^2))+8/15*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^6*d)-4/15*x^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^4*d)+1/5*x^4*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^2*d)],
[x^4*(a+b*arcsinh(c*x))^2/sqrt(d+c^2*d*x^2),x,10,-15/64*b^2*x*(1+c^2*x^2)/(c^4*sqrt(d+c^2*d*x^2))+1/32*b^2*x^3*(1+c^2*x^2)/(c^2*sqrt(d+c^2*d*x^2))+15/64*b^2*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c^5*sqrt(d+c^2*d*x^2))+3/8*b*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c^3*sqrt(d+c^2*d*x^2))-1/8*b*x^4*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c*sqrt(d+c^2*d*x^2))+1/8*(a+b*arcsinh(c*x))^3*sqrt(1+c^2*x^2)/(b*c^5*sqrt(d+c^2*d*x^2))-3/8*x*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^4*d)+1/4*x^3*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^2*d)],
[x^3*(a+b*arcsinh(c*x))^2/sqrt(d+c^2*d*x^2),x,9,-14/9*b^2*(1+c^2*x^2)/(c^4*sqrt(d+c^2*d*x^2))+2/27*b^2*(1+c^2*x^2)^2/(c^4*sqrt(d+c^2*d*x^2))+4/3*a*b*x*sqrt(1+c^2*x^2)/(c^3*sqrt(d+c^2*d*x^2))+4/3*b^2*x*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c^3*sqrt(d+c^2*d*x^2))-2/9*b*x^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c*sqrt(d+c^2*d*x^2))-2/3*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^4*d)+1/3*x^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^2*d)],
[x^2*(a+b*arcsinh(c*x))^2/sqrt(d+c^2*d*x^2),x,5,1/4*b^2*x*(1+c^2*x^2)/(c^2*sqrt(d+c^2*d*x^2))-1/4*b^2*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c^3*sqrt(d+c^2*d*x^2))-1/2*b*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c*sqrt(d+c^2*d*x^2))-1/6*(a+b*arcsinh(c*x))^3*sqrt(1+c^2*x^2)/(b*c^3*sqrt(d+c^2*d*x^2))+1/2*x*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^2*d)],
[x*(a+b*arcsinh(c*x))^2/sqrt(d+c^2*d*x^2),x,4,2*b^2*(1+c^2*x^2)/(c^2*sqrt(d+c^2*d*x^2))-2*a*b*x*sqrt(1+c^2*x^2)/(c*sqrt(d+c^2*d*x^2))-2*b^2*x*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c*sqrt(d+c^2*d*x^2))+(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^2*d)],
[(a+b*arcsinh(c*x))^2/sqrt(d+c^2*d*x^2),x,1,1/3*(a+b*arcsinh(c*x))^3*sqrt(1+c^2*x^2)/(b*c*sqrt(d+c^2*d*x^2))],
[(a+b*arcsinh(c*x))^2/(x*sqrt(d+c^2*d*x^2)),x,8,-2*(a+b*arcsinh(c*x))^2*arctanh(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)-2*b*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)+2*b*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)+2*b^2*polylog(3,-exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)-2*b^2*polylog(3,exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)],
[(a+b*arcsinh(c*x))^2/(x^2*sqrt(d+c^2*d*x^2)),x,6,c*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)+2*b*c*(a+b*arcsinh(c*x))*log(1+(-1)/exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)-b^2*c*polylog(2,exp(-2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)-(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(d*x)],
[(a+b*arcsinh(c*x))^2/(x^3*sqrt(d+c^2*d*x^2)),x,13,-b*c*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(x*sqrt(d+c^2*d*x^2))+c^2*(a+b*arcsinh(c*x))^2*arctanh(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)-b^2*c^2*arctanh(sqrt(1+c^2*x^2))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)+b*c^2*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)-b*c^2*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)-b^2*c^2*polylog(3,-exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)+b^2*c^2*polylog(3,exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)-1/2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(d*x^2)],
[(a+b*arcsinh(c*x))^2/(x^4*sqrt(d+c^2*d*x^2)),x,9,-1/3*b^2*c^2*(1+c^2*x^2)/(x*sqrt(d+c^2*d*x^2))-1/3*b*c*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(x^2*sqrt(d+c^2*d*x^2))-2/3*c^3*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)-4/3*b*c^3*(a+b*arcsinh(c*x))*log(1+(-1)/exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)+2/3*b^2*c^3*polylog(2,exp(-2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/sqrt(d+c^2*d*x^2)-1/3*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(d*x^3)+2/3*c^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(d*x)],
[x^5*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(3/2),x,22,-32/9*b^2*(1+c^2*x^2)/(c^6*d*sqrt(d+c^2*d*x^2))+2/27*b^2*(1+c^2*x^2)^2/(c^6*d*sqrt(d+c^2*d*x^2))-x^4*(a+b*arcsinh(c*x))^2/(c^2*d*sqrt(d+c^2*d*x^2))+16/3*a*b*x*sqrt(1+c^2*x^2)/(c^5*d*sqrt(d+c^2*d*x^2))+16/3*b^2*x*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c^5*d*sqrt(d+c^2*d*x^2))-2*b*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c^5*d*sqrt(d+c^2*d*x^2))-2/9*b*x^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c^3*d*sqrt(d+c^2*d*x^2))+4*b*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^6*d*sqrt(d+c^2*d*x^2))-2*I*b^2*polylog(2,-I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^6*d*sqrt(d+c^2*d*x^2))+2*I*b^2*polylog(2,I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^6*d*sqrt(d+c^2*d*x^2))-8/3*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^6*d^2)+4/3*x^2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^4*d^2)],
[x^4*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(3/2),x,14,1/4*b^2*x*(1+c^2*x^2)/(c^4*d*sqrt(d+c^2*d*x^2))-x^3*(a+b*arcsinh(c*x))^2/(c^2*d*sqrt(d+c^2*d*x^2))-1/4*b^2*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c^5*d*sqrt(d+c^2*d*x^2))-1/2*b*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c^3*d*sqrt(d+c^2*d*x^2))+(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(c^5*d*sqrt(d+c^2*d*x^2))-1/2*(a+b*arcsinh(c*x))^3*sqrt(1+c^2*x^2)/(b*c^5*d*sqrt(d+c^2*d*x^2))-2*b*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^5*d*sqrt(d+c^2*d*x^2))-b^2*polylog(2,-exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^5*d*sqrt(d+c^2*d*x^2))+3/2*x*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^4*d^2)],
[x^3*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(3/2),x,13,2*b^2*(1+c^2*x^2)/(c^4*d*sqrt(d+c^2*d*x^2))-x^2*(a+b*arcsinh(c*x))^2/(c^2*d*sqrt(d+c^2*d*x^2))-4*a*b*x*sqrt(1+c^2*x^2)/(c^3*d*sqrt(d+c^2*d*x^2))-4*b^2*x*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c^3*d*sqrt(d+c^2*d*x^2))+2*b*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c^3*d*sqrt(d+c^2*d*x^2))-4*b*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^4*d*sqrt(d+c^2*d*x^2))+2*I*b^2*polylog(2,-I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^4*d*sqrt(d+c^2*d*x^2))-2*I*b^2*polylog(2,I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^4*d*sqrt(d+c^2*d*x^2))+2*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^4*d^2)],
[x^2*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(3/2),x,7,-x*(a+b*arcsinh(c*x))^2/(c^2*d*sqrt(d+c^2*d*x^2))-(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(c^3*d*sqrt(d+c^2*d*x^2))+1/3*(a+b*arcsinh(c*x))^3*sqrt(1+c^2*x^2)/(b*c^3*d*sqrt(d+c^2*d*x^2))+2*b*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^3*d*sqrt(d+c^2*d*x^2))+b^2*polylog(2,-exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^3*d*sqrt(d+c^2*d*x^2))],
[x*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(3/2),x,7,-(a+b*arcsinh(c*x))^2/(c^2*d*sqrt(d+c^2*d*x^2))+4*b*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^2*d*sqrt(d+c^2*d*x^2))-2*I*b^2*polylog(2,-I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^2*d*sqrt(d+c^2*d*x^2))+2*I*b^2*polylog(2,I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^2*d*sqrt(d+c^2*d*x^2))],
[(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(3/2),x,6,x*(a+b*arcsinh(c*x))^2/(d*sqrt(d+c^2*d*x^2))+(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(c*d*sqrt(d+c^2*d*x^2))-2*b*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c*d*sqrt(d+c^2*d*x^2))-b^2*polylog(2,-exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c*d*sqrt(d+c^2*d*x^2))],
[(a+b*arcsinh(c*x))^2/(x*(d+c^2*d*x^2)^(3/2)),x,15,(a+b*arcsinh(c*x))^2/(d*sqrt(d+c^2*d*x^2))-4*b*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))-2*(a+b*arcsinh(c*x))^2*arctanh(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))-2*b*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))+2*I*b^2*polylog(2,-I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))-2*I*b^2*polylog(2,I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))+2*b*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))+2*b^2*polylog(3,-exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))-2*b^2*polylog(3,exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))],
[(a+b*arcsinh(c*x))^2/(x^2*(d+c^2*d*x^2)^(3/2)),x,14,-(a+b*arcsinh(c*x))^2/(d*x*sqrt(d+c^2*d*x^2))-2*c^2*x*(a+b*arcsinh(c*x))^2/(d*sqrt(d+c^2*d*x^2))-2*c*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))-4*b*c*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))+4*b*c*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))+b^2*c*polylog(2,-exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))+b^2*c*polylog(2,exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))],
[(a+b*arcsinh(c*x))^2/(x^3*(d+c^2*d*x^2)^(3/2)),x,26,-3/2*c^2*(a+b*arcsinh(c*x))^2/(d*sqrt(d+c^2*d*x^2))-1/2*(a+b*arcsinh(c*x))^2/(d*x^2*sqrt(d+c^2*d*x^2))-b*c*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(d*x*sqrt(d+c^2*d*x^2))+4*b*c^2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))+3*c^2*(a+b*arcsinh(c*x))^2*arctanh(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))-b^2*c^2*arctanh(sqrt(1+c^2*x^2))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))+3*b*c^2*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))-2*I*b^2*c^2*polylog(2,-I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))+2*I*b^2*c^2*polylog(2,I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))-3*b*c^2*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))-3*b^2*c^2*polylog(3,-exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))+3*b^2*c^2*polylog(3,exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))],
[(a+b*arcsinh(c*x))^2/(x^4*(d+c^2*d*x^2)^(3/2)),x,24,-1/3*b^2*c^2*(1+c^2*x^2)/(d*x*sqrt(d+c^2*d*x^2))-1/3*(a+b*arcsinh(c*x))^2/(d*x^3*sqrt(d+c^2*d*x^2))+4/3*c^2*(a+b*arcsinh(c*x))^2/(d*x*sqrt(d+c^2*d*x^2))+8/3*c^4*x*(a+b*arcsinh(c*x))^2/(d*sqrt(d+c^2*d*x^2))-1/3*b*c*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(d*x^2*sqrt(d+c^2*d*x^2))+8/3*c^3*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))+20/3*b*c^3*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))-16/3*b*c^3*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))-b^2*c^3*polylog(2,-exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))-5/3*b^2*c^3*polylog(2,exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d*sqrt(d+c^2*d*x^2))],
[x^5*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(5/2),x,26,-1/3*x^4*(a+b*arcsinh(c*x))^2/(c^2*d*(d+c^2*d*x^2)^(3/2))+1/3*b^2/(c^6*d^2*sqrt(d+c^2*d*x^2))+2*b^2*(1+c^2*x^2)/(c^6*d^2*sqrt(d+c^2*d*x^2))-4/3*x^2*(a+b*arcsinh(c*x))^2/(c^4*d^2*sqrt(d+c^2*d*x^2))-1/3*b*x^3*(a+b*arcsinh(c*x))/(c^3*d^2*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2))-16/3*a*b*x*sqrt(1+c^2*x^2)/(c^5*d^2*sqrt(d+c^2*d*x^2))-16/3*b^2*x*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c^5*d^2*sqrt(d+c^2*d*x^2))+11/3*b*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(c^5*d^2*sqrt(d+c^2*d*x^2))-22/3*b*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^6*d^2*sqrt(d+c^2*d*x^2))+11/3*I*b^2*polylog(2,-I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^6*d^2*sqrt(d+c^2*d*x^2))-11/3*I*b^2*polylog(2,I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^6*d^2*sqrt(d+c^2*d*x^2))+8/3*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(c^6*d^3)],
[x^4*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(5/2),x,16,-1/3*x^3*(a+b*arcsinh(c*x))^2/(c^2*d*(d+c^2*d*x^2)^(3/2))-1/3*b^2*x/(c^4*d^2*sqrt(d+c^2*d*x^2))-x*(a+b*arcsinh(c*x))^2/(c^4*d^2*sqrt(d+c^2*d*x^2))-1/3*b*x^2*(a+b*arcsinh(c*x))/(c^3*d^2*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2))+1/3*b^2*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c^5*d^2*sqrt(d+c^2*d*x^2))-4/3*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(c^5*d^2*sqrt(d+c^2*d*x^2))+1/3*(a+b*arcsinh(c*x))^3*sqrt(1+c^2*x^2)/(b*c^5*d^2*sqrt(d+c^2*d*x^2))+8/3*b*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^5*d^2*sqrt(d+c^2*d*x^2))+4/3*b^2*polylog(2,-exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^5*d^2*sqrt(d+c^2*d*x^2))],
[x^3*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(5/2),x,16,-1/3*x^2*(a+b*arcsinh(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*arcsinh(c*x))^2/(c^4*d^2*sqrt(d+c^2*d*x^2))-1/3*b*x*(a+b*arcsinh(c*x))/(c^3*d^2*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2))+10/3*b*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^4*d^2*sqrt(d+c^2*d*x^2))-5/3*I*b^2*polylog(2,-I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^4*d^2*sqrt(d+c^2*d*x^2))+5/3*I*b^2*polylog(2,I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^4*d^2*sqrt(d+c^2*d*x^2))],
[x^2*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(5/2),x,9,1/3*x^3*(a+b*arcsinh(c*x))^2/(d*(d+c^2*d*x^2)^(3/2))+1/3*b^2*x/(c^2*d^2*sqrt(d+c^2*d*x^2))+1/3*b*x^2*(a+b*arcsinh(c*x))/(c*d^2*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2))-1/3*b^2*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c^3*d^2*sqrt(d+c^2*d*x^2))+1/3*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(c^3*d^2*sqrt(d+c^2*d*x^2))-2/3*b*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^3*d^2*sqrt(d+c^2*d*x^2))-1/3*b^2*polylog(2,-exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^3*d^2*sqrt(d+c^2*d*x^2))],
[x*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(5/2),x,9,-1/3*(a+b*arcsinh(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*arcsinh(c*x))/(c*d^2*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2))+2/3*b*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^2*d^2*sqrt(d+c^2*d*x^2))-1/3*I*b^2*polylog(2,-I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^2*d^2*sqrt(d+c^2*d*x^2))+1/3*I*b^2*polylog(2,I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c^2*d^2*sqrt(d+c^2*d*x^2))],
[(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(5/2),x,9,1/3*x*(a+b*arcsinh(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*arcsinh(c*x))^2/(d^2*sqrt(d+c^2*d*x^2))+1/3*b*(a+b*arcsinh(c*x))/(c*d^2*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2))+2/3*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(c*d^2*sqrt(d+c^2*d*x^2))-4/3*b*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c*d^2*sqrt(d+c^2*d*x^2))-2/3*b^2*polylog(2,-exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(c*d^2*sqrt(d+c^2*d*x^2))],
[(a+b*arcsinh(c*x))^2/(x*(d+c^2*d*x^2)^(5/2)),x,24,1/3*(a+b*arcsinh(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*arcsinh(c*x))^2/(d^2*sqrt(d+c^2*d*x^2))-1/3*b*c*x*(a+b*arcsinh(c*x))/(d^2*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2))-14/3*b*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))-2*(a+b*arcsinh(c*x))^2*arctanh(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))-2*b*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))+7/3*I*b^2*polylog(2,-I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))-7/3*I*b^2*polylog(2,I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))+2*b*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))+2*b^2*polylog(3,-exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))-2*b^2*polylog(3,exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))],
[(a+b*arcsinh(c*x))^2/(x^2*(d+c^2*d*x^2)^(5/2)),x,19,-(a+b*arcsinh(c*x))^2/(d*x*(d+c^2*d*x^2)^(3/2))-4/3*c^2*x*(a+b*arcsinh(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*arcsinh(c*x))^2/(d^2*sqrt(d+c^2*d*x^2))-1/3*b*c*(a+b*arcsinh(c*x))/(d^2*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2))-8/3*c*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))-4*b*c*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))+16/3*b*c*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))+5/3*b^2*c*polylog(2,-exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))+b^2*c*polylog(2,exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))],
[(a+b*arcsinh(c*x))^2/(x^3*(d+c^2*d*x^2)^(5/2)),x,38,-5/6*c^2*(a+b*arcsinh(c*x))^2/(d*(d+c^2*d*x^2)^(3/2))-1/2*(a+b*arcsinh(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*arcsinh(c*x))^2/(d^2*sqrt(d+c^2*d*x^2))-b*c*(a+b*arcsinh(c*x))/(d^2*x*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2))-2/3*b*c^3*x*(a+b*arcsinh(c*x))/(d^2*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2))+26/3*b*c^2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))+5*c^2*(a+b*arcsinh(c*x))^2*arctanh(exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))-b^2*c^2*arctanh(sqrt(1+c^2*x^2))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))+5*b*c^2*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))-13/3*I*b^2*c^2*polylog(2,-I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))+13/3*I*b^2*c^2*polylog(2,I*exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))-5*b*c^2*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))-5*b^2*c^2*polylog(3,-exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))+5*b^2*c^2*polylog(3,exp(arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))],
[(a+b*arcsinh(c*x))^2/(x^4*(d+c^2*d*x^2)^(5/2)),x,32,-1/3*(a+b*arcsinh(c*x))^2/(d*x^3*(d+c^2*d*x^2)^(3/2))+2*c^2*(a+b*arcsinh(c*x))^2/(d*x*(d+c^2*d*x^2)^(3/2))+8/3*c^4*x*(a+b*arcsinh(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*arcsinh(c*x))^2/(d^2*sqrt(d+c^2*d*x^2))-1/3*b*c*(a+b*arcsinh(c*x))/(d^2*x^2*sqrt(1+c^2*x^2)*sqrt(d+c^2*d*x^2))+16/3*c^3*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))+32/3*b*c^3*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))-32/3*b*c^3*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))-8/3*b^2*c^3*polylog(2,-exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))-8/3*b^2*c^3*polylog(2,exp(2*arcsinh(c*x)))*sqrt(1+c^2*x^2)/(d^2*sqrt(d+c^2*d*x^2))],
[arcsinh(a*x)^2/(c+a^2*c*x^2)^(7/2),x,13,1/5*x*arcsinh(a*x)^2/(c*(c+a^2*c*x^2)^(5/2))+4/15*x*arcsinh(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^2*x^2)*sqrt(c+a^2*c*x^2))+1/10*arcsinh(a*x)/(a*c^3*(1+a^2*x^2)^(3/2)*sqrt(c+a^2*c*x^2))+8/15*x*arcsinh(a*x)^2/(c^3*sqrt(c+a^2*c*x^2))+4/15*arcsinh(a*x)/(a*c^3*sqrt(1+a^2*x^2)*sqrt(c+a^2*c*x^2))+8/15*arcsinh(a*x)^2*sqrt(1+a^2*x^2)/(a*c^3*sqrt(c+a^2*c*x^2))-16/15*arcsinh(a*x)*log(1+exp(2*arcsinh(a*x)))*sqrt(1+a^2*x^2)/(a*c^3*sqrt(c+a^2*c*x^2))-8/15*polylog(2,-exp(2*arcsinh(a*x)))*sqrt(1+a^2*x^2)/(a*c^3*sqrt(c+a^2*c*x^2))],

# Integrands of the form (f x)^m (d+c^2 d x^2)^p (a+b ArcSinh[c x])^2 and m symbolic
[x^m*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2,x,12,5*d*x^(1+m)*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/((4+m)*(6+m))+x^(1+m)*(d+c^2*d*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/(6+m)+10*b^2*c^2*d^2*x^(3+m)*sqrt(d+c^2*d*x^2)/((4+m)^3*(6+m))+2*b^2*c^2*d^2*(52+15*m+m^2)*x^(3+m)*sqrt(d+c^2*d*x^2)/((4+m)^2*(6+m)^3)+2*b^2*c^4*d^2*x^(5+m)*sqrt(d+c^2*d*x^2)/(6+m)^3+15*d^2*x^(1+m)*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/((6+m)*(8+6*m+m^2))-30*b*c*d^2*x^(2+m)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/((2+m)^2*(4+m)*(6+m)*sqrt(1+c^2*x^2))-10*b*c*d^2*x^(2+m)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/((6+m)*(8+6*m+m^2)*sqrt(1+c^2*x^2))-2*b*c*d^2*x^(2+m)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/((12+8*m+m^2)*sqrt(1+c^2*x^2))-10*b*c^3*d^2*x^(4+m)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/((4+m)^2*(6+m)*sqrt(1+c^2*x^2))-4*b*c^3*d^2*x^(4+m)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/((4+m)*(6+m)*sqrt(1+c^2*x^2))-2*b*c^5*d^2*x^(6+m)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/((6+m)^2*sqrt(1+c^2*x^2))+10*b^2*c^2*d^2*(10+3*m)*x^(3+m)*hypergeom([1/2,1/2*(3+m)],[1/2*(5+m)],-c^2*x^2)*sqrt(d+c^2*d*x^2)/((4+m)^3*(6+m)*(6+5*m+m^2)*sqrt(1+c^2*x^2))+30*b^2*c^2*d^2*x^(3+m)*hypergeom([1/2,1/2*(3+m)],[1/2*(5+m)],-c^2*x^2)*sqrt(d+c^2*d*x^2)/((2+m)^2*(6+m)*(12+7*m+m^2)*sqrt(1+c^2*x^2))+2*b^2*c^2*d^2*(264+130*m+15*m^2)*x^(3+m)*hypergeom([1/2,1/2*(3+m)],[1/2*(5+m)],-c^2*x^2)*sqrt(d+c^2*d*x^2)/((4+m)^2*(6+m)^3*(6+5*m+m^2)*sqrt(1+c^2*x^2))+15*d^3*Unintegrable(x^m*(a+b*arcsinh(c*x))^2/sqrt(d+c^2*d*x^2),x)/((6+m)*(8+6*m+m^2))],
[x^m*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2,x,7,x^(1+m)*(d+c^2*d*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(4+m)+2*b^2*c^2*d*x^(3+m)*sqrt(d+c^2*d*x^2)/(4+m)^3+3*d*x^(1+m)*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(8+6*m+m^2)-6*b*c*d*x^(2+m)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/((2+m)^2*(4+m)*sqrt(1+c^2*x^2))-2*b*c*d*x^(2+m)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/((8+6*m+m^2)*sqrt(1+c^2*x^2))-2*b*c^3*d*x^(4+m)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/((4+m)^2*sqrt(1+c^2*x^2))+2*b^2*c^2*d*(10+3*m)*x^(3+m)*hypergeom([1/2,1/2*(3+m)],[1/2*(5+m)],-c^2*x^2)*sqrt(d+c^2*d*x^2)/((4+m)^3*(6+5*m+m^2)*sqrt(1+c^2*x^2))+6*b^2*c^2*d*x^(3+m)*hypergeom([1/2,1/2*(3+m)],[1/2*(5+m)],-c^2*x^2)*sqrt(d+c^2*d*x^2)/((2+m)^2*(12+7*m+m^2)*sqrt(1+c^2*x^2))+3*d^2*Unintegrable(x^m*(a+b*arcsinh(c*x))^2/sqrt(d+c^2*d*x^2),x)/(8+6*m+m^2)],
[x^m*(d+c^2*d*x^2)^(1/2)*(a+b*arcsinh(c*x))^2,x,3,x^(1+m)*(a+b*arcsinh(c*x))^2*sqrt(d+c^2*d*x^2)/(2+m)-2*b*c*x^(2+m)*(a+b*arcsinh(c*x))*sqrt(d+c^2*d*x^2)/((2+m)^2*sqrt(1+c^2*x^2))+2*b^2*c^2*x^(3+m)*hypergeom([1/2,1/2*(3+m)],[1/2*(5+m)],-c^2*x^2)*sqrt(d+c^2*d*x^2)/((2+m)^2*(3+m)*sqrt(1+c^2*x^2))+d*Unintegrable(x^m*(a+b*arcsinh(c*x))^2/sqrt(d+c^2*d*x^2),x)/(2+m)],
[x^m*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(1/2),x,0,Unintegrable(x^m*(a+b*arcsinh(c*x))^2/sqrt(d+c^2*d*x^2),x)],
[x^m*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(3/2),x,0,Unintegrable(x^m*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(3/2),x)],
[x^m*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(5/2),x,0,Unintegrable(x^m*(a+b*arcsinh(c*x))^2/(d+c^2*d*x^2)^(5/2),x)],
[x^m*arcsinh(a*x)^2/sqrt(1+a^2*x^2),x,0,Unintegrable(x^m*arcsinh(a*x)^2/sqrt(1+a^2*x^2),x)],

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

# Integrands of the form (f x)^m (d+c^2 d x^2)^p (a+b ArcSinh[c x])^3
[(c+a^2*c*x^2)^3*arcsinh(a*x)^3,x,24,-30256/385875*c^3*(1+a^2*x^2)^(3/2)/a-2664/214375*c^3*(1+a^2*x^2)^(5/2)/a-6/2401*c^3*(1+a^2*x^2)^(7/2)/a+4322/1225*c^3*x*arcsinh(a*x)+1514/3675*a^2*c^3*x^3*arcsinh(a*x)+702/6125*a^4*c^3*x^5*arcsinh(a*x)+6/343*a^6*c^3*x^7*arcsinh(a*x)-8/35*c^3*(1+a^2*x^2)^(3/2)*arcsinh(a*x)^2/a-18/175*c^3*(1+a^2*x^2)^(5/2)*arcsinh(a*x)^2/a-3/49*c^3*(1+a^2*x^2)^(7/2)*arcsinh(a*x)^2/a+16/35*c^3*x*arcsinh(a*x)^3+8/35*c^3*x*(1+a^2*x^2)*arcsinh(a*x)^3+6/35*c^3*x*(1+a^2*x^2)^2*arcsinh(a*x)^3+1/7*c^3*x*(1+a^2*x^2)^3*arcsinh(a*x)^3-413312/128625*c^3*sqrt(1+a^2*x^2)/a-48/35*c^3*arcsinh(a*x)^2*sqrt(1+a^2*x^2)/a],
[(c+a^2*c*x^2)^2*arcsinh(a*x)^3,x,17,-272/3375*c^2*(1+a^2*x^2)^(3/2)/a-6/625*c^2*(1+a^2*x^2)^(5/2)/a+298/75*c^2*x*arcsinh(a*x)+76/225*a^2*c^2*x^3*arcsinh(a*x)+6/125*a^4*c^2*x^5*arcsinh(a*x)-4/15*c^2*(1+a^2*x^2)^(3/2)*arcsinh(a*x)^2/a-3/25*c^2*(1+a^2*x^2)^(5/2)*arcsinh(a*x)^2/a+8/15*c^2*x*arcsinh(a*x)^3+4/15*c^2*x*(1+a^2*x^2)*arcsinh(a*x)^3+1/5*c^2*x*(1+a^2*x^2)^2*arcsinh(a*x)^3-4144/1125*c^2*sqrt(1+a^2*x^2)/a-8/5*c^2*arcsinh(a*x)^2*sqrt(1+a^2*x^2)/a],
[(c+a^2*c*x^2)*arcsinh(a*x)^3,x,10,-2/27*c*(1+a^2*x^2)^(3/2)/a+14/3*c*x*arcsinh(a*x)+2/9*a^2*c*x^3*arcsinh(a*x)-1/3*c*(1+a^2*x^2)^(3/2)*arcsinh(a*x)^2/a+2/3*c*x*arcsinh(a*x)^3+1/3*c*x*(1+a^2*x^2)*arcsinh(a*x)^3-40/9*c*sqrt(1+a^2*x^2)/a-2*c*arcsinh(a*x)^2*sqrt(1+a^2*x^2)/a],
[arcsinh(a*x)^3/(c+a^2*c*x^2),x,10,2*arcsinh(a*x)^3*arctan(exp(arcsinh(a*x)))/(a*c)-3*I*arcsinh(a*x)^2*polylog(2,-I*exp(arcsinh(a*x)))/(a*c)+3*I*arcsinh(a*x)^2*polylog(2,I*exp(arcsinh(a*x)))/(a*c)+6*I*arcsinh(a*x)*polylog(3,-I*exp(arcsinh(a*x)))/(a*c)-6*I*arcsinh(a*x)*polylog(3,I*exp(arcsinh(a*x)))/(a*c)-6*I*polylog(4,-I*exp(arcsinh(a*x)))/(a*c)+6*I*polylog(4,I*exp(arcsinh(a*x)))/(a*c)],
[arcsinh(a*x)^3/(c+a^2*c*x^2)^2,x,18,1/2*x*arcsinh(a*x)^3/(c^2*(1+a^2*x^2))-6*arcsinh(a*x)*arctan(exp(arcsinh(a*x)))/(a*c^2)+arcsinh(a*x)^3*arctan(exp(arcsinh(a*x)))/(a*c^2)+3*I*polylog(2,-I*exp(arcsinh(a*x)))/(a*c^2)-3/2*I*arcsinh(a*x)^2*polylog(2,-I*exp(arcsinh(a*x)))/(a*c^2)-3*I*polylog(2,I*exp(arcsinh(a*x)))/(a*c^2)+3/2*I*arcsinh(a*x)^2*polylog(2,I*exp(arcsinh(a*x)))/(a*c^2)+3*I*arcsinh(a*x)*polylog(3,-I*exp(arcsinh(a*x)))/(a*c^2)-3*I*arcsinh(a*x)*polylog(3,I*exp(arcsinh(a*x)))/(a*c^2)-3*I*polylog(4,-I*exp(arcsinh(a*x)))/(a*c^2)+3*I*polylog(4,I*exp(arcsinh(a*x)))/(a*c^2)+3/2*arcsinh(a*x)^2/(a*c^2*sqrt(1+a^2*x^2))],
[arcsinh(a*x)^3/(c+a^2*c*x^2)^3,x,28,-1/4*x*arcsinh(a*x)/(c^3*(1+a^2*x^2))+1/4*arcsinh(a*x)^2/(a*c^3*(1+a^2*x^2)^(3/2))+1/4*x*arcsinh(a*x)^3/(c^3*(1+a^2*x^2)^2)+3/8*x*arcsinh(a*x)^3/(c^3*(1+a^2*x^2))-5*arcsinh(a*x)*arctan(exp(arcsinh(a*x)))/(a*c^3)+3/4*arcsinh(a*x)^3*arctan(exp(arcsinh(a*x)))/(a*c^3)+5/2*I*polylog(2,-I*exp(arcsinh(a*x)))/(a*c^3)-9/8*I*arcsinh(a*x)^2*polylog(2,-I*exp(arcsinh(a*x)))/(a*c^3)-5/2*I*polylog(2,I*exp(arcsinh(a*x)))/(a*c^3)+9/8*I*arcsinh(a*x)^2*polylog(2,I*exp(arcsinh(a*x)))/(a*c^3)+9/4*I*arcsinh(a*x)*polylog(3,-I*exp(arcsinh(a*x)))/(a*c^3)-9/4*I*arcsinh(a*x)*polylog(3,I*exp(arcsinh(a*x)))/(a*c^3)-9/4*I*polylog(4,-I*exp(arcsinh(a*x)))/(a*c^3)+9/4*I*polylog(4,I*exp(arcsinh(a*x)))/(a*c^3)+(-1/4)/(a*c^3*sqrt(1+a^2*x^2))+9/8*arcsinh(a*x)^2/(a*c^3*sqrt(1+a^2*x^2))],

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

# p>0
[(c+a^2*c*x^2)^(5/2)*arcsinh(a*x)^3,x,24,5/24*c*x*(c+a^2*c*x^2)^(3/2)*arcsinh(a*x)^3+1/6*x*(c+a^2*c*x^2)^(5/2)*arcsinh(a*x)^3-1/216*c^2*(1+a^2*x^2)^(5/2)*sqrt(c+a^2*c*x^2)/a+245/384*c^2*x*arcsinh(a*x)*sqrt(c+a^2*c*x^2)+65/576*c^2*x*(1+a^2*x^2)*arcsinh(a*x)*sqrt(c+a^2*c*x^2)+1/36*c^2*x*(1+a^2*x^2)^2*arcsinh(a*x)*sqrt(c+a^2*c*x^2)-5/32*c^2*(1+a^2*x^2)^(3/2)*arcsinh(a*x)^2*sqrt(c+a^2*c*x^2)/a-1/12*c^2*(1+a^2*x^2)^(5/2)*arcsinh(a*x)^2*sqrt(c+a^2*c*x^2)/a+5/16*c^2*x*arcsinh(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^2*x^2)-65/2304*a^3*c^2*x^4*sqrt(c+a^2*c*x^2)/sqrt(1+a^2*x^2)-115/768*c^2*arcsinh(a*x)^2*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-15/32*a*c^2*x^2*arcsinh(a*x)^2*sqrt(c+a^2*c*x^2)/sqrt(1+a^2*x^2)+5/64*c^2*arcsinh(a*x)^4*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))],
[(c+a^2*c*x^2)^(3/2)*arcsinh(a*x)^3,x,14,1/4*x*(c+a^2*c*x^2)^(3/2)*arcsinh(a*x)^3+45/64*c*x*arcsinh(a*x)*sqrt(c+a^2*c*x^2)+3/32*c*x*(1+a^2*x^2)*arcsinh(a*x)*sqrt(c+a^2*c*x^2)-3/16*c*(1+a^2*x^2)^(3/2)*arcsinh(a*x)^2*sqrt(c+a^2*c*x^2)/a+3/8*c*x*arcsinh(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^2*x^2)-3/128*a^3*c*x^4*sqrt(c+a^2*c*x^2)/sqrt(1+a^2*x^2)-27/128*c*arcsinh(a*x)^2*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-9/16*a*c*x^2*arcsinh(a*x)^2*sqrt(c+a^2*c*x^2)/sqrt(1+a^2*x^2)+3/32*c*arcsinh(a*x)^4*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))],
[arcsinh(a*x)^3*sqrt(c+a^2*c*x^2),x,6,3/4*x*arcsinh(a*x)*sqrt(c+a^2*c*x^2)+1/2*x*arcsinh(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^2*x^2)-3/8*arcsinh(a*x)^2*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-3/4*a*x^2*arcsinh(a*x)^2*sqrt(c+a^2*c*x^2)/sqrt(1+a^2*x^2)+1/8*arcsinh(a*x)^4*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))],

# p<0
[arcsinh(a*x)^3/sqrt(c+a^2*c*x^2),x,1,1/4*arcsinh(a*x)^4*sqrt(1+a^2*x^2)/(a*sqrt(c+a^2*c*x^2))],
[arcsinh(a*x)^3/(c+a^2*c*x^2)^(3/2),x,7,x*arcsinh(a*x)^3/(c*sqrt(c+a^2*c*x^2))+arcsinh(a*x)^3*sqrt(1+a^2*x^2)/(a*c*sqrt(c+a^2*c*x^2))-3*arcsinh(a*x)^2*log(1+exp(2*arcsinh(a*x)))*sqrt(1+a^2*x^2)/(a*c*sqrt(c+a^2*c*x^2))-3*arcsinh(a*x)*polylog(2,-exp(2*arcsinh(a*x)))*sqrt(1+a^2*x^2)/(a*c*sqrt(c+a^2*c*x^2))+3/2*polylog(3,-exp(2*arcsinh(a*x)))*sqrt(1+a^2*x^2)/(a*c*sqrt(c+a^2*c*x^2))],
[arcsinh(a*x)^3/(c+a^2*c*x^2)^(5/2),x,11,1/3*x*arcsinh(a*x)^3/(c*(c+a^2*c*x^2)^(3/2))-x*arcsinh(a*x)/(c^2*sqrt(c+a^2*c*x^2))+2/3*x*arcsinh(a*x)^3/(c^2*sqrt(c+a^2*c*x^2))+1/2*arcsinh(a*x)^2/(a*c^2*sqrt(1+a^2*x^2)*sqrt(c+a^2*c*x^2))+2/3*arcsinh(a*x)^3*sqrt(1+a^2*x^2)/(a*c^2*sqrt(c+a^2*c*x^2))-2*arcsinh(a*x)^2*log(1+exp(2*arcsinh(a*x)))*sqrt(1+a^2*x^2)/(a*c^2*sqrt(c+a^2*c*x^2))+1/2*log(1+a^2*x^2)*sqrt(1+a^2*x^2)/(a*c^2*sqrt(c+a^2*c*x^2))-2*arcsinh(a*x)*polylog(2,-exp(2*arcsinh(a*x)))*sqrt(1+a^2*x^2)/(a*c^2*sqrt(c+a^2*c*x^2))+polylog(3,-exp(2*arcsinh(a*x)))*sqrt(1+a^2*x^2)/(a*c^2*sqrt(c+a^2*c*x^2))],
[arcsinh(a*x)^3/(c+a^2*c*x^2)^(7/2),x,17,1/5*x*arcsinh(a*x)^3/(c*(c+a^2*c*x^2)^(5/2))+4/15*x*arcsinh(a*x)^3/(c^2*(c+a^2*c*x^2)^(3/2))-x*arcsinh(a*x)/(c^3*sqrt(c+a^2*c*x^2))-1/10*x*arcsinh(a*x)/(c^3*(1+a^2*x^2)*sqrt(c+a^2*c*x^2))+3/20*arcsinh(a*x)^2/(a*c^3*(1+a^2*x^2)^(3/2)*sqrt(c+a^2*c*x^2))+8/15*x*arcsinh(a*x)^3/(c^3*sqrt(c+a^2*c*x^2))+(-1/20)/(a*c^3*sqrt(1+a^2*x^2)*sqrt(c+a^2*c*x^2))+2/5*arcsinh(a*x)^2/(a*c^3*sqrt(1+a^2*x^2)*sqrt(c+a^2*c*x^2))+8/15*arcsinh(a*x)^3*sqrt(1+a^2*x^2)/(a*c^3*sqrt(c+a^2*c*x^2))-8/5*arcsinh(a*x)^2*log(1+exp(2*arcsinh(a*x)))*sqrt(1+a^2*x^2)/(a*c^3*sqrt(c+a^2*c*x^2))+1/2*log(1+a^2*x^2)*sqrt(1+a^2*x^2)/(a*c^3*sqrt(c+a^2*c*x^2))-8/5*arcsinh(a*x)*polylog(2,-exp(2*arcsinh(a*x)))*sqrt(1+a^2*x^2)/(a*c^3*sqrt(c+a^2*c*x^2))+4/5*polylog(3,-exp(2*arcsinh(a*x)))*sqrt(1+a^2*x^2)/(a*c^3*sqrt(c+a^2*c*x^2))],
[x^m*arcsinh(a*x)^3/sqrt(1+a^2*x^2),x,0,Unintegrable(x^m*arcsinh(a*x)^3/sqrt(1+a^2*x^2),x)],
[x^4*arcsinh(a*x)^3/sqrt(1+a^2*x^2),x,13,45/128*x^2/a^3-3/128*x^4/a+45/128*arcsinh(a*x)^2/a^5+9/16*x^2*arcsinh(a*x)^2/a^3-3/16*x^4*arcsinh(a*x)^2/a+3/32*arcsinh(a*x)^4/a^5-45/64*x*arcsinh(a*x)*sqrt(1+a^2*x^2)/a^4+3/32*x^3*arcsinh(a*x)*sqrt(1+a^2*x^2)/a^2-3/8*x*arcsinh(a*x)^3*sqrt(1+a^2*x^2)/a^4+1/4*x^3*arcsinh(a*x)^3*sqrt(1+a^2*x^2)/a^2],
[x^3*arcsinh(a*x)^3/sqrt(1+a^2*x^2),x,10,40/9*x/a^3-2/27*x^3/a+2*x*arcsinh(a*x)^2/a^3-1/3*x^3*arcsinh(a*x)^2/a-40/9*arcsinh(a*x)*sqrt(1+a^2*x^2)/a^4+2/9*x^2*arcsinh(a*x)*sqrt(1+a^2*x^2)/a^2-2/3*arcsinh(a*x)^3*sqrt(1+a^2*x^2)/a^4+1/3*x^2*arcsinh(a*x)^3*sqrt(1+a^2*x^2)/a^2],
[x^2*arcsinh(a*x)^3/sqrt(1+a^2*x^2),x,6,-3/8*x^2/a-3/8*arcsinh(a*x)^2/a^3-3/4*x^2*arcsinh(a*x)^2/a-1/8*arcsinh(a*x)^4/a^3+3/4*x*arcsinh(a*x)*sqrt(1+a^2*x^2)/a^2+1/2*x*arcsinh(a*x)^3*sqrt(1+a^2*x^2)/a^2],
[x*arcsinh(a*x)^3/sqrt(1+a^2*x^2),x,4,-6*x/a-3*x*arcsinh(a*x)^2/a+6*arcsinh(a*x)*sqrt(1+a^2*x^2)/a^2+arcsinh(a*x)^3*sqrt(1+a^2*x^2)/a^2],
[arcsinh(a*x)^3/sqrt(1+a^2*x^2),x,1,1/4*arcsinh(a*x)^4/a],
[arcsinh(a*x)^3/(x*sqrt(1+a^2*x^2)),x,10,-2*arcsinh(a*x)^3*arctanh(exp(arcsinh(a*x)))-3*arcsinh(a*x)^2*polylog(2,-exp(arcsinh(a*x)))+3*arcsinh(a*x)^2*polylog(2,exp(arcsinh(a*x)))+6*arcsinh(a*x)*polylog(3,-exp(arcsinh(a*x)))-6*arcsinh(a*x)*polylog(3,exp(arcsinh(a*x)))-6*polylog(4,-exp(arcsinh(a*x)))+6*polylog(4,exp(arcsinh(a*x)))],
[arcsinh(a*x)^3/(x^2*sqrt(1+a^2*x^2)),x,7,-a*arcsinh(a*x)^3+3*a*arcsinh(a*x)^2*log(1-exp(2*arcsinh(a*x)))+3*a*arcsinh(a*x)*polylog(2,exp(2*arcsinh(a*x)))-3/2*a*polylog(3,exp(2*arcsinh(a*x)))-arcsinh(a*x)^3*sqrt(1+a^2*x^2)/x],
[arcsinh(a*x)^3/(x^3*sqrt(1+a^2*x^2)),x,18,-3/2*a*arcsinh(a*x)^2/x-6*a^2*arcsinh(a*x)*arctanh(exp(arcsinh(a*x)))+a^2*arcsinh(a*x)^3*arctanh(exp(arcsinh(a*x)))-3*a^2*polylog(2,-exp(arcsinh(a*x)))+3/2*a^2*arcsinh(a*x)^2*polylog(2,-exp(arcsinh(a*x)))+3*a^2*polylog(2,exp(arcsinh(a*x)))-3/2*a^2*arcsinh(a*x)^2*polylog(2,exp(arcsinh(a*x)))-3*a^2*arcsinh(a*x)*polylog(3,-exp(arcsinh(a*x)))+3*a^2*arcsinh(a*x)*polylog(3,exp(arcsinh(a*x)))+3*a^2*polylog(4,-exp(arcsinh(a*x)))-3*a^2*polylog(4,exp(arcsinh(a*x)))-1/2*arcsinh(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 ArcSinh[c x])^1

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

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

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

# p<0
[x^4/(arcsinh(a*x)*sqrt(1+a^2*x^2)),x,5,-1/2*Chi(2*arcsinh(a*x))/a^5+1/8*Chi(4*arcsinh(a*x))/a^5+3/8*log(arcsinh(a*x))/a^5],
[x^3/(arcsinh(a*x)*sqrt(1+a^2*x^2)),x,5,-3/4*Shi(arcsinh(a*x))/a^4+1/4*Shi(3*arcsinh(a*x))/a^4],
[x^2/(arcsinh(a*x)*sqrt(1+a^2*x^2)),x,4,1/2*Chi(2*arcsinh(a*x))/a^3-1/2*log(arcsinh(a*x))/a^3],
[x^2/(arcsinh(a*x)*sqrt(1+a^2*x^2)),x,4,1/2*Chi(2*arcsinh(a*x))/a^3-1/2*log(arcsinh(a*x))/a^3],
[x/(arcsinh(a*x)*sqrt(1+a^2*x^2)),x,2,Shi(arcsinh(a*x))/a^2],
[1/(arcsinh(a*x)*sqrt(1+a^2*x^2)),x,1,log(arcsinh(a*x))/a],
[1/(x*arcsinh(a*x)*sqrt(1+a^2*x^2)),x,0,Unintegrable(1/(x*arcsinh(a*x)*sqrt(1+a^2*x^2)),x)],
[1/(x^2*arcsinh(a*x)*sqrt(1+a^2*x^2)),x,0,Unintegrable(1/(x^2*arcsinh(a*x)*sqrt(1+a^2*x^2)),x)],
[x^5/((a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)),x,12,5/8*cosh(a/b)*Shi((a+b*arcsinh(c*x))/b)/(b*c^6)-5/16*cosh(3*a/b)*Shi(3*(a+b*arcsinh(c*x))/b)/(b*c^6)+1/16*cosh(5*a/b)*Shi(5*(a+b*arcsinh(c*x))/b)/(b*c^6)-5/8*Chi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b*c^6)+5/16*Chi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b*c^6)-1/16*Chi(5*(a+b*arcsinh(c*x))/b)*sinh(5*a/b)/(b*c^6)],
[x^4/((a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)),x,9,-1/2*Chi(2*(a+b*arcsinh(c*x))/b)*cosh(2*a/b)/(b*c^5)+1/8*Chi(4*(a+b*arcsinh(c*x))/b)*cosh(4*a/b)/(b*c^5)+3/8*log(a+b*arcsinh(c*x))/(b*c^5)+1/2*Shi(2*(a+b*arcsinh(c*x))/b)*sinh(2*a/b)/(b*c^5)-1/8*Shi(4*(a+b*arcsinh(c*x))/b)*sinh(4*a/b)/(b*c^5)],
[x^3/((a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)),x,9,-3/4*cosh(a/b)*Shi((a+b*arcsinh(c*x))/b)/(b*c^4)+1/4*cosh(3*a/b)*Shi(3*(a+b*arcsinh(c*x))/b)/(b*c^4)+3/4*Chi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b*c^4)-1/4*Chi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b*c^4)],
[x^2/((a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)),x,6,1/2*Chi(2*(a+b*arcsinh(c*x))/b)*cosh(2*a/b)/(b*c^3)-1/2*log(a+b*arcsinh(c*x))/(b*c^3)-1/2*Shi(2*(a+b*arcsinh(c*x))/b)*sinh(2*a/b)/(b*c^3)],
[x/((a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)),x,4,cosh(a/b)*Shi((a+b*arcsinh(c*x))/b)/(b*c^2)-Chi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b*c^2)],
[1/((a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)),x,1,log(a+b*arcsinh(c*x))/(b*c)],
[1/(x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)),x,0,Unintegrable(1/(x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)),x)],
[1/(x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)),x,0,Unintegrable(1/(x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)),x)],
[x^2/((1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))),x,0,Unintegrable(x^2/((1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))),x)],
[x/((1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))),x,0,Unintegrable(x/((1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))),x)],
[1/((1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))),x,0,Unintegrable(1/((1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))),x)],
[1/(x*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))),x,0,Unintegrable(1/(x*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))),x)],
[1/(x^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))),x,0,Unintegrable(1/(x^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))),x)],

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

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

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

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

# p>0
[x^3*sqrt(1+c^2*x^2)/(a+b*arcsinh(c*x))^2,x,22,-x^3*(1+c^2*x^2)/(b*c*(a+b*arcsinh(c*x)))-1/8*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b^2*c^4)-3/16*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/(b^2*c^4)+5/16*Chi(5*(a+b*arcsinh(c*x))/b)*cosh(5*a/b)/(b^2*c^4)+1/8*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b^2*c^4)+3/16*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b^2*c^4)-5/16*Shi(5*(a+b*arcsinh(c*x))/b)*sinh(5*a/b)/(b^2*c^4)],
[x^2*sqrt(1+c^2*x^2)/(a+b*arcsinh(c*x))^2,x,16,-x^2*(1+c^2*x^2)/(b*c*(a+b*arcsinh(c*x)))+1/2*cosh(4*a/b)*Shi(4*(a+b*arcsinh(c*x))/b)/(b^2*c^3)-1/2*Chi(4*(a+b*arcsinh(c*x))/b)*sinh(4*a/b)/(b^2*c^3)],
[x*sqrt(1+c^2*x^2)/(a+b*arcsinh(c*x))^2,x,14,-x*(1+c^2*x^2)/(b*c*(a+b*arcsinh(c*x)))+1/4*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b^2*c^2)+3/4*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/(b^2*c^2)-1/4*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b^2*c^2)-3/4*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b^2*c^2)],
[sqrt(1+c^2*x^2)/(a+b*arcsinh(c*x))^2,x,7,(-1-c^2*x^2)/(b*c*(a+b*arcsinh(c*x)))+cosh(2*a/b)*Shi(2*(a+b*arcsinh(c*x))/b)/(b^2*c)-Chi(2*(a+b*arcsinh(c*x))/b)*sinh(2*a/b)/(b^2*c)],
[sqrt(1+c^2*x^2)/(x*(a+b*arcsinh(c*x))^2),x,5,(-1-c^2*x^2)/(b*c*x*(a+b*arcsinh(c*x)))+Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/b^2-Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/b^2-Unintegrable(1/(x^2*(a+b*arcsinh(c*x))),x)/(b*c)],
[sqrt(1+c^2*x^2)/(x^2*(a+b*arcsinh(c*x))^2),x,1,(-1-c^2*x^2)/(b*c*x^2*(a+b*arcsinh(c*x)))-2*Unintegrable(1/(x^3*(a+b*arcsinh(c*x))),x)/(b*c)],
[sqrt(1+c^2*x^2)/(x^3*(a+b*arcsinh(c*x))^2),x,0,Unintegrable(sqrt(1+c^2*x^2)/(x^3*(a+b*arcsinh(c*x))^2),x)],
[sqrt(1+c^2*x^2)/(x^4*(a+b*arcsinh(c*x))^2),x,0,Unintegrable(sqrt(1+c^2*x^2)/(x^4*(a+b*arcsinh(c*x))^2),x)],
[x^3*(1+c^2*x^2)^(3/2)/(a+b*arcsinh(c*x))^2,x,28,-x^3*(1+c^2*x^2)^2/(b*c*(a+b*arcsinh(c*x)))-3/64*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b^2*c^4)-9/64*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/(b^2*c^4)+5/64*Chi(5*(a+b*arcsinh(c*x))/b)*cosh(5*a/b)/(b^2*c^4)+7/64*Chi(7*(a+b*arcsinh(c*x))/b)*cosh(7*a/b)/(b^2*c^4)+3/64*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b^2*c^4)+9/64*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b^2*c^4)-5/64*Shi(5*(a+b*arcsinh(c*x))/b)*sinh(5*a/b)/(b^2*c^4)-7/64*Shi(7*(a+b*arcsinh(c*x))/b)*sinh(7*a/b)/(b^2*c^4)],
[x^2*(1+c^2*x^2)^(3/2)/(a+b*arcsinh(c*x))^2,x,19,-x^2*(1+c^2*x^2)^2/(b*c*(a+b*arcsinh(c*x)))-1/16*cosh(2*a/b)*Shi(2*(a+b*arcsinh(c*x))/b)/(b^2*c^3)+1/4*cosh(4*a/b)*Shi(4*(a+b*arcsinh(c*x))/b)/(b^2*c^3)+3/16*cosh(6*a/b)*Shi(6*(a+b*arcsinh(c*x))/b)/(b^2*c^3)+1/16*Chi(2*(a+b*arcsinh(c*x))/b)*sinh(2*a/b)/(b^2*c^3)-1/4*Chi(4*(a+b*arcsinh(c*x))/b)*sinh(4*a/b)/(b^2*c^3)-3/16*Chi(6*(a+b*arcsinh(c*x))/b)*sinh(6*a/b)/(b^2*c^3)],
[x*(1+c^2*x^2)^(3/2)/(a+b*arcsinh(c*x))^2,x,22,-x*(1+c^2*x^2)^2/(b*c*(a+b*arcsinh(c*x)))+1/8*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b^2*c^2)+9/16*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/(b^2*c^2)+5/16*Chi(5*(a+b*arcsinh(c*x))/b)*cosh(5*a/b)/(b^2*c^2)-1/8*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b^2*c^2)-9/16*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b^2*c^2)-5/16*Shi(5*(a+b*arcsinh(c*x))/b)*sinh(5*a/b)/(b^2*c^2)],
[(1+c^2*x^2)^(3/2)/(a+b*arcsinh(c*x))^2,x,10,-(1+c^2*x^2)^2/(b*c*(a+b*arcsinh(c*x)))+cosh(2*a/b)*Shi(2*(a+b*arcsinh(c*x))/b)/(b^2*c)+1/2*cosh(4*a/b)*Shi(4*(a+b*arcsinh(c*x))/b)/(b^2*c)-Chi(2*(a+b*arcsinh(c*x))/b)*sinh(2*a/b)/(b^2*c)-1/2*Chi(4*(a+b*arcsinh(c*x))/b)*sinh(4*a/b)/(b^2*c)],
[(1+c^2*x^2)^(3/2)/(x*(a+b*arcsinh(c*x))^2),x,10,-(1+c^2*x^2)^2/(b*c*x*(a+b*arcsinh(c*x)))+9/4*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/b^2+3/4*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/b^2-9/4*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/b^2-3/4*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/b^2-Unintegrable((1+c^2*x^2)/(x^2*(a+b*arcsinh(c*x))),x)/(b*c)],
[(1+c^2*x^2)^(3/2)/(x^2*(a+b*arcsinh(c*x))^2),x,1,-(1+c^2*x^2)^2/(b*c*x^2*(a+b*arcsinh(c*x)))-2*Unintegrable((1+c^2*x^2)/(x^3*(a+b*arcsinh(c*x))),x)/(b*c)+2*c*Unintegrable((1+c^2*x^2)/(x*(a+b*arcsinh(c*x))),x)/b],
[(1+c^2*x^2)^(3/2)/(x^3*(a+b*arcsinh(c*x))^2),x,0,Unintegrable((1+c^2*x^2)^(3/2)/(x^3*(a+b*arcsinh(c*x))^2),x)],
[(1+c^2*x^2)^(3/2)/(x^4*(a+b*arcsinh(c*x))^2),x,1,-(1+c^2*x^2)^2/(b*c*x^4*(a+b*arcsinh(c*x)))-4*Unintegrable((1+c^2*x^2)/(x^5*(a+b*arcsinh(c*x))),x)/(b*c)],
[x^3*(1+c^2*x^2)^(5/2)/(a+b*arcsinh(c*x))^2,x,34,-x^3*(1+c^2*x^2)^3/(b*c*(a+b*arcsinh(c*x)))-3/128*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b^2*c^4)-3/32*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/(b^2*c^4)+21/256*Chi(7*(a+b*arcsinh(c*x))/b)*cosh(7*a/b)/(b^2*c^4)+9/256*Chi(9*(a+b*arcsinh(c*x))/b)*cosh(9*a/b)/(b^2*c^4)+3/128*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b^2*c^4)+3/32*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b^2*c^4)-21/256*Shi(7*(a+b*arcsinh(c*x))/b)*sinh(7*a/b)/(b^2*c^4)-9/256*Shi(9*(a+b*arcsinh(c*x))/b)*sinh(9*a/b)/(b^2*c^4)],
[x^2*(1+c^2*x^2)^(5/2)/(a+b*arcsinh(c*x))^2,x,28,-x^2*(1+c^2*x^2)^3/(b*c*(a+b*arcsinh(c*x)))-1/16*cosh(2*a/b)*Shi(2*(a+b*arcsinh(c*x))/b)/(b^2*c^3)+1/8*cosh(4*a/b)*Shi(4*(a+b*arcsinh(c*x))/b)/(b^2*c^3)+3/16*cosh(6*a/b)*Shi(6*(a+b*arcsinh(c*x))/b)/(b^2*c^3)+1/16*cosh(8*a/b)*Shi(8*(a+b*arcsinh(c*x))/b)/(b^2*c^3)+1/16*Chi(2*(a+b*arcsinh(c*x))/b)*sinh(2*a/b)/(b^2*c^3)-1/8*Chi(4*(a+b*arcsinh(c*x))/b)*sinh(4*a/b)/(b^2*c^3)-3/16*Chi(6*(a+b*arcsinh(c*x))/b)*sinh(6*a/b)/(b^2*c^3)-1/16*Chi(8*(a+b*arcsinh(c*x))/b)*sinh(8*a/b)/(b^2*c^3)],
[x*(1+c^2*x^2)^(5/2)/(a+b*arcsinh(c*x))^2,x,28,-x*(1+c^2*x^2)^3/(b*c*(a+b*arcsinh(c*x)))+5/64*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b^2*c^2)+27/64*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/(b^2*c^2)+25/64*Chi(5*(a+b*arcsinh(c*x))/b)*cosh(5*a/b)/(b^2*c^2)+7/64*Chi(7*(a+b*arcsinh(c*x))/b)*cosh(7*a/b)/(b^2*c^2)-5/64*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b^2*c^2)-27/64*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b^2*c^2)-25/64*Shi(5*(a+b*arcsinh(c*x))/b)*sinh(5*a/b)/(b^2*c^2)-7/64*Shi(7*(a+b*arcsinh(c*x))/b)*sinh(7*a/b)/(b^2*c^2)],
[(1+c^2*x^2)^(5/2)/(a+b*arcsinh(c*x))^2,x,13,-(1+c^2*x^2)^3/(b*c*(a+b*arcsinh(c*x)))+15/16*cosh(2*a/b)*Shi(2*(a+b*arcsinh(c*x))/b)/(b^2*c)+3/4*cosh(4*a/b)*Shi(4*(a+b*arcsinh(c*x))/b)/(b^2*c)+3/16*cosh(6*a/b)*Shi(6*(a+b*arcsinh(c*x))/b)/(b^2*c)-15/16*Chi(2*(a+b*arcsinh(c*x))/b)*sinh(2*a/b)/(b^2*c)-3/4*Chi(4*(a+b*arcsinh(c*x))/b)*sinh(4*a/b)/(b^2*c)-3/16*Chi(6*(a+b*arcsinh(c*x))/b)*sinh(6*a/b)/(b^2*c)],
[(1+c^2*x^2)^(5/2)/(x*(a+b*arcsinh(c*x))^2),x,13,-(1+c^2*x^2)^3/(b*c*x*(a+b*arcsinh(c*x)))+25/8*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/b^2+25/16*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/b^2+5/16*Chi(5*(a+b*arcsinh(c*x))/b)*cosh(5*a/b)/b^2-25/8*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/b^2-25/16*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/b^2-5/16*Shi(5*(a+b*arcsinh(c*x))/b)*sinh(5*a/b)/b^2-Unintegrable((1+c^2*x^2)^2/(x^2*(a+b*arcsinh(c*x))),x)/(b*c)],
[(1+c^2*x^2)^(5/2)/(x^2*(a+b*arcsinh(c*x))^2),x,1,-(1+c^2*x^2)^3/(b*c*x^2*(a+b*arcsinh(c*x)))-2*Unintegrable((1+c^2*x^2)^2/(x^3*(a+b*arcsinh(c*x))),x)/(b*c)+4*c*Unintegrable((1+c^2*x^2)^2/(x*(a+b*arcsinh(c*x))),x)/b],
[(1+c^2*x^2)^(5/2)/(x^3*(a+b*arcsinh(c*x))^2),x,0,Unintegrable((1+c^2*x^2)^(5/2)/(x^3*(a+b*arcsinh(c*x))^2),x)],
[(1+c^2*x^2)^(5/2)/(x^4*(a+b*arcsinh(c*x))^2),x,0,Unintegrable((1+c^2*x^2)^(5/2)/(x^4*(a+b*arcsinh(c*x))^2),x)],

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

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

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

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

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

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

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

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

# p<0

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

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

# n>0
[(c+a^2*c*x^2)^(3/2)*sqrt(arcsinh(a*x)),x,24,1/4*c*arcsinh(a*x)^(3/2)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+1/16*c*erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-1/16*c*erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+1/256*c*erf(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-1/256*c*erfi(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+1/4*x*(c+a^2*c*x^2)^(3/2)*sqrt(arcsinh(a*x))+3/8*c*x*sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))],
[sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x)),x,10,1/3*arcsinh(a*x)^(3/2)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+1/16*erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-1/16*erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+1/2*x*sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))],
[sqrt(arcsinh(a*x))/sqrt(c+a^2*c*x^2),x,1,2/3*arcsinh(a*x)^(3/2)*sqrt(1+a^2*x^2)/(a*sqrt(c+a^2*c*x^2))],
[sqrt(arcsinh(a*x))/(c+a^2*c*x^2)^(3/2),x,1,x*sqrt(arcsinh(a*x))/(c*sqrt(c+a^2*c*x^2))-1/2*a*sqrt(1+a^2*x^2)*Unintegrable(x/((1+a^2*x^2)*sqrt(arcsinh(a*x))),x)/(c*sqrt(c+a^2*c*x^2))],
[sqrt(arcsinh(a*x))/(c+a^2*c*x^2)^(5/2),x,2,1/3*x*sqrt(arcsinh(a*x))/(c*(c+a^2*c*x^2)^(3/2))+2/3*x*sqrt(arcsinh(a*x))/(c^2*sqrt(c+a^2*c*x^2))-1/6*a*sqrt(1+a^2*x^2)*Unintegrable(x/((1+a^2*x^2)^2*sqrt(arcsinh(a*x))),x)/(c^2*sqrt(c+a^2*c*x^2))-1/3*a*sqrt(1+a^2*x^2)*Unintegrable(x/((1+a^2*x^2)*sqrt(arcsinh(a*x))),x)/(c^2*sqrt(c+a^2*c*x^2))],
[(c+a^2*c*x^2)^(3/2)*arcsinh(a*x)^(3/2),x,26,1/4*x*(c+a^2*c*x^2)^(3/2)*arcsinh(a*x)^(3/2)+3/8*c*x*arcsinh(a*x)^(3/2)*sqrt(c+a^2*c*x^2)+3/20*c*arcsinh(a*x)^(5/2)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+3/64*c*erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+3/64*c*erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+3/2048*c*erf(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+3/2048*c*erfi(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-3/32*c*(1+a^2*x^2)^(3/2)*sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))/a-27/256*c*sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))/(a*sqrt(1+a^2*x^2))-9/32*a*c*x^2*sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))/sqrt(1+a^2*x^2)],
[arcsinh(a*x)^(3/2)*sqrt(c+a^2*c*x^2),x,11,1/2*x*arcsinh(a*x)^(3/2)*sqrt(c+a^2*c*x^2)+1/5*arcsinh(a*x)^(5/2)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+3/64*erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+3/64*erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-3/16*sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))/(a*sqrt(1+a^2*x^2))-3/8*a*x^2*sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))/sqrt(1+a^2*x^2)],
[arcsinh(a*x)^(3/2)/sqrt(c+a^2*c*x^2),x,1,2/5*arcsinh(a*x)^(5/2)*sqrt(1+a^2*x^2)/(a*sqrt(c+a^2*c*x^2))],
[arcsinh(a*x)^(3/2)/(c+a^2*c*x^2)^(3/2),x,1,x*arcsinh(a*x)^(3/2)/(c*sqrt(c+a^2*c*x^2))-3/2*a*sqrt(1+a^2*x^2)*Unintegrable(x*sqrt(arcsinh(a*x))/(1+a^2*x^2),x)/(c*sqrt(c+a^2*c*x^2))],
[(c+a^2*c*x^2)^(3/2)*arcsinh(a*x)^(5/2),x,39,1/4*x*(c+a^2*c*x^2)^(3/2)*arcsinh(a*x)^(5/2)-5/32*c*(1+a^2*x^2)^(3/2)*arcsinh(a*x)^(3/2)*sqrt(c+a^2*c*x^2)/a+3/8*c*x*arcsinh(a*x)^(5/2)*sqrt(c+a^2*c*x^2)-45/256*c*arcsinh(a*x)^(3/2)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-15/32*a*c*x^2*arcsinh(a*x)^(3/2)*sqrt(c+a^2*c*x^2)/sqrt(1+a^2*x^2)+3/28*c*arcsinh(a*x)^(7/2)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+15/256*c*erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-15/256*c*erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+15/16384*c*erf(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-15/16384*c*erfi(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+225/512*c*x*sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))+15/256*c*x*(1+a^2*x^2)*sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))],
[arcsinh(a*x)^(5/2)*sqrt(c+a^2*c*x^2),x,13,1/2*x*arcsinh(a*x)^(5/2)*sqrt(c+a^2*c*x^2)-5/16*arcsinh(a*x)^(3/2)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-5/8*a*x^2*arcsinh(a*x)^(3/2)*sqrt(c+a^2*c*x^2)/sqrt(1+a^2*x^2)+1/7*arcsinh(a*x)^(7/2)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+15/256*erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-15/256*erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+15/32*x*sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))],
[arcsinh(a*x)^(5/2)/sqrt(c+a^2*c*x^2),x,1,2/7*arcsinh(a*x)^(7/2)*sqrt(1+a^2*x^2)/(a*sqrt(c+a^2*c*x^2))],
[arcsinh(a*x)^(5/2)/(c+a^2*c*x^2)^(3/2),x,1,x*arcsinh(a*x)^(5/2)/(c*sqrt(c+a^2*c*x^2))-5/2*a*sqrt(1+a^2*x^2)*Unintegrable(x*arcsinh(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(arcsinh(x/a)),x,24,1/4*a^3*arcsinh(x/a)^(3/2)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)+1/16*a^3*erf(sqrt(2)*sqrt(arcsinh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)-1/16*a^3*erfi(sqrt(2)*sqrt(arcsinh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)+1/256*a^3*erf(2*sqrt(arcsinh(x/a)))*sqrt(Pi)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)-1/256*a^3*erfi(2*sqrt(arcsinh(x/a)))*sqrt(Pi)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)+1/4*x*(a^2+x^2)^(3/2)*sqrt(arcsinh(x/a))+3/8*a^2*x*sqrt(a^2+x^2)*sqrt(arcsinh(x/a))],
[sqrt(a^2+x^2)*sqrt(arcsinh(x/a)),x,10,1/3*a*arcsinh(x/a)^(3/2)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)+1/16*a*erf(sqrt(2)*sqrt(arcsinh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)-1/16*a*erfi(sqrt(2)*sqrt(arcsinh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)+1/2*x*sqrt(a^2+x^2)*sqrt(arcsinh(x/a))],
[sqrt(arcsinh(x/a))/sqrt(a^2+x^2),x,1,2/3*a*arcsinh(x/a)^(3/2)*sqrt(1+x^2/a^2)/sqrt(a^2+x^2)],
[sqrt(arcsinh(x/a))/(a^2+x^2)^(3/2),x,1,x*sqrt(arcsinh(x/a))/(a^2*sqrt(a^2+x^2))-1/2*sqrt(1+x^2/a^2)*Unintegrable(x/((1+x^2/a^2)*sqrt(arcsinh(x/a))),x)/(a^3*sqrt(a^2+x^2))],
[sqrt(arcsinh(x/a))/(a^2+x^2)^(5/2),x,2,1/3*x*sqrt(arcsinh(x/a))/(a^2*(a^2+x^2)^(3/2))+2/3*x*sqrt(arcsinh(x/a))/(a^4*sqrt(a^2+x^2))-1/6*sqrt(1+x^2/a^2)*Unintegrable(x/((1+x^2/a^2)^2*sqrt(arcsinh(x/a))),x)/(a^5*sqrt(a^2+x^2))-1/3*sqrt(1+x^2/a^2)*Unintegrable(x/((1+x^2/a^2)*sqrt(arcsinh(x/a))),x)/(a^5*sqrt(a^2+x^2))],
[(a^2+x^2)^(3/2)*arcsinh(x/a)^(3/2),x,26,1/4*x*(a^2+x^2)^(3/2)*arcsinh(x/a)^(3/2)+3/8*a^2*x*arcsinh(x/a)^(3/2)*sqrt(a^2+x^2)+3/20*a^3*arcsinh(x/a)^(5/2)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)+3/64*a^3*erf(sqrt(2)*sqrt(arcsinh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)+3/64*a^3*erfi(sqrt(2)*sqrt(arcsinh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)+3/2048*a^3*erf(2*sqrt(arcsinh(x/a)))*sqrt(Pi)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)+3/2048*a^3*erfi(2*sqrt(arcsinh(x/a)))*sqrt(Pi)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)-3/32*(a^2+x^2)^(5/2)*sqrt(arcsinh(x/a))/(a*sqrt(1+x^2/a^2))-27/256*a^3*sqrt(a^2+x^2)*sqrt(arcsinh(x/a))/sqrt(1+x^2/a^2)-9/32*a*x^2*sqrt(a^2+x^2)*sqrt(arcsinh(x/a))/sqrt(1+x^2/a^2)],
[arcsinh(x/a)^(3/2)*sqrt(a^2+x^2),x,11,1/2*x*arcsinh(x/a)^(3/2)*sqrt(a^2+x^2)+1/5*a*arcsinh(x/a)^(5/2)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)+3/64*a*erf(sqrt(2)*sqrt(arcsinh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)+3/64*a*erfi(sqrt(2)*sqrt(arcsinh(x/a)))*sqrt(1/2*Pi)*sqrt(a^2+x^2)/sqrt(1+x^2/a^2)-3/16*a*sqrt(a^2+x^2)*sqrt(arcsinh(x/a))/sqrt(1+x^2/a^2)-3/8*x^2*sqrt(a^2+x^2)*sqrt(arcsinh(x/a))/(a*sqrt(1+x^2/a^2))],
[arcsinh(x/a)^(3/2)/sqrt(a^2+x^2),x,1,2/5*a*arcsinh(x/a)^(5/2)*sqrt(1+x^2/a^2)/sqrt(a^2+x^2)],
[arcsinh(x/a)^(3/2)/(a^2+x^2)^(3/2),x,1,x*arcsinh(x/a)^(3/2)/(a^2*sqrt(a^2+x^2))-3/2*sqrt(1+x^2/a^2)*Unintegrable(x*sqrt(arcsinh(x/a))/(1+x^2/a^2),x)/(a^3*sqrt(a^2+x^2))],

# n<0
[x/(sqrt(1+x^2)*sqrt(arcsinh(x))),x,6,-1/2*erf(sqrt(arcsinh(x)))*sqrt(Pi)+1/2*erfi(sqrt(arcsinh(x)))*sqrt(Pi)],
[(c+a^2*c*x^2)^(5/2)/sqrt(arcsinh(a*x)),x,18,1/64*c^2*erf(sqrt(6)*sqrt(arcsinh(a*x)))*sqrt(1/6*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+1/64*c^2*erfi(sqrt(6)*sqrt(arcsinh(a*x)))*sqrt(1/6*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+15/64*c^2*erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+15/64*c^2*erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+3/64*c^2*erf(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+3/64*c^2*erfi(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+5/8*c^2*sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))/(a*sqrt(1+a^2*x^2))],
[(c+a^2*c*x^2)^(3/2)/sqrt(arcsinh(a*x)),x,13,1/4*c*erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+1/4*c*erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+1/32*c*erf(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+1/32*c*erfi(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+3/4*c*sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))/(a*sqrt(1+a^2*x^2))],
[sqrt(c+a^2*c*x^2)/sqrt(arcsinh(a*x)),x,8,1/4*erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+1/4*erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))/(a*sqrt(1+a^2*x^2))],
[1/(sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x))),x,1,2*sqrt(1+a^2*x^2)*sqrt(arcsinh(a*x))/(a*sqrt(c+a^2*c*x^2))],
[1/((c+a^2*c*x^2)^(3/2)*sqrt(arcsinh(a*x))),x,0,Unintegrable(1/((c+a^2*c*x^2)^(3/2)*sqrt(arcsinh(a*x))),x)],
[1/((c+a^2*c*x^2)^(5/2)*sqrt(arcsinh(a*x))),x,0,Unintegrable(1/((c+a^2*c*x^2)^(5/2)*sqrt(arcsinh(a*x))),x)],
[(c+a^2*c*x^2)^(5/2)/arcsinh(a*x)^(3/2),x,19,-15/16*c^2*erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+15/16*c^2*erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-3/8*c^2*erf(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+3/8*c^2*erfi(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-1/16*c^2*erf(sqrt(6)*sqrt(arcsinh(a*x)))*sqrt(3/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+1/16*c^2*erfi(sqrt(6)*sqrt(arcsinh(a*x)))*sqrt(3/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-2*(c+a^2*c*x^2)^(5/2)*sqrt(1+a^2*x^2)/(a*sqrt(arcsinh(a*x)))],
[(c+a^2*c*x^2)^(3/2)/arcsinh(a*x)^(3/2),x,14,-c*erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+c*erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-1/4*c*erf(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+1/4*c*erfi(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-2*(c+a^2*c*x^2)^(3/2)*sqrt(1+a^2*x^2)/(a*sqrt(arcsinh(a*x)))],
[sqrt(c+a^2*c*x^2)/arcsinh(a*x)^(3/2),x,9,-erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(1/2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-2*sqrt(1+a^2*x^2)*sqrt(c+a^2*c*x^2)/(a*sqrt(arcsinh(a*x)))],
[1/(arcsinh(a*x)^(3/2)*sqrt(c+a^2*c*x^2)),x,1,-2*sqrt(1+a^2*x^2)/(a*sqrt(c+a^2*c*x^2)*sqrt(arcsinh(a*x)))],
[1/((c+a^2*c*x^2)^(3/2)*arcsinh(a*x)^(3/2)),x,1,-2*sqrt(1+a^2*x^2)/(a*(c+a^2*c*x^2)^(3/2)*sqrt(arcsinh(a*x)))-4*a*sqrt(1+a^2*x^2)*Unintegrable(x/((1+a^2*x^2)^2*sqrt(arcsinh(a*x))),x)/(c*sqrt(c+a^2*c*x^2))],
[1/((c+a^2*c*x^2)^(5/2)*arcsinh(a*x)^(3/2)),x,1,-2*sqrt(1+a^2*x^2)/(a*(c+a^2*c*x^2)^(5/2)*sqrt(arcsinh(a*x)))-8*a*sqrt(1+a^2*x^2)*Unintegrable(x/((1+a^2*x^2)^3*sqrt(arcsinh(a*x))),x)/(c^2*sqrt(c+a^2*c*x^2))],
[(c+a^2*c*x^2)^(3/2)/arcsinh(a*x)^(5/2),x,18,-2/3*(c+a^2*c*x^2)^(3/2)*sqrt(1+a^2*x^2)/(a*arcsinh(a*x)^(3/2))+2/3*c*erf(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+2/3*c*erfi(2*sqrt(arcsinh(a*x)))*sqrt(Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+2/3*c*erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+2/3*c*erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-16/3*c*x*(1+a^2*x^2)*sqrt(c+a^2*c*x^2)/sqrt(arcsinh(a*x))],
[sqrt(c+a^2*c*x^2)/arcsinh(a*x)^(5/2),x,7,2/3*erf(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))+2/3*erfi(sqrt(2)*sqrt(arcsinh(a*x)))*sqrt(2*Pi)*sqrt(c+a^2*c*x^2)/(a*sqrt(1+a^2*x^2))-2/3*sqrt(1+a^2*x^2)*sqrt(c+a^2*c*x^2)/(a*arcsinh(a*x)^(3/2))-8/3*x*sqrt(c+a^2*c*x^2)/sqrt(arcsinh(a*x))],
[1/(arcsinh(a*x)^(5/2)*sqrt(c+a^2*c*x^2)),x,1,-2/3*sqrt(1+a^2*x^2)/(a*arcsinh(a*x)^(3/2)*sqrt(c+a^2*c*x^2))],
[1/((c+a^2*c*x^2)^(3/2)*arcsinh(a*x)^(5/2)),x,1,-2/3*sqrt(1+a^2*x^2)/(a*(c+a^2*c*x^2)^(3/2)*arcsinh(a*x)^(3/2))-4/3*a*sqrt(1+a^2*x^2)*Unintegrable(x/((1+a^2*x^2)^2*arcsinh(a*x)^(3/2)),x)/(c*sqrt(c+a^2*c*x^2))],
[1/((c+a^2*c*x^2)^(5/2)*arcsinh(a*x)^(5/2)),x,1,-2/3*sqrt(1+a^2*x^2)/(a*(c+a^2*c*x^2)^(5/2)*arcsinh(a*x)^(3/2))-8/3*a*sqrt(1+a^2*x^2)*Unintegrable(x/((1+a^2*x^2)^3*arcsinh(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 ArcSinh[c x])^n with n symbolic

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

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

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

# p<0
[x^m*arcsinh(a*x)^n/sqrt(1+a^2*x^2),x,0,Unintegrable(x^m*arcsinh(a*x)^n/sqrt(1+a^2*x^2),x)],
[x^3*arcsinh(a*x)^n/sqrt(1+a^2*x^2),x,9,1/8*3^(-1-n)*arcsinh(a*x)^n*GAMMA(1+n,-3*arcsinh(a*x))/(a^4*(-arcsinh(a*x))^n)-3/8*arcsinh(a*x)^n*GAMMA(1+n,-arcsinh(a*x))/(a^4*(-arcsinh(a*x))^n)-3/8*GAMMA(1+n,arcsinh(a*x))/a^4+1/8*3^(-1-n)*GAMMA(1+n,3*arcsinh(a*x))/a^4],
[x^2*arcsinh(a*x)^n/sqrt(1+a^2*x^2),x,6,-1/2*arcsinh(a*x)^(1+n)/(a^3*(1+n))+2^(-3-n)*arcsinh(a*x)^n*GAMMA(1+n,-2*arcsinh(a*x))/(a^3*(-arcsinh(a*x))^n)-2^(-3-n)*GAMMA(1+n,2*arcsinh(a*x))/a^3],
[x*arcsinh(a*x)^n/sqrt(1+a^2*x^2),x,4,1/2*arcsinh(a*x)^n*GAMMA(1+n,-arcsinh(a*x))/(a^2*(-arcsinh(a*x))^n)+1/2*GAMMA(1+n,arcsinh(a*x))/a^2],
[arcsinh(a*x)^n/sqrt(1+a^2*x^2),x,1,arcsinh(a*x)^(1+n)/(a*(1+n))],
[arcsinh(a*x)^n/(x*sqrt(1+a^2*x^2)),x,0,Unintegrable(arcsinh(a*x)^n/(x*sqrt(1+a^2*x^2)),x)],
[arcsinh(a*x)^n/(x^2*sqrt(1+a^2*x^2)),x,0,Unintegrable(arcsinh(a*x)^n/(x^2*sqrt(1+a^2*x^2)),x)],

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

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

# Integrands of the form (d+e x)^(p/2) (f+g x)^(q/2) (a+b ArcSinh[c x])^1 with e f+d g=0 and c^2 d^2+e^2=0

# q>0
[(d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))*sqrt(f-I*c*f*x),x,13,3/8*d^2*x*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-1/4*c^2*d^2*x^3*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)+2/3*I*d^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c-2/3*I*b*d^2*x*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)-3/16*b*c*d^2*x^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)-2/9*I*b*c^2*d^2*x^3*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+1/16*b*c^3*d^2*x^4*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+5/16*d^2*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(b*c*sqrt(1+c^2*x^2))],
[(d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))*sqrt(f-I*c*f*x),x,8,1/2*d*x*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)+1/3*I*d*(1+c^2*x^2)*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c-1/3*I*b*d*x*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)-1/4*b*c*d*x^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)-1/9*I*b*c^2*d*x^3*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+1/4*d*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(b*c*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x),x,4,1/2*x*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-1/4*b*c*x^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+1/4*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(b*c*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))*sqrt(f-I*c*f*x)/sqrt(d+I*c*d*x),x,6,-I*f*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+I*b*f*x*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/2*f*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(a+b*arcsinh(c*x))*sqrt(f-I*c*f*x)/(d+I*c*d*x)^(3/2),x,8,2*I*f^2*(1-I*c*x)*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-1/2*f^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(b*c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-2*b*f^2*(1+c^2*x^2)^(3/2)*log(I-c*x)/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(a+b*arcsinh(c*x))*sqrt(f-I*c*f*x)/(d+I*c*d*x)^(5/2),x,6,2/3*I*b*f^3*(1+c^2*x^2)^(5/2)/(c*(I-c*x)*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*I*f^3*(1-I*c*x)^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*b*f^3*(1+c^2*x^2)^(5/2)*log(I-c*x)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x)),x,12,-1/5*I*b*d*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)^(3/2)-5/16*b*c*d*x^2*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)^(3/2)-2/15*I*b*c^2*d*x^3*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)^(3/2)-1/16*b*c^3*d*x^4*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)^(3/2)-1/25*I*b*c^4*d*x^5*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)^(3/2)+1/4*d*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))+3/8*d*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)+1/5*I*d*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(1+c^2*x^2)*(a+b*arcsinh(c*x))/c+3/16*d*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(b*c*(1+c^2*x^2)^(3/2))],
[(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x)),x,7,-5/16*b*c*x^2*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)^(3/2)-1/16*b*c^3*x^4*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)^(3/2)+1/4*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))+3/8*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)+3/16*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(b*c*(1+c^2*x^2)^(3/2))],
[(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x),x,8,1/2*f*x*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-1/3*I*f*(1+c^2*x^2)*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c+1/3*I*b*f*x*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)-1/4*b*c*f*x^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+1/9*I*b*c^2*f*x^3*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+1/4*f*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(b*c*sqrt(1+c^2*x^2))],
[(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/sqrt(d+I*c*d*x),x,9,-2*I*f^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-1/2*f^2*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+2*I*b*f^2*x*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/4*b*c*f^2*x^2*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+3/4*f^2*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2),x,10,-I*b*f^3*x*(1+c^2*x^2)^(3/2)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+4*I*f^3*(1-I*c*x)*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+I*f^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-3/2*f^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(b*c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-4*b*f^3*(1+c^2*x^2)^(3/2)*log(I-c*x)/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2),x,9,4/3*I*b*f^4*(1+c^2*x^2)^(5/2)/(c*(I-c*x)*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/2*b*f^4*(1+c^2*x^2)^(5/2)*arcsinh(c*x)^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*I*f^4*(1-I*c*x)^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2*I*f^4*(1-I*c*x)*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+f^4*(1+c^2*x^2)^(5/2)*arcsinh(c*x)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+8/3*b*f^4*(1+c^2*x^2)^(5/2)*log(I-c*x)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x)),x,9,-25/96*b*c*x^2*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)/(1+c^2*x^2)^(5/2)-5/96*b*c^3*x^4*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)/(1+c^2*x^2)^(5/2)+1/6*x*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))+5/16*x*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)^2+5/24*x*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)+5/32*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(b*c*(1+c^2*x^2)^(5/2))-1/36*b*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*sqrt(1+c^2*x^2)/c],
[(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x)),x,12,1/5*I*b*f*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)^(3/2)-5/16*b*c*f*x^2*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)^(3/2)+2/15*I*b*c^2*f*x^3*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)^(3/2)-1/16*b*c^3*f*x^4*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)^(3/2)+1/25*I*b*c^4*f*x^5*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)^(3/2)+1/4*f*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))+3/8*f*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)-1/5*I*f*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(1+c^2*x^2)*(a+b*arcsinh(c*x))/c+3/16*f*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(b*c*(1+c^2*x^2)^(3/2))],
[(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x),x,13,3/8*f^2*x*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-1/4*c^2*f^2*x^3*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-2/3*I*f^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c+2/3*I*b*f^2*x*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)-3/16*b*c*f^2*x^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+2/9*I*b*c^2*f^2*x^3*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+1/16*b*c^3*f^2*x^4*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+5/16*f^2*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(b*c*sqrt(1+c^2*x^2))],
[(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/sqrt(d+I*c*d*x),x,13,-11/3*I*f^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-3/2*f^3*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/3*I*c*f^3*x^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+11/3*I*b*f^3*x*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+3/4*b*c*f^3*x^2*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-1/9*I*b*c^2*f^3*x^3*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+5/4*f^3*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(3/2),x,7,-3/2*I*b*f^4*x*(1+c^2*x^2)^(3/2)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+b*c*f^4*x^2*(1+c^2*x^2)^(3/2)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+5/4*b*f^4*(1-I*c*x)^2*(1+c^2*x^2)^(3/2)/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+15/4*b*f^4*(1+c^2*x^2)^(3/2)*arcsinh(c*x)^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+2*I*f^4*(1-I*c*x)^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+15/2*I*f^4*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+5/2*I*f^4*(1-I*c*x)*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-15/2*f^4*(1+c^2*x^2)^(3/2)*arcsinh(c*x)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-8*b*f^4*(1+c^2*x^2)^(3/2)*log(I-c*x)/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(d+I*c*d*x)^(5/2),x,10,I*b*f^5*x*(1+c^2*x^2)^(5/2)/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+8/3*I*b*f^5*(1+c^2*x^2)^(5/2)/(c*(I-c*x)*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-5/2*b*f^5*(1+c^2*x^2)^(5/2)*arcsinh(c*x)^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*I*f^5*(1-I*c*x)^4*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-10/3*I*f^5*(1-I*c*x)^2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-5*I*f^5*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+5*f^5*(1+c^2*x^2)^(5/2)*arcsinh(c*x)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+28/3*b*f^5*(1+c^2*x^2)^(5/2)*log(I-c*x)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],

# q<0
[(d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))/sqrt(f-I*c*f*x),x,13,11/3*I*d^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-3/2*d^3*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-1/3*I*c*d^3*x^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-11/3*I*b*d^3*x*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+3/4*b*c*d^3*x^2*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/9*I*b*c^2*d^3*x^3*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+5/4*d^3*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))/sqrt(f-I*c*f*x),x,9,2*I*d^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-1/2*d^2*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-2*I*b*d^2*x*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/4*b*c*d^2*x^2*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+3/4*d^2*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)/sqrt(f-I*c*f*x),x,6,I*d*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-I*b*d*x*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/2*d*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(a+b*arcsinh(c*x))/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)),x,2,1/2*(a+b*arcsinh(c*x))^2*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(a+b*arcsinh(c*x))/((d+I*c*d*x)^(3/2)*sqrt(f-I*c*f*x)),x,5,f*(I+c*x)*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-b*f*(1+c^2*x^2)^(3/2)*log(I-c*x)/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*sqrt(f-I*c*f*x)),x,8,1/3*I*b*f^2*(1+c^2*x^2)^(5/2)/(c*(I-c*x)*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*I*f^2*(1-I*c*x)*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*f^2*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*I*b*f^2*(1+c^2*x^2)^(5/2)*arctan(c*x)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/6*b*f^2*(1+c^2*x^2)^(5/2)*log(1+c^2*x^2)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(3/2),x,7,3/2*I*b*d^4*x*(1+c^2*x^2)^(3/2)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+b*c*d^4*x^2*(1+c^2*x^2)^(3/2)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+5/4*b*d^4*(1+I*c*x)^2*(1+c^2*x^2)^(3/2)/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+15/4*b*d^4*(1+c^2*x^2)^(3/2)*arcsinh(c*x)^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-2*I*d^4*(1+I*c*x)^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-15/2*I*d^4*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-5/2*I*d^4*(1+I*c*x)*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-15/2*d^4*(1+c^2*x^2)^(3/2)*arcsinh(c*x)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-8*b*d^4*(1+c^2*x^2)^(3/2)*log(I+c*x)/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(3/2),x,10,I*b*d^3*x*(1+c^2*x^2)^(3/2)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-4*I*d^3*(1+I*c*x)*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-I*d^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-3/2*d^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(b*c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-4*b*d^3*(1+c^2*x^2)^(3/2)*log(I+c*x)/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)/(f-I*c*f*x)^(3/2),x,8,-2*I*d^2*(1+I*c*x)*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-1/2*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(b*c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-2*b*d^2*(1+c^2*x^2)^(3/2)*log(I+c*x)/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(a+b*arcsinh(c*x))/((f-I*c*f*x)^(3/2)*sqrt(d+I*c*d*x)),x,5,-d*(I-c*x)*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-b*d*(1+c^2*x^2)^(3/2)*log(I+c*x)/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(a+b*arcsinh(c*x))/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)),x,3,x*(1+c^2*x^2)*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-1/2*b*(1+c^2*x^2)^(3/2)*log(1+c^2*x^2)/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(3/2)),x,8,1/6*I*b*f*(1+c^2*x^2)^(5/2)/(c*(I-c*x)*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*f*(I+c*x)*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*f*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/6*I*b*f*(1+c^2*x^2)^(5/2)*arctan(c*x)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*b*f*(1+c^2*x^2)^(5/2)*log(1+c^2*x^2)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(5/2),x,10,-I*b*d^5*x*(1+c^2*x^2)^(5/2)/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+8/3*I*b*d^5*(1+c^2*x^2)^(5/2)/(c*(I+c*x)*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-5/2*b*d^5*(1+c^2*x^2)^(5/2)*arcsinh(c*x)^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*I*d^5*(1+I*c*x)^4*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+10/3*I*d^5*(1+I*c*x)^2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+5*I*d^5*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+5*d^5*(1+c^2*x^2)^(5/2)*arcsinh(c*x)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+28/3*b*d^5*(1+c^2*x^2)^(5/2)*log(I+c*x)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))/(f-I*c*f*x)^(5/2),x,9,4/3*I*b*d^4*(1+c^2*x^2)^(5/2)/(c*(I+c*x)*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/2*b*d^4*(1+c^2*x^2)^(5/2)*arcsinh(c*x)^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*I*d^4*(1+I*c*x)^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2*I*d^4*(1+I*c*x)*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+d^4*(1+c^2*x^2)^(5/2)*arcsinh(c*x)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+8/3*b*d^4*(1+c^2*x^2)^(5/2)*log(I+c*x)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)/(f-I*c*f*x)^(5/2),x,6,2/3*I*b*d^3*(1+c^2*x^2)^(5/2)/(c*(I+c*x)*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*I*d^3*(1+I*c*x)^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*b*d^3*(1+c^2*x^2)^(5/2)*log(I+c*x)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(a+b*arcsinh(c*x))/((f-I*c*f*x)^(5/2)*sqrt(d+I*c*d*x)),x,8,1/3*I*b*d^2*(1+c^2*x^2)^(5/2)/(c*(I+c*x)*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*I*d^2*(1+I*c*x)*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*d^2*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*I*b*d^2*(1+c^2*x^2)^(5/2)*arctan(c*x)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/6*b*d^2*(1+c^2*x^2)^(5/2)*log(1+c^2*x^2)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(a+b*arcsinh(c*x))/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(5/2)),x,8,1/6*I*b*d*(1+c^2*x^2)^(5/2)/(c*(I+c*x)*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*d*(I-c*x)*(1+c^2*x^2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*d*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/6*I*b*d*(1+c^2*x^2)^(5/2)*arctan(c*x)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*b*d*(1+c^2*x^2)^(5/2)*log(1+c^2*x^2)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)),x,5,1/6*b*(1+c^2*x^2)^(3/2)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*b*(1+c^2*x^2)^(5/2)*log(1+c^2*x^2)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],

# Integrands of the form (d+e x)^(p/2) (f+g x)^(q/2) (a+b ArcSinh[c x])^2 with e f+d g=0 and c^2 d^2+e^2=0

# q>0
[(d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2*sqrt(f-I*c*f*x),x,23,8/9*I*b^2*d^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c+15/64*b^2*d^2*x*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-1/32*b^2*c^2*d^2*x^3*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)+4/27*I*b^2*d^2*(1+c^2*x^2)*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c+3/8*d^2*x*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-1/4*c^2*d^2*x^3*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)+2/3*I*d^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c-15/64*b^2*d^2*arcsinh(c*x)*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(c*sqrt(1+c^2*x^2))-4/3*I*b*d^2*x*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)-3/8*b*c*d^2*x^2*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)-4/9*I*b*c^2*d^2*x^3*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+1/8*b*c^3*d^2*x^4*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+5/24*d^2*(a+b*arcsinh(c*x))^3*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(b*c*sqrt(1+c^2*x^2))],
[(d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2*sqrt(f-I*c*f*x),x,13,4/9*I*b^2*d*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c+1/4*b^2*d*x*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)+2/27*I*b^2*d*(1+c^2*x^2)*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c+1/2*d*x*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)+1/3*I*d*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c-1/4*b^2*d*arcsinh(c*x)*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(c*sqrt(1+c^2*x^2))-2/3*I*b*d*x*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)-1/2*b*c*d*x^2*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)-2/9*I*b*c^2*d*x^3*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+1/6*d*(a+b*arcsinh(c*x))^3*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(b*c*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x),x,6,1/4*b^2*x*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)+1/2*x*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-1/4*b^2*arcsinh(c*x)*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(c*sqrt(1+c^2*x^2))-1/2*b*c*x^2*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+1/6*(a+b*arcsinh(c*x))^3*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(b*c*sqrt(1+c^2*x^2))],
[(a+b*arcsinh(c*x))^2*sqrt(f-I*c*f*x)/sqrt(d+I*c*d*x),x,8,-2*I*b^2*f*(1+c^2*x^2)/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-I*f*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+2*I*a*b*f*x*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+2*I*b^2*f*x*arcsinh(c*x)*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/3*f*(a+b*arcsinh(c*x))^3*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(a+b*arcsinh(c*x))^2*sqrt(f-I*c*f*x)/(d+I*c*d*x)^(3/2),x,19,2*I*f^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+2*f^2*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+2*f^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-1/3*f^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^3/(b*c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-8*I*b*f^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-4*b*f^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-4*b^2*f^2*(1+c^2*x^2)^(3/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+4*b^2*f^2*(1+c^2*x^2)^(3/2)*polylog(2,I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-2*b^2*f^2*(1+c^2*x^2)^(3/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(a+b*arcsinh(c*x))^2*sqrt(f-I*c*f*x)/(d+I*c*d*x)^(5/2),x,20,-1/3*f^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-4/3*I*b^2*f^3*(1+c^2*x^2)^(5/2)*cot(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*I*f^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2*cot(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*b*f^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*csc(1/4*Pi+1/2*I*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*I*f^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2*cot(1/4*Pi+1/2*I*arcsinh(c*x))*csc(1/4*Pi+1/2*I*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+4/3*b*f^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*log(1+I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+4/3*b^2*f^3*(1+c^2*x^2)^(5/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2,x,19,8/225*I*b^2*d*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/c+1/32*b^2*d*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)+16/75*I*b^2*d*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(c*(1+c^2*x^2))+15/64*b^2*d*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)+2/125*I*b^2*d*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(1+c^2*x^2)/c-9/64*b^2*d*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*arcsinh(c*x)/(c*(1+c^2*x^2)^(3/2))-2/5*I*b*d*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)^(3/2)-3/8*b*c*d*x^2*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)^(3/2)-4/15*I*b*c^2*d*x^3*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)^(3/2)-2/25*I*b*c^4*d*x^5*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)^(3/2)+1/4*d*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2+3/8*d*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(1+c^2*x^2)+1/5*I*d*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/c+1/8*d*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^3/(b*c*(1+c^2*x^2)^(3/2))-1/8*b*d*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2,x,11,1/32*b^2*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)+15/64*b^2*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)-9/64*b^2*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*arcsinh(c*x)/(c*(1+c^2*x^2)^(3/2))-3/8*b*c*x^2*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)^(3/2)+1/4*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2+3/8*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(1+c^2*x^2)+1/8*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^3/(b*c*(1+c^2*x^2)^(3/2))-1/8*b*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x),x,13,-4/9*I*b^2*f*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c+1/4*b^2*f*x*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-2/27*I*b^2*f*(1+c^2*x^2)*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c+1/2*f*x*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-1/3*I*f*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c-1/4*b^2*f*arcsinh(c*x)*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(c*sqrt(1+c^2*x^2))+2/3*I*b*f*x*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)-1/2*b*c*f*x^2*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+2/9*I*b*c^2*f*x^3*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+1/6*f*(a+b*arcsinh(c*x))^3*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(b*c*sqrt(1+c^2*x^2))],
[(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/sqrt(d+I*c*d*x),x,11,-4*I*b^2*f^2*(1+c^2*x^2)/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-1/4*b^2*f^2*x*(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-2*I*f^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-1/2*f^2*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/4*b^2*f^2*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+4*I*b*f^2*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/2*b*c*f^2*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/2*f^2*(a+b*arcsinh(c*x))^3*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2),x,23,-2*I*a*b*f^3*x*(1+c^2*x^2)^(3/2)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+2*I*b^2*f^3*(1+c^2*x^2)^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-2*I*b^2*f^3*x*(1+c^2*x^2)^(3/2)*arcsinh(c*x)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+4*I*f^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+4*f^3*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+4*f^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+I*f^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-f^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^3/(b*c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-16*I*b*f^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-8*b*f^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-8*b^2*f^3*(1+c^2*x^2)^(3/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+8*b^2*f^3*(1+c^2*x^2)^(3/2)*polylog(2,I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-4*b^2*f^3*(1+c^2*x^2)^(3/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2),x,21,-8/3*f^4*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*f^4*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^3/(b*c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-8/3*I*b^2*f^4*(1+c^2*x^2)^(5/2)*cot(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-8/3*I*f^4*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2*cot(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+4/3*b*f^4*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*csc(1/4*Pi+1/2*I*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*I*f^4*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2*cot(1/4*Pi+1/2*I*arcsinh(c*x))*csc(1/4*Pi+1/2*I*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+32/3*b*f^4*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*log(1+I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+32/3*b^2*f^4*(1+c^2*x^2)^(5/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2,x,17,1/108*b^2*x*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)+245/1152*b^2*x*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)/(1+c^2*x^2)^2+65/1728*b^2*x*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)/(1+c^2*x^2)-115/1152*b^2*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*arcsinh(c*x)/(c*(1+c^2*x^2)^(5/2))-5/16*b*c*x^2*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)^(5/2)+1/6*x*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2+5/16*x*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(1+c^2*x^2)^2+5/24*x*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(1+c^2*x^2)+5/48*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^3/(b*c*(1+c^2*x^2)^(5/2))-5/48*b*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))/(c*sqrt(1+c^2*x^2))-1/18*b*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2,x,19,-8/225*I*b^2*f*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/c+1/32*b^2*f*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)-16/75*I*b^2*f*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(c*(1+c^2*x^2))+15/64*b^2*f*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)/(1+c^2*x^2)-2/125*I*b^2*f*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(1+c^2*x^2)/c-9/64*b^2*f*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*arcsinh(c*x)/(c*(1+c^2*x^2)^(3/2))+2/5*I*b*f*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)^(3/2)-3/8*b*c*f*x^2*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)^(3/2)+4/15*I*b*c^2*f*x^3*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)^(3/2)+2/25*I*b*c^4*f*x^5*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))/(1+c^2*x^2)^(3/2)+1/4*f*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2+3/8*f*x*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^2/(1+c^2*x^2)-1/5*I*f*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/c+1/8*f*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))^3/(b*c*(1+c^2*x^2)^(3/2))-1/8*b*f*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x),x,23,-8/9*I*b^2*f^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c+15/64*b^2*f^2*x*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-1/32*b^2*c^2*f^2*x^3*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-4/27*I*b^2*f^2*(1+c^2*x^2)*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c+3/8*f^2*x*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-1/4*c^2*f^2*x^3*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)-2/3*I*f^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/c-15/64*b^2*f^2*arcsinh(c*x)*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(c*sqrt(1+c^2*x^2))+4/3*I*b*f^2*x*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)-3/8*b*c*f^2*x^2*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+4/9*I*b*c^2*f^2*x^3*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+1/8*b*c^3*f^2*x^4*(a+b*arcsinh(c*x))*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/sqrt(1+c^2*x^2)+5/24*f^2*(a+b*arcsinh(c*x))^3*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)/(b*c*sqrt(1+c^2*x^2))],
[(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/sqrt(d+I*c*d*x),x,17,-68/9*I*b^2*f^3*(1+c^2*x^2)/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-3/4*b^2*f^3*x*(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+2/27*I*b^2*f^3*(1+c^2*x^2)^2/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-11/3*I*f^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-3/2*f^3*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/3*I*c*f^3*x^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+3/4*b^2*f^3*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+22/3*I*b*f^3*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+3/2*b*c*f^3*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-2/9*I*b*c^2*f^3*x^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+5/6*f^3*(a+b*arcsinh(c*x))^3*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(3/2),x,28,-8*I*a*b*f^4*x*(1+c^2*x^2)^(3/2)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+8*I*b^2*f^4*(1+c^2*x^2)^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+1/4*b^2*f^4*x*(1+c^2*x^2)^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-1/4*b^2*f^4*(1+c^2*x^2)^(3/2)*arcsinh(c*x)/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-8*I*b^2*f^4*x*(1+c^2*x^2)^(3/2)*arcsinh(c*x)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-1/2*b*c*f^4*x^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+8*I*f^4*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+8*f^4*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+8*f^4*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+4*I*f^4*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+1/2*f^4*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-5/2*f^4*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^3/(b*c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-32*I*b*f^4*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-16*b*f^4*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-16*b^2*f^4*(1+c^2*x^2)^(3/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+16*b^2*f^4*(1+c^2*x^2)^(3/2)*polylog(2,I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-8*b^2*f^4*(1+c^2*x^2)^(3/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(f-I*c*f*x)^(5/2)*(a+b*arcsinh(c*x))^2/(d+I*c*d*x)^(5/2),x,25,2*I*a*b*f^5*x*(1+c^2*x^2)^(5/2)/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2*I*b^2*f^5*(1+c^2*x^2)^3/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2*I*b^2*f^5*x*(1+c^2*x^2)^(5/2)*arcsinh(c*x)/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-28/3*f^5*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-I*f^5*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+5/3*f^5*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^3/(b*c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-16/3*I*b^2*f^5*(1+c^2*x^2)^(5/2)*cot(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-28/3*I*f^5*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2*cot(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+8/3*b*f^5*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*csc(1/4*Pi+1/2*I*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+4/3*I*f^5*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2*cot(1/4*Pi+1/2*I*arcsinh(c*x))*csc(1/4*Pi+1/2*I*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+112/3*b*f^5*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*log(1+I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+112/3*b^2*f^5*(1+c^2*x^2)^(5/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],

# q<0
[(d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2/sqrt(f-I*c*f*x),x,17,68/9*I*b^2*d^3*(1+c^2*x^2)/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-3/4*b^2*d^3*x*(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-2/27*I*b^2*d^3*(1+c^2*x^2)^2/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+11/3*I*d^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-3/2*d^3*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-1/3*I*c*d^3*x^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+3/4*b^2*d^3*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-22/3*I*b*d^3*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+3/2*b*c*d^3*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+2/9*I*b*c^2*d^3*x^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+5/6*d^3*(a+b*arcsinh(c*x))^3*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2/sqrt(f-I*c*f*x),x,11,4*I*b^2*d^2*(1+c^2*x^2)/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-1/4*b^2*d^2*x*(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+2*I*d^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-1/2*d^2*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/4*b^2*d^2*arcsinh(c*x)*sqrt(1+c^2*x^2)/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-4*I*b*d^2*x*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/2*b*c*d^2*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/2*d^2*(a+b*arcsinh(c*x))^3*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)/sqrt(f-I*c*f*x),x,8,2*I*b^2*d*(1+c^2*x^2)/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+I*d*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-2*I*a*b*d*x*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))-2*I*b^2*d*x*arcsinh(c*x)*sqrt(1+c^2*x^2)/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))+1/3*d*(a+b*arcsinh(c*x))^3*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(a+b*arcsinh(c*x))^2/(sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x)),x,2,1/3*(a+b*arcsinh(c*x))^3*sqrt(1+c^2*x^2)/(b*c*sqrt(d+I*c*d*x)*sqrt(f-I*c*f*x))],
[(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*sqrt(f-I*c*f*x)),x,16,I*f*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+f*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+f*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-4*I*b*f*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-2*b*f*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-2*b^2*f*(1+c^2*x^2)^(3/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+2*b^2*f*(1+c^2*x^2)^(3/2)*polylog(2,I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-b^2*f*(1+c^2*x^2)^(3/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*sqrt(f-I*c*f*x)),x,30,-2/3*I*b^2*f^2*(1+c^2*x^2)^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*b^2*f^2*x*(1+c^2*x^2)^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*b^2*f^2*(1+c^2*x^2)^(5/2)*arcsinh(c*x)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*b*f^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*I*b*f^2*x*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*b*c*f^2*x^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*I*f^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*f^2*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*c^2*f^2*x^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*f^2*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*f^2*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-4/3*I*b*f^2*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*b*f^2*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*b^2*f^2*(1+c^2*x^2)^(5/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*b^2*f^2*(1+c^2*x^2)^(5/2)*polylog(2,I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*b^2*f^2*(1+c^2*x^2)^(5/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(3/2),x,28,8*I*a*b*d^4*x*(1+c^2*x^2)^(3/2)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-8*I*b^2*d^4*(1+c^2*x^2)^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+1/4*b^2*d^4*x*(1+c^2*x^2)^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-1/4*b^2*d^4*(1+c^2*x^2)^(3/2)*arcsinh(c*x)/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+8*I*b^2*d^4*x*(1+c^2*x^2)^(3/2)*arcsinh(c*x)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-1/2*b*c*d^4*x^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-8*I*d^4*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+8*d^4*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+8*d^4*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-4*I*d^4*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+1/2*d^4*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-5/2*d^4*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^3/(b*c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+32*I*b*d^4*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-16*b*d^4*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+16*b^2*d^4*(1+c^2*x^2)^(3/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-16*b^2*d^4*(1+c^2*x^2)^(3/2)*polylog(2,I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-8*b^2*d^4*(1+c^2*x^2)^(3/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(3/2),x,23,2*I*a*b*d^3*x*(1+c^2*x^2)^(3/2)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-2*I*b^2*d^3*(1+c^2*x^2)^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+2*I*b^2*d^3*x*(1+c^2*x^2)^(3/2)*arcsinh(c*x)/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-4*I*d^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+4*d^3*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+4*d^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-I*d^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-d^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^3/(b*c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+16*I*b*d^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-8*b*d^3*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+8*b^2*d^3*(1+c^2*x^2)^(3/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-8*b^2*d^3*(1+c^2*x^2)^(3/2)*polylog(2,I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-4*b^2*d^3*(1+c^2*x^2)^(3/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)/(f-I*c*f*x)^(3/2),x,19,-2*I*d^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+2*d^2*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+2*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-1/3*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^3/(b*c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+8*I*b*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-4*b*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+4*b^2*d^2*(1+c^2*x^2)^(3/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-4*b^2*d^2*(1+c^2*x^2)^(3/2)*polylog(2,I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-2*b^2*d^2*(1+c^2*x^2)^(3/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(a+b*arcsinh(c*x))^2/((f-I*c*f*x)^(3/2)*sqrt(d+I*c*d*x)),x,16,-I*d*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+d*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+d*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+4*I*b*d*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-2*b*d*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+2*b^2*d*(1+c^2*x^2)^(3/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-2*b^2*d*(1+c^2*x^2)^(3/2)*polylog(2,I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-b^2*d*(1+c^2*x^2)^(3/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2)),x,7,x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))+(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-2*b*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))-b^2*(1+c^2*x^2)^(3/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(3/2))],
[(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(3/2)),x,21,-1/3*I*b^2*f*(1+c^2*x^2)^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*b^2*f*x*(1+c^2*x^2)^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*b*f*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*I*b*f*x*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*I*f*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*f*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*f*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*f*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*I*b*f*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-4/3*b*f*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*b^2*f*(1+c^2*x^2)^(5/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*b^2*f*(1+c^2*x^2)^(5/2)*polylog(2,I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*b^2*f*(1+c^2*x^2)^(5/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(d+I*c*d*x)^(5/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(5/2),x,25,-2*I*a*b*d^5*x*(1+c^2*x^2)^(5/2)/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2*I*b^2*d^5*(1+c^2*x^2)^3/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2*I*b^2*d^5*x*(1+c^2*x^2)^(5/2)*arcsinh(c*x)/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+28/3*d^5*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+I*d^5*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+5/3*d^5*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^3/(b*c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+112/3*b*d^5*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*log(1+I/exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-112/3*b^2*d^5*(1+c^2*x^2)^(5/2)*polylog(2,(-I)/exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+8/3*b*d^5*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*sec(1/4*Pi+1/2*I*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+16/3*I*b^2*d^5*(1+c^2*x^2)^(5/2)*tan(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+28/3*I*d^5*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2*tan(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-4/3*I*d^5*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2*sec(1/4*Pi+1/2*I*arcsinh(c*x))^2*tan(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(d+I*c*d*x)^(3/2)*(a+b*arcsinh(c*x))^2/(f-I*c*f*x)^(5/2),x,21,8/3*d^4*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*d^4*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^3/(b*c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+32/3*b*d^4*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*log(1+I/exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-32/3*b^2*d^4*(1+c^2*x^2)^(5/2)*polylog(2,(-I)/exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+4/3*b*d^4*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*sec(1/4*Pi+1/2*I*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+8/3*I*b^2*d^4*(1+c^2*x^2)^(5/2)*tan(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+8/3*I*d^4*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2*tan(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*I*d^4*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2*sec(1/4*Pi+1/2*I*arcsinh(c*x))^2*tan(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(a+b*arcsinh(c*x))^2*sqrt(d+I*c*d*x)/(f-I*c*f*x)^(5/2),x,20,1/3*d^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+4/3*b*d^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*log(1+I/exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-4/3*b^2*d^3*(1+c^2*x^2)^(5/2)*polylog(2,(-I)/exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*b*d^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*sec(1/4*Pi+1/2*I*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+4/3*I*b^2*d^3*(1+c^2*x^2)^(5/2)*tan(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*I*d^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2*tan(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*I*d^3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2*sec(1/4*Pi+1/2*I*arcsinh(c*x))^2*tan(1/4*Pi+1/2*I*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(a+b*arcsinh(c*x))^2/((f-I*c*f*x)^(5/2)*sqrt(d+I*c*d*x)),x,30,2/3*I*b^2*d^2*(1+c^2*x^2)^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*b^2*d^2*x*(1+c^2*x^2)^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*b^2*d^2*(1+c^2*x^2)^(5/2)*arcsinh(c*x)/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*b*d^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*I*b*d^2*x*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*b*c*d^2*x^2*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*I*d^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*d^2*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*c^2*d^2*x^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*d^2*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*d^2*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+4/3*I*b*d^2*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*b*d^2*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*b^2*d^2*(1+c^2*x^2)^(5/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*b^2*d^2*(1+c^2*x^2)^(5/2)*polylog(2,I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*b^2*d^2*(1+c^2*x^2)^(5/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(3/2)*(f-I*c*f*x)^(5/2)),x,21,1/3*I*b^2*d*(1+c^2*x^2)^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*b^2*d*x*(1+c^2*x^2)^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*b*d*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*I*b*d*x*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*I*d*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*d*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*d*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*d*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*I*b*d*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-4/3*b*d*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*b^2*d*(1+c^2*x^2)^(5/2)*polylog(2,-I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-1/3*b^2*d*(1+c^2*x^2)^(5/2)*polylog(2,I*exp(arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*b^2*d*(1+c^2*x^2)^(5/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],
[(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2)),x,10,-1/3*b^2*x*(1+c^2*x^2)^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*b*(1+c^2*x^2)^(3/2)*(a+b*arcsinh(c*x))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+1/3*x*(1+c^2*x^2)*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2/((d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))+2/3*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))^2/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-4/3*b*(1+c^2*x^2)^(5/2)*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))-2/3*b^2*(1+c^2*x^2)^(5/2)*polylog(2,-exp(2*arcsinh(c*x)))/(c*(d+I*c*d*x)^(5/2)*(f-I*c*f*x)^(5/2))],

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

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

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

# n>0
[(d+e*x^2)^4*(a+b*arcsinh(c*x)),x,5,-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)^(3/2)/c^9-2/525*b*e^2*(63*c^4*d^2-90*c^2*d*e+35*e^2)*(1+c^2*x^2)^(5/2)/c^9-4/441*b*(9*c^2*d-7*e)*e^3*(1+c^2*x^2)^(7/2)/c^9-1/81*b*e^4*(1+c^2*x^2)^(9/2)/c^9+d^4*x*(a+b*arcsinh(c*x))+4/3*d^3*e*x^3*(a+b*arcsinh(c*x))+6/5*d^2*e^2*x^5*(a+b*arcsinh(c*x))+4/7*d*e^3*x^7*(a+b*arcsinh(c*x))+1/9*e^4*x^9*(a+b*arcsinh(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)*sqrt(1+c^2*x^2)/c^9],
[(d+e*x^2)^3*(a+b*arcsinh(c*x)),x,5,-1/105*b*e*(35*c^4*d^2-42*c^2*d*e+15*e^2)*(1+c^2*x^2)^(3/2)/c^7-3/175*b*(7*c^2*d-5*e)*e^2*(1+c^2*x^2)^(5/2)/c^7-1/49*b*e^3*(1+c^2*x^2)^(7/2)/c^7+d^3*x*(a+b*arcsinh(c*x))+d^2*e*x^3*(a+b*arcsinh(c*x))+3/5*d*e^2*x^5*(a+b*arcsinh(c*x))+1/7*e^3*x^7*(a+b*arcsinh(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)*sqrt(1+c^2*x^2)/c^7],
[(d+e*x^2)^2*(a+b*arcsinh(c*x)),x,5,-2/45*b*(5*c^2*d-3*e)*e*(1+c^2*x^2)^(3/2)/c^5-1/25*b*e^2*(1+c^2*x^2)^(5/2)/c^5+d^2*x*(a+b*arcsinh(c*x))+2/3*d*e*x^3*(a+b*arcsinh(c*x))+1/5*e^2*x^5*(a+b*arcsinh(c*x))-1/15*b*(15*c^4*d^2-10*c^2*d*e+3*e^2)*sqrt(1+c^2*x^2)/c^5],
[(d+e*x^2)*(a+b*arcsinh(c*x)),x,4,-1/9*b*e*(1+c^2*x^2)^(3/2)/c^3+d*x*(a+b*arcsinh(c*x))+1/3*e*x^3*(a+b*arcsinh(c*x))-1/3*b*(3*c^2*d-e)*sqrt(1+c^2*x^2)/c^3],
[a+b*arcsinh(c*x),x,3,a*x+b*x*arcsinh(c*x)-b*sqrt(1+c^2*x^2)/c],
[(a+b*arcsinh(c*x))/(d+e*x^2),x,18,1/2*(a+b*arcsinh(c*x))*log(1-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))-1/2*(a+b*arcsinh(c*x))*log(1+exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))+1/2*(a+b*arcsinh(c*x))*log(1-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))-1/2*(a+b*arcsinh(c*x))*log(1+exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))-1/2*b*polylog(2,-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))+1/2*b*polylog(2,exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))-1/2*b*polylog(2,-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))+1/2*b*polylog(2,exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))],
[(a+b*arcsinh(c*x))/(d+e*x^2)^2,x,26,-1/4*(a+b*arcsinh(c*x))*log(1-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/((-d)^(3/2)*sqrt(e))+1/4*(a+b*arcsinh(c*x))*log(1+exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/((-d)^(3/2)*sqrt(e))-1/4*(a+b*arcsinh(c*x))*log(1-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/((-d)^(3/2)*sqrt(e))+1/4*(a+b*arcsinh(c*x))*log(1+exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/((-d)^(3/2)*sqrt(e))+1/4*b*polylog(2,-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/((-d)^(3/2)*sqrt(e))-1/4*b*polylog(2,exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/((-d)^(3/2)*sqrt(e))+1/4*b*polylog(2,-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/((-d)^(3/2)*sqrt(e))-1/4*b*polylog(2,exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/((-d)^(3/2)*sqrt(e))-1/4*b*c*arctan((-c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d-e)*sqrt(1+c^2*x^2)))/(d*sqrt(c^2*d-e)*sqrt(e))-1/4*b*c*arctan((c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d-e)*sqrt(1+c^2*x^2)))/(d*sqrt(c^2*d-e)*sqrt(e))+1/4*(-a-b*arcsinh(c*x))/(d*sqrt(e)*(sqrt(-d)-x*sqrt(e)))+1/4*(a+b*arcsinh(c*x))/(d*sqrt(e)*(sqrt(-d)+x*sqrt(e)))],
[(d+e*x^2)^3*(a+b*arcsinh(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*arcsinh(c*x))^2+d^2*e*x^3*(a+b*arcsinh(c*x))^2+3/5*d*e^2*x^5*(a+b*arcsinh(c*x))^2+1/7*e^3*x^7*(a+b*arcsinh(c*x))^2-2*b*d^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c+4/3*b*d^2*e*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-16/25*b*d*e^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^5+32/245*b*e^3*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^7-2/3*b*d^2*e*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c+8/25*b*d*e^2*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-16/245*b*e^3*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^5-6/25*b*d*e^2*x^4*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c+12/245*b*e^3*x^4*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-2/49*b*e^3*x^6*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(d+e*x^2)^2*(a+b*arcsinh(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*arcsinh(c*x))^2+2/3*d*e*x^3*(a+b*arcsinh(c*x))^2+1/5*e^2*x^5*(a+b*arcsinh(c*x))^2-2*b*d^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c+8/9*b*d*e*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-16/75*b*e^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^5-4/9*b*d*e*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c+8/75*b*e^2*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-2/25*b*e^2*x^4*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(d+e*x^2)*(a+b*arcsinh(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*arcsinh(c*x))^2+1/3*e*x^3*(a+b*arcsinh(c*x))^2-2*b*d*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c+4/9*b*e*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c^3-2/9*b*e*x^2*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(a+b*arcsinh(c*x))^2,x,3,2*b^2*x+x*(a+b*arcsinh(c*x))^2-2*b*(a+b*arcsinh(c*x))*sqrt(1+c^2*x^2)/c],
[(a+b*arcsinh(c*x))^2/(d+e*x^2),x,22,1/2*(a+b*arcsinh(c*x))^2*log(1-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))-1/2*(a+b*arcsinh(c*x))^2*log(1+exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))+1/2*(a+b*arcsinh(c*x))^2*log(1-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))-1/2*(a+b*arcsinh(c*x))^2*log(1+exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))-b*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))+b*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))-b*(a+b*arcsinh(c*x))*polylog(2,-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))+b*(a+b*arcsinh(c*x))*polylog(2,exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))+b^2*polylog(3,-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))-b^2*polylog(3,exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)-sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))+b^2*polylog(3,-exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))-b^2*polylog(3,exp(arcsinh(c*x))*sqrt(e)/(c*sqrt(-d)+sqrt(-c^2*d+e)))/(sqrt(-d)*sqrt(e))],

# n<0
[(d+e*x^2)^3/(a+b*arcsinh(c*x)),x,42,d^3*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b*c)-3/4*d^2*e*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b*c^3)+3/8*d*e^2*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b*c^5)-5/64*e^3*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b*c^7)+3/4*d^2*e*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/(b*c^3)-9/16*d*e^2*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/(b*c^5)+9/64*e^3*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/(b*c^7)+3/16*d*e^2*Chi(5*(a+b*arcsinh(c*x))/b)*cosh(5*a/b)/(b*c^5)-5/64*e^3*Chi(5*(a+b*arcsinh(c*x))/b)*cosh(5*a/b)/(b*c^7)+1/64*e^3*Chi(7*(a+b*arcsinh(c*x))/b)*cosh(7*a/b)/(b*c^7)-d^3*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b*c)+3/4*d^2*e*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b*c^3)-3/8*d*e^2*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b*c^5)+5/64*e^3*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b*c^7)-3/4*d^2*e*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b*c^3)+9/16*d*e^2*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b*c^5)-9/64*e^3*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b*c^7)-3/16*d*e^2*Shi(5*(a+b*arcsinh(c*x))/b)*sinh(5*a/b)/(b*c^5)+5/64*e^3*Shi(5*(a+b*arcsinh(c*x))/b)*sinh(5*a/b)/(b*c^7)-1/64*e^3*Shi(7*(a+b*arcsinh(c*x))/b)*sinh(7*a/b)/(b*c^7)],
[(d+e*x^2)^2/(a+b*arcsinh(c*x)),x,27,d^2*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b*c)-1/2*d*e*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b*c^3)+1/8*e^2*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b*c^5)+1/2*d*e*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/(b*c^3)-3/16*e^2*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/(b*c^5)+1/16*e^2*Chi(5*(a+b*arcsinh(c*x))/b)*cosh(5*a/b)/(b*c^5)-d^2*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b*c)+1/2*d*e*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b*c^3)-1/8*e^2*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b*c^5)-1/2*d*e*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b*c^3)+3/16*e^2*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b*c^5)-1/16*e^2*Shi(5*(a+b*arcsinh(c*x))/b)*sinh(5*a/b)/(b*c^5)],
[(d+e*x^2)/(a+b*arcsinh(c*x)),x,15,d*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b*c)-1/4*e*Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b*c^3)+1/4*e*Chi(3*(a+b*arcsinh(c*x))/b)*cosh(3*a/b)/(b*c^3)-d*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b*c)+1/4*e*Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b*c^3)-1/4*e*Shi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b*c^3)],
[1/(a+b*arcsinh(c*x)),x,4,Chi((a+b*arcsinh(c*x))/b)*cosh(a/b)/(b*c)-Shi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b*c)],
[1/((d+e*x^2)*(a+b*arcsinh(c*x))),x,0,Unintegrable(1/((d+e*x^2)*(a+b*arcsinh(c*x))),x)],
[1/((d+e*x^2)^2*(a+b*arcsinh(c*x))),x,0,Unintegrable(1/((d+e*x^2)^2*(a+b*arcsinh(c*x))),x)],
[(d+e*x^2)^2/(a+b*arcsinh(c*x))^2,x,26,d^2*cosh(a/b)*Shi((a+b*arcsinh(c*x))/b)/(b^2*c)-1/2*d*e*cosh(a/b)*Shi((a+b*arcsinh(c*x))/b)/(b^2*c^3)+1/8*e^2*cosh(a/b)*Shi((a+b*arcsinh(c*x))/b)/(b^2*c^5)+3/2*d*e*cosh(3*a/b)*Shi(3*(a+b*arcsinh(c*x))/b)/(b^2*c^3)-9/16*e^2*cosh(3*a/b)*Shi(3*(a+b*arcsinh(c*x))/b)/(b^2*c^5)+5/16*e^2*cosh(5*a/b)*Shi(5*(a+b*arcsinh(c*x))/b)/(b^2*c^5)-d^2*Chi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b^2*c)+1/2*d*e*Chi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b^2*c^3)-1/8*e^2*Chi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b^2*c^5)-3/2*d*e*Chi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b^2*c^3)+9/16*e^2*Chi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b^2*c^5)-5/16*e^2*Chi(5*(a+b*arcsinh(c*x))/b)*sinh(5*a/b)/(b^2*c^5)-d^2*sqrt(1+c^2*x^2)/(b*c*(a+b*arcsinh(c*x)))-2*d*e*x^2*sqrt(1+c^2*x^2)/(b*c*(a+b*arcsinh(c*x)))-e^2*x^4*sqrt(1+c^2*x^2)/(b*c*(a+b*arcsinh(c*x)))],
[(d+e*x^2)/(a+b*arcsinh(c*x))^2,x,15,d*cosh(a/b)*Shi((a+b*arcsinh(c*x))/b)/(b^2*c)-1/4*e*cosh(a/b)*Shi((a+b*arcsinh(c*x))/b)/(b^2*c^3)+3/4*e*cosh(3*a/b)*Shi(3*(a+b*arcsinh(c*x))/b)/(b^2*c^3)-d*Chi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b^2*c)+1/4*e*Chi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b^2*c^3)-3/4*e*Chi(3*(a+b*arcsinh(c*x))/b)*sinh(3*a/b)/(b^2*c^3)-d*sqrt(1+c^2*x^2)/(b*c*(a+b*arcsinh(c*x)))-e*x^2*sqrt(1+c^2*x^2)/(b*c*(a+b*arcsinh(c*x)))],
[1/(a+b*arcsinh(c*x))^2,x,5,cosh(a/b)*Shi((a+b*arcsinh(c*x))/b)/(b^2*c)-Chi((a+b*arcsinh(c*x))/b)*sinh(a/b)/(b^2*c)-sqrt(1+c^2*x^2)/(b*c*(a+b*arcsinh(c*x)))],
[1/((d+e*x^2)*(a+b*arcsinh(c*x))^2),x,0,Unintegrable(1/((d+e*x^2)*(a+b*arcsinh(c*x))^2),x)],
[1/((d+e*x^2)^2*(a+b*arcsinh(c*x))^2),x,0,Unintegrable(1/((d+e*x^2)^2*(a+b*arcsinh(c*x))^2),x)],

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

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

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

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

# n>0
[(a+b*arcsinh(c*x))*sqrt(d+e*x^2),x,0,Unintegrable((a+b*arcsinh(c*x))*sqrt(d+e*x^2),x)],
[(a+b*arcsinh(c*x))/sqrt(d+e*x^2),x,0,Unintegrable((a+b*arcsinh(c*x))/sqrt(d+e*x^2),x)],
[(a+b*arcsinh(c*x))/(d+e*x^2)^(3/2),x,6,-b*arctanh(sqrt(e)*sqrt(1+c^2*x^2)/(c*sqrt(d+e*x^2)))/(d*sqrt(e))+x*(a+b*arcsinh(c*x))/(d*sqrt(d+e*x^2))],
[(a+b*arcsinh(c*x))/(d+e*x^2)^(5/2),x,7,1/3*x*(a+b*arcsinh(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)))/(d^2*sqrt(e))+2/3*x*(a+b*arcsinh(c*x))/(d^2*sqrt(d+e*x^2))-1/3*b*c*sqrt(1+c^2*x^2)/(d*(c^2*d-e)*sqrt(d+e*x^2))],
[(a+b*arcsinh(c*x))/(d+e*x^2)^(7/2),x,8,1/5*x*(a+b*arcsinh(c*x))/(d*(d+e*x^2)^(5/2))+4/15*x*(a+b*arcsinh(c*x))/(d^2*(d+e*x^2)^(3/2))-8/15*b*arctanh(sqrt(e)*sqrt(1+c^2*x^2)/(c*sqrt(d+e*x^2)))/(d^3*sqrt(e))-1/15*b*c*sqrt(1+c^2*x^2)/(d*(c^2*d-e)*(d+e*x^2)^(3/2))+8/15*x*(a+b*arcsinh(c*x))/(d^3*sqrt(d+e*x^2))-2/15*b*c*(3*c^2*d-2*e)*sqrt(1+c^2*x^2)/(d^2*(c^2*d-e)^2*sqrt(d+e*x^2))],
[(a+b*arcsinh(c*x))^2*sqrt(d+e*x^2),x,0,Unintegrable((a+b*arcsinh(c*x))^2*sqrt(d+e*x^2),x)],
[(a+b*arcsinh(c*x))^2/sqrt(d+e*x^2),x,0,Unintegrable((a+b*arcsinh(c*x))^2/sqrt(d+e*x^2),x)],
[(a+b*arcsinh(c*x))^2/(d+e*x^2)^(3/2),x,0,Unintegrable((a+b*arcsinh(c*x))^2/(d+e*x^2)^(3/2),x)],
[(a+b*arcsinh(c*x))^2/(d+e*x^2)^(5/2),x,0,Unintegrable((a+b*arcsinh(c*x))^2/(d+e*x^2)^(5/2),x)],

# n<0
[sqrt(d+e*x^2)/(a+b*arcsinh(c*x)),x,0,Unintegrable(sqrt(d+e*x^2)/(a+b*arcsinh(c*x)),x)],
[1/((a+b*arcsinh(c*x))*sqrt(d+e*x^2)),x,0,Unintegrable(1/((a+b*arcsinh(c*x))*sqrt(d+e*x^2)),x)],
[1/((d+e*x^2)^(3/2)*(a+b*arcsinh(c*x))),x,0,Unintegrable(1/((d+e*x^2)^(3/2)*(a+b*arcsinh(c*x))),x)],
[1/((d+e*x^2)^(5/2)*(a+b*arcsinh(c*x))),x,0,Unintegrable(1/((d+e*x^2)^(5/2)*(a+b*arcsinh(c*x))),x)],
[sqrt(d+e*x^2)/(a+b*arcsinh(c*x))^2,x,0,Unintegrable(sqrt(d+e*x^2)/(a+b*arcsinh(c*x))^2,x)],
[1/((a+b*arcsinh(c*x))^2*sqrt(d+e*x^2)),x,0,Unintegrable(1/((a+b*arcsinh(c*x))^2*sqrt(d+e*x^2)),x)],
[1/((d+e*x^2)^(3/2)*(a+b*arcsinh(c*x))^2),x,0,Unintegrable(1/((d+e*x^2)^(3/2)*(a+b*arcsinh(c*x))^2),x)],
[1/((d+e*x^2)^(5/2)*(a+b*arcsinh(c*x))^2),x,0,Unintegrable(1/((d+e*x^2)^(5/2)*(a+b*arcsinh(c*x))^2),x)]]:
