# Maple integration test file: "5 Inverse trig functions\5.1 Inverse sine\5.1.4 (f x)^m (d+e x^2)^p (a+b arcsin(c x))^n.txt"

lst:=[

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

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

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

# p>0
[x^4*(d-c^2*d*x^2)*(a+b*arcsin(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*arcsin(c*x))-1/7*c^2*d*x^7*(a+b*arcsin(c*x))+2/35*b*d*sqrt(1-c^2*x^2)/c^5],
[x^3*(d-c^2*d*x^2)*(a+b*arcsin(c*x)),x,6,-1/24*b*d*arcsin(c*x)/c^4+1/4*d*x^4*(a+b*arcsin(c*x))-1/6*c^2*d*x^6*(a+b*arcsin(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*arcsin(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*arcsin(c*x))-1/5*c^2*d*x^5*(a+b*arcsin(c*x))+2/15*b*d*sqrt(1-c^2*x^2)/c^3],
[x*(d-c^2*d*x^2)*(a+b*arcsin(c*x)),x,4,1/16*b*d*x*(1-c^2*x^2)^(3/2)/c+3/32*b*d*arcsin(c*x)/c^2-1/4*d*(1-c^2*x^2)^2*(a+b*arcsin(c*x))/c^2+3/32*b*d*x*sqrt(1-c^2*x^2)/c],
[(d-c^2*d*x^2)*(a+b*arcsin(c*x)),x,5,1/9*b*d*(1-c^2*x^2)^(3/2)/c+d*x*(a+b*arcsin(c*x))-1/3*c^2*d*x^3*(a+b*arcsin(c*x))+2/3*b*d*sqrt(1-c^2*x^2)/c],
[(d-c^2*d*x^2)*(a+b*arcsin(c*x))/x,x,8,-1/4*b*d*arcsin(c*x)+1/2*d*(1-c^2*x^2)*(a+b*arcsin(c*x))-1/2*I*d*(a+b*arcsin(c*x))^2/b+d*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))-1/2*I*b*d*polylog(2,exp(2*I*arcsin(c*x)))-1/4*b*c*d*x*sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)*(a+b*arcsin(c*x))/x^2,x,6,-d*(a+b*arcsin(c*x))/x-c^2*d*x*(a+b*arcsin(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*arcsin(c*x))/x^3,x,8,-1/2*b*c^2*d*arcsin(c*x)-1/2*d*(1-c^2*x^2)*(a+b*arcsin(c*x))/x^2+1/2*I*c^2*d*(a+b*arcsin(c*x))^2/b-c^2*d*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))+1/2*I*b*c^2*d*polylog(2,exp(2*I*arcsin(c*x)))-1/2*b*c*d*sqrt(1-c^2*x^2)/x],
[(d-c^2*d*x^2)*(a+b*arcsin(c*x))/x^4,x,6,-1/3*d*(a+b*arcsin(c*x))/x^3+c^2*d*(a+b*arcsin(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*arcsin(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*arcsin(c*x))-2/7*c^2*d^2*x^7*(a+b*arcsin(c*x))+1/9*c^4*d^2*x^9*(a+b*arcsin(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*arcsin(c*x)),x,7,-73/3072*b*d^2*arcsin(c*x)/c^4+1/4*d^2*x^4*(a+b*arcsin(c*x))-1/3*c^2*d^2*x^6*(a+b*arcsin(c*x))+1/8*c^4*d^2*x^8*(a+b*arcsin(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*arcsin(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*arcsin(c*x))-2/5*c^2*d^2*x^5*(a+b*arcsin(c*x))+1/7*c^4*d^2*x^7*(a+b*arcsin(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*arcsin(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*arcsin(c*x)/c^2-1/6*d^2*(1-c^2*x^2)^3*(a+b*arcsin(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*arcsin(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*arcsin(c*x))-2/3*c^2*d^2*x^3*(a+b*arcsin(c*x))+1/5*c^4*d^2*x^5*(a+b*arcsin(c*x))+8/15*b*d^2*sqrt(1-c^2*x^2)/c],
[(d-c^2*d*x^2)^2*(a+b*arcsin(c*x))/x,x,12,-1/16*b*c*d^2*x*(1-c^2*x^2)^(3/2)-11/32*b*d^2*arcsin(c*x)+1/2*d^2*(1-c^2*x^2)*(a+b*arcsin(c*x))+1/4*d^2*(1-c^2*x^2)^2*(a+b*arcsin(c*x))-1/2*I*d^2*(a+b*arcsin(c*x))^2/b+d^2*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))-1/2*I*b*d^2*polylog(2,exp(2*I*arcsin(c*x)))-11/32*b*c*d^2*x*sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)^2*(a+b*arcsin(c*x))/x^2,x,7,-1/9*b*c*d^2*(1-c^2*x^2)^(3/2)-d^2*(a+b*arcsin(c*x))/x-2*c^2*d^2*x*(a+b*arcsin(c*x))+1/3*c^4*d^2*x^3*(a+b*arcsin(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*arcsin(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*arcsin(c*x)-c^2*d^2*(1-c^2*x^2)*(a+b*arcsin(c*x))-1/2*d^2*(1-c^2*x^2)^2*(a+b*arcsin(c*x))/x^2+I*c^2*d^2*(a+b*arcsin(c*x))^2/b-2*c^2*d^2*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))+I*b*c^2*d^2*polylog(2,exp(2*I*arcsin(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*arcsin(c*x))/x^4,x,7,-1/3*d^2*(a+b*arcsin(c*x))/x^3+2*c^2*d^2*(a+b*arcsin(c*x))/x+c^4*d^2*x*(a+b*arcsin(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*arcsin(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*arcsin(c*x))-3/7*c^2*d^3*x^7*(a+b*arcsin(c*x))+1/3*c^4*d^3*x^9*(a+b*arcsin(c*x))-1/11*c^6*d^3*x^11*(a+b*arcsin(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*arcsin(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*arcsin(c*x)/c^4-1/8*d^3*(1-c^2*x^2)^4*(a+b*arcsin(c*x))/c^4+1/10*d^3*(1-c^2*x^2)^5*(a+b*arcsin(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*arcsin(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*arcsin(c*x))-3/5*c^2*d^3*x^5*(a+b*arcsin(c*x))+3/7*c^4*d^3*x^7*(a+b*arcsin(c*x))-1/9*c^6*d^3*x^9*(a+b*arcsin(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*arcsin(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*arcsin(c*x)/c^2-1/8*d^3*(1-c^2*x^2)^4*(a+b*arcsin(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*arcsin(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*arcsin(c*x))-c^2*d^3*x^3*(a+b*arcsin(c*x))+3/5*c^4*d^3*x^5*(a+b*arcsin(c*x))-1/7*c^6*d^3*x^7*(a+b*arcsin(c*x))+16/35*b*d^3*sqrt(1-c^2*x^2)/c],
[(d-c^2*d*x^2)^3*(a+b*arcsin(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*arcsin(c*x)+1/2*d^3*(1-c^2*x^2)*(a+b*arcsin(c*x))+1/4*d^3*(1-c^2*x^2)^2*(a+b*arcsin(c*x))+1/6*d^3*(1-c^2*x^2)^3*(a+b*arcsin(c*x))-1/2*I*d^3*(a+b*arcsin(c*x))^2/b+d^3*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))-1/2*I*b*d^3*polylog(2,exp(2*I*arcsin(c*x)))-19/48*b*c*d^3*x*sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)^3*(a+b*arcsin(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*arcsin(c*x))/x-3*c^2*d^3*x*(a+b*arcsin(c*x))+c^4*d^3*x^3*(a+b*arcsin(c*x))-1/5*c^6*d^3*x^5*(a+b*arcsin(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*arcsin(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*arcsin(c*x)-3/2*c^2*d^3*(1-c^2*x^2)*(a+b*arcsin(c*x))-3/4*c^2*d^3*(1-c^2*x^2)^2*(a+b*arcsin(c*x))-1/2*d^3*(1-c^2*x^2)^3*(a+b*arcsin(c*x))/x^2+3/2*I*c^2*d^3*(a+b*arcsin(c*x))^2/b-3*c^2*d^3*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))+3/2*I*b*c^2*d^3*polylog(2,exp(2*I*arcsin(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*arcsin(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*arcsin(c*x))/x^3+3*c^2*d^3*(a+b*arcsin(c*x))/x+3*c^4*d^3*x*(a+b*arcsin(c*x))-1/3*c^6*d^3*x^3*(a+b*arcsin(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*arcsin(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*arcsin(c*x))/(c^4*d)-1/3*x^3*(a+b*arcsin(c*x))/(c^2*d)-2*I*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))/(c^5*d)+I*b*polylog(2,-I*exp(I*arcsin(c*x)))/(c^5*d)-I*b*polylog(2,I*exp(I*arcsin(c*x)))/(c^5*d)-4/3*b*sqrt(1-c^2*x^2)/(c^5*d)],
[x^3*(a+b*arcsin(c*x))/(d-c^2*d*x^2),x,8,1/4*b*arcsin(c*x)/(c^4*d)-1/2*x^2*(a+b*arcsin(c*x))/(c^2*d)+1/2*I*(a+b*arcsin(c*x))^2/(b*c^4*d)-(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))/(c^4*d)+1/2*I*b*polylog(2,-exp(2*I*arcsin(c*x)))/(c^4*d)-1/4*b*x*sqrt(1-c^2*x^2)/(c^3*d)],
[x^2*(a+b*arcsin(c*x))/(d-c^2*d*x^2),x,8,-x*(a+b*arcsin(c*x))/(c^2*d)-2*I*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))/(c^3*d)+I*b*polylog(2,-I*exp(I*arcsin(c*x)))/(c^3*d)-I*b*polylog(2,I*exp(I*arcsin(c*x)))/(c^3*d)-b*sqrt(1-c^2*x^2)/(c^3*d)],
[x*(a+b*arcsin(c*x))/(d-c^2*d*x^2),x,5,1/2*I*(a+b*arcsin(c*x))^2/(b*c^2*d)-(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))/(c^2*d)+1/2*I*b*polylog(2,-exp(2*I*arcsin(c*x)))/(c^2*d)],
[(a+b*arcsin(c*x))/(d-c^2*d*x^2),x,6,-2*I*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))/(c*d)+I*b*polylog(2,-I*exp(I*arcsin(c*x)))/(c*d)-I*b*polylog(2,I*exp(I*arcsin(c*x)))/(c*d)],
[(a+b*arcsin(c*x))/(x*(d-c^2*d*x^2)),x,7,-2*(a+b*arcsin(c*x))*arctanh(exp(2*I*arcsin(c*x)))/d+1/2*I*b*polylog(2,-exp(2*I*arcsin(c*x)))/d-1/2*I*b*polylog(2,exp(2*I*arcsin(c*x)))/d],
[(a+b*arcsin(c*x))/(x^2*(d-c^2*d*x^2)),x,10,(-a-b*arcsin(c*x))/(d*x)-2*I*c*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))/d-b*c*arctanh(sqrt(1-c^2*x^2))/d+I*b*c*polylog(2,-I*exp(I*arcsin(c*x)))/d-I*b*c*polylog(2,I*exp(I*arcsin(c*x)))/d],
[(a+b*arcsin(c*x))/(x^3*(d-c^2*d*x^2)),x,9,1/2*(-a-b*arcsin(c*x))/(d*x^2)-2*c^2*(a+b*arcsin(c*x))*arctanh(exp(2*I*arcsin(c*x)))/d+1/2*I*b*c^2*polylog(2,-exp(2*I*arcsin(c*x)))/d-1/2*I*b*c^2*polylog(2,exp(2*I*arcsin(c*x)))/d-1/2*b*c*sqrt(1-c^2*x^2)/(d*x)],
[(a+b*arcsin(c*x))/(x^4*(d-c^2*d*x^2)),x,15,1/3*(-a-b*arcsin(c*x))/(d*x^3)-c^2*(a+b*arcsin(c*x))/(d*x)-2*I*c^3*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))/d-7/6*b*c^3*arctanh(sqrt(1-c^2*x^2))/d+I*b*c^3*polylog(2,-I*exp(I*arcsin(c*x)))/d-I*b*c^3*polylog(2,I*exp(I*arcsin(c*x)))/d-1/6*b*c*sqrt(1-c^2*x^2)/(d*x^2)],
[x^4*(a+b*arcsin(c*x))/(d-c^2*d*x^2)^2,x,12,3/2*x*(a+b*arcsin(c*x))/(c^4*d^2)+1/2*x^3*(a+b*arcsin(c*x))/(c^2*d^2*(1-c^2*x^2))+3*I*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))/(c^5*d^2)-3/2*I*b*polylog(2,-I*exp(I*arcsin(c*x)))/(c^5*d^2)+3/2*I*b*polylog(2,I*exp(I*arcsin(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*arcsin(c*x))/(d-c^2*d*x^2)^2,x,8,1/2*b*arcsin(c*x)/(c^4*d^2)+1/2*x^2*(a+b*arcsin(c*x))/(c^2*d^2*(1-c^2*x^2))-1/2*I*(a+b*arcsin(c*x))^2/(b*c^4*d^2)+(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))/(c^4*d^2)-1/2*I*b*polylog(2,-exp(2*I*arcsin(c*x)))/(c^4*d^2)-1/2*b*x/(c^3*d^2*sqrt(1-c^2*x^2))],
[x^2*(a+b*arcsin(c*x))/(d-c^2*d*x^2)^2,x,8,1/2*x*(a+b*arcsin(c*x))/(c^2*d^2*(1-c^2*x^2))+I*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))/(c^3*d^2)-1/2*I*b*polylog(2,-I*exp(I*arcsin(c*x)))/(c^3*d^2)+1/2*I*b*polylog(2,I*exp(I*arcsin(c*x)))/(c^3*d^2)-1/2*b/(c^3*d^2*sqrt(1-c^2*x^2))],
[x*(a+b*arcsin(c*x))/(d-c^2*d*x^2)^2,x,2,1/2*(a+b*arcsin(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*arcsin(c*x))/(d-c^2*d*x^2)^2,x,8,1/2*x*(a+b*arcsin(c*x))/(d^2*(1-c^2*x^2))-I*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))/(c*d^2)+1/2*I*b*polylog(2,-I*exp(I*arcsin(c*x)))/(c*d^2)-1/2*I*b*polylog(2,I*exp(I*arcsin(c*x)))/(c*d^2)-1/2*b/(c*d^2*sqrt(1-c^2*x^2))],
[(a+b*arcsin(c*x))/(x*(d-c^2*d*x^2)^2),x,9,1/2*(a+b*arcsin(c*x))/(d^2*(1-c^2*x^2))-2*(a+b*arcsin(c*x))*arctanh(exp(2*I*arcsin(c*x)))/d^2+1/2*I*b*polylog(2,-exp(2*I*arcsin(c*x)))/d^2-1/2*I*b*polylog(2,exp(2*I*arcsin(c*x)))/d^2-1/2*b*c*x/(d^2*sqrt(1-c^2*x^2))],
[(a+b*arcsin(c*x))/(x^2*(d-c^2*d*x^2)^2),x,13,(-a-b*arcsin(c*x))/(d^2*x*(1-c^2*x^2))+3/2*c^2*x*(a+b*arcsin(c*x))/(d^2*(1-c^2*x^2))-3*I*c*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))/d^2-b*c*arctanh(sqrt(1-c^2*x^2))/d^2+3/2*I*b*c*polylog(2,-I*exp(I*arcsin(c*x)))/d^2-3/2*I*b*c*polylog(2,I*exp(I*arcsin(c*x)))/d^2-1/2*b*c/(d^2*sqrt(1-c^2*x^2))],
[(a+b*arcsin(c*x))/(x^3*(d-c^2*d*x^2)^2),x,12,c^2*(a+b*arcsin(c*x))/(d^2*(1-c^2*x^2))+1/2*(-a-b*arcsin(c*x))/(d^2*x^2*(1-c^2*x^2))-4*c^2*(a+b*arcsin(c*x))*arctanh(exp(2*I*arcsin(c*x)))/d^2+I*b*c^2*polylog(2,-exp(2*I*arcsin(c*x)))/d^2-I*b*c^2*polylog(2,exp(2*I*arcsin(c*x)))/d^2-1/2*b*c/(d^2*x*sqrt(1-c^2*x^2))],
[(a+b*arcsin(c*x))/(x^4*(d-c^2*d*x^2)^2),x,19,1/3*(-a-b*arcsin(c*x))/(d^2*x^3*(1-c^2*x^2))-5/3*c^2*(a+b*arcsin(c*x))/(d^2*x*(1-c^2*x^2))+5/2*c^4*x*(a+b*arcsin(c*x))/(d^2*(1-c^2*x^2))-5*I*c^3*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(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(I*arcsin(c*x)))/d^2-5/2*I*b*c^3*polylog(2,I*exp(I*arcsin(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*arcsin(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*arcsin(c*x))/(c^2*d^3*(1-c^2*x^2)^2)-3/8*x*(a+b*arcsin(c*x))/(c^4*d^3*(1-c^2*x^2))-3/4*I*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))/(c^5*d^3)+3/8*I*b*polylog(2,-I*exp(I*arcsin(c*x)))/(c^5*d^3)-3/8*I*b*polylog(2,I*exp(I*arcsin(c*x)))/(c^5*d^3)+5/8*b/(c^5*d^3*sqrt(1-c^2*x^2))],
[x^3*(a+b*arcsin(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*arcsin(c*x)/(c^4*d^3)+1/4*x^4*(a+b*arcsin(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*arcsin(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*arcsin(c*x))/(c^2*d^3*(1-c^2*x^2)^2)-1/8*x*(a+b*arcsin(c*x))/(c^2*d^3*(1-c^2*x^2))+1/4*I*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))/(c^3*d^3)-1/8*I*b*polylog(2,-I*exp(I*arcsin(c*x)))/(c^3*d^3)+1/8*I*b*polylog(2,I*exp(I*arcsin(c*x)))/(c^3*d^3)+1/8*b/(c^3*d^3*sqrt(1-c^2*x^2))],
[x*(a+b*arcsin(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*arcsin(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*arcsin(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*arcsin(c*x))/(d^3*(1-c^2*x^2)^2)+3/8*x*(a+b*arcsin(c*x))/(d^3*(1-c^2*x^2))-3/4*I*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))/(c*d^3)+3/8*I*b*polylog(2,-I*exp(I*arcsin(c*x)))/(c*d^3)-3/8*I*b*polylog(2,I*exp(I*arcsin(c*x)))/(c*d^3)-3/8*b/(c*d^3*sqrt(1-c^2*x^2))],
[(a+b*arcsin(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*arcsin(c*x))/(d^3*(1-c^2*x^2)^2)+1/2*(a+b*arcsin(c*x))/(d^3*(1-c^2*x^2))-2*(a+b*arcsin(c*x))*arctanh(exp(2*I*arcsin(c*x)))/d^3+1/2*I*b*polylog(2,-exp(2*I*arcsin(c*x)))/d^3-1/2*I*b*polylog(2,exp(2*I*arcsin(c*x)))/d^3-2/3*b*c*x/(d^3*sqrt(1-c^2*x^2))],
[(a+b*arcsin(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*arcsin(c*x))/(d^3*x*(1-c^2*x^2)^2)+5/4*c^2*x*(a+b*arcsin(c*x))/(d^3*(1-c^2*x^2)^2)+15/8*c^2*x*(a+b*arcsin(c*x))/(d^3*(1-c^2*x^2))-15/4*I*c*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))/d^3-b*c*arctanh(sqrt(1-c^2*x^2))/d^3+15/8*I*b*c*polylog(2,-I*exp(I*arcsin(c*x)))/d^3-15/8*I*b*c*polylog(2,I*exp(I*arcsin(c*x)))/d^3-7/8*b*c/(d^3*sqrt(1-c^2*x^2))],
[(a+b*arcsin(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*arcsin(c*x))/(d^3*(1-c^2*x^2)^2)+1/2*(-a-b*arcsin(c*x))/(d^3*x^2*(1-c^2*x^2)^2)+3/2*c^2*(a+b*arcsin(c*x))/(d^3*(1-c^2*x^2))-6*c^2*(a+b*arcsin(c*x))*arctanh(exp(2*I*arcsin(c*x)))/d^3+3/2*I*b*c^2*polylog(2,-exp(2*I*arcsin(c*x)))/d^3-3/2*I*b*c^2*polylog(2,exp(2*I*arcsin(c*x)))/d^3-2/3*b*c^3*x/(d^3*sqrt(1-c^2*x^2))],
[(a+b*arcsin(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*arcsin(c*x))/(d^3*x^3*(1-c^2*x^2)^2)-7/3*c^2*(a+b*arcsin(c*x))/(d^3*x*(1-c^2*x^2)^2)+35/12*c^4*x*(a+b*arcsin(c*x))/(d^3*(1-c^2*x^2)^2)+35/8*c^4*x*(a+b*arcsin(c*x))/(d^3*(1-c^2*x^2))-35/4*I*c^3*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(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(I*arcsin(c*x)))/d^3-35/8*I*b*c^3*polylog(2,I*exp(I*arcsin(c*x)))/d^3-29/24*b*c^3/(d^3*sqrt(1-c^2*x^2))],

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

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

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

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

# p>0

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

# Integrands of the form (f x)^m (d-c^2 d x^2)^p (a+b ArcSin[c x) and m symbolic
[x^m*(d-c^2*d*x^2)^3*(a+b*arcsin(c*x)),x,6,d^3*x^(1+m)*(a+b*arcsin(c*x))/(1+m)-3*c^2*d^3*x^(3+m)*(a+b*arcsin(c*x))/(3+m)+3*c^4*d^3*x^(5+m)*(a+b*arcsin(c*x))/(5+m)-c^6*d^3*x^(7+m)*(a+b*arcsin(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*arcsin(c*x)),x,5,d^2*x^(1+m)*(a+b*arcsin(c*x))/(1+m)-2*c^2*d^2*x^(3+m)*(a+b*arcsin(c*x))/(3+m)+c^4*d^2*x^(5+m)*(a+b*arcsin(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*arcsin(c*x)),x,4,d*x^(1+m)*(a+b*arcsin(c*x))/(1+m)-c^2*d*x^(3+m)*(a+b*arcsin(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*arcsin(c*x))/(d-c^2*d*x^2),x,0,Unintegrable(x^m*(a+b*arcsin(c*x))/(d-c^2*d*x^2),x)],
[x^m*(a+b*arcsin(c*x))/(d-c^2*d*x^2)^2,x,2,1/2*x^(1+m)*(a+b*arcsin(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*arcsin(c*x))/(d-c^2*d*x^2),x)/d],
[x^m*(a+b*arcsin(c*x))/(d-c^2*d*x^2)^3,x,4,1/4*x^(1+m)*(a+b*arcsin(c*x))/(d^3*(1-c^2*x^2)^2)+1/8*(3-m)*x^(1+m)*(a+b*arcsin(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*arcsin(c*x))/(d-c^2*d*x^2),x)/d^2],
[x^m*(d-c^2*d*x^2)^(5/2)*(a+b*arcsin(c*x)),x,9,5*d*x^(1+m)*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(c*x))/((4+m)*(6+m))+x^(1+m)*(d-c^2*d*x^2)^(5/2)*(a+b*arcsin(c*x))/(6+m)+15*d^2*x^(1+m)*(a+b*arcsin(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*arcsin(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*arcsin(c*x)),x,6,x^(1+m)*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(c*x))/(4+m)+3*d*x^(1+m)*(a+b*arcsin(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*arcsin(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*arcsin(c*x)),x,3,x^(1+m)*(a+b*arcsin(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*arcsin(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*arcsin(c*x))/(d-c^2*d*x^2)^(1/2),x,1,x^(1+m)*(a+b*arcsin(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*arcsin(c*x))/(d-c^2*d*x^2)^(3/2),x,3,x^(1+m)*(a+b*arcsin(c*x))/(d*sqrt(d-c^2*d*x^2))-m*x^(1+m)*(a+b*arcsin(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*arcsin(c*x))/(d-c^2*d*x^2)^(5/2),x,5,1/3*x^(1+m)*(a+b*arcsin(c*x))/(d*(d-c^2*d*x^2)^(3/2))+1/3*(2-m)*x^(1+m)*(a+b*arcsin(c*x))/(d^2*sqrt(d-c^2*d*x^2))-1/3*(2-m)*m*x^(1+m)*(a+b*arcsin(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*arcsin(a*x)/sqrt(1-a^2*x^2),x,1,x^(1+m)*arcsin(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 ArcSin[c x])^2

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

# p>0
[x^4*(d-c^2*d*x^2)*(a+b*arcsin(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*arcsin(c*x))/c^5-4/35*b*d*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))/c^5+2/49*b*d*(1-c^2*x^2)^(7/2)*(a+b*arcsin(c*x))/c^5+2/35*d*x^5*(a+b*arcsin(c*x))^2+1/7*d*x^5*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+32/525*b*d*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^5+16/525*b*d*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+4/175*b*d*x^4*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[x^3*(d-c^2*d*x^2)*(a+b*arcsin(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*arcsin(c*x))^2/c^4+1/12*d*x^4*(a+b*arcsin(c*x))^2+1/6*d*x^4*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+1/12*b*d*x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+1/18*b*d*x^3*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c-1/18*b*c*d*x^5*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)],
[x^2*(d-c^2*d*x^2)*(a+b*arcsin(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*arcsin(c*x))/c^3-2/25*b*d*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))/c^3+2/15*d*x^3*(a+b*arcsin(c*x))^2+1/5*d*x^3*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+8/45*b*d*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+4/45*b*d*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[x*(d-c^2*d*x^2)*(a+b*arcsin(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*arcsin(c*x))/c+3/32*d*(a+b*arcsin(c*x))^2/c^2-1/4*d*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2/c^2+3/16*b*d*x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[(d-c^2*d*x^2)*(a+b*arcsin(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*arcsin(c*x))/c+2/3*d*x*(a+b*arcsin(c*x))^2+1/3*d*x*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+4/3*b*d*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[(d-c^2*d*x^2)*(a+b*arcsin(c*x))^2/x,x,10,1/4*b^2*c^2*d*x^2-1/4*d*(a+b*arcsin(c*x))^2+1/2*d*(1-c^2*x^2)*(a+b*arcsin(c*x))^2-1/3*I*d*(a+b*arcsin(c*x))^3/b+d*(a+b*arcsin(c*x))^2*log(1-exp(2*I*arcsin(c*x)))-I*b*d*(a+b*arcsin(c*x))*polylog(2,exp(2*I*arcsin(c*x)))+1/2*b^2*d*polylog(3,exp(2*I*arcsin(c*x)))-1/2*b*c*d*x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)*(a+b*arcsin(c*x))^2/x^2,x,12,2*b^2*c^2*d*x-2*c^2*d*x*(a+b*arcsin(c*x))^2-d*(1-c^2*x^2)*(a+b*arcsin(c*x))^2/x-4*b*c*d*(a+b*arcsin(c*x))*arctanh(exp(I*arcsin(c*x)))+2*I*b^2*c*d*polylog(2,-exp(I*arcsin(c*x)))-2*I*b^2*c*d*polylog(2,exp(I*arcsin(c*x)))-2*b*c*d*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)*(a+b*arcsin(c*x))^2/x^3,x,10,-1/2*c^2*d*(a+b*arcsin(c*x))^2-1/2*d*(1-c^2*x^2)*(a+b*arcsin(c*x))^2/x^2+1/3*I*c^2*d*(a+b*arcsin(c*x))^3/b-c^2*d*(a+b*arcsin(c*x))^2*log(1-exp(2*I*arcsin(c*x)))+b^2*c^2*d*log(x)+I*b*c^2*d*(a+b*arcsin(c*x))*polylog(2,exp(2*I*arcsin(c*x)))-1/2*b^2*c^2*d*polylog(3,exp(2*I*arcsin(c*x)))-b*c*d*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/x],
[(d-c^2*d*x^2)*(a+b*arcsin(c*x))^2/x^4,x,16,-1/3*b^2*c^2*d/x+2/3*c^2*d*(a+b*arcsin(c*x))^2/x-1/3*d*(1-c^2*x^2)*(a+b*arcsin(c*x))^2/x^3+10/3*b*c^3*d*(a+b*arcsin(c*x))*arctanh(exp(I*arcsin(c*x)))-5/3*I*b^2*c^3*d*polylog(2,-exp(I*arcsin(c*x)))+5/3*I*b^2*c^3*d*polylog(2,exp(I*arcsin(c*x)))-1/3*b*c*d*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/x^2],
[x^4*(d-c^2*d*x^2)^2*(a+b*arcsin(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*arcsin(c*x))/c^5-2/315*b*d^2*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))/c^5-20/441*b*d^2*(1-c^2*x^2)^(7/2)*(a+b*arcsin(c*x))/c^5+2/81*b*d^2*(1-c^2*x^2)^(9/2)*(a+b*arcsin(c*x))/c^5+8/315*d^2*x^5*(a+b*arcsin(c*x))^2+4/63*d^2*x^5*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+1/9*d^2*x^5*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2+128/4725*b*d^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^5+64/4725*b*d^2*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+16/1575*b*d^2*x^4*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[x^3*(d-c^2*d*x^2)^2*(a+b*arcsin(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*arcsin(c*x))-73/3072*d^2*(a+b*arcsin(c*x))^2/c^4+1/24*d^2*x^4*(a+b*arcsin(c*x))^2+1/12*d^2*x^4*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+1/8*d^2*x^4*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2+73/1536*b*d^2*x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+73/2304*b*d^2*x^3*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c-25/576*b*c*d^2*x^5*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)],
[x^2*(d-c^2*d*x^2)^2*(a+b*arcsin(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*arcsin(c*x))/c^3+2/175*b*d^2*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))/c^3-2/49*b*d^2*(1-c^2*x^2)^(7/2)*(a+b*arcsin(c*x))/c^3+8/105*d^2*x^3*(a+b*arcsin(c*x))^2+4/35*d^2*x^3*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+1/7*d^2*x^3*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2+32/315*b*d^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+16/315*b*d^2*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[x*(d-c^2*d*x^2)^2*(a+b*arcsin(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*arcsin(c*x))/c+1/18*b*d^2*x*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))/c+5/96*d^2*(a+b*arcsin(c*x))^2/c^2-1/6*d^2*(1-c^2*x^2)^3*(a+b*arcsin(c*x))^2/c^2+5/48*b*d^2*x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[(d-c^2*d*x^2)^2*(a+b*arcsin(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*arcsin(c*x))/c+2/25*b*d^2*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))/c+8/15*d^2*x*(a+b*arcsin(c*x))^2+4/15*d^2*x*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+1/5*d^2*x*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2+16/15*b*d^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[(d-c^2*d*x^2)^2*(a+b*arcsin(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*arcsin(c*x))-11/32*d^2*(a+b*arcsin(c*x))^2+1/2*d^2*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+1/4*d^2*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2-1/3*I*d^2*(a+b*arcsin(c*x))^3/b+d^2*(a+b*arcsin(c*x))^2*log(1-exp(2*I*arcsin(c*x)))-I*b*d^2*(a+b*arcsin(c*x))*polylog(2,exp(2*I*arcsin(c*x)))+1/2*b^2*d^2*polylog(3,exp(2*I*arcsin(c*x)))-11/16*b*c*d^2*x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)^2*(a+b*arcsin(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*arcsin(c*x))-8/3*c^2*d^2*x*(a+b*arcsin(c*x))^2-4/3*c^2*d^2*x*(1-c^2*x^2)*(a+b*arcsin(c*x))^2-d^2*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2/x-4*b*c*d^2*(a+b*arcsin(c*x))*arctanh(exp(I*arcsin(c*x)))+2*I*b^2*c*d^2*polylog(2,-exp(I*arcsin(c*x)))-2*I*b^2*c*d^2*polylog(2,exp(I*arcsin(c*x)))-10/3*b*c*d^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)^2*(a+b*arcsin(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*arcsin(c*x))/x-1/4*c^2*d^2*(a+b*arcsin(c*x))^2-c^2*d^2*(1-c^2*x^2)*(a+b*arcsin(c*x))^2-1/2*d^2*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2/x^2+2/3*I*c^2*d^2*(a+b*arcsin(c*x))^3/b-2*c^2*d^2*(a+b*arcsin(c*x))^2*log(1-exp(2*I*arcsin(c*x)))+b^2*c^2*d^2*log(x)+2*I*b*c^2*d^2*(a+b*arcsin(c*x))*polylog(2,exp(2*I*arcsin(c*x)))-b^2*c^2*d^2*polylog(3,exp(2*I*arcsin(c*x)))-1/2*b*c^3*d^2*x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)^2*(a+b*arcsin(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*arcsin(c*x))/x^2+8/3*c^4*d^2*x*(a+b*arcsin(c*x))^2+4/3*c^2*d^2*(1-c^2*x^2)*(a+b*arcsin(c*x))^2/x-1/3*d^2*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2/x^3+22/3*b*c^3*d^2*(a+b*arcsin(c*x))*arctanh(exp(I*arcsin(c*x)))-11/3*I*b^2*c^3*d^2*polylog(2,-exp(I*arcsin(c*x)))+11/3*I*b^2*c^3*d^2*polylog(2,exp(I*arcsin(c*x)))+5/3*b*c^3*d^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)],
[x^4*(d-c^2*d*x^2)^3*(a+b*arcsin(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*arcsin(c*x))/c^5-4/1155*b*d^3*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))/c^5+2/1617*b*d^3*(1-c^2*x^2)^(7/2)*(a+b*arcsin(c*x))/c^5-8/297*b*d^3*(1-c^2*x^2)^(9/2)*(a+b*arcsin(c*x))/c^5+2/121*b*d^3*(1-c^2*x^2)^(11/2)*(a+b*arcsin(c*x))/c^5+16/1155*d^3*x^5*(a+b*arcsin(c*x))^2+8/231*d^3*x^5*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+2/33*d^3*x^5*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2+1/11*d^3*x^5*(1-c^2*x^2)^3*(a+b*arcsin(c*x))^2+256/17325*b*d^3*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^5+128/17325*b*d^3*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+32/5775*b*d^3*x^4*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[x^3*(d-c^2*d*x^2)^3*(a+b*arcsin(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*arcsin(c*x))-1/50*b*c*d^3*x^5*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))-79/5120*d^3*(a+b*arcsin(c*x))^2/c^4+1/40*d^3*x^4*(a+b*arcsin(c*x))^2+1/20*d^3*x^4*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+3/40*d^3*x^4*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2+1/10*d^3*x^4*(1-c^2*x^2)^3*(a+b*arcsin(c*x))^2+79/2560*b*d^3*x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+79/3840*b*d^3*x^3*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c-31/960*b*c*d^3*x^5*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)],
[x^2*(d-c^2*d*x^2)^3*(a+b*arcsin(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*arcsin(c*x))/c^3+4/525*b*d^3*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))/c^3+2/441*b*d^3*(1-c^2*x^2)^(7/2)*(a+b*arcsin(c*x))/c^3-2/81*b*d^3*(1-c^2*x^2)^(9/2)*(a+b*arcsin(c*x))/c^3+16/315*d^3*x^3*(a+b*arcsin(c*x))^2+8/105*d^3*x^3*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+2/21*d^3*x^3*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2+1/9*d^3*x^3*(1-c^2*x^2)^3*(a+b*arcsin(c*x))^2+64/945*b*d^3*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+32/945*b*d^3*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[x*(d-c^2*d*x^2)^3*(a+b*arcsin(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*arcsin(c*x))/c+7/192*b*d^3*x*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))/c+1/32*b*d^3*x*(1-c^2*x^2)^(7/2)*(a+b*arcsin(c*x))/c+35/1024*d^3*(a+b*arcsin(c*x))^2/c^2-1/8*d^3*(1-c^2*x^2)^4*(a+b*arcsin(c*x))^2/c^2+35/512*b*d^3*x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[(d-c^2*d*x^2)^3*(a+b*arcsin(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*arcsin(c*x))/c+12/175*b*d^3*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))/c+2/49*b*d^3*(1-c^2*x^2)^(7/2)*(a+b*arcsin(c*x))/c+16/35*d^3*x*(a+b*arcsin(c*x))^2+8/35*d^3*x*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+6/35*d^3*x*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2+1/7*d^3*x*(1-c^2*x^2)^3*(a+b*arcsin(c*x))^2+32/35*b*d^3*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[(d-c^2*d*x^2)^3*(a+b*arcsin(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*arcsin(c*x))-1/18*b*c*d^3*x*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))-19/48*d^3*(a+b*arcsin(c*x))^2+1/2*d^3*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+1/4*d^3*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2+1/6*d^3*(1-c^2*x^2)^3*(a+b*arcsin(c*x))^2-1/3*I*d^3*(a+b*arcsin(c*x))^3/b+d^3*(a+b*arcsin(c*x))^2*log(1-exp(2*I*arcsin(c*x)))-I*b*d^3*(a+b*arcsin(c*x))*polylog(2,exp(2*I*arcsin(c*x)))+1/2*b^2*d^3*polylog(3,exp(2*I*arcsin(c*x)))-19/24*b*c*d^3*x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)^3*(a+b*arcsin(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*arcsin(c*x))-2/25*b*c*d^3*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))-16/5*c^2*d^3*x*(a+b*arcsin(c*x))^2-8/5*c^2*d^3*x*(1-c^2*x^2)*(a+b*arcsin(c*x))^2-6/5*c^2*d^3*x*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2-d^3*(1-c^2*x^2)^3*(a+b*arcsin(c*x))^2/x-4*b*c*d^3*(a+b*arcsin(c*x))*arctanh(exp(I*arcsin(c*x)))+2*I*b^2*c*d^3*polylog(2,-exp(I*arcsin(c*x)))-2*I*b^2*c*d^3*polylog(2,exp(I*arcsin(c*x)))-22/5*b*c*d^3*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)^3*(a+b*arcsin(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*arcsin(c*x))-b*c*d^3*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))/x+3/32*c^2*d^3*(a+b*arcsin(c*x))^2-3/2*c^2*d^3*(1-c^2*x^2)*(a+b*arcsin(c*x))^2-3/4*c^2*d^3*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2-1/2*d^3*(1-c^2*x^2)^3*(a+b*arcsin(c*x))^2/x^2+I*c^2*d^3*(a+b*arcsin(c*x))^3/b-3*c^2*d^3*(a+b*arcsin(c*x))^2*log(1-exp(2*I*arcsin(c*x)))+b^2*c^2*d^3*log(x)+3*I*b*c^2*d^3*(a+b*arcsin(c*x))*polylog(2,exp(2*I*arcsin(c*x)))-3/2*b^2*c^2*d^3*polylog(3,exp(2*I*arcsin(c*x)))+3/16*b*c^3*d^3*x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)^3*(a+b*arcsin(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*arcsin(c*x))-1/3*b*c*d^3*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))/x^2+16/3*c^4*d^3*x*(a+b*arcsin(c*x))^2+8/3*c^4*d^3*x*(1-c^2*x^2)*(a+b*arcsin(c*x))^2+2*c^2*d^3*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2/x-1/3*d^3*(1-c^2*x^2)^3*(a+b*arcsin(c*x))^2/x^3+34/3*b*c^3*d^3*(a+b*arcsin(c*x))*arctanh(exp(I*arcsin(c*x)))-17/3*I*b^2*c^3*d^3*polylog(2,-exp(I*arcsin(c*x)))+17/3*I*b^2*c^3*d^3*polylog(2,exp(I*arcsin(c*x)))+5*b*c^3*d^3*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)],

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

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

# p>0
[x^3*(d-c^2*d*x^2)^(1/2)*(a+b*arcsin(c*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*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/c^4-1/15*x^2*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/c^2+1/5*x^4*(a+b*arcsin(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*arcsin(c*x)*sqrt(d-c^2*d*x^2)/(c^3*sqrt(1-c^2*x^2))+2/45*b*x^3*(a+b*arcsin(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(1-c^2*x^2))-2/25*b*c*x^5*(a+b*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)],
[x^2*(d-c^2*d*x^2)^(1/2)*(a+b*arcsin(c*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*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/c^2+1/4*x^3*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)-1/64*b^2*arcsin(c*x)*sqrt(d-c^2*d*x^2)/(c^3*sqrt(1-c^2*x^2))+1/8*b*x^2*(a+b*arcsin(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(1-c^2*x^2))-1/8*b*c*x^4*(a+b*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+1/24*(a+b*arcsin(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)^(1/2)*(a+b*arcsin(c*x))^2,x,5,-1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/(c*sqrt(1-c^2*x^2))-2/9*b*c*x^3*(a+b*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)^(1/2)*(a+b*arcsin(c*x))^2,x,5,-1/4*b^2*x*sqrt(d-c^2*d*x^2)+1/2*x*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)+1/4*b^2*arcsin(c*x)*sqrt(d-c^2*d*x^2)/(c*sqrt(1-c^2*x^2))-1/2*b*c*x^2*(a+b*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+1/6*(a+b*arcsin(c*x))^3*sqrt(d-c^2*d*x^2)/(b*c*sqrt(1-c^2*x^2))],
[(d-c^2*d*x^2)^(1/2)*(a+b*arcsin(c*x))^2/x,x,12,-2*b^2*sqrt(d-c^2*d*x^2)+(a+b*arcsin(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*arcsin(c*x)*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-2*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+2*I*b*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-2*I*b*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-2*b^2*polylog(3,-exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+2*b^2*polylog(3,exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)^(1/2)*(a+b*arcsin(c*x))^2/x^2,x,7,-(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/x-I*c*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-1/3*c*(a+b*arcsin(c*x))^3*sqrt(d-c^2*d*x^2)/(b*sqrt(1-c^2*x^2))+2*b*c*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-I*b^2*c*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)^(1/2)*(a+b*arcsin(c*x))^2/x^3,x,13,-1/2*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/x^2-b*c*(a+b*arcsin(c*x))*sqrt(d-c^2*d*x^2)/(x*sqrt(1-c^2*x^2))+c^2*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(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)-I*b*c^2*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+I*b*c^2*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+b^2*c^2*polylog(3,-exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-b^2*c^2*polylog(3,exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)],
[(d-c^2*d*x^2)^(1/2)*(a+b*arcsin(c*x))^2/x^4,x,9,-1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(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*arcsin(c*x)*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+1/3*I*c^3*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-2/3*b*c^3*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+1/3*I*b^2*c^3*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-1/3*b*c*(a+b*arcsin(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*arcsin(c*x))^2,x,20,1/7*x^4*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(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*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/c^4-1/35*d*x^2*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/c^2+3/35*d*x^4*(a+b*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(c*x))^2,x,17,1/6*x^3*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(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*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/c^2+1/8*d*x^3*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)+7/1152*b^2*d*arcsin(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*arcsin(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*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+1/48*d*(a+b*arcsin(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*arcsin(c*x))^2,x,6,-1/5*(d-c^2*d*x^2)^(5/2)*(a+b*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(c*x))^2,x,10,1/4*x*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(c*x))^2-17/64*b^2*d*x*sqrt(d-c^2*d*x^2)+1/32*b^2*c^2*d*x^3*sqrt(d-c^2*d*x^2)+3/8*d*x*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)+17/64*b^2*d*arcsin(c*x)*sqrt(d-c^2*d*x^2)/(c*sqrt(1-c^2*x^2))-5/8*b*c*d*x^2*(a+b*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+1/8*b*c^3*d*x^4*(a+b*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+1/8*d*(a+b*arcsin(c*x))^3*sqrt(d-c^2*d*x^2)/(b*c*sqrt(1-c^2*x^2)),1/4*x*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/c+3/8*d*x*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)+9/64*b^2*d*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+1/8*d*(a+b*arcsin(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*arcsin(c*x))^2/x,x,17,1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(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*arcsin(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*arcsin(c*x)*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-2/3*b*c*d*x*(a+b*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-2*d*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+2*I*b*d*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-2*I*b*d*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-2*b^2*d*polylog(3,-exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+2*b^2*d*polylog(3,exp(I*arcsin(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*arcsin(c*x))^2/x^2,x,14,-(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(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*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)-5/4*b^2*c*d*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-I*c*d*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-1/2*c*d*(a+b*arcsin(c*x))^3*sqrt(d-c^2*d*x^2)/(b*sqrt(1-c^2*x^2))+2*b*c*d*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-I*b^2*c*d*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+b*c*d*(a+b*arcsin(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*arcsin(c*x))^2/x^3,x,18,-1/2*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(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*arcsin(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*arcsin(c*x)*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-b*c*d*(a+b*arcsin(c*x))*sqrt(d-c^2*d*x^2)/(x*sqrt(1-c^2*x^2))-b*c^3*d*x*(a+b*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+3*c^2*d*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(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*I*b*c^2*d*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+3*I*b*c^2*d*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+3*b^2*c^2*d*polylog(3,-exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-3*b^2*c^2*d*polylog(3,exp(I*arcsin(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*arcsin(c*x))^2/x^4,x,16,-1/3*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(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*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/x-1/3*b^2*c^3*d*arcsin(c*x)*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+4/3*I*c^3*d*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+1/3*c^3*d*(a+b*arcsin(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*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+4/3*I*b^2*c^3*d*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-1/3*b*c*d*(a+b*arcsin(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*arcsin(c*x))^2,x,27,5/63*d*x^4*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(c*x))^2+1/9*x^4*(d-c^2*d*x^2)^(5/2)*(a+b*arcsin(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*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/c^4-1/63*d^2*x^2*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/c^2+1/21*d^2*x^4*(a+b*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(c*x))^2,x,25,5/48*d*x^3*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(c*x))^2+1/8*x^3*(d-c^2*d*x^2)^(5/2)*(a+b*arcsin(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*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/c^2+5/64*d^2*x^3*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)+359/36864*b^2*d^2*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+5/384*d^2*(a+b*arcsin(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*arcsin(c*x))^2,x,6,-1/7*(d-c^2*d*x^2)^(7/2)*(a+b*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(c*x))^2,x,16,5/24*d*x*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(c*x))^2+1/6*x*(d-c^2*d*x^2)^(5/2)*(a+b*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/c+1/18*b*d^2*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))*sqrt(d-c^2*d*x^2)/c+5/16*d^2*x*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)+115/1152*b^2*d^2*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+5/48*d^2*(a+b*arcsin(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*arcsin(c*x))^2/x,x,23,1/3*d*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(c*x))^2+1/5*(d-c^2*d*x^2)^(5/2)*(a+b*arcsin(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*arcsin(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*arcsin(c*x)*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-16/15*b*c*d^2*x*(a+b*arcsin(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*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-2*d^2*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+2*I*b*d^2*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-2*I*b*d^2*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-2*b^2*d^2*polylog(3,-exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+2*b^2*d^2*polylog(3,exp(I*arcsin(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*arcsin(c*x))^2/x^2,x,23,-5/4*c^2*d*x*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(c*x))^2-(d-c^2*d*x^2)^(5/2)*(a+b*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)-15/8*c^2*d^2*x*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)-89/64*b^2*c*d^2*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-I*c*d^2*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-5/8*c*d^2*(a+b*arcsin(c*x))^3*sqrt(d-c^2*d*x^2)/(b*sqrt(1-c^2*x^2))+2*b*c*d^2*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-I*b^2*c*d^2*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+b*c*d^2*(a+b*arcsin(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*arcsin(c*x))^2/x^3,x,25,-5/6*c^2*d*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(c*x))^2-1/2*(d-c^2*d*x^2)^(5/2)*(a+b*arcsin(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*arcsin(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*arcsin(c*x)*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-b*c*d^2*(a+b*arcsin(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*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+5*c^2*d^2*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(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*I*b*c^2*d^2*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+5*I*b*c^2*d^2*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(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(I*arcsin(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(I*arcsin(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*arcsin(c*x))^2/x^4,x,27,5/3*c^2*d*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(c*x))^2/x-1/3*(d-c^2*d*x^2)^(5/2)*(a+b*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/x^2+5/2*c^4*d^2*x*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)+23/12*b^2*c^3*d^2*arcsin(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*arcsin(c*x))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+7/3*I*c^3*d^2*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+5/6*c^3*d^2*(a+b*arcsin(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*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)+7/3*I*b^2*c^3*d^2*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(d-c^2*d*x^2)/sqrt(1-c^2*x^2)-7/3*b*c^3*d^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2)],

# p<0
[x^5*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(1/2),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*arcsin(c*x)*sqrt(1-c^2*x^2)/(c^5*sqrt(d-c^2*d*x^2))+8/45*b*x^3*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/(c^3*sqrt(d-c^2*d*x^2))+2/25*b*x^5*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/(c*sqrt(d-c^2*d*x^2))-8/15*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^6*d)-4/15*x^2*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^4*d)-1/5*x^4*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^2*d)],
[x^4*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(1/2),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*arcsin(c*x)*sqrt(1-c^2*x^2)/(c^5*sqrt(d-c^2*d*x^2))+3/8*b*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/(c^3*sqrt(d-c^2*d*x^2))+1/8*b*x^4*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/(c*sqrt(d-c^2*d*x^2))+1/8*(a+b*arcsin(c*x))^3*sqrt(1-c^2*x^2)/(b*c^5*sqrt(d-c^2*d*x^2))-3/8*x*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^4*d)-1/4*x^3*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^2*d)],
[x^3*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(1/2),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*arcsin(c*x)*sqrt(1-c^2*x^2)/(c^3*sqrt(d-c^2*d*x^2))+2/9*b*x^3*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/(c*sqrt(d-c^2*d*x^2))-2/3*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^4*d)-1/3*x^2*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^2*d)],
[x^2*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(1/2),x,5,-1/4*b^2*arcsin(c*x)*sqrt(1-c^2*x^2)/(c^3*sqrt(d-c^2*d*x^2))+1/2*b*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/(c*sqrt(d-c^2*d*x^2))+1/6*(a+b*arcsin(c*x))^3*sqrt(1-c^2*x^2)/(b*c^3*sqrt(d-c^2*d*x^2))+1/4*b^2*x*sqrt(d-c^2*d*x^2)/(c^2*d)-1/2*x*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^2*d),1/4*b^2*x*(1-c^2*x^2)/(c^2*sqrt(d-c^2*d*x^2))-1/4*b^2*arcsin(c*x)*sqrt(1-c^2*x^2)/(c^3*sqrt(d-c^2*d*x^2))+1/2*b*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/(c*sqrt(d-c^2*d*x^2))+1/6*(a+b*arcsin(c*x))^3*sqrt(1-c^2*x^2)/(b*c^3*sqrt(d-c^2*d*x^2))-1/2*x*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^2*d)],
[x*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(1/2),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*arcsin(c*x)*sqrt(1-c^2*x^2)/(c*sqrt(d-c^2*d*x^2))-(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^2*d)],
[(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(1/2),x,1,1/3*(a+b*arcsin(c*x))^3*sqrt(1-c^2*x^2)/(b*c*sqrt(d-c^2*d*x^2))],
[(a+b*arcsin(c*x))^2/(x*(d-c^2*d*x^2)^(1/2)),x,8,-2*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)+2*I*b*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)-2*I*b*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)-2*b^2*polylog(3,-exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)+2*b^2*polylog(3,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)],
[(a+b*arcsin(c*x))^2/(x^2*(d-c^2*d*x^2)^(1/2)),x,6,-I*c*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)+2*b*c*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)-I*b^2*c*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)-(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(d*x)],
[(a+b*arcsin(c*x))^2/(x^3*(d-c^2*d*x^2)^(1/2)),x,13,-b*c*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/(x*sqrt(d-c^2*d*x^2))-c^2*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(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)+I*b*c^2*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)-I*b*c^2*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)-b^2*c^2*polylog(3,-exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)+b^2*c^2*polylog(3,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)-1/2*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(d*x^2)],
[(a+b*arcsin(c*x))^2/(x^4*(d-c^2*d*x^2)^(1/2)),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*arcsin(c*x))*sqrt(1-c^2*x^2)/(x^2*sqrt(d-c^2*d*x^2))-2/3*I*c^3*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)+4/3*b*c^3*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)-2/3*I*b^2*c^3*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/sqrt(d-c^2*d*x^2)-1/3*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(d*x^3)-2/3*c^2*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(d*x)],
[x^5*(a+b*arcsin(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*arcsin(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*arcsin(c*x)*sqrt(1-c^2*x^2)/(c^5*d*sqrt(d-c^2*d*x^2))+2*b*x*(a+b*arcsin(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*arcsin(c*x))*sqrt(1-c^2*x^2)/(c^3*d*sqrt(d-c^2*d*x^2))+4*I*b*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(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(I*arcsin(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(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^6*d*sqrt(d-c^2*d*x^2))+8/3*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^6*d^2)+4/3*x^2*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^4*d^2)],
[x^4*(a+b*arcsin(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*arcsin(c*x))^2/(c^2*d*sqrt(d-c^2*d*x^2))+1/4*b^2*arcsin(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*arcsin(c*x))*sqrt(1-c^2*x^2)/(c^3*d*sqrt(d-c^2*d*x^2))-I*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)/(c^5*d*sqrt(d-c^2*d*x^2))-1/2*(a+b*arcsin(c*x))^3*sqrt(1-c^2*x^2)/(b*c^5*d*sqrt(d-c^2*d*x^2))+2*b*(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^5*d*sqrt(d-c^2*d*x^2))-I*b^2*polylog(2,-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^5*d*sqrt(d-c^2*d*x^2))+3/2*x*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^4*d^2)],
[x^3*(a+b*arcsin(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*arcsin(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*arcsin(c*x)*sqrt(1-c^2*x^2)/(c^3*d*sqrt(d-c^2*d*x^2))+2*b*x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/(c^3*d*sqrt(d-c^2*d*x^2))+4*I*b*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(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(I*arcsin(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(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^4*d*sqrt(d-c^2*d*x^2))+2*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^4*d^2)],
[x^2*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(3/2),x,7,x*(a+b*arcsin(c*x))^2/(c^2*d*sqrt(d-c^2*d*x^2))-I*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)/(c^3*d*sqrt(d-c^2*d*x^2))-1/3*(a+b*arcsin(c*x))^3*sqrt(1-c^2*x^2)/(b*c^3*d*sqrt(d-c^2*d*x^2))+2*b*(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^3*d*sqrt(d-c^2*d*x^2))-I*b^2*polylog(2,-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^3*d*sqrt(d-c^2*d*x^2))],
[x*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(3/2),x,7,(a+b*arcsin(c*x))^2/(c^2*d*sqrt(d-c^2*d*x^2))+4*I*b*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(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(I*arcsin(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(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^2*d*sqrt(d-c^2*d*x^2))],
[(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(3/2),x,6,x*(a+b*arcsin(c*x))^2/(d*sqrt(d-c^2*d*x^2))-I*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)/(c*d*sqrt(d-c^2*d*x^2))+2*b*(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c*d*sqrt(d-c^2*d*x^2))-I*b^2*polylog(2,-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c*d*sqrt(d-c^2*d*x^2))],
[(a+b*arcsin(c*x))^2/(x*(d-c^2*d*x^2)^(3/2)),x,15,(a+b*arcsin(c*x))^2/(d*sqrt(d-c^2*d*x^2))+4*I*b*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))-2*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))+2*I*b*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))-2*I*b^2*polylog(2,-I*exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))+2*I*b^2*polylog(2,I*exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))-2*I*b*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))-2*b^2*polylog(3,-exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))+2*b^2*polylog(3,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))],
[(a+b*arcsin(c*x))^2/(x^2*(d-c^2*d*x^2)^(3/2)),x,14,-(a+b*arcsin(c*x))^2/(d*x*sqrt(d-c^2*d*x^2))+2*c^2*x*(a+b*arcsin(c*x))^2/(d*sqrt(d-c^2*d*x^2))-2*I*c*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))-4*b*c*(a+b*arcsin(c*x))*arctanh(exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))+4*b*c*(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))-I*b^2*c*polylog(2,-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))-I*b^2*c*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))],
[(a+b*arcsin(c*x))^2/(x^3*(d-c^2*d*x^2)^(3/2)),x,26,3/2*c^2*(a+b*arcsin(c*x))^2/(d*sqrt(d-c^2*d*x^2))-1/2*(a+b*arcsin(c*x))^2/(d*x^2*sqrt(d-c^2*d*x^2))-b*c*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/(d*x*sqrt(d-c^2*d*x^2))+4*I*b*c^2*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))-3*c^2*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(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*I*b*c^2*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(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(I*arcsin(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(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))-3*I*b*c^2*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))-3*b^2*c^2*polylog(3,-exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))+3*b^2*c^2*polylog(3,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))],
[(a+b*arcsin(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*arcsin(c*x))^2/(d*x^3*sqrt(d-c^2*d*x^2))-4/3*c^2*(a+b*arcsin(c*x))^2/(d*x*sqrt(d-c^2*d*x^2))+8/3*c^4*x*(a+b*arcsin(c*x))^2/(d*sqrt(d-c^2*d*x^2))-1/3*b*c*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/(d*x^2*sqrt(d-c^2*d*x^2))-8/3*I*c^3*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))-20/3*b*c^3*(a+b*arcsin(c*x))*arctanh(exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))+16/3*b*c^3*(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))-I*b^2*c^3*polylog(2,-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))-5/3*I*b^2*c^3*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*sqrt(d-c^2*d*x^2))],
[x^5*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(5/2),x,26,1/3*x^4*(a+b*arcsin(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*arcsin(c*x))^2/(c^4*d^2*sqrt(d-c^2*d*x^2))-1/3*b*x^3*(a+b*arcsin(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*arcsin(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*arcsin(c*x))*sqrt(1-c^2*x^2)/(c^5*d^2*sqrt(d-c^2*d*x^2))-22/3*I*b*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(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(I*arcsin(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(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^6*d^2*sqrt(d-c^2*d*x^2))-8/3*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(c^6*d^3)],
[x^4*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(5/2),x,16,1/3*x^3*(a+b*arcsin(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*arcsin(c*x))^2/(c^4*d^2*sqrt(d-c^2*d*x^2))-1/3*b*x^2*(a+b*arcsin(c*x))/(c^3*d^2*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2))-1/3*b^2*arcsin(c*x)*sqrt(1-c^2*x^2)/(c^5*d^2*sqrt(d-c^2*d*x^2))+4/3*I*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)/(c^5*d^2*sqrt(d-c^2*d*x^2))+1/3*(a+b*arcsin(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*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^5*d^2*sqrt(d-c^2*d*x^2))+4/3*I*b^2*polylog(2,-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^5*d^2*sqrt(d-c^2*d*x^2))],
[x^3*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(5/2),x,16,1/3*x^2*(a+b*arcsin(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*arcsin(c*x))^2/(c^4*d^2*sqrt(d-c^2*d*x^2))-1/3*b*x*(a+b*arcsin(c*x))/(c^3*d^2*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2))-10/3*I*b*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(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(I*arcsin(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(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^4*d^2*sqrt(d-c^2*d*x^2))],
[x^2*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(5/2),x,9,1/3*x^3*(a+b*arcsin(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*arcsin(c*x))/(c*d^2*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2))-1/3*b^2*arcsin(c*x)*sqrt(1-c^2*x^2)/(c^3*d^2*sqrt(d-c^2*d*x^2))+1/3*I*(a+b*arcsin(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*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^3*d^2*sqrt(d-c^2*d*x^2))+1/3*I*b^2*polylog(2,-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^3*d^2*sqrt(d-c^2*d*x^2))],
[x*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(5/2),x,9,1/3*(a+b*arcsin(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*arcsin(c*x))/(c*d^2*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+2/3*I*b*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(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(I*arcsin(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(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^2*d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(5/2),x,9,1/3*x*(a+b*arcsin(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*arcsin(c*x))^2/(d^2*sqrt(d-c^2*d*x^2))-1/3*b*(a+b*arcsin(c*x))/(c*d^2*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2))-2/3*I*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)/(c*d^2*sqrt(d-c^2*d*x^2))+4/3*b*(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c*d^2*sqrt(d-c^2*d*x^2))-2/3*I*b^2*polylog(2,-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c*d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arcsin(c*x))^2/(x*(d-c^2*d*x^2)^(5/2)),x,24,1/3*(a+b*arcsin(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*arcsin(c*x))^2/(d^2*sqrt(d-c^2*d*x^2))-1/3*b*c*x*(a+b*arcsin(c*x))/(d^2*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+14/3*I*b*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))-2*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))+2*I*b*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(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(I*arcsin(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(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))-2*I*b*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))-2*b^2*polylog(3,-exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))+2*b^2*polylog(3,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arcsin(c*x))^2/(x^2*(d-c^2*d*x^2)^(5/2)),x,19,-(a+b*arcsin(c*x))^2/(d*x*(d-c^2*d*x^2)^(3/2))+4/3*c^2*x*(a+b*arcsin(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*arcsin(c*x))^2/(d^2*sqrt(d-c^2*d*x^2))-1/3*b*c*(a+b*arcsin(c*x))/(d^2*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2))-8/3*I*c*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))-4*b*c*(a+b*arcsin(c*x))*arctanh(exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))+16/3*b*c*(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))-5/3*I*b^2*c*polylog(2,-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))-I*b^2*c*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arcsin(c*x))^2/(x^3*(d-c^2*d*x^2)^(5/2)),x,38,5/6*c^2*(a+b*arcsin(c*x))^2/(d*(d-c^2*d*x^2)^(3/2))-1/2*(a+b*arcsin(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*arcsin(c*x))^2/(d^2*sqrt(d-c^2*d*x^2))-b*c*(a+b*arcsin(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*arcsin(c*x))/(d^2*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2))+26/3*I*b*c^2*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))-5*c^2*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(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*I*b*c^2*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(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(I*arcsin(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(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))-5*I*b*c^2*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(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(I*arcsin(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(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))],
[(a+b*arcsin(c*x))^2/(x^4*(d-c^2*d*x^2)^(5/2)),x,32,-1/3*(a+b*arcsin(c*x))^2/(d*x^3*(d-c^2*d*x^2)^(3/2))-2*c^2*(a+b*arcsin(c*x))^2/(d*x*(d-c^2*d*x^2)^(3/2))+8/3*c^4*x*(a+b*arcsin(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*arcsin(c*x))^2/(d^2*sqrt(d-c^2*d*x^2))-1/3*b*c*(a+b*arcsin(c*x))/(d^2*x^2*sqrt(1-c^2*x^2)*sqrt(d-c^2*d*x^2))-16/3*I*c^3*(a+b*arcsin(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*arcsin(c*x))*arctanh(exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))+32/3*b*c^3*(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))-8/3*I*b^2*c^3*polylog(2,-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))-8/3*I*b^2*c^3*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d^2*sqrt(d-c^2*d*x^2))],
[x^4*arcsin(a*x)^2/sqrt(1-a^2*x^2),x,10,-15/64*arcsin(a*x)/a^5+3/8*x^2*arcsin(a*x)/a^3+1/8*x^4*arcsin(a*x)/a+1/8*arcsin(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*arcsin(a*x)^2*sqrt(1-a^2*x^2)/a^4-1/4*x^3*arcsin(a*x)^2*sqrt(1-a^2*x^2)/a^2],
[x^3*arcsin(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*arcsin(a*x)/a^3+2/9*x^3*arcsin(a*x)/a+14/9*sqrt(1-a^2*x^2)/a^4-2/3*arcsin(a*x)^2*sqrt(1-a^2*x^2)/a^4-1/3*x^2*arcsin(a*x)^2*sqrt(1-a^2*x^2)/a^2],
[x^2*arcsin(a*x)^2/sqrt(1-a^2*x^2),x,5,-1/4*arcsin(a*x)/a^3+1/2*x^2*arcsin(a*x)/a+1/6*arcsin(a*x)^3/a^3+1/4*x*sqrt(1-a^2*x^2)/a^2-1/2*x*arcsin(a*x)^2*sqrt(1-a^2*x^2)/a^2],
[x*arcsin(a*x)^2/sqrt(1-a^2*x^2),x,3,2*x*arcsin(a*x)/a+2*sqrt(1-a^2*x^2)/a^2-arcsin(a*x)^2*sqrt(1-a^2*x^2)/a^2],
[arcsin(a*x)^2/sqrt(1-a^2*x^2),x,1,1/3*arcsin(a*x)^3/a],
[arcsin(a*x)^2/(x*sqrt(1-a^2*x^2)),x,8,-2*arcsin(a*x)^2*arctanh(exp(I*arcsin(a*x)))+2*I*arcsin(a*x)*polylog(2,-exp(I*arcsin(a*x)))-2*I*arcsin(a*x)*polylog(2,exp(I*arcsin(a*x)))-2*polylog(3,-exp(I*arcsin(a*x)))+2*polylog(3,exp(I*arcsin(a*x)))],
[arcsin(a*x)^2/(x^2*sqrt(1-a^2*x^2)),x,6,-I*a*arcsin(a*x)^2+2*a*arcsin(a*x)*log(1-exp(2*I*arcsin(a*x)))-I*a*polylog(2,exp(2*I*arcsin(a*x)))-arcsin(a*x)^2*sqrt(1-a^2*x^2)/x],
[arcsin(a*x)^2/(x^3*sqrt(1-a^2*x^2)),x,13,-a*arcsin(a*x)/x-a^2*arcsin(a*x)^2*arctanh(exp(I*arcsin(a*x)))-a^2*arctanh(sqrt(1-a^2*x^2))+I*a^2*arcsin(a*x)*polylog(2,-exp(I*arcsin(a*x)))-I*a^2*arcsin(a*x)*polylog(2,exp(I*arcsin(a*x)))-a^2*polylog(3,-exp(I*arcsin(a*x)))+a^2*polylog(3,exp(I*arcsin(a*x)))-1/2*arcsin(a*x)^2*sqrt(1-a^2*x^2)/x^2],
[arcsin(a*x)^2/(c-a^2*c*x^2)^(1/2),x,1,1/3*arcsin(a*x)^3*sqrt(1-a^2*x^2)/(a*sqrt(c-a^2*c*x^2))],
[arcsin(a*x)^2/(c-a^2*c*x^2)^(3/2),x,6,x*arcsin(a*x)^2/(c*sqrt(c-a^2*c*x^2))-I*arcsin(a*x)^2*sqrt(1-a^2*x^2)/(a*c*sqrt(c-a^2*c*x^2))+2*arcsin(a*x)*log(1+exp(2*I*arcsin(a*x)))*sqrt(1-a^2*x^2)/(a*c*sqrt(c-a^2*c*x^2))-I*polylog(2,-exp(2*I*arcsin(a*x)))*sqrt(1-a^2*x^2)/(a*c*sqrt(c-a^2*c*x^2))],
[arcsin(a*x)^2/(c-a^2*c*x^2)^(5/2),x,9,1/3*x*arcsin(a*x)^2/(c*(c-a^2*c*x^2)^(3/2))+1/3*x/(c^2*sqrt(c-a^2*c*x^2))+2/3*x*arcsin(a*x)^2/(c^2*sqrt(c-a^2*c*x^2))-1/3*arcsin(a*x)/(a*c^2*sqrt(1-a^2*x^2)*sqrt(c-a^2*c*x^2))-2/3*I*arcsin(a*x)^2*sqrt(1-a^2*x^2)/(a*c^2*sqrt(c-a^2*c*x^2))+4/3*arcsin(a*x)*log(1+exp(2*I*arcsin(a*x)))*sqrt(1-a^2*x^2)/(a*c^2*sqrt(c-a^2*c*x^2))-2/3*I*polylog(2,-exp(2*I*arcsin(a*x)))*sqrt(1-a^2*x^2)/(a*c^2*sqrt(c-a^2*c*x^2))],
[arcsin(a*x)^2/(c-a^2*c*x^2)^(7/2),x,13,1/5*x*arcsin(a*x)^2/(c*(c-a^2*c*x^2)^(5/2))+4/15*x*arcsin(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*arcsin(a*x)/(a*c^3*(1-a^2*x^2)^(3/2)*sqrt(c-a^2*c*x^2))+8/15*x*arcsin(a*x)^2/(c^3*sqrt(c-a^2*c*x^2))-4/15*arcsin(a*x)/(a*c^3*sqrt(1-a^2*x^2)*sqrt(c-a^2*c*x^2))-8/15*I*arcsin(a*x)^2*sqrt(1-a^2*x^2)/(a*c^3*sqrt(c-a^2*c*x^2))+16/15*arcsin(a*x)*log(1+exp(2*I*arcsin(a*x)))*sqrt(1-a^2*x^2)/(a*c^3*sqrt(c-a^2*c*x^2))-8/15*I*polylog(2,-exp(2*I*arcsin(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 ArcSin[c x)^2 and m symbolic
[x^m*(d-c^2*d*x^2)^3*(a+b*arcsin(c*x))^2,x,23,2*b^2*c^2*d^3*x^(3+m)/((3+m)*(7+m)^2)+30*b^2*c^2*d^3*x^(3+m)/((3+m)^2*(5+m)*(7+m)^2)+12*b^2*c^2*d^3*x^(3+m)/((3+m)*(5+m)^2*(7+m))+48*b^2*c^2*d^3*x^(3+m)/((3+m)^3*(5+m)*(7+m))+36*b^2*c^2*d^3*x^(3+m)/((7+m)*(15+8*m+m^2)^2)+10*b^2*c^2*d^3*x^(3+m)/((7+m)^2*(15+8*m+m^2))-10*b^2*c^4*d^3*x^(5+m)/((5+m)^2*(7+m)^2)-4*b^2*c^4*d^3*x^(5+m)/((5+m)*(7+m)^2)-12*b^2*c^4*d^3*x^(5+m)/((5+m)^3*(7+m))+2*b^2*c^6*d^3*x^(7+m)/(7+m)^3-10*b*c*d^3*x^(2+m)*(1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))/((5+m)*(7+m)^2)-12*b*c*d^3*x^(2+m)*(1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))/((5+m)^2*(7+m))-2*b*c*d^3*x^(2+m)*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))/(7+m)^2+48*d^3*x^(1+m)*(a+b*arcsin(c*x))^2/((5+m)*(7+m)*(3+4*m+m^2))+24*d^3*x^(1+m)*(1-c^2*x^2)*(a+b*arcsin(c*x))^2/((7+m)*(15+8*m+m^2))+6*d^3*x^(1+m)*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2/((5+m)*(7+m))+d^3*x^(1+m)*(1-c^2*x^2)^3*(a+b*arcsin(c*x))^2/(7+m)-30*b*c*d^3*x^(2+m)*(a+b*arcsin(c*x))*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)/((5+m)*(7+m)^2*(6+5*m+m^2))-36*b*c*d^3*x^(2+m)*(a+b*arcsin(c*x))*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)/((5+m)^2*(7+m)*(6+5*m+m^2))-48*b*c*d^3*x^(2+m)*(a+b*arcsin(c*x))*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)/((3+m)^2*(7+m)*(10+7*m+m^2))-96*b*c*d^3*x^(2+m)*(a+b*arcsin(c*x))*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)/((5+m)*(7+m)*(6+11*m+6*m^2+m^3))+96*b^2*c^2*d^3*x^(3+m)*HypergeometricPFQ([1,3/2+1/2*m,3/2+1/2*m],[2+1/2*m,5/2+1/2*m],c^2*x^2)/((3+m)^2*(5+m)*(7+m)*(2+3*m+m^2))+30*b^2*c^2*d^3*x^(3+m)*HypergeometricPFQ([1,3/2+1/2*m,3/2+1/2*m],[2+1/2*m,5/2+1/2*m],c^2*x^2)/((3+m)^2*(7+m)^2*(10+7*m+m^2))+48*b^2*c^2*d^3*x^(3+m)*HypergeometricPFQ([1,3/2+1/2*m,3/2+1/2*m],[2+1/2*m,5/2+1/2*m],c^2*x^2)/((3+m)^3*(7+m)*(10+7*m+m^2))+36*b^2*c^2*d^3*x^(3+m)*HypergeometricPFQ([1,3/2+1/2*m,3/2+1/2*m],[2+1/2*m,5/2+1/2*m],c^2*x^2)/((15+8*m+m^2)^2*(14+9*m+m^2))-36*b*c*d^3*x^(2+m)*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/((3+m)*(5+m)^2*(7+m))-48*b*c*d^3*x^(2+m)*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/((3+m)^2*(5+m)*(7+m))-30*b*c*d^3*x^(2+m)*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/((7+m)^2*(15+8*m+m^2))],
[x^m*(d-c^2*d*x^2)^2*(a+b*arcsin(c*x))^2,x,13,6*b^2*c^2*d^2*x^(3+m)/((3+m)^2*(5+m)^2)+2*b^2*c^2*d^2*x^(3+m)/((3+m)*(5+m)^2)+8*b^2*c^2*d^2*x^(3+m)/((3+m)^3*(5+m))-2*b^2*c^4*d^2*x^(5+m)/(5+m)^3-2*b*c*d^2*x^(2+m)*(1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))/(5+m)^2+8*d^2*x^(1+m)*(a+b*arcsin(c*x))^2/((5+m)*(3+4*m+m^2))+4*d^2*x^(1+m)*(1-c^2*x^2)*(a+b*arcsin(c*x))^2/(15+8*m+m^2)+d^2*x^(1+m)*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2/(5+m)-6*b*c*d^2*x^(2+m)*(a+b*arcsin(c*x))*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)/((5+m)^2*(6+5*m+m^2))-8*b*c*d^2*x^(2+m)*(a+b*arcsin(c*x))*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)/((3+m)^2*(10+7*m+m^2))-16*b*c*d^2*x^(2+m)*(a+b*arcsin(c*x))*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)/((5+m)*(6+11*m+6*m^2+m^3))+8*b^2*c^2*d^2*x^(3+m)*HypergeometricPFQ([1,3/2+1/2*m,3/2+1/2*m],[2+1/2*m,5/2+1/2*m],c^2*x^2)/((2+m)*(3+m)^3*(5+m))+16*b^2*c^2*d^2*x^(3+m)*HypergeometricPFQ([1,3/2+1/2*m,3/2+1/2*m],[2+1/2*m,5/2+1/2*m],c^2*x^2)/((3+m)^2*(5+m)*(2+3*m+m^2))+6*b^2*c^2*d^2*x^(3+m)*HypergeometricPFQ([1,3/2+1/2*m,3/2+1/2*m],[2+1/2*m,5/2+1/2*m],c^2*x^2)/((2+m)*(15+8*m+m^2)^2)-6*b*c*d^2*x^(2+m)*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/((3+m)*(5+m)^2)-8*b*c*d^2*x^(2+m)*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/((3+m)^2*(5+m))],
[x^m*(d-c^2*d*x^2)*(a+b*arcsin(c*x))^2,x,6,2*b^2*c^2*d*x^(3+m)/(3+m)^3+2*d*x^(1+m)*(a+b*arcsin(c*x))^2/(3+4*m+m^2)+d*x^(1+m)*(1-c^2*x^2)*(a+b*arcsin(c*x))^2/(3+m)-2*b*c*d*x^(2+m)*(a+b*arcsin(c*x))*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)/((2+m)*(3+m)^2)-4*b*c*d*x^(2+m)*(a+b*arcsin(c*x))*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)/(6+11*m+6*m^2+m^3)+2*b^2*c^2*d*x^(3+m)*HypergeometricPFQ([1,3/2+1/2*m,3/2+1/2*m],[2+1/2*m,5/2+1/2*m],c^2*x^2)/((2+m)*(3+m)^3)+4*b^2*c^2*d*x^(3+m)*HypergeometricPFQ([1,3/2+1/2*m,3/2+1/2*m],[2+1/2*m,5/2+1/2*m],c^2*x^2)/((3+m)^2*(2+3*m+m^2))-2*b*c*d*x^(2+m)*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/(3+m)^2],
[x^m*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2),x,0,Unintegrable(x^m*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2),x)],
[x^m*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^2,x,4,1/2*x^(1+m)*(a+b*arcsin(c*x))^2/(d^2*(1-c^2*x^2))+b*c*(1+m)*x^(2+m)*(a+b*arcsin(c*x))*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)/(d^2*(2+m))+b^2*c^2*x^(3+m)*hypergeom([1,1/2*(3+m)],[1/2*(5+m)],c^2*x^2)/(d^2*(3+m))-b^2*c^2*(1+m)*x^(3+m)*HypergeometricPFQ([1,3/2+1/2*m,3/2+1/2*m],[2+1/2*m,5/2+1/2*m],c^2*x^2)/(d^2*(6+5*m+m^2))-b*c*x^(2+m)*(a+b*arcsin(c*x))/(d^2*sqrt(1-c^2*x^2))+1/2*(1-m)*Unintegrable(x^m*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2),x)/d],
[x^m*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^3,x,10,-1/6*b*c*x^(2+m)*(a+b*arcsin(c*x))/(d^3*(1-c^2*x^2)^(3/2))+1/4*x^(1+m)*(a+b*arcsin(c*x))^2/(d^3*(1-c^2*x^2)^2)+1/8*(3-m)*x^(1+m)*(a+b*arcsin(c*x))^2/(d^3*(1-c^2*x^2))+1/6*b*c*(1-m)*(1+m)*x^(2+m)*(a+b*arcsin(c*x))*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)/(d^3*(2+m))+1/4*b*c*(3-m)*(1+m)*x^(2+m)*(a+b*arcsin(c*x))*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],c^2*x^2)/(d^3*(2+m))+1/6*b^2*c^2*(1-m)*x^(3+m)*hypergeom([1,1/2*(3+m)],[1/2*(5+m)],c^2*x^2)/(d^3*(3+m))+1/4*b^2*c^2*(3-m)*x^(3+m)*hypergeom([1,1/2*(3+m)],[1/2*(5+m)],c^2*x^2)/(d^3*(3+m))+1/6*b^2*c^2*x^(3+m)*hypergeom([2,1/2*(3+m)],[1/2*(5+m)],c^2*x^2)/(d^3*(3+m))-1/6*b^2*c^2*(1-m)*(1+m)*x^(3+m)*HypergeometricPFQ([1,3/2+1/2*m,3/2+1/2*m],[2+1/2*m,5/2+1/2*m],c^2*x^2)/(d^3*(6+5*m+m^2))-1/4*b^2*c^2*(3-m)*(1+m)*x^(3+m)*HypergeometricPFQ([1,3/2+1/2*m,3/2+1/2*m],[2+1/2*m,5/2+1/2*m],c^2*x^2)/(d^3*(6+5*m+m^2))-1/6*b*c*(1-m)*x^(2+m)*(a+b*arcsin(c*x))/(d^3*sqrt(1-c^2*x^2))-1/4*b*c*(3-m)*x^(2+m)*(a+b*arcsin(c*x))/(d^3*sqrt(1-c^2*x^2))+1/8*(1-m)*(3-m)*Unintegrable(x^m*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2),x)/d^2],
[x^m*(d-c^2*d*x^2)^(5/2)*(a+b*arcsin(c*x))^2,x,12,5*d*x^(1+m)*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(c*x))^2/((4+m)*(6+m))+x^(1+m)*(d-c^2*d*x^2)^(5/2)*(a+b*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(c*x))^2,x,7,x^(1+m)*(d-c^2*d*x^2)^(3/2)*(a+b*arcsin(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*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(8+6*m+m^2)-6*b*c*d*x^(2+m)*(a+b*arcsin(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*arcsin(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*arcsin(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*arcsin(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*arcsin(c*x))^2,x,3,x^(1+m)*(a+b*arcsin(c*x))^2*sqrt(d-c^2*d*x^2)/(2+m)-2*b*c*x^(2+m)*(a+b*arcsin(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*arcsin(c*x))^2/sqrt(d-c^2*d*x^2),x)/(2+m)],
[x^m*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(1/2),x,0,Unintegrable(x^m*(a+b*arcsin(c*x))^2/sqrt(d-c^2*d*x^2),x)],
[x^m*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(3/2),x,0,Unintegrable(x^m*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(3/2),x)],
[x^m*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(5/2),x,0,Unintegrable(x^m*(a+b*arcsin(c*x))^2/(d-c^2*d*x^2)^(5/2),x)],
[x^m*arcsin(a*x)^2/sqrt(1-a^2*x^2),x,0,Unintegrable(x^m*arcsin(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 ArcSin[c x])^3

# Integrands of the form (f x)^m (d-c^2 d x^2)^p (a+b ArcSin[c x)^3
[(c-a^2*c*x^2)^3*arcsin(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*arcsin(a*x)+1514/3675*a^2*c^3*x^3*arcsin(a*x)-702/6125*a^4*c^3*x^5*arcsin(a*x)+6/343*a^6*c^3*x^7*arcsin(a*x)+8/35*c^3*(1-a^2*x^2)^(3/2)*arcsin(a*x)^2/a+18/175*c^3*(1-a^2*x^2)^(5/2)*arcsin(a*x)^2/a+3/49*c^3*(1-a^2*x^2)^(7/2)*arcsin(a*x)^2/a+16/35*c^3*x*arcsin(a*x)^3+8/35*c^3*x*(1-a^2*x^2)*arcsin(a*x)^3+6/35*c^3*x*(1-a^2*x^2)^2*arcsin(a*x)^3+1/7*c^3*x*(1-a^2*x^2)^3*arcsin(a*x)^3-413312/128625*c^3*sqrt(1-a^2*x^2)/a+48/35*c^3*arcsin(a*x)^2*sqrt(1-a^2*x^2)/a],
[(c-a^2*c*x^2)^2*arcsin(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*arcsin(a*x)+76/225*a^2*c^2*x^3*arcsin(a*x)-6/125*a^4*c^2*x^5*arcsin(a*x)+4/15*c^2*(1-a^2*x^2)^(3/2)*arcsin(a*x)^2/a+3/25*c^2*(1-a^2*x^2)^(5/2)*arcsin(a*x)^2/a+8/15*c^2*x*arcsin(a*x)^3+4/15*c^2*x*(1-a^2*x^2)*arcsin(a*x)^3+1/5*c^2*x*(1-a^2*x^2)^2*arcsin(a*x)^3-4144/1125*c^2*sqrt(1-a^2*x^2)/a+8/5*c^2*arcsin(a*x)^2*sqrt(1-a^2*x^2)/a],
[(c-a^2*c*x^2)*arcsin(a*x)^3,x,10,-2/27*c*(1-a^2*x^2)^(3/2)/a-14/3*c*x*arcsin(a*x)+2/9*a^2*c*x^3*arcsin(a*x)+1/3*c*(1-a^2*x^2)^(3/2)*arcsin(a*x)^2/a+2/3*c*x*arcsin(a*x)^3+1/3*c*x*(1-a^2*x^2)*arcsin(a*x)^3-40/9*c*sqrt(1-a^2*x^2)/a+2*c*arcsin(a*x)^2*sqrt(1-a^2*x^2)/a],
[arcsin(a*x)^3/(c-a^2*c*x^2),x,10,-2*I*arcsin(a*x)^3*arctan(exp(I*arcsin(a*x)))/(a*c)+3*I*arcsin(a*x)^2*polylog(2,-I*exp(I*arcsin(a*x)))/(a*c)-3*I*arcsin(a*x)^2*polylog(2,I*exp(I*arcsin(a*x)))/(a*c)-6*arcsin(a*x)*polylog(3,-I*exp(I*arcsin(a*x)))/(a*c)+6*arcsin(a*x)*polylog(3,I*exp(I*arcsin(a*x)))/(a*c)-6*I*polylog(4,-I*exp(I*arcsin(a*x)))/(a*c)+6*I*polylog(4,I*exp(I*arcsin(a*x)))/(a*c)],
[arcsin(a*x)^3/(c-a^2*c*x^2)^2,x,18,1/2*x*arcsin(a*x)^3/(c^2*(1-a^2*x^2))-6*I*arcsin(a*x)*arctan(exp(I*arcsin(a*x)))/(a*c^2)-I*arcsin(a*x)^3*arctan(exp(I*arcsin(a*x)))/(a*c^2)+3*I*polylog(2,-I*exp(I*arcsin(a*x)))/(a*c^2)+3/2*I*arcsin(a*x)^2*polylog(2,-I*exp(I*arcsin(a*x)))/(a*c^2)-3*I*polylog(2,I*exp(I*arcsin(a*x)))/(a*c^2)-3/2*I*arcsin(a*x)^2*polylog(2,I*exp(I*arcsin(a*x)))/(a*c^2)-3*arcsin(a*x)*polylog(3,-I*exp(I*arcsin(a*x)))/(a*c^2)+3*arcsin(a*x)*polylog(3,I*exp(I*arcsin(a*x)))/(a*c^2)-3*I*polylog(4,-I*exp(I*arcsin(a*x)))/(a*c^2)+3*I*polylog(4,I*exp(I*arcsin(a*x)))/(a*c^2)-3/2*arcsin(a*x)^2/(a*c^2*sqrt(1-a^2*x^2))],
[arcsin(a*x)^3/(c-a^2*c*x^2)^3,x,28,1/4*x*arcsin(a*x)/(c^3*(1-a^2*x^2))-1/4*arcsin(a*x)^2/(a*c^3*(1-a^2*x^2)^(3/2))+1/4*x*arcsin(a*x)^3/(c^3*(1-a^2*x^2)^2)+3/8*x*arcsin(a*x)^3/(c^3*(1-a^2*x^2))-5*I*arcsin(a*x)*arctan(exp(I*arcsin(a*x)))/(a*c^3)-3/4*I*arcsin(a*x)^3*arctan(exp(I*arcsin(a*x)))/(a*c^3)+5/2*I*polylog(2,-I*exp(I*arcsin(a*x)))/(a*c^3)+9/8*I*arcsin(a*x)^2*polylog(2,-I*exp(I*arcsin(a*x)))/(a*c^3)-5/2*I*polylog(2,I*exp(I*arcsin(a*x)))/(a*c^3)-9/8*I*arcsin(a*x)^2*polylog(2,I*exp(I*arcsin(a*x)))/(a*c^3)-9/4*arcsin(a*x)*polylog(3,-I*exp(I*arcsin(a*x)))/(a*c^3)+9/4*arcsin(a*x)*polylog(3,I*exp(I*arcsin(a*x)))/(a*c^3)-9/4*I*polylog(4,-I*exp(I*arcsin(a*x)))/(a*c^3)+9/4*I*polylog(4,I*exp(I*arcsin(a*x)))/(a*c^3)+(-1/4)/(a*c^3*sqrt(1-a^2*x^2))-9/8*arcsin(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 ArcSin[c x])^3

# p>0
[(c-a^2*c*x^2)^(5/2)*arcsin(a*x)^3,x,24,5/24*c*x*(c-a^2*c*x^2)^(3/2)*arcsin(a*x)^3+1/6*x*(c-a^2*c*x^2)^(5/2)*arcsin(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*arcsin(a*x)*sqrt(c-a^2*c*x^2)-65/576*c^2*x*(1-a^2*x^2)*arcsin(a*x)*sqrt(c-a^2*c*x^2)-1/36*c^2*x*(1-a^2*x^2)^2*arcsin(a*x)*sqrt(c-a^2*c*x^2)+5/32*c^2*(1-a^2*x^2)^(3/2)*arcsin(a*x)^2*sqrt(c-a^2*c*x^2)/a+1/12*c^2*(1-a^2*x^2)^(5/2)*arcsin(a*x)^2*sqrt(c-a^2*c*x^2)/a+5/16*c^2*x*arcsin(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*arcsin(a*x)^2*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-15/32*a*c^2*x^2*arcsin(a*x)^2*sqrt(c-a^2*c*x^2)/sqrt(1-a^2*x^2)+5/64*c^2*arcsin(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)*arcsin(a*x)^3,x,14,1/4*x*(c-a^2*c*x^2)^(3/2)*arcsin(a*x)^3-45/64*c*x*arcsin(a*x)*sqrt(c-a^2*c*x^2)-3/32*c*x*(1-a^2*x^2)*arcsin(a*x)*sqrt(c-a^2*c*x^2)+3/16*c*(1-a^2*x^2)^(3/2)*arcsin(a*x)^2*sqrt(c-a^2*c*x^2)/a+3/8*c*x*arcsin(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*arcsin(a*x)^2*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-9/16*a*c*x^2*arcsin(a*x)^2*sqrt(c-a^2*c*x^2)/sqrt(1-a^2*x^2)+3/32*c*arcsin(a*x)^4*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))],
[(c-a^2*c*x^2)^(1/2)*arcsin(a*x)^3,x,6,-3/4*x*arcsin(a*x)*sqrt(c-a^2*c*x^2)+1/2*x*arcsin(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*arcsin(a*x)^2*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-3/4*a*x^2*arcsin(a*x)^2*sqrt(c-a^2*c*x^2)/sqrt(1-a^2*x^2)+1/8*arcsin(a*x)^4*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))],

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

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

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

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

# p<0
[x^4/(arcsin(a*x)*sqrt(1-a^2*x^2)),x,5,-1/2*Ci(2*arcsin(a*x))/a^5+1/8*Ci(4*arcsin(a*x))/a^5+3/8*log(arcsin(a*x))/a^5],
[x^3/(arcsin(a*x)*sqrt(1-a^2*x^2)),x,5,3/4*Si(arcsin(a*x))/a^4-1/4*Si(3*arcsin(a*x))/a^4],
[x^2/(arcsin(a*x)*sqrt(1-a^2*x^2)),x,4,-1/2*Ci(2*arcsin(a*x))/a^3+1/2*log(arcsin(a*x))/a^3],
[x^2/(arcsin(a*x)*sqrt(1-a^2*x^2)),x,4,-1/2*Ci(2*arcsin(a*x))/a^3+1/2*log(arcsin(a*x))/a^3],
[x/(arcsin(a*x)*sqrt(1-a^2*x^2)),x,2,Si(arcsin(a*x))/a^2],
[1/(arcsin(a*x)*sqrt(1-a^2*x^2)),x,1,log(arcsin(a*x))/a],
[1/(x*arcsin(a*x)*sqrt(1-a^2*x^2)),x,0,Unintegrable(1/(x*arcsin(a*x)*sqrt(1-a^2*x^2)),x)],
[1/(x^2*arcsin(a*x)*sqrt(1-a^2*x^2)),x,0,Unintegrable(1/(x^2*arcsin(a*x)*sqrt(1-a^2*x^2)),x)],
[x^5/((a+b*arcsin(c*x))*sqrt(1-c^2*x^2)),x,12,5/8*cos(a/b)*Si((a+b*arcsin(c*x))/b)/(b*c^6)-5/16*cos(3*a/b)*Si(3*(a+b*arcsin(c*x))/b)/(b*c^6)+1/16*cos(5*a/b)*Si(5*(a+b*arcsin(c*x))/b)/(b*c^6)-5/8*Ci((a+b*arcsin(c*x))/b)*sin(a/b)/(b*c^6)+5/16*Ci(3*(a+b*arcsin(c*x))/b)*sin(3*a/b)/(b*c^6)-1/16*Ci(5*(a+b*arcsin(c*x))/b)*sin(5*a/b)/(b*c^6)],
[x^4/((a+b*arcsin(c*x))*sqrt(1-c^2*x^2)),x,9,-1/2*Ci(2*(a+b*arcsin(c*x))/b)*cos(2*a/b)/(b*c^5)+1/8*Ci(4*(a+b*arcsin(c*x))/b)*cos(4*a/b)/(b*c^5)+3/8*log(a+b*arcsin(c*x))/(b*c^5)-1/2*Si(2*(a+b*arcsin(c*x))/b)*sin(2*a/b)/(b*c^5)+1/8*Si(4*(a+b*arcsin(c*x))/b)*sin(4*a/b)/(b*c^5)],
[x^3/((a+b*arcsin(c*x))*sqrt(1-c^2*x^2)),x,9,3/4*cos(a/b)*Si((a+b*arcsin(c*x))/b)/(b*c^4)-1/4*cos(3*a/b)*Si(3*(a+b*arcsin(c*x))/b)/(b*c^4)-3/4*Ci((a+b*arcsin(c*x))/b)*sin(a/b)/(b*c^4)+1/4*Ci(3*(a+b*arcsin(c*x))/b)*sin(3*a/b)/(b*c^4)],
[x^2/((a+b*arcsin(c*x))*sqrt(1-c^2*x^2)),x,6,-1/2*Ci(2*(a+b*arcsin(c*x))/b)*cos(2*a/b)/(b*c^3)+1/2*log(a+b*arcsin(c*x))/(b*c^3)-1/2*Si(2*(a+b*arcsin(c*x))/b)*sin(2*a/b)/(b*c^3)],
[x/((a+b*arcsin(c*x))*sqrt(1-c^2*x^2)),x,4,cos(a/b)*Si((a+b*arcsin(c*x))/b)/(b*c^2)-Ci((a+b*arcsin(c*x))/b)*sin(a/b)/(b*c^2)],
[1/((a+b*arcsin(c*x))*sqrt(1-c^2*x^2)),x,1,log(a+b*arcsin(c*x))/(b*c)],
[1/(x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)),x,0,Unintegrable(1/(x*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)),x)],
[1/(x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)),x,0,Unintegrable(1/(x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)),x)],
[x^2/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))),x,0,Unintegrable(x^2/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))),x)],
[x/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))),x,0,Unintegrable(x/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))),x)],
[1/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))),x,0,Unintegrable(1/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))),x)],
[1/(x*(1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))),x,0,Unintegrable(1/(x*(1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))),x)],
[1/(x^2*(1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))),x,0,Unintegrable(1/(x^2*(1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))),x)],
[x^2/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))),x,0,Unintegrable(x^2/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))),x)],
[x/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))),x,0,Unintegrable(x/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))),x)],
[1/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))),x,0,Unintegrable(1/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))),x)],
[1/(x*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))),x,0,Unintegrable(1/(x*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))),x)],
[1/(x^2*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))),x,0,Unintegrable(1/(x^2*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))),x)],

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

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

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

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

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

# p<0
[x^m/((a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)),x,1,-x^m/(b*c*(a+b*arcsin(c*x)))+m*Unintegrable(x^(-1+m)/(a+b*arcsin(c*x)),x)/(b*c)],
[x^5/((a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)),x,13,-x^5/(b*c*(a+b*arcsin(c*x)))+5/8*Ci((a+b*arcsin(c*x))/b)*cos(a/b)/(b^2*c^6)-15/16*Ci(3*(a+b*arcsin(c*x))/b)*cos(3*a/b)/(b^2*c^6)+5/16*Ci(5*(a+b*arcsin(c*x))/b)*cos(5*a/b)/(b^2*c^6)+5/8*Si((a+b*arcsin(c*x))/b)*sin(a/b)/(b^2*c^6)-15/16*Si(3*(a+b*arcsin(c*x))/b)*sin(3*a/b)/(b^2*c^6)+5/16*Si(5*(a+b*arcsin(c*x))/b)*sin(5*a/b)/(b^2*c^6)],
[x^4/((a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)),x,10,-x^4/(b*c*(a+b*arcsin(c*x)))+cos(2*a/b)*Si(2*(a+b*arcsin(c*x))/b)/(b^2*c^5)-1/2*cos(4*a/b)*Si(4*(a+b*arcsin(c*x))/b)/(b^2*c^5)-Ci(2*(a+b*arcsin(c*x))/b)*sin(2*a/b)/(b^2*c^5)+1/2*Ci(4*(a+b*arcsin(c*x))/b)*sin(4*a/b)/(b^2*c^5)],
[x^3/((a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)),x,10,-x^3/(b*c*(a+b*arcsin(c*x)))+3/4*Ci((a+b*arcsin(c*x))/b)*cos(a/b)/(b^2*c^4)-3/4*Ci(3*(a+b*arcsin(c*x))/b)*cos(3*a/b)/(b^2*c^4)+3/4*Si((a+b*arcsin(c*x))/b)*sin(a/b)/(b^2*c^4)-3/4*Si(3*(a+b*arcsin(c*x))/b)*sin(3*a/b)/(b^2*c^4)],
[x^2/((a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)),x,7,-x^2/(b*c*(a+b*arcsin(c*x)))+cos(2*a/b)*Si(2*(a+b*arcsin(c*x))/b)/(b^2*c^3)-Ci(2*(a+b*arcsin(c*x))/b)*sin(2*a/b)/(b^2*c^3)],
[x/((a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)),x,5,-x/(b*c*(a+b*arcsin(c*x)))+Ci((a+b*arcsin(c*x))/b)*cos(a/b)/(b^2*c^2)+Si((a+b*arcsin(c*x))/b)*sin(a/b)/(b^2*c^2)],
[1/((a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)),x,1,(-1)/(b*c*(a+b*arcsin(c*x)))],
[1/(x*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)),x,1,(-1)/(b*c*x*(a+b*arcsin(c*x)))-Unintegrable(1/(x^2*(a+b*arcsin(c*x))),x)/(b*c)],
[1/(x^2*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)),x,1,(-1)/(b*c*x^2*(a+b*arcsin(c*x)))-2*Unintegrable(1/(x^3*(a+b*arcsin(c*x))),x)/(b*c)],
[x^m/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))^2),x,0,Unintegrable(x^m/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))^2),x)],
[x^3/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))^2),x,0,Unintegrable(x^3/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))^2),x)],
[x^2/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))^2),x,1,-x^2/(b*c*(1-c^2*x^2)*(a+b*arcsin(c*x)))+2*Unintegrable(x/((1-c^2*x^2)^2*(a+b*arcsin(c*x))),x)/(b*c)],
[x/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))^2),x,0,Unintegrable(x/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))^2),x)],
[1/((1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))^2),x,1,(-1)/(b*c*(1-c^2*x^2)*(a+b*arcsin(c*x)))+2*c*Unintegrable(x/((1-c^2*x^2)^2*(a+b*arcsin(c*x))),x)/b],
[1/(x*(1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))^2),x,0,Unintegrable(1/(x*(1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))^2),x)],
[1/(x^2*(1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))^2),x,0,Unintegrable(1/(x^2*(1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))^2),x)],
[x^m/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))^2),x,0,Unintegrable(x^m/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))^2),x)],
[x^3/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))^2),x,0,Unintegrable(x^3/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))^2),x)],
[x^2/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))^2),x,0,Unintegrable(x^2/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))^2),x)],
[x/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))^2),x,0,Unintegrable(x/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))^2),x)],
[1/((1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))^2),x,1,(-1)/(b*c*(1-c^2*x^2)^2*(a+b*arcsin(c*x)))+4*c*Unintegrable(x/((1-c^2*x^2)^3*(a+b*arcsin(c*x))),x)/b],
[1/(x*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))^2),x,0,Unintegrable(1/(x*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))^2),x)],
[1/(x^2*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))^2),x,0,Unintegrable(1/(x^2*(1-c^2*x^2)^(5/2)*(a+b*arcsin(c*x))^2),x)],

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

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

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

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

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

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

# p>0
[x^3*(d-c^2*d*x^2)/(a+b*arcsin(c*x))^(3/2),x,27,3/8*d*cos(2*a/b)*FresnelC(2*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sqrt(Pi)/(b^(3/2)*c^4)+3/8*d*FresnelS(2*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sin(2*a/b)*sqrt(Pi)/(b^(3/2)*c^4)-1/8*d*cos(6*a/b)*FresnelC(2*sqrt(3/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*c^4)-1/8*d*FresnelS(2*sqrt(3/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(6*a/b)*sqrt(3*Pi)/(b^(3/2)*c^4)-2*d*x^3*(1-c^2*x^2)^(3/2)/(b*c*sqrt(a+b*arcsin(c*x)))],
[x^2*(d-c^2*d*x^2)/(a+b*arcsin(c*x))^(3/2),x,32,-5/4*d*cos(3*a/b)*FresnelS(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/6*Pi)/(b^(3/2)*c^3)+5/4*d*FresnelC(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(3*a/b)*sqrt(1/6*Pi)/(b^(3/2)*c^3)-5/2*d*cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^3)+5/2*d*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(1/2*Pi)/(b^(3/2)*c^3)+d*cos(3*a/b)*FresnelS(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(2/3*Pi)/(b^(3/2)*c^3)-d*FresnelC(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(3*a/b)*sqrt(2/3*Pi)/(b^(3/2)*c^3)+d*cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(2*Pi)/(b^(3/2)*c^3)-d*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(2*Pi)/(b^(3/2)*c^3)+1/4*d*cos(5*a/b)*FresnelS(sqrt(10/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(5/2*Pi)/(b^(3/2)*c^3)-1/4*d*FresnelC(sqrt(10/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(5*a/b)*sqrt(5/2*Pi)/(b^(3/2)*c^3)-2*d*x^2*(1-c^2*x^2)^(3/2)/(b*c*sqrt(a+b*arcsin(c*x)))],
[x*(d-c^2*d*x^2)/(a+b*arcsin(c*x))^(3/2),x,17,d*cos(4*a/b)*FresnelC(2*sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^2)+d*FresnelS(2*sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(4*a/b)*sqrt(1/2*Pi)/(b^(3/2)*c^2)+d*cos(2*a/b)*FresnelC(2*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sqrt(Pi)/(b^(3/2)*c^2)+d*FresnelS(2*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sin(2*a/b)*sqrt(Pi)/(b^(3/2)*c^2)-2*d*x*(1-c^2*x^2)^(3/2)/(b*c*sqrt(a+b*arcsin(c*x)))],
[(d-c^2*d*x^2)/(a+b*arcsin(c*x))^(3/2),x,14,-3*d*cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c)+3*d*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(1/2*Pi)/(b^(3/2)*c)-d*cos(3*a/b)*FresnelS(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(3/2*Pi)/(b^(3/2)*c)+d*FresnelC(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(3*a/b)*sqrt(3/2*Pi)/(b^(3/2)*c)-2*d*(1-c^2*x^2)^(3/2)/(b*c*sqrt(a+b*arcsin(c*x)))],
[(d-c^2*d*x^2)/(x*(a+b*arcsin(c*x))^(3/2)),x,12,-2*d*cos(2*a/b)*FresnelC(2*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sqrt(Pi)/b^(3/2)-2*d*FresnelS(2*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sin(2*a/b)*sqrt(Pi)/b^(3/2)-2*d*(1-c^2*x^2)^(3/2)/(b*c*x*sqrt(a+b*arcsin(c*x)))-2*d*Unintegrable(1/(x^2*sqrt(1-c^2*x^2)*sqrt(a+b*arcsin(c*x))),x)/(b*c)],
[x^3*(d-c^2*d*x^2)^2/(a+b*arcsin(c*x))^(3/2),x,32,1/8*d^2*cos(4*a/b)*FresnelC(2*sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^4)+1/8*d^2*FresnelS(2*sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(4*a/b)*sqrt(1/2*Pi)/(b^(3/2)*c^4)+3/16*d^2*cos(2*a/b)*FresnelC(2*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sqrt(Pi)/(b^(3/2)*c^4)-1/16*d^2*cos(8*a/b)*FresnelC(4*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sqrt(Pi)/(b^(3/2)*c^4)+3/16*d^2*FresnelS(2*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sin(2*a/b)*sqrt(Pi)/(b^(3/2)*c^4)-1/16*d^2*FresnelS(4*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sin(8*a/b)*sqrt(Pi)/(b^(3/2)*c^4)-1/16*d^2*cos(6*a/b)*FresnelC(2*sqrt(3/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*c^4)-1/16*d^2*FresnelS(2*sqrt(3/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(6*a/b)*sqrt(3*Pi)/(b^(3/2)*c^4)-2*d^2*x^3*(1-c^2*x^2)^(5/2)/(b*c*sqrt(a+b*arcsin(c*x)))],
[x^2*(d-c^2*d*x^2)^2/(a+b*arcsin(c*x))^(3/2),x,42,-5/16*d^2*cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^3)+5/16*d^2*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(1/2*Pi)/(b^(3/2)*c^3)+1/16*d^2*cos(3*a/b)*FresnelS(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(3/2*Pi)/(b^(3/2)*c^3)-1/16*d^2*FresnelC(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(3*a/b)*sqrt(3/2*Pi)/(b^(3/2)*c^3)+3/16*d^2*cos(5*a/b)*FresnelS(sqrt(10/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(5/2*Pi)/(b^(3/2)*c^3)-3/16*d^2*FresnelC(sqrt(10/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(5*a/b)*sqrt(5/2*Pi)/(b^(3/2)*c^3)+1/16*d^2*cos(7*a/b)*FresnelS(sqrt(14/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(7/2*Pi)/(b^(3/2)*c^3)-1/16*d^2*FresnelC(sqrt(14/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(7*a/b)*sqrt(7/2*Pi)/(b^(3/2)*c^3)-2*d^2*x^2*(1-c^2*x^2)^(5/2)/(b*c*sqrt(a+b*arcsin(c*x)))],
[x*(d-c^2*d*x^2)^2/(a+b*arcsin(c*x))^(3/2),x,32,d^2*cos(4*a/b)*FresnelC(2*sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^2)+d^2*FresnelS(2*sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(4*a/b)*sqrt(1/2*Pi)/(b^(3/2)*c^2)+5/8*d^2*cos(2*a/b)*FresnelC(2*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sqrt(Pi)/(b^(3/2)*c^2)+5/8*d^2*FresnelS(2*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sin(2*a/b)*sqrt(Pi)/(b^(3/2)*c^2)+1/8*d^2*cos(6*a/b)*FresnelC(2*sqrt(3/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(3*Pi)/(b^(3/2)*c^2)+1/8*d^2*FresnelS(2*sqrt(3/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(6*a/b)*sqrt(3*Pi)/(b^(3/2)*c^2)-2*d^2*x*(1-c^2*x^2)^(5/2)/(b*c*sqrt(a+b*arcsin(c*x)))],
[(d-c^2*d*x^2)^2/(a+b*arcsin(c*x))^(3/2),x,19,-5/2*d^2*cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c)+5/2*d^2*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(1/2*Pi)/(b^(3/2)*c)-5/4*d^2*cos(3*a/b)*FresnelS(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(3/2*Pi)/(b^(3/2)*c)+5/4*d^2*FresnelC(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(3*a/b)*sqrt(3/2*Pi)/(b^(3/2)*c)-1/4*d^2*cos(5*a/b)*FresnelS(sqrt(10/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(5/2*Pi)/(b^(3/2)*c)+1/4*d^2*FresnelC(sqrt(10/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(5*a/b)*sqrt(5/2*Pi)/(b^(3/2)*c)-2*d^2*(1-c^2*x^2)^(5/2)/(b*c*sqrt(a+b*arcsin(c*x)))],
[(d-c^2*d*x^2)^2/(x*(a+b*arcsin(c*x))^(3/2)),x,25,-d^2*cos(4*a/b)*FresnelC(2*sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/b^(3/2)-d^2*FresnelS(2*sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(4*a/b)*sqrt(1/2*Pi)/b^(3/2)-3*d^2*cos(2*a/b)*FresnelC(2*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sqrt(Pi)/b^(3/2)-3*d^2*FresnelS(2*sqrt(a+b*arcsin(c*x))/(sqrt(b)*sqrt(Pi)))*sin(2*a/b)*sqrt(Pi)/b^(3/2)-2*d^2*(1-c^2*x^2)^(5/2)/(b*c*x*sqrt(a+b*arcsin(c*x)))-2*d^2*Unintegrable(1/(x^2*sqrt(1-c^2*x^2)*sqrt(a+b*arcsin(c*x))),x)/(b*c)],

# p<0

#  An excellent example of the importance of reducing even unintegrable expressions to simplest form so cancellations can occur. 
[x*arcsin(x)^(3/2)/(1-x^2)^2-3/8*x/((1-x^2)*sqrt(arcsin(x))),x,3,1/2*arcsin(x)^(3/2)/(1-x^2)-3/4*x*sqrt(arcsin(x))/sqrt(1-x^2)],

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

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

# n>0
[(c-a^2*c*x^2)^(3/2)*sqrt(arcsin(a*x)),x,15,1/4*c*arcsin(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-1/64*c*FresnelS(2*sqrt(2/Pi)*sqrt(arcsin(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-1/8*c*FresnelS(2*sqrt(arcsin(a*x))/sqrt(Pi))*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(arcsin(a*x))+3/8*c*x*sqrt(c-a^2*c*x^2)*sqrt(arcsin(a*x))],
[(c-a^2*c*x^2)^(1/2)*sqrt(arcsin(a*x)),x,7,1/3*arcsin(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-1/8*FresnelS(2*sqrt(arcsin(a*x))/sqrt(Pi))*sqrt(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(arcsin(a*x))],
[sqrt(arcsin(a*x))/(c-a^2*c*x^2)^(1/2),x,1,2/3*arcsin(a*x)^(3/2)*sqrt(1-a^2*x^2)/(a*(c-a^2*c*x^2)^(1/2))],
[sqrt(arcsin(a*x))/(c-a^2*c*x^2)^(3/2),x,1,x*sqrt(arcsin(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(arcsin(a*x))),x)/(c*sqrt(c-a^2*c*x^2))],
[sqrt(arcsin(a*x))/(c-a^2*c*x^2)^(5/2),x,2,1/3*x*sqrt(arcsin(a*x))/(c*(c-a^2*c*x^2)^(3/2))+2/3*x*sqrt(arcsin(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(arcsin(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(arcsin(a*x))),x)/(c^2*sqrt(c-a^2*c*x^2))],
[(c-a^2*c*x^2)^(3/2)*arcsin(a*x)^(3/2),x,17,1/4*x*(c-a^2*c*x^2)^(3/2)*arcsin(a*x)^(3/2)+3/8*c*x*arcsin(a*x)^(3/2)*sqrt(c-a^2*c*x^2)+3/20*c*arcsin(a*x)^(5/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-3/512*c*FresnelC(2*sqrt(2/Pi)*sqrt(arcsin(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-3/32*c*FresnelC(2*sqrt(arcsin(a*x))/sqrt(Pi))*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(arcsin(a*x))/a+27/256*c*sqrt(c-a^2*c*x^2)*sqrt(arcsin(a*x))/(a*sqrt(1-a^2*x^2))-9/32*a*c*x^2*sqrt(c-a^2*c*x^2)*sqrt(arcsin(a*x))/sqrt(1-a^2*x^2)],
[(c-a^2*c*x^2)^(1/2)*arcsin(a*x)^(3/2),x,8,1/2*x*arcsin(a*x)^(3/2)*sqrt(c-a^2*c*x^2)+1/5*arcsin(a*x)^(5/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-3/32*FresnelC(2*sqrt(arcsin(a*x))/sqrt(Pi))*sqrt(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(arcsin(a*x))/(a*sqrt(1-a^2*x^2))-3/8*a*x^2*sqrt(c-a^2*c*x^2)*sqrt(arcsin(a*x))/sqrt(1-a^2*x^2)],
[arcsin(a*x)^(3/2)/(c-a^2*c*x^2)^(1/2),x,1,2/5*arcsin(a*x)^(5/2)*sqrt(1-a^2*x^2)/(a*(c-a^2*c*x^2)^(1/2))],
[arcsin(a*x)^(3/2)/(c-a^2*c*x^2)^(3/2),x,1,x*arcsin(a*x)^(3/2)/(c*sqrt(c-a^2*c*x^2))-3/2*a*sqrt(1-a^2*x^2)*Unintegrable(x*sqrt(arcsin(a*x))/(1-a^2*x^2),x)/(c*sqrt(c-a^2*c*x^2))],
[(c-a^2*c*x^2)^(3/2)*arcsin(a*x)^(5/2),x,27,1/4*x*(c-a^2*c*x^2)^(3/2)*arcsin(a*x)^(5/2)+5/32*c*(1-a^2*x^2)^(3/2)*arcsin(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/a+3/8*c*x*arcsin(a*x)^(5/2)*sqrt(c-a^2*c*x^2)+45/256*c*arcsin(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-15/32*a*c*x^2*arcsin(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/sqrt(1-a^2*x^2)+3/28*c*arcsin(a*x)^(7/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))+15/4096*c*FresnelS(2*sqrt(2/Pi)*sqrt(arcsin(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))+15/128*c*FresnelS(2*sqrt(arcsin(a*x))/sqrt(Pi))*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(arcsin(a*x))-15/256*c*x*(1-a^2*x^2)*sqrt(c-a^2*c*x^2)*sqrt(arcsin(a*x))],
[(c-a^2*c*x^2)^(1/2)*arcsin(a*x)^(5/2),x,10,1/2*x*arcsin(a*x)^(5/2)*sqrt(c-a^2*c*x^2)+5/16*arcsin(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-5/8*a*x^2*arcsin(a*x)^(3/2)*sqrt(c-a^2*c*x^2)/sqrt(1-a^2*x^2)+1/7*arcsin(a*x)^(7/2)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))+15/128*FresnelS(2*sqrt(arcsin(a*x))/sqrt(Pi))*sqrt(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(arcsin(a*x))],
[arcsin(a*x)^(5/2)/(c-a^2*c*x^2)^(1/2),x,1,2/7*arcsin(a*x)^(7/2)*sqrt(1-a^2*x^2)/(a*(c-a^2*c*x^2)^(1/2))],
[arcsin(a*x)^(5/2)/(c-a^2*c*x^2)^(3/2),x,1,x*arcsin(a*x)^(5/2)/(c*sqrt(c-a^2*c*x^2))-5/2*a*sqrt(1-a^2*x^2)*Unintegrable(x*arcsin(a*x)^(3/2)/(1-a^2*x^2),x)/(c*sqrt(c-a^2*c*x^2))],
[(a^2-x^2)^(3/2)*arcsin(x/a)^(1/2),x,15,1/4*a^3*arcsin(x/a)^(3/2)*sqrt(a^2-x^2)/sqrt(1-x^2/a^2)-1/64*a^3*FresnelS(2*sqrt(2/Pi)*sqrt(arcsin(x/a)))*sqrt(1/2*Pi)*sqrt(a^2-x^2)/sqrt(1-x^2/a^2)-1/8*a^3*FresnelS(2*sqrt(arcsin(x/a))/sqrt(Pi))*sqrt(Pi)*sqrt(a^2-x^2)/sqrt(1-x^2/a^2)+1/4*x*(a^2-x^2)^(3/2)*sqrt(arcsin(x/a))+3/8*a^2*x*sqrt(a^2-x^2)*sqrt(arcsin(x/a))],
[(a^2-x^2)^(1/2)*arcsin(x/a)^(1/2),x,7,1/3*a*arcsin(x/a)^(3/2)*sqrt(a^2-x^2)/sqrt(1-x^2/a^2)-1/8*a*FresnelS(2*sqrt(arcsin(x/a))/sqrt(Pi))*sqrt(Pi)*sqrt(a^2-x^2)/sqrt(1-x^2/a^2)+1/2*x*sqrt(a^2-x^2)*sqrt(arcsin(x/a))],
[arcsin(x/a)^(1/2)/(a^2-x^2)^(1/2),x,1,2/3*a*arcsin(x/a)^(3/2)*sqrt(1-x^2/a^2)/sqrt(a^2-x^2)],
[arcsin(x/a)^(1/2)/(a^2-x^2)^(3/2),x,1,x*sqrt(arcsin(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(arcsin(x/a))),x)/(a^3*sqrt(a^2-x^2))],
[arcsin(x/a)^(1/2)/(a^2-x^2)^(5/2),x,2,1/3*x*sqrt(arcsin(x/a))/(a^2*(a^2-x^2)^(3/2))+2/3*x*sqrt(arcsin(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(arcsin(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(arcsin(x/a))),x)/(a^5*sqrt(a^2-x^2))],
[(a^2-x^2)^(3/2)*arcsin(x/a)^(3/2),x,17,1/4*x*(a^2-x^2)^(3/2)*arcsin(x/a)^(3/2)+3/8*a^2*x*arcsin(x/a)^(3/2)*sqrt(a^2-x^2)+3/20*a^3*arcsin(x/a)^(5/2)*sqrt(a^2-x^2)/sqrt(1-x^2/a^2)-3/512*a^3*FresnelC(2*sqrt(2/Pi)*sqrt(arcsin(x/a)))*sqrt(1/2*Pi)*sqrt(a^2-x^2)/sqrt(1-x^2/a^2)-3/32*a^3*FresnelC(2*sqrt(arcsin(x/a))/sqrt(Pi))*sqrt(Pi)*sqrt(a^2-x^2)/sqrt(1-x^2/a^2)+3/32*(a^2-x^2)^(5/2)*sqrt(arcsin(x/a))/(a*sqrt(1-x^2/a^2))+27/256*a^3*sqrt(a^2-x^2)*sqrt(arcsin(x/a))/sqrt(1-x^2/a^2)-9/32*a*x^2*sqrt(a^2-x^2)*sqrt(arcsin(x/a))/sqrt(1-x^2/a^2)],
[(a^2-x^2)^(1/2)*arcsin(x/a)^(3/2),x,8,1/2*x*arcsin(x/a)^(3/2)*sqrt(a^2-x^2)+1/5*a*arcsin(x/a)^(5/2)*sqrt(a^2-x^2)/sqrt(1-x^2/a^2)-3/32*a*FresnelC(2*sqrt(arcsin(x/a))/sqrt(Pi))*sqrt(Pi)*sqrt(a^2-x^2)/sqrt(1-x^2/a^2)+3/16*a*sqrt(a^2-x^2)*sqrt(arcsin(x/a))/sqrt(1-x^2/a^2)-3/8*x^2*sqrt(a^2-x^2)*sqrt(arcsin(x/a))/(a*sqrt(1-x^2/a^2))],
[arcsin(x/a)^(3/2)/(a^2-x^2)^(1/2),x,1,2/5*a*arcsin(x/a)^(5/2)*sqrt(1-x^2/a^2)/sqrt(a^2-x^2)],
[arcsin(x/a)^(3/2)/(a^2-x^2)^(3/2),x,1,x*arcsin(x/a)^(3/2)/(a^2*sqrt(a^2-x^2))-3/2*sqrt(1-x^2/a^2)*Unintegrable(x*sqrt(arcsin(x/a))/(1-x^2/a^2),x)/(a^3*sqrt(a^2-x^2))],

# n<0
[x/(sqrt(1-x^2)*sqrt(arcsin(x))),x,3,FresnelS(sqrt(2/Pi)*sqrt(arcsin(x)))*sqrt(2*Pi)],
[(c-a^2*c*x^2)^(5/2)/sqrt(arcsin(a*x)),x,9,1/32*c^2*(c-a^2*c*x^2)^(1/2)*FresnelC(2*sqrt(3/Pi)*sqrt(arcsin(a*x)))*sqrt(1/3*Pi)/(a*sqrt(1-a^2*x^2))+3/16*c^2*(c-a^2*c*x^2)^(1/2)*FresnelC(2*sqrt(2/Pi)*sqrt(arcsin(a*x)))*sqrt(1/2*Pi)/(a*sqrt(1-a^2*x^2))+15/32*c^2*(c-a^2*c*x^2)^(1/2)*FresnelC(2*sqrt(arcsin(a*x))/sqrt(Pi))*sqrt(Pi)/(a*sqrt(1-a^2*x^2))+5/8*c^2*(c-a^2*c*x^2)^(1/2)*sqrt(arcsin(a*x))/(a*sqrt(1-a^2*x^2))],
[(c-a^2*c*x^2)^(3/2)/sqrt(arcsin(a*x)),x,7,1/8*c*(c-a^2*c*x^2)^(1/2)*FresnelC(2*sqrt(2/Pi)*sqrt(arcsin(a*x)))*sqrt(1/2*Pi)/(a*sqrt(1-a^2*x^2))+1/2*c*(c-a^2*c*x^2)^(1/2)*FresnelC(2*sqrt(arcsin(a*x))/sqrt(Pi))*sqrt(Pi)/(a*sqrt(1-a^2*x^2))+3/4*c*(c-a^2*c*x^2)^(1/2)*sqrt(arcsin(a*x))/(a*sqrt(1-a^2*x^2))],
[(c-a^2*c*x^2)^(1/2)/sqrt(arcsin(a*x)),x,5,1/2*(c-a^2*c*x^2)^(1/2)*FresnelC(2*sqrt(arcsin(a*x))/sqrt(Pi))*sqrt(Pi)/(a*sqrt(1-a^2*x^2))+(c-a^2*c*x^2)^(1/2)*sqrt(arcsin(a*x))/(a*sqrt(1-a^2*x^2))],
[1/((c-a^2*c*x^2)^(1/2)*sqrt(arcsin(a*x))),x,1,2*sqrt(1-a^2*x^2)*sqrt(arcsin(a*x))/(a*(c-a^2*c*x^2)^(1/2))],
[1/((c-a^2*c*x^2)^(3/2)*sqrt(arcsin(a*x))),x,0,Unintegrable(1/((c-a^2*c*x^2)^(3/2)*sqrt(arcsin(a*x))),x)],
[1/((c-a^2*c*x^2)^(5/2)*sqrt(arcsin(a*x))),x,0,Unintegrable(1/((c-a^2*c*x^2)^(5/2)*sqrt(arcsin(a*x))),x)],
[(c-a^2*c*x^2)^(5/2)/arcsin(a*x)^(3/2),x,10,-3/2*c^2*FresnelS(2*sqrt(2/Pi)*sqrt(arcsin(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-15/8*c^2*FresnelS(2*sqrt(arcsin(a*x))/sqrt(Pi))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-1/8*c^2*FresnelS(2*sqrt(3/Pi)*sqrt(arcsin(a*x)))*sqrt(3*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(arcsin(a*x)))],
[(c-a^2*c*x^2)^(3/2)/arcsin(a*x)^(3/2),x,8,-c*FresnelS(2*sqrt(2/Pi)*sqrt(arcsin(a*x)))*sqrt(1/2*Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-2*c*FresnelS(2*sqrt(arcsin(a*x))/sqrt(Pi))*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(arcsin(a*x)))],
[(c-a^2*c*x^2)^(1/2)/arcsin(a*x)^(3/2),x,6,-2*(c-a^2*c*x^2)^(1/2)*FresnelS(2*sqrt(arcsin(a*x))/sqrt(Pi))*sqrt(Pi)/(a*sqrt(1-a^2*x^2))-2*(c-a^2*c*x^2)^(1/2)*sqrt(1-a^2*x^2)/(a*sqrt(arcsin(a*x)))],
[1/((c-a^2*c*x^2)^(1/2)*arcsin(a*x)^(3/2)),x,1,-2*sqrt(1-a^2*x^2)/(a*(c-a^2*c*x^2)^(1/2)*sqrt(arcsin(a*x)))],
[1/((c-a^2*c*x^2)^(3/2)*arcsin(a*x)^(3/2)),x,1,-2*sqrt(1-a^2*x^2)/(a*(c-a^2*c*x^2)^(3/2)*sqrt(arcsin(a*x)))+4*a*sqrt(1-a^2*x^2)*Unintegrable(x/((1-a^2*x^2)^2*sqrt(arcsin(a*x))),x)/(c*sqrt(c-a^2*c*x^2))],
[1/((c-a^2*c*x^2)^(5/2)*arcsin(a*x)^(3/2)),x,1,-2*sqrt(1-a^2*x^2)/(a*(c-a^2*c*x^2)^(5/2)*sqrt(arcsin(a*x)))+8*a*sqrt(1-a^2*x^2)*Unintegrable(x/((1-a^2*x^2)^3*sqrt(arcsin(a*x))),x)/(c^2*sqrt(c-a^2*c*x^2))],
[(c-a^2*c*x^2)^(3/2)/arcsin(a*x)^(5/2),x,12,-2/3*(c-a^2*c*x^2)^(3/2)*sqrt(1-a^2*x^2)/(a*arcsin(a*x)^(3/2))-8/3*c*FresnelC(2*sqrt(arcsin(a*x))/sqrt(Pi))*sqrt(Pi)*sqrt(c-a^2*c*x^2)/(a*sqrt(1-a^2*x^2))-4/3*c*FresnelC(2*sqrt(2/Pi)*sqrt(arcsin(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(arcsin(a*x))],
[(c-a^2*c*x^2)^(1/2)/arcsin(a*x)^(5/2),x,4,-8/3*(c-a^2*c*x^2)^(1/2)*FresnelC(2*sqrt(arcsin(a*x))/sqrt(Pi))*sqrt(Pi)/(a*sqrt(1-a^2*x^2))-2/3*(c-a^2*c*x^2)^(1/2)*sqrt(1-a^2*x^2)/(a*arcsin(a*x)^(3/2))+8/3*x*(c-a^2*c*x^2)^(1/2)/sqrt(arcsin(a*x))],
[1/((c-a^2*c*x^2)^(1/2)*arcsin(a*x)^(5/2)),x,1,-2/3*sqrt(1-a^2*x^2)/(a*(c-a^2*c*x^2)^(1/2)*arcsin(a*x)^(3/2))],
[1/((c-a^2*c*x^2)^(3/2)*arcsin(a*x)^(5/2)),x,1,-2/3*sqrt(1-a^2*x^2)/(a*(c-a^2*c*x^2)^(3/2)*arcsin(a*x)^(3/2))+4/3*a*sqrt(1-a^2*x^2)*Unintegrable(x/((1-a^2*x^2)^2*arcsin(a*x)^(3/2)),x)/(c*sqrt(c-a^2*c*x^2))],
[1/((c-a^2*c*x^2)^(5/2)*arcsin(a*x)^(5/2)),x,1,-2/3*sqrt(1-a^2*x^2)/(a*(c-a^2*c*x^2)^(5/2)*arcsin(a*x)^(3/2))+8/3*a*sqrt(1-a^2*x^2)*Unintegrable(x/((1-a^2*x^2)^3*arcsin(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 ArcSin[c x])^n with n symbolic

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

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

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

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

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

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

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

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

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

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

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

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

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

# Integrands of the form x^m (d+e x)^(p/2) (f+g x)^(p/2) (a+b ArcSin[c x])^2 where e f+d g=0

# p>0
[x^2*(d+c*d*x)^(1/2)*(e-c*e*x)^(1/2)*(a+b*arcsin(c*x))^2,x,11,1/64*b^2*x*sqrt(d+c*d*x)*sqrt(e-c*e*x)/c^2-1/32*b^2*x^3*sqrt(d+c*d*x)*sqrt(e-c*e*x)-1/8*x*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)/c^2+1/4*x^3*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)-1/64*b^2*arcsin(c*x)*sqrt(d+c*d*x)*sqrt(e-c*e*x)/(c^3*sqrt(1-c^2*x^2))+1/8*b*x^2*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/(c*sqrt(1-c^2*x^2))-1/8*b*c*x^4*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)+1/24*(a+b*arcsin(c*x))^3*sqrt(d+c*d*x)*sqrt(e-c*e*x)/(b*c^3*sqrt(1-c^2*x^2))],
[x*(d+c*d*x)^(1/2)*(e-c*e*x)^(1/2)*(a+b*arcsin(c*x))^2,x,6,4/9*b^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)/c^2+2/27*b^2*(1-c^2*x^2)*sqrt(d+c*d*x)*sqrt(e-c*e*x)/c^2-1/3*(1-c^2*x^2)*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)/c^2+2/3*b*x*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/(c*sqrt(1-c^2*x^2))-2/9*b*c*x^3*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)],
[(d+c*d*x)^(1/2)*(e-c*e*x)^(1/2)*(a+b*arcsin(c*x))^2,x,6,-1/4*b^2*x*sqrt(d+c*d*x)*sqrt(e-c*e*x)+1/2*x*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)+1/4*b^2*arcsin(c*x)*sqrt(d+c*d*x)*sqrt(e-c*e*x)/(c*sqrt(1-c^2*x^2))-1/2*b*c*x^2*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)+1/6*(a+b*arcsin(c*x))^3*sqrt(d+c*d*x)*sqrt(e-c*e*x)/(b*c*sqrt(1-c^2*x^2))],
[(d+c*d*x)^(1/2)*(e-c*e*x)^(1/2)*(a+b*arcsin(c*x))^2/x,x,13,-2*b^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)+(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)-2*a*b*c*x*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-2*b^2*c*x*arcsin(c*x)*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-2*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)+2*I*b*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-2*I*b*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-2*b^2*polylog(3,-exp(I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)+2*b^2*polylog(3,exp(I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)],
[(d+c*d*x)^(1/2)*(e-c*e*x)^(1/2)*(a+b*arcsin(c*x))^2/x^2,x,8,-(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)/x-I*c*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-1/3*c*(a+b*arcsin(c*x))^3*sqrt(d+c*d*x)*sqrt(e-c*e*x)/(b*sqrt(1-c^2*x^2))+2*b*c*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-I*b^2*c*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)],
[x^2*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)*(a+b*arcsin(c*x))^2,x,18,-7/1152*b^2*d*e*x*sqrt(d+c*d*x)*sqrt(e-c*e*x)/c^2-43/1728*b^2*d*e*x^3*sqrt(d+c*d*x)*sqrt(e-c*e*x)+1/108*b^2*c^2*d*e*x^5*sqrt(d+c*d*x)*sqrt(e-c*e*x)-1/16*d*e*x*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)/c^2+1/8*d*e*x^3*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)+1/6*d*e*x^3*(1-c^2*x^2)*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)+7/1152*b^2*d*e*arcsin(c*x)*sqrt(d+c*d*x)*sqrt(e-c*e*x)/(c^3*sqrt(1-c^2*x^2))+1/16*b*d*e*x^2*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/(c*sqrt(1-c^2*x^2))-7/48*b*c*d*e*x^4*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)+1/18*b*c^3*d*e*x^6*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)+1/48*d*e*(a+b*arcsin(c*x))^3*sqrt(d+c*d*x)*sqrt(e-c*e*x)/(b*c^3*sqrt(1-c^2*x^2))],
[x*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)*(a+b*arcsin(c*x))^2,x,7,16/75*b^2*d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x)/c^2+8/225*b^2*d*e*(1-c^2*x^2)*sqrt(d+c*d*x)*sqrt(e-c*e*x)/c^2+2/125*b^2*d*e*(1-c^2*x^2)^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)/c^2-1/5*d*e*(1-c^2*x^2)^2*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)/c^2+2/5*b*d*e*x*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/(c*sqrt(1-c^2*x^2))-4/15*b*c*d*e*x^3*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)+2/25*b*c^3*d*e*x^5*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)],
[(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)*(a+b*arcsin(c*x))^2,x,11,-1/32*b^2*x*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)-15/64*b^2*x*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)/(1-c^2*x^2)+9/64*b^2*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)*arcsin(c*x)/(c*(1-c^2*x^2)^(3/2))-3/8*b*c*x^2*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)*(a+b*arcsin(c*x))/(1-c^2*x^2)^(3/2)+1/4*x*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)*(a+b*arcsin(c*x))^2+3/8*x*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)*(a+b*arcsin(c*x))^2/(1-c^2*x^2)+1/8*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)*(a+b*arcsin(c*x))^3/(b*c*(1-c^2*x^2)^(3/2))+1/8*b*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)*(a+b*arcsin(c*x))^2/x,x,18,-22/9*b^2*d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x)-2/27*b^2*d*e*(1-c^2*x^2)*sqrt(d+c*d*x)*sqrt(e-c*e*x)+d*e*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)+1/3*d*e*(1-c^2*x^2)*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)-2*a*b*c*d*e*x*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-2*b^2*c*d*e*x*arcsin(c*x)*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-2/3*b*c*d*e*x*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)+2/9*b*c^3*d*e*x^3*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-2*d*e*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)+2*I*b*d*e*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-2*I*b*d*e*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-2*b^2*d*e*polylog(3,-exp(I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)+2*b^2*d*e*polylog(3,exp(I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)],
[(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)*(a+b*arcsin(c*x))^2/x^2,x,15,1/4*b^2*c^2*d*e*x*sqrt(d+c*d*x)*sqrt(e-c*e*x)-3/2*c^2*d*e*x*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)-d*e*(1-c^2*x^2)*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)/x-5/4*b^2*c*d*e*arcsin(c*x)*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)+3/2*b*c^3*d*e*x^2*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-I*c*d*e*(a+b*arcsin(c*x))^2*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-1/2*c*d*e*(a+b*arcsin(c*x))^3*sqrt(d+c*d*x)*sqrt(e-c*e*x)/(b*sqrt(1-c^2*x^2))+2*b*c*d*e*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)-I*b^2*c*d*e*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(d+c*d*x)*sqrt(e-c*e*x)/sqrt(1-c^2*x^2)+b*c*d*e*(a+b*arcsin(c*x))*sqrt(d+c*d*x)*sqrt(e-c*e*x)*sqrt(1-c^2*x^2)],

# p<0
[x^2*(a+b*arcsin(c*x))^2/((d+c*d*x)^(1/2)*(e-c*e*x)^(1/2)),x,6,1/4*b^2*x*(1-c^2*x^2)/(c^2*sqrt(d+c*d*x)*sqrt(e-c*e*x))-1/2*x*(1-c^2*x^2)*(a+b*arcsin(c*x))^2/(c^2*sqrt(d+c*d*x)*sqrt(e-c*e*x))-1/4*b^2*arcsin(c*x)*sqrt(1-c^2*x^2)/(c^3*sqrt(d+c*d*x)*sqrt(e-c*e*x))+1/2*b*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/(c*sqrt(d+c*d*x)*sqrt(e-c*e*x))+1/6*(a+b*arcsin(c*x))^3*sqrt(1-c^2*x^2)/(b*c^3*sqrt(d+c*d*x)*sqrt(e-c*e*x))],
[x*(a+b*arcsin(c*x))^2/((d+c*d*x)^(1/2)*(e-c*e*x)^(1/2)),x,5,2*b^2*(1-c^2*x^2)/(c^2*sqrt(d+c*d*x)*sqrt(e-c*e*x))-(1-c^2*x^2)*(a+b*arcsin(c*x))^2/(c^2*sqrt(d+c*d*x)*sqrt(e-c*e*x))+2*a*b*x*sqrt(1-c^2*x^2)/(c*sqrt(d+c*d*x)*sqrt(e-c*e*x))+2*b^2*x*arcsin(c*x)*sqrt(1-c^2*x^2)/(c*sqrt(d+c*d*x)*sqrt(e-c*e*x))],
[(a+b*arcsin(c*x))^2/((d+c*d*x)^(1/2)*(e-c*e*x)^(1/2)),x,2,1/3*(a+b*arcsin(c*x))^3*sqrt(1-c^2*x^2)/(b*c*sqrt(d+c*d*x)*sqrt(e-c*e*x))],
[(a+b*arcsin(c*x))^2/(x*(d+c*d*x)^(1/2)*(e-c*e*x)^(1/2)),x,9,-2*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(d+c*d*x)*sqrt(e-c*e*x))+2*I*b*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(d+c*d*x)*sqrt(e-c*e*x))-2*I*b*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(d+c*d*x)*sqrt(e-c*e*x))-2*b^2*polylog(3,-exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(d+c*d*x)*sqrt(e-c*e*x))+2*b^2*polylog(3,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(d+c*d*x)*sqrt(e-c*e*x))],
[(a+b*arcsin(c*x))^2/(x^2*(d+c*d*x)^(1/2)*(e-c*e*x)^(1/2)),x,7,-(1-c^2*x^2)*(a+b*arcsin(c*x))^2/(x*sqrt(d+c*d*x)*sqrt(e-c*e*x))-I*c*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)/(sqrt(d+c*d*x)*sqrt(e-c*e*x))+2*b*c*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(d+c*d*x)*sqrt(e-c*e*x))-I*b^2*c*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(sqrt(d+c*d*x)*sqrt(e-c*e*x))],
[x^2*(a+b*arcsin(c*x))^2/((d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)),x,8,x*(a+b*arcsin(c*x))^2/(c^2*d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))-I*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)/(c^3*d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))-1/3*(a+b*arcsin(c*x))^3*sqrt(1-c^2*x^2)/(b*c^3*d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))+2*b*(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^3*d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))-I*b^2*polylog(2,-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^3*d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))],
[x*(a+b*arcsin(c*x))^2/((d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)),x,8,(a+b*arcsin(c*x))^2/(c^2*d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))+4*I*b*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^2*d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))-2*I*b^2*polylog(2,-I*exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^2*d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))+2*I*b^2*polylog(2,I*exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(c^2*d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))],
[(a+b*arcsin(c*x))^2/((d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)),x,7,x*(1-c^2*x^2)*(a+b*arcsin(c*x))^2/((d+c*d*x)^(3/2)*(e-c*e*x)^(3/2))-I*(1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))^2/(c*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2))+2*b*(1-c^2*x^2)^(3/2)*(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))/(c*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2))-I*b^2*(1-c^2*x^2)^(3/2)*polylog(2,-exp(2*I*arcsin(c*x)))/(c*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2))],
[(a+b*arcsin(c*x))^2/(x*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)),x,16,(a+b*arcsin(c*x))^2/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))+4*I*b*(a+b*arcsin(c*x))*arctan(exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))-2*(a+b*arcsin(c*x))^2*arctanh(exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))+2*I*b*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))-2*I*b^2*polylog(2,-I*exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))+2*I*b^2*polylog(2,I*exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))-2*I*b*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))-2*b^2*polylog(3,-exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))+2*b^2*polylog(3,exp(I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))],
[(a+b*arcsin(c*x))^2/(x^2*(d+c*d*x)^(3/2)*(e-c*e*x)^(3/2)),x,15,-(a+b*arcsin(c*x))^2/(d*e*x*sqrt(d+c*d*x)*sqrt(e-c*e*x))+2*c^2*x*(a+b*arcsin(c*x))^2/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))-2*I*c*(a+b*arcsin(c*x))^2*sqrt(1-c^2*x^2)/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))-4*b*c*(a+b*arcsin(c*x))*arctanh(exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))+4*b*c*(a+b*arcsin(c*x))*log(1+exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))-I*b^2*c*polylog(2,-exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))-I*b^2*c*polylog(2,exp(2*I*arcsin(c*x)))*sqrt(1-c^2*x^2)/(d*e*sqrt(d+c*d*x)*sqrt(e-c*e*x))],

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

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

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

# p>0
[x^4*(d+e*x^2)*(a+b*arcsin(c*x)),x,5,-1/105*b*(14*c^2*d+15*e)*(1-c^2*x^2)^(3/2)/c^7+1/175*b*(7*c^2*d+15*e)*(1-c^2*x^2)^(5/2)/c^7-1/49*b*e*(1-c^2*x^2)^(7/2)/c^7+1/5*d*x^5*(a+b*arcsin(c*x))+1/7*e*x^7*(a+b*arcsin(c*x))+1/35*b*(7*c^2*d+5*e)*sqrt(1-c^2*x^2)/c^7],
[x^3*(d+e*x^2)*(a+b*arcsin(c*x)),x,6,-1/96*b*(9*c^2*d+5*e)*arcsin(c*x)/c^6+1/4*d*x^4*(a+b*arcsin(c*x))+1/6*e*x^6*(a+b*arcsin(c*x))+1/96*b*(9*c^2*d+5*e)*x*sqrt(1-c^2*x^2)/c^5+1/144*b*(9*c^2*d+5*e)*x^3*sqrt(1-c^2*x^2)/c^3+1/36*b*e*x^5*sqrt(1-c^2*x^2)/c],
[x^2*(d+e*x^2)*(a+b*arcsin(c*x)),x,5,-1/45*b*(5*c^2*d+6*e)*(1-c^2*x^2)^(3/2)/c^5+1/25*b*e*(1-c^2*x^2)^(5/2)/c^5+1/3*d*x^3*(a+b*arcsin(c*x))+1/5*e*x^5*(a+b*arcsin(c*x))+1/15*b*(5*c^2*d+3*e)*sqrt(1-c^2*x^2)/c^5],
[x*(d+e*x^2)*(a+b*arcsin(c*x)),x,4,-1/32*b*(8*c^4*d^2+8*c^2*d*e+3*e^2)*arcsin(c*x)/(c^4*e)+1/4*(d+e*x^2)^2*(a+b*arcsin(c*x))/e+3/32*b*(2*c^2*d+e)*x*sqrt(1-c^2*x^2)/c^3+1/16*b*x*(d+e*x^2)*sqrt(1-c^2*x^2)/c],
[(d+e*x^2)*(a+b*arcsin(c*x)),x,4,-1/9*b*e*(1-c^2*x^2)^(3/2)/c^3+d*x*(a+b*arcsin(c*x))+1/3*e*x^3*(a+b*arcsin(c*x))+1/3*b*(3*c^2*d+e)*sqrt(1-c^2*x^2)/c^3],
[(d+e*x^2)*(a+b*arcsin(c*x))/x,x,12,-1/4*b*e*arcsin(c*x)/c^2-1/2*I*b*d*arcsin(c*x)^2+1/2*e*x^2*(a+b*arcsin(c*x))+b*d*arcsin(c*x)*log(1-exp(2*I*arcsin(c*x)))-b*d*arcsin(c*x)*log(x)+d*(a+b*arcsin(c*x))*log(x)-1/2*I*b*d*polylog(2,exp(2*I*arcsin(c*x)))+1/4*b*e*x*sqrt(1-c^2*x^2)/c],
[(d+e*x^2)*(a+b*arcsin(c*x))/x^2,x,5,-d*(a+b*arcsin(c*x))/x+e*x*(a+b*arcsin(c*x))-b*c*d*arctanh(sqrt(1-c^2*x^2))+b*e*sqrt(1-c^2*x^2)/c],
[(d+e*x^2)*(a+b*arcsin(c*x))/x^3,x,10,-1/2*I*b*e*arcsin(c*x)^2-1/2*d*(a+b*arcsin(c*x))/x^2+b*e*arcsin(c*x)*log(1-exp(2*I*arcsin(c*x)))-b*e*arcsin(c*x)*log(x)+e*(a+b*arcsin(c*x))*log(x)-1/2*I*b*e*polylog(2,exp(2*I*arcsin(c*x)))-1/2*b*c*d*sqrt(1-c^2*x^2)/x],
[(d+e*x^2)*(a+b*arcsin(c*x))/x^4,x,6,-1/3*d*(a+b*arcsin(c*x))/x^3-e*(a+b*arcsin(c*x))/x-1/6*b*c*(c^2*d+6*e)*arctanh(sqrt(1-c^2*x^2))-1/6*b*c*d*sqrt(1-c^2*x^2)/x^2],
[x^4*(d+e*x^2)^2*(a+b*arcsin(c*x)),x,6,-2/945*b*(63*c^4*d^2+135*c^2*d*e+70*e^2)*(1-c^2*x^2)^(3/2)/c^9+1/525*b*(21*c^4*d^2+90*c^2*d*e+70*e^2)*(1-c^2*x^2)^(5/2)/c^9-2/441*b*e*(9*c^2*d+14*e)*(1-c^2*x^2)^(7/2)/c^9+1/81*b*e^2*(1-c^2*x^2)^(9/2)/c^9+1/5*d^2*x^5*(a+b*arcsin(c*x))+2/7*d*e*x^7*(a+b*arcsin(c*x))+1/9*e^2*x^9*(a+b*arcsin(c*x))+1/315*b*(63*c^4*d^2+90*c^2*d*e+35*e^2)*sqrt(1-c^2*x^2)/c^9],
[x^3*(d+e*x^2)^2*(a+b*arcsin(c*x)),x,7,-1/3072*b*(288*c^4*d^2+320*c^2*d*e+105*e^2)*arcsin(c*x)/c^8+1/4*d^2*x^4*(a+b*arcsin(c*x))+1/3*d*e*x^6*(a+b*arcsin(c*x))+1/8*e^2*x^8*(a+b*arcsin(c*x))+1/3072*b*(288*c^4*d^2+320*c^2*d*e+105*e^2)*x*sqrt(1-c^2*x^2)/c^7+1/4608*b*(288*c^4*d^2+320*c^2*d*e+105*e^2)*x^3*sqrt(1-c^2*x^2)/c^5+1/1152*b*e*(64*c^2*d+21*e)*x^5*sqrt(1-c^2*x^2)/c^3+1/64*b*e^2*x^7*sqrt(1-c^2*x^2)/c],
[x^2*(d+e*x^2)^2*(a+b*arcsin(c*x)),x,5,-1/315*b*(35*c^4*d^2+84*c^2*d*e+45*e^2)*(1-c^2*x^2)^(3/2)/c^7+1/175*b*e*(14*c^2*d+15*e)*(1-c^2*x^2)^(5/2)/c^7-1/49*b*e^2*(1-c^2*x^2)^(7/2)/c^7+1/3*d^2*x^3*(a+b*arcsin(c*x))+2/5*d*e*x^5*(a+b*arcsin(c*x))+1/7*e^2*x^7*(a+b*arcsin(c*x))+1/105*b*(35*c^4*d^2+42*c^2*d*e+15*e^2)*sqrt(1-c^2*x^2)/c^7],
[x*(d+e*x^2)^2*(a+b*arcsin(c*x)),x,5,-1/96*b*(2*c^2*d+e)*(8*c^4*d^2+8*c^2*d*e+5*e^2)*arcsin(c*x)/(c^6*e)+1/6*(d+e*x^2)^3*(a+b*arcsin(c*x))/e+1/288*b*(44*c^4*d^2+44*c^2*d*e+15*e^2)*x*sqrt(1-c^2*x^2)/c^5+5/144*b*(2*c^2*d+e)*x*(d+e*x^2)*sqrt(1-c^2*x^2)/c^3+1/36*b*x*(d+e*x^2)^2*sqrt(1-c^2*x^2)/c],
[(d+e*x^2)^2*(a+b*arcsin(c*x)),x,5,-2/45*b*e*(5*c^2*d+3*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*arcsin(c*x))+2/3*d*e*x^3*(a+b*arcsin(c*x))+1/5*e^2*x^5*(a+b*arcsin(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)^2*(a+b*arcsin(c*x))/x,x,14,-1/2*b*d*e*arcsin(c*x)/c^2-3/32*b*e^2*arcsin(c*x)/c^4-1/2*I*b*d^2*arcsin(c*x)^2+d*e*x^2*(a+b*arcsin(c*x))+1/4*e^2*x^4*(a+b*arcsin(c*x))+b*d^2*arcsin(c*x)*log(1-exp(2*I*arcsin(c*x)))-b*d^2*arcsin(c*x)*log(x)+d^2*(a+b*arcsin(c*x))*log(x)-1/2*I*b*d^2*polylog(2,exp(2*I*arcsin(c*x)))+1/2*b*d*e*x*sqrt(1-c^2*x^2)/c+3/32*b*e^2*x*sqrt(1-c^2*x^2)/c^3+1/16*b*e^2*x^3*sqrt(1-c^2*x^2)/c],
[(d+e*x^2)^2*(a+b*arcsin(c*x))/x^2,x,6,-1/9*b*e^2*(1-c^2*x^2)^(3/2)/c^3-d^2*(a+b*arcsin(c*x))/x+2*d*e*x*(a+b*arcsin(c*x))+1/3*e^2*x^3*(a+b*arcsin(c*x))-b*c*d^2*arctanh(sqrt(1-c^2*x^2))+1/3*b*e*(6*c^2*d+e)*sqrt(1-c^2*x^2)/c^3],
[(d+e*x^2)^2*(a+b*arcsin(c*x))/x^3,x,13,-1/4*b*e^2*arcsin(c*x)/c^2-I*b*d*e*arcsin(c*x)^2-1/2*d^2*(a+b*arcsin(c*x))/x^2+1/2*e^2*x^2*(a+b*arcsin(c*x))+2*b*d*e*arcsin(c*x)*log(1-exp(2*I*arcsin(c*x)))-2*b*d*e*arcsin(c*x)*log(x)+2*d*e*(a+b*arcsin(c*x))*log(x)-I*b*d*e*polylog(2,exp(2*I*arcsin(c*x)))-1/2*b*c*d^2*sqrt(1-c^2*x^2)/x+1/4*b*e^2*x*sqrt(1-c^2*x^2)/c],
[(d+e*x^2)^2*(a+b*arcsin(c*x))/x^4,x,6,-1/3*d^2*(a+b*arcsin(c*x))/x^3-2*d*e*(a+b*arcsin(c*x))/x+e^2*x*(a+b*arcsin(c*x))-1/6*b*c*d*(c^2*d+12*e)*arctanh(sqrt(1-c^2*x^2))+b*e^2*sqrt(1-c^2*x^2)/c-1/6*b*c*d^2*sqrt(1-c^2*x^2)/x^2],
[x^4*(d+e*x^2)^3*(a+b*arcsin(c*x)),x,5,-1/3465*b*(462*c^6*d^3+1485*c^4*d^2*e+1540*c^2*d*e^2+525*e^3)*(1-c^2*x^2)^(3/2)/c^11+1/1925*b*(77*c^6*d^3+495*c^4*d^2*e+770*c^2*d*e^2+350*e^3)*(1-c^2*x^2)^(5/2)/c^11-1/1617*b*e*(99*c^4*d^2+308*c^2*d*e+210*e^2)*(1-c^2*x^2)^(7/2)/c^11+1/297*b*e^2*(11*c^2*d+15*e)*(1-c^2*x^2)^(9/2)/c^11-1/121*b*e^3*(1-c^2*x^2)^(11/2)/c^11+1/5*d^3*x^5*(a+b*arcsin(c*x))+3/7*d^2*e*x^7*(a+b*arcsin(c*x))+1/3*d*e^2*x^9*(a+b*arcsin(c*x))+1/11*e^3*x^11*(a+b*arcsin(c*x))+1/1155*b*(231*c^6*d^3+495*c^4*d^2*e+385*c^2*d*e^2+105*e^3)*sqrt(1-c^2*x^2)/c^11],
[x^3*(d+e*x^2)^3*(a+b*arcsin(c*x)),x,8,1/5120*b*(128*c^10*d^5-480*c^6*d^3*e^2-800*c^4*d^2*e^3-525*c^2*d*e^4-126*e^5)*arcsin(c*x)/(c^10*e^2)-1/8*d*(d+e*x^2)^4*(a+b*arcsin(c*x))/e^2+1/10*(d+e*x^2)^5*(a+b*arcsin(c*x))/e^2-1/76800*b*(1232*c^8*d^4-2536*c^6*d^3*e-7758*c^4*d^2*e^2-6615*c^2*d*e^3-1890*e^4)*x*sqrt(1-c^2*x^2)/(c^9*e)-1/38400*b*(136*c^6*d^3-1096*c^4*d^2*e-1617*c^2*d*e^2-630*e^3)*x*(d+e*x^2)*sqrt(1-c^2*x^2)/(c^7*e)+1/9600*b*(26*c^4*d^2+201*c^2*d*e+126*e^2)*x*(d+e*x^2)^2*sqrt(1-c^2*x^2)/(c^5*e)+1/1600*b*(11*c^2*d+18*e)*x*(d+e*x^2)^3*sqrt(1-c^2*x^2)/(c^3*e)+1/100*b*x*(d+e*x^2)^4*sqrt(1-c^2*x^2)/(c*e)],
[x^2*(d+e*x^2)^3*(a+b*arcsin(c*x)),x,5,-1/945*b*(105*c^6*d^3+378*c^4*d^2*e+405*c^2*d*e^2+140*e^3)*(1-c^2*x^2)^(3/2)/c^9+1/525*b*e*(63*c^4*d^2+135*c^2*d*e+70*e^2)*(1-c^2*x^2)^(5/2)/c^9-1/441*b*e^2*(27*c^2*d+28*e)*(1-c^2*x^2)^(7/2)/c^9+1/81*b*e^3*(1-c^2*x^2)^(9/2)/c^9+1/3*d^3*x^3*(a+b*arcsin(c*x))+3/5*d^2*e*x^5*(a+b*arcsin(c*x))+3/7*d*e^2*x^7*(a+b*arcsin(c*x))+1/9*e^3*x^9*(a+b*arcsin(c*x))+1/315*b*(105*c^6*d^3+189*c^4*d^2*e+135*c^2*d*e^2+35*e^3)*sqrt(1-c^2*x^2)/c^9],
[x*(d+e*x^2)^3*(a+b*arcsin(c*x)),x,6,-1/1024*b*(128*c^8*d^4+256*c^6*d^3*e+288*c^4*d^2*e^2+160*c^2*d*e^3+35*e^4)*arcsin(c*x)/(c^8*e)+1/8*(d+e*x^2)^4*(a+b*arcsin(c*x))/e+5/3072*b*(2*c^2*d+e)*(40*c^4*d^2+40*c^2*d*e+21*e^2)*x*sqrt(1-c^2*x^2)/c^7+1/1536*b*(104*c^4*d^2+104*c^2*d*e+35*e^2)*x*(d+e*x^2)*sqrt(1-c^2*x^2)/c^5+7/384*b*(2*c^2*d+e)*x*(d+e*x^2)^2*sqrt(1-c^2*x^2)/c^3+1/64*b*x*(d+e*x^2)^3*sqrt(1-c^2*x^2)/c],
[(d+e*x^2)^3*(a+b*arcsin(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*e^2*(7*c^2*d+5*e)*(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*arcsin(c*x))+d^2*e*x^3*(a+b*arcsin(c*x))+3/5*d*e^2*x^5*(a+b*arcsin(c*x))+1/7*e^3*x^7*(a+b*arcsin(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)^3*(a+b*arcsin(c*x))/x,x,19,-3/4*b*d^2*e*arcsin(c*x)/c^2-9/32*b*d*e^2*arcsin(c*x)/c^4-5/96*b*e^3*arcsin(c*x)/c^6-1/2*I*b*d^3*arcsin(c*x)^2+3/2*d^2*e*x^2*(a+b*arcsin(c*x))+3/4*d*e^2*x^4*(a+b*arcsin(c*x))+1/6*e^3*x^6*(a+b*arcsin(c*x))+b*d^3*arcsin(c*x)*log(1-exp(2*I*arcsin(c*x)))-b*d^3*arcsin(c*x)*log(x)+d^3*(a+b*arcsin(c*x))*log(x)-1/2*I*b*d^3*polylog(2,exp(2*I*arcsin(c*x)))+3/4*b*d^2*e*x*sqrt(1-c^2*x^2)/c+9/32*b*d*e^2*x*sqrt(1-c^2*x^2)/c^3+5/96*b*e^3*x*sqrt(1-c^2*x^2)/c^5+3/16*b*d*e^2*x^3*sqrt(1-c^2*x^2)/c+5/144*b*e^3*x^3*sqrt(1-c^2*x^2)/c^3+1/36*b*e^3*x^5*sqrt(1-c^2*x^2)/c],
[(d+e*x^2)^3*(a+b*arcsin(c*x))/x^2,x,6,-1/15*b*e^2*(5*c^2*d+2*e)*(1-c^2*x^2)^(3/2)/c^5+1/25*b*e^3*(1-c^2*x^2)^(5/2)/c^5-d^3*(a+b*arcsin(c*x))/x+3*d^2*e*x*(a+b*arcsin(c*x))+d*e^2*x^3*(a+b*arcsin(c*x))+1/5*e^3*x^5*(a+b*arcsin(c*x))-b*c*d^3*arctanh(sqrt(1-c^2*x^2))+1/5*b*e*(15*c^4*d^2+5*c^2*d*e+e^2)*sqrt(1-c^2*x^2)/c^5],
[(d+e*x^2)^3*(a+b*arcsin(c*x))/x^3,x,15,-3/32*b*e^2*(8*c^2*d+e)*arcsin(c*x)/c^4-3/2*I*b*d^2*e*arcsin(c*x)^2-1/2*d^3*(a+b*arcsin(c*x))/x^2+3/2*d*e^2*x^2*(a+b*arcsin(c*x))+1/4*e^3*x^4*(a+b*arcsin(c*x))+3*b*d^2*e*arcsin(c*x)*log(1-exp(2*I*arcsin(c*x)))-3*b*d^2*e*arcsin(c*x)*log(x)+3*d^2*e*(a+b*arcsin(c*x))*log(x)-3/2*I*b*d^2*e*polylog(2,exp(2*I*arcsin(c*x)))-1/2*b*c*d^3*sqrt(1-c^2*x^2)/x+3/32*b*e^2*(8*c^2*d+e)*x*sqrt(1-c^2*x^2)/c^3+1/16*b*e^3*x^3*sqrt(1-c^2*x^2)/c],
[(d+e*x^2)^3*(a+b*arcsin(c*x))/x^4,x,8,-1/9*b*e^3*(1-c^2*x^2)^(3/2)/c^3-1/3*d^3*(a+b*arcsin(c*x))/x^3-3*d^2*e*(a+b*arcsin(c*x))/x+3*d*e^2*x*(a+b*arcsin(c*x))+1/3*e^3*x^3*(a+b*arcsin(c*x))-1/6*b*c*d^2*(c^2*d+18*e)*arctanh(sqrt(1-c^2*x^2))+1/3*b*e^2*(9*c^2*d+e)*sqrt(1-c^2*x^2)/c^3-1/6*b*c*d^3*sqrt(1-c^2*x^2)/x^2],
[(d+e*x^2)^4*(a+b*arcsin(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*e^3*(9*c^2*d+7*e)*(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*arcsin(c*x))+4/3*d^3*e*x^3*(a+b*arcsin(c*x))+6/5*d^2*e^2*x^5*(a+b*arcsin(c*x))+4/7*d*e^3*x^7*(a+b*arcsin(c*x))+1/9*e^4*x^9*(a+b*arcsin(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],

# p<0
[x^4*(a+b*arcsin(c*x))/(d+e*x^2),x,27,-a*d*x/e^2-1/9*b*(1-c^2*x^2)^(3/2)/(c^3*e)-b*d*x*arcsin(c*x)/e^2+1/3*x^3*(a+b*arcsin(c*x))/e+1/2*(-d)^(3/2)*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^(5/2)-1/2*(-d)^(3/2)*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^(5/2)+1/2*(-d)^(3/2)*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^(5/2)-1/2*(-d)^(3/2)*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^(5/2)+1/2*I*b*(-d)^(3/2)*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^(5/2)-1/2*I*b*(-d)^(3/2)*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^(5/2)+1/2*I*b*(-d)^(3/2)*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^(5/2)-1/2*I*b*(-d)^(3/2)*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^(5/2)-b*d*sqrt(1-c^2*x^2)/(c*e^2)+1/3*b*sqrt(1-c^2*x^2)/(c^3*e)],
[x^3*(a+b*arcsin(c*x))/(d+e*x^2),x,23,-1/4*b*arcsin(c*x)/(c^2*e)+1/2*x^2*(a+b*arcsin(c*x))/e+1/2*I*d*(a+b*arcsin(c*x))^2/(b*e^2)-1/2*d*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^2-1/2*d*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^2-1/2*d*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^2-1/2*d*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^2+1/2*I*b*d*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^2+1/2*I*b*d*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^2+1/2*I*b*d*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^2+1/2*I*b*d*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^2+1/4*b*x*sqrt(1-c^2*x^2)/(c*e)],
[x^2*(a+b*arcsin(c*x))/(d+e*x^2),x,23,a*x/e+b*x*arcsin(c*x)/e+1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(-d)/e^(3/2)-1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(-d)/e^(3/2)+1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(-d)/e^(3/2)-1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(-d)/e^(3/2)+1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(-d)/e^(3/2)-1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(-d)/e^(3/2)+1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(-d)/e^(3/2)-1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(-d)/e^(3/2)+b*sqrt(1-c^2*x^2)/(c*e)],
[x*(a+b*arcsin(c*x))/(d+e*x^2),x,18,-1/2*I*(a+b*arcsin(c*x))^2/(b*e)+1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e+1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e+1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e+1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e-1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e-1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e-1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e-1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e],
[(a+b*arcsin(c*x))/(d+e*x^2),x,18,1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))-1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))+1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))-1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))+1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))-1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))+1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))-1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))],
[(a+b*arcsin(c*x))/(x*(d+e*x^2)),x,25,(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))/d-1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d-1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d-1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d-1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d-1/2*I*b*polylog(2,exp(2*I*arcsin(c*x)))/d+1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d+1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d+1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d+1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d],
[(a+b*arcsin(c*x))/(x^2*(d+e*x^2)),x,24,(-a-b*arcsin(c*x))/(d*x)-b*c*arctanh(sqrt(1-c^2*x^2))/d+1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(e)/(-d)^(3/2)-1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(e)/(-d)^(3/2)+1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(e)/(-d)^(3/2)-1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(e)/(-d)^(3/2)+1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(e)/(-d)^(3/2)-1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(e)/(-d)^(3/2)+1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(e)/(-d)^(3/2)-1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(e)/(-d)^(3/2)],
[(a+b*arcsin(c*x))/(x^3*(d+e*x^2)),x,27,1/2*(-a-b*arcsin(c*x))/(d*x^2)-e*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))/d^2+1/2*e*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^2+1/2*e*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^2+1/2*e*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^2+1/2*e*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^2+1/2*I*b*e*polylog(2,exp(2*I*arcsin(c*x)))/d^2-1/2*I*b*e*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^2-1/2*I*b*e*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^2-1/2*I*b*e*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^2-1/2*I*b*e*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^2-1/2*b*c*sqrt(1-c^2*x^2)/(d*x)],
[(a+b*arcsin(c*x))/(x^4*(d+e*x^2)),x,29,1/3*(-a-b*arcsin(c*x))/(d*x^3)+e*(a+b*arcsin(c*x))/(d^2*x)-1/6*b*c^3*arctanh(sqrt(1-c^2*x^2))/d+b*c*e*arctanh(sqrt(1-c^2*x^2))/d^2+1/2*e^(3/2)*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(-d)^(5/2)-1/2*e^(3/2)*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(-d)^(5/2)+1/2*e^(3/2)*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(-d)^(5/2)-1/2*e^(3/2)*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(-d)^(5/2)+1/2*I*b*e^(3/2)*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(-d)^(5/2)-1/2*I*b*e^(3/2)*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(-d)^(5/2)+1/2*I*b*e^(3/2)*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(-d)^(5/2)-1/2*I*b*e^(3/2)*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(-d)^(5/2)-1/6*b*c*sqrt(1-c^2*x^2)/(d*x^2)],
[x^3*(a+b*arcsin(c*x))/(d+e*x^2)^2,x,23,1/2*d*(a+b*arcsin(c*x))/(e^2*(d+e*x^2))-1/2*I*(a+b*arcsin(c*x))^2/(b*e^2)+1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^2+1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^2+1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^2+1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^2-1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^2-1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^2-1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^2-1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^2-1/2*b*c*arctan(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(1-c^2*x^2)))*sqrt(d)/(e^2*sqrt(c^2*d+e))],
[x*(a+b*arcsin(c*x))/(d+e*x^2)^2,x,3,1/2*(-a-b*arcsin(c*x))/(e*(d+e*x^2))+1/2*b*c*arctan(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(1-c^2*x^2)))/(e*sqrt(d)*sqrt(c^2*d+e))],
[(a+b*arcsin(c*x))/(x*(d+e*x^2)^2),x,28,1/2*(a+b*arcsin(c*x))/(d*(d+e*x^2))+(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))/d^2-1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^2-1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^2-1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^2-1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^2-1/2*I*b*polylog(2,exp(2*I*arcsin(c*x)))/d^2+1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^2+1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^2+1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^2+1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^2-1/2*b*c*arctan(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(1-c^2*x^2)))/(d^(3/2)*sqrt(c^2*d+e))],
[(a+b*arcsin(c*x))/(x^3*(d+e*x^2)^2),x,30,1/2*(-a-b*arcsin(c*x))/(d^2*x^2)-1/2*e*(a+b*arcsin(c*x))/(d^2*(d+e*x^2))-2*e*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))/d^3+e*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^3+e*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^3+e*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^3+e*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^3+I*b*e*polylog(2,exp(2*I*arcsin(c*x)))/d^3-I*b*e*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^3-I*b*e*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^3-I*b*e*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^3-I*b*e*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^3+1/2*b*c*e*arctan(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(1-c^2*x^2)))/(d^(5/2)*sqrt(c^2*d+e))-1/2*b*c*sqrt(1-c^2*x^2)/(d^2*x)],
[x^4*(a+b*arcsin(c*x))/(d+e*x^2)^2,x,49,a*x/e^2+b*x*arcsin(c*x)/e^2+3/4*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(-d)/e^(5/2)-3/4*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(-d)/e^(5/2)+3/4*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(-d)/e^(5/2)-3/4*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(-d)/e^(5/2)+3/4*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(-d)/e^(5/2)-3/4*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(-d)/e^(5/2)+3/4*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(-d)/e^(5/2)-3/4*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(-d)/e^(5/2)-1/4*d*(a+b*arcsin(c*x))/(e^(5/2)*(sqrt(-d)-x*sqrt(e)))+1/4*d*(a+b*arcsin(c*x))/(e^(5/2)*(sqrt(-d)+x*sqrt(e)))+1/4*b*c*d*arctanh((-c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(e^(5/2)*sqrt(c^2*d+e))+1/4*b*c*d*arctanh((c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(e^(5/2)*sqrt(c^2*d+e))+b*sqrt(1-c^2*x^2)/(c*e^2)],
[x^2*(a+b*arcsin(c*x))/(d+e*x^2)^2,x,46,1/4*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(e^(3/2)*sqrt(-d))-1/4*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(e^(3/2)*sqrt(-d))+1/4*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(e^(3/2)*sqrt(-d))-1/4*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(e^(3/2)*sqrt(-d))+1/4*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(e^(3/2)*sqrt(-d))-1/4*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(e^(3/2)*sqrt(-d))+1/4*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(e^(3/2)*sqrt(-d))-1/4*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(e^(3/2)*sqrt(-d))+1/4*(a+b*arcsin(c*x))/(e^(3/2)*(sqrt(-d)-x*sqrt(e)))+1/4*(-a-b*arcsin(c*x))/(e^(3/2)*(sqrt(-d)+x*sqrt(e)))-1/4*b*c*arctanh((-c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(e^(3/2)*sqrt(c^2*d+e))-1/4*b*c*arctanh((c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(e^(3/2)*sqrt(c^2*d+e))],
[(a+b*arcsin(c*x))/(d+e*x^2)^2,x,26,-1/4*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/((-d)^(3/2)*sqrt(e))+1/4*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/((-d)^(3/2)*sqrt(e))-1/4*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/((-d)^(3/2)*sqrt(e))+1/4*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/((-d)^(3/2)*sqrt(e))-1/4*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/((-d)^(3/2)*sqrt(e))+1/4*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/((-d)^(3/2)*sqrt(e))-1/4*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/((-d)^(3/2)*sqrt(e))+1/4*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/((-d)^(3/2)*sqrt(e))+1/4*(-a-b*arcsin(c*x))/(d*sqrt(e)*(sqrt(-d)-x*sqrt(e)))+1/4*(a+b*arcsin(c*x))/(d*sqrt(e)*(sqrt(-d)+x*sqrt(e)))+1/4*b*c*arctanh((-c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(d*sqrt(e)*sqrt(c^2*d+e))+1/4*b*c*arctanh((c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(d*sqrt(e)*sqrt(c^2*d+e))],
[(a+b*arcsin(c*x))/(x^2*(d+e*x^2)^2),x,50,(-a-b*arcsin(c*x))/(d^2*x)-b*c*arctanh(sqrt(1-c^2*x^2))/d^2-3/4*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(e)/(-d)^(5/2)+3/4*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(e)/(-d)^(5/2)-3/4*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(e)/(-d)^(5/2)+3/4*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(e)/(-d)^(5/2)-3/4*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(e)/(-d)^(5/2)+3/4*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))*sqrt(e)/(-d)^(5/2)-3/4*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(e)/(-d)^(5/2)+3/4*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))*sqrt(e)/(-d)^(5/2)+1/4*(a+b*arcsin(c*x))*sqrt(e)/(d^2*(sqrt(-d)-x*sqrt(e)))-1/4*(a+b*arcsin(c*x))*sqrt(e)/(d^2*(sqrt(-d)+x*sqrt(e)))-1/4*b*c*arctanh((-c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))*sqrt(e)/(d^2*sqrt(c^2*d+e))-1/4*b*c*arctanh((c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))*sqrt(e)/(d^2*sqrt(c^2*d+e))],
[x^5*(a+b*arcsin(c*x))/(d+e*x^2)^3,x,27,-1/4*d^2*(a+b*arcsin(c*x))/(e^3*(d+e*x^2)^2)+d*(a+b*arcsin(c*x))/(e^3*(d+e*x^2))-1/2*I*(a+b*arcsin(c*x))^2/(b*e^3)+1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^3+1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^3+1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^3+1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^3-1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^3-1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/e^3-1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^3-1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/e^3+1/8*b*c*(2*c^2*d+e)*arctan(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(1-c^2*x^2)))*sqrt(d)/(e^3*(c^2*d+e)^(3/2))-b*c*arctan(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(1-c^2*x^2)))*sqrt(d)/(e^3*sqrt(c^2*d+e))+1/8*b*c*d*x*sqrt(1-c^2*x^2)/(e^2*(c^2*d+e)*(d+e*x^2))],
[x^3*(a+b*arcsin(c*x))/(d+e*x^2)^3,x,7,-1/4*b*arcsin(c*x)/(d*e^2)+1/4*x^4*(a+b*arcsin(c*x))/(d*(d+e*x^2)^2)+1/8*b*c*(2*c^2*d+3*e)*arctan(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(1-c^2*x^2)))/(e^2*(c^2*d+e)^(3/2)*sqrt(d))-1/8*b*c*x*sqrt(1-c^2*x^2)/(e*(c^2*d+e)*(d+e*x^2))],
[x*(a+b*arcsin(c*x))/(d+e*x^2)^3,x,4,1/4*(-a-b*arcsin(c*x))/(e*(d+e*x^2)^2)+1/8*b*c*(2*c^2*d+e)*arctan(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(1-c^2*x^2)))/(d^(3/2)*e*(c^2*d+e)^(3/2))+1/8*b*c*x*sqrt(1-c^2*x^2)/(d*(c^2*d+e)*(d+e*x^2))],
[(a+b*arcsin(c*x))/(x*(d+e*x^2)^3),x,32,1/4*(a+b*arcsin(c*x))/(d*(d+e*x^2)^2)+1/2*(a+b*arcsin(c*x))/(d^2*(d+e*x^2))-1/8*b*c*(2*c^2*d+e)*arctan(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(1-c^2*x^2)))/(d^(5/2)*(c^2*d+e)^(3/2))+(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))/d^3-1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^3-1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^3-1/2*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^3-1/2*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^3-1/2*I*b*polylog(2,exp(2*I*arcsin(c*x)))/d^3+1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^3+1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^3+1/2*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^3+1/2*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^3-1/2*b*c*arctan(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(1-c^2*x^2)))/(d^(5/2)*sqrt(c^2*d+e))-1/8*b*c*e*x*sqrt(1-c^2*x^2)/(d^2*(c^2*d+e)*(d+e*x^2))],
[(a+b*arcsin(c*x))/(x^3*(d+e*x^2)^3),x,34,1/2*(-a-b*arcsin(c*x))/(d^3*x^2)-1/4*e*(a+b*arcsin(c*x))/(d^2*(d+e*x^2)^2)-e*(a+b*arcsin(c*x))/(d^3*(d+e*x^2))+1/8*b*c*e*(2*c^2*d+e)*arctan(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(1-c^2*x^2)))/(d^(7/2)*(c^2*d+e)^(3/2))-3*e*(a+b*arcsin(c*x))*log(1-exp(2*I*arcsin(c*x)))/d^4+3/2*e*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^4+3/2*e*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^4+3/2*e*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^4+3/2*e*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^4+3/2*I*b*e*polylog(2,exp(2*I*arcsin(c*x)))/d^4-3/2*I*b*e*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^4-3/2*I*b*e*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/d^4-3/2*I*b*e*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^4-3/2*I*b*e*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/d^4+b*c*e*arctan(x*sqrt(c^2*d+e)/(sqrt(d)*sqrt(1-c^2*x^2)))/(d^(7/2)*sqrt(c^2*d+e))-1/2*b*c*sqrt(1-c^2*x^2)/(d^3*x)+1/8*b*c*e^2*x*sqrt(1-c^2*x^2)/(d^3*(c^2*d+e)*(d+e*x^2))],
[x^4*(a+b*arcsin(c*x))/(d+e*x^2)^3,x,80,1/16*b*c^3*d*arctanh((-c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(e^(5/2)*(c^2*d+e)^(3/2))+1/16*b*c^3*d*arctanh((c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(e^(5/2)*(c^2*d+e)^(3/2))+3/16*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(e^(5/2)*sqrt(-d))-3/16*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(e^(5/2)*sqrt(-d))+3/16*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(e^(5/2)*sqrt(-d))-3/16*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(e^(5/2)*sqrt(-d))+3/16*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(e^(5/2)*sqrt(-d))-3/16*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(e^(5/2)*sqrt(-d))+3/16*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(e^(5/2)*sqrt(-d))-3/16*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(e^(5/2)*sqrt(-d))-1/16*(a+b*arcsin(c*x))*sqrt(-d)/(e^(5/2)*(sqrt(-d)-x*sqrt(e))^2)+5/16*(a+b*arcsin(c*x))/(e^(5/2)*(sqrt(-d)-x*sqrt(e)))+1/16*(a+b*arcsin(c*x))*sqrt(-d)/(e^(5/2)*(sqrt(-d)+x*sqrt(e))^2)-5/16*(a+b*arcsin(c*x))/(e^(5/2)*(sqrt(-d)+x*sqrt(e)))-5/16*b*c*arctanh((-c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(e^(5/2)*sqrt(c^2*d+e))-5/16*b*c*arctanh((c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(e^(5/2)*sqrt(c^2*d+e))+1/16*b*c*sqrt(-d)*sqrt(1-c^2*x^2)/(e^2*(c^2*d+e)*(sqrt(-d)-x*sqrt(e)))+1/16*b*c*sqrt(-d)*sqrt(1-c^2*x^2)/(e^2*(c^2*d+e)*(sqrt(-d)+x*sqrt(e)))],
[x^2*(a+b*arcsin(c*x))/(d+e*x^2)^3,x,62,-1/16*b*c^3*arctanh((-c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(e^(3/2)*(c^2*d+e)^(3/2))-1/16*b*c^3*arctanh((c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(e^(3/2)*(c^2*d+e)^(3/2))-1/16*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/((-d)^(3/2)*e^(3/2))+1/16*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/((-d)^(3/2)*e^(3/2))-1/16*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/((-d)^(3/2)*e^(3/2))+1/16*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/((-d)^(3/2)*e^(3/2))-1/16*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/((-d)^(3/2)*e^(3/2))+1/16*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/((-d)^(3/2)*e^(3/2))-1/16*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/((-d)^(3/2)*e^(3/2))+1/16*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/((-d)^(3/2)*e^(3/2))+1/16*(-a-b*arcsin(c*x))/(e^(3/2)*sqrt(-d)*(sqrt(-d)-x*sqrt(e))^2)+1/16*(-a-b*arcsin(c*x))/(d*e^(3/2)*(sqrt(-d)-x*sqrt(e)))+1/16*(a+b*arcsin(c*x))/(e^(3/2)*sqrt(-d)*(sqrt(-d)+x*sqrt(e))^2)+1/16*(a+b*arcsin(c*x))/(d*e^(3/2)*(sqrt(-d)+x*sqrt(e)))+1/16*b*c*arctanh((-c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(d*e^(3/2)*sqrt(c^2*d+e))+1/16*b*c*arctanh((c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(d*e^(3/2)*sqrt(c^2*d+e))+1/16*b*c*sqrt(1-c^2*x^2)/(e*(c^2*d+e)*sqrt(-d)*(sqrt(-d)-x*sqrt(e)))+1/16*b*c*sqrt(1-c^2*x^2)/(e*(c^2*d+e)*sqrt(-d)*(sqrt(-d)+x*sqrt(e)))],
[(a+b*arcsin(c*x))/(d+e*x^2)^3,x,34,1/16*b*c^3*arctanh((-c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(d*(c^2*d+e)^(3/2)*sqrt(e))+1/16*b*c^3*arctanh((c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(d*(c^2*d+e)^(3/2)*sqrt(e))+3/16*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/((-d)^(5/2)*sqrt(e))-3/16*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/((-d)^(5/2)*sqrt(e))+3/16*(a+b*arcsin(c*x))*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/((-d)^(5/2)*sqrt(e))-3/16*(a+b*arcsin(c*x))*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/((-d)^(5/2)*sqrt(e))+3/16*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/((-d)^(5/2)*sqrt(e))-3/16*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/((-d)^(5/2)*sqrt(e))+3/16*I*b*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/((-d)^(5/2)*sqrt(e))-3/16*I*b*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/((-d)^(5/2)*sqrt(e))+1/16*(-a-b*arcsin(c*x))/((-d)^(3/2)*sqrt(e)*(sqrt(-d)-x*sqrt(e))^2)-3/16*(a+b*arcsin(c*x))/(d^2*sqrt(e)*(sqrt(-d)-x*sqrt(e)))+1/16*(a+b*arcsin(c*x))/((-d)^(3/2)*sqrt(e)*(sqrt(-d)+x*sqrt(e))^2)+3/16*(a+b*arcsin(c*x))/(d^2*sqrt(e)*(sqrt(-d)+x*sqrt(e)))+3/16*b*c*arctanh((-c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(d^2*sqrt(e)*sqrt(c^2*d+e))+3/16*b*c*arctanh((c^2*x*sqrt(-d)+sqrt(e))/(sqrt(c^2*d+e)*sqrt(1-c^2*x^2)))/(d^2*sqrt(e)*sqrt(c^2*d+e))+1/16*b*c*sqrt(1-c^2*x^2)/((-d)^(3/2)*(c^2*d+e)*(sqrt(-d)-x*sqrt(e)))+1/16*b*c*sqrt(1-c^2*x^2)/((-d)^(3/2)*(c^2*d+e)*(sqrt(-d)+x*sqrt(e)))],

#  {(a + b*ArcSin[c*x])/(x^2*(d + e*x^2)^3), x, 84, (b*c*e*Sqrt[1 - c^2*x^2])/(16*(-d)^(5/2)*(c^2*d + e)*(Sqrt[-d] - Sqrt[e]*x)) + (b*c*e*Sqrt[1 - c^2*x^2])/(16*(-d)^(5/2)*(c^2*d + e)*(Sqrt[-d] + Sqrt[e]*x)) - (a + b*ArcSin[c*x])/(d^3*x) - (Sqrt[e]*(a + b*ArcSin[c*x]))/(16*(-d)^(5/2)*(Sqrt[-d] - Sqrt[e]*x)^2) + (7*Sqrt[e]*(a + b*ArcSin[c*x]))/(16*d^3*(Sqrt[-d] - Sqrt[e]*x)) + (Sqrt[e]*(a + b*ArcSin[c*x]))/(16*(-d)^(5/2)*(Sqrt[-d] + Sqrt[e]*x)^2) - (7*Sqrt[e]*(a + b*ArcSin[c*x]))/(16*d^3*(Sqrt[-d] + Sqrt[e]*x)) - (b*c^3*Sqrt[e]*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d^2*(c^2*d + e)^(3/2)) - (7*b*c*Sqrt[e]*ArcTanh[(Sqrt[e] - c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d^3*Sqrt[c^2*d + e]) - (b*c^3*Sqrt[e]*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d^2*(c^2*d + e)^(3/2)) - (7*b*c*Sqrt[e]*ArcTanh[(Sqrt[e] + c^2*Sqrt[-d]*x)/(Sqrt[c^2*d + e]*Sqrt[1 - c^2*x^2])])/(16*d^3*Sqrt[c^2*d + e]) - (b*c*ArcTanh[Sqrt[1 - c^2*x^2]])/d^3 + (15*Sqrt[e]*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(16*(-d)^(7/2)) - (15*Sqrt[e]*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(16*(-d)^(7/2)) + (15*Sqrt[e]*(a + b*ArcSin[c*x])*Log[1 - (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(16*(-d)^(7/2)) - (15*Sqrt[e]*(a + b*ArcSin[c*x])*Log[1 + (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(16*(-d)^(7/2)) + (15*I*b*Sqrt[e]*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e]))])/(16*(-d)^(7/2)) - (15*I*b*Sqrt[e]*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] - Sqrt[c^2*d + e])])/(16*(-d)^(7/2)) + (15*I*b*Sqrt[e]*PolyLog[2, -((Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e]))])/(16*(-d)^(7/2)) - (15*I*b*Sqrt[e]*PolyLog[2, (Sqrt[e]*E^(I*ArcSin[c*x]))/(I*c*Sqrt[-d] + Sqrt[c^2*d + e])])/(16*(-d)^(7/2))} 

# Integrands of the form x^m (d+e x^2)^(p/2) (a+b ArcSin[c x])
[(d+e*x^2)^(1/2)*(a+b*arcsin(c*x)),x,0,Unintegrable((a+b*arcsin(c*x))*sqrt(d+e*x^2),x)],
[(a+b*arcsin(c*x))/(d+e*x^2)^(1/2),x,0,Unintegrable((a+b*arcsin(c*x))/sqrt(d+e*x^2),x)],
[(a+b*arcsin(c*x))/(d+e*x^2)^(3/2),x,6,b*arctan(sqrt(e)*sqrt(1-c^2*x^2)/(c*sqrt(d+e*x^2)))/(d*sqrt(e))+x*(a+b*arcsin(c*x))/(d*sqrt(d+e*x^2))],
[(a+b*arcsin(c*x))/(d+e*x^2)^(5/2),x,7,1/3*x*(a+b*arcsin(c*x))/(d*(d+e*x^2)^(3/2))+2/3*b*arctan(sqrt(e)*sqrt(1-c^2*x^2)/(c*sqrt(d+e*x^2)))/(d^2*sqrt(e))+2/3*x*(a+b*arcsin(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*arcsin(c*x))/(d+e*x^2)^(7/2),x,8,1/5*x*(a+b*arcsin(c*x))/(d*(d+e*x^2)^(5/2))+4/15*x*(a+b*arcsin(c*x))/(d^2*(d+e*x^2)^(3/2))+8/15*b*arctan(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*arcsin(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))],

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

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

# Integrands of the form (f x)^m (d+e x^2)^p (a+b ArcSin[c x])^2
[(d+e*x^2)^3*(a+b*arcsin(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*arcsin(c*x))^2+d^2*e*x^3*(a+b*arcsin(c*x))^2+3/5*d*e^2*x^5*(a+b*arcsin(c*x))^2+1/7*e^3*x^7*(a+b*arcsin(c*x))^2+2*b*d^3*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c+4/3*b*d^2*e*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+16/25*b*d*e^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^5+32/245*b*e^3*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^7+2/3*b*d^2*e*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c+8/25*b*d*e^2*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+16/245*b*e^3*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^5+6/25*b*d*e^2*x^4*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c+12/245*b*e^3*x^4*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+2/49*b*e^3*x^6*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[(d+e*x^2)^2*(a+b*arcsin(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*arcsin(c*x))^2+2/3*d*e*x^3*(a+b*arcsin(c*x))^2+1/5*e^2*x^5*(a+b*arcsin(c*x))^2+2*b*d^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c+8/9*b*d*e*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+16/75*b*e^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^5+4/9*b*d*e*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c+8/75*b*e^2*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+2/25*b*e^2*x^4*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[(d+e*x^2)*(a+b*arcsin(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*arcsin(c*x))^2+1/3*e*x^3*(a+b*arcsin(c*x))^2+2*b*d*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c+4/9*b*e*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c^3+2/9*b*e*x^2*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[(a+b*arcsin(c*x))^2,x,3,-2*b^2*x+x*(a+b*arcsin(c*x))^2+2*b*(a+b*arcsin(c*x))*sqrt(1-c^2*x^2)/c],
[(a+b*arcsin(c*x))^2/(d+e*x^2),x,22,1/2*(a+b*arcsin(c*x))^2*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))-1/2*(a+b*arcsin(c*x))^2*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))+1/2*(a+b*arcsin(c*x))^2*log(1-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))-1/2*(a+b*arcsin(c*x))^2*log(1+exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))+I*b*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))-I*b*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))+I*b*(a+b*arcsin(c*x))*polylog(2,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))-I*b*(a+b*arcsin(c*x))*polylog(2,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))-b^2*polylog(3,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))+b^2*polylog(3,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)-sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))-b^2*polylog(3,-exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))+b^2*polylog(3,exp(I*arcsin(c*x))*sqrt(e)/(I*c*sqrt(-d)+sqrt(c^2*d+e)))/(sqrt(-d)*sqrt(e))],

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

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

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

# Integrands of the form (f x)^m (d+e x^2)^p / (a+b ArcSin[c x])
[(d+e*x^2)^2/(a+b*arcsin(c*x)),x,27,d^2*Ci((a+b*arcsin(c*x))/b)*cos(a/b)/(b*c)+1/2*d*e*Ci((a+b*arcsin(c*x))/b)*cos(a/b)/(b*c^3)+1/8*e^2*Ci((a+b*arcsin(c*x))/b)*cos(a/b)/(b*c^5)-1/2*d*e*Ci(3*(a+b*arcsin(c*x))/b)*cos(3*a/b)/(b*c^3)-3/16*e^2*Ci(3*(a+b*arcsin(c*x))/b)*cos(3*a/b)/(b*c^5)+1/16*e^2*Ci(5*(a+b*arcsin(c*x))/b)*cos(5*a/b)/(b*c^5)+d^2*Si((a+b*arcsin(c*x))/b)*sin(a/b)/(b*c)+1/2*d*e*Si((a+b*arcsin(c*x))/b)*sin(a/b)/(b*c^3)+1/8*e^2*Si((a+b*arcsin(c*x))/b)*sin(a/b)/(b*c^5)-1/2*d*e*Si(3*(a+b*arcsin(c*x))/b)*sin(3*a/b)/(b*c^3)-3/16*e^2*Si(3*(a+b*arcsin(c*x))/b)*sin(3*a/b)/(b*c^5)+1/16*e^2*Si(5*(a+b*arcsin(c*x))/b)*sin(5*a/b)/(b*c^5)],
[(d+e*x^2)/(a+b*arcsin(c*x)),x,15,d*Ci((a+b*arcsin(c*x))/b)*cos(a/b)/(b*c)+1/4*e*Ci((a+b*arcsin(c*x))/b)*cos(a/b)/(b*c^3)-1/4*e*Ci(3*(a+b*arcsin(c*x))/b)*cos(3*a/b)/(b*c^3)+d*Si((a+b*arcsin(c*x))/b)*sin(a/b)/(b*c)+1/4*e*Si((a+b*arcsin(c*x))/b)*sin(a/b)/(b*c^3)-1/4*e*Si(3*(a+b*arcsin(c*x))/b)*sin(3*a/b)/(b*c^3)],
[1/(a+b*arcsin(c*x)),x,4,Ci((a+b*arcsin(c*x))/b)*cos(a/b)/(b*c)+Si((a+b*arcsin(c*x))/b)*sin(a/b)/(b*c)],
[1/((d+e*x^2)*(a+b*arcsin(c*x))),x,0,Unintegrable(1/((d+e*x^2)*(a+b*arcsin(c*x))),x)],
[1/((d+e*x^2)^2*(a+b*arcsin(c*x))),x,0,Unintegrable(1/((d+e*x^2)^2*(a+b*arcsin(c*x))),x)],

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

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

# Integrands of the form (f x)^m (d+e x^2)^p / (a+b ArcSin[c x])^2
[(d+e*x^2)^2/(a+b*arcsin(c*x))^2,x,26,-d^2*cos(a/b)*Si((a+b*arcsin(c*x))/b)/(b^2*c)-1/2*d*e*cos(a/b)*Si((a+b*arcsin(c*x))/b)/(b^2*c^3)-1/8*e^2*cos(a/b)*Si((a+b*arcsin(c*x))/b)/(b^2*c^5)+3/2*d*e*cos(3*a/b)*Si(3*(a+b*arcsin(c*x))/b)/(b^2*c^3)+9/16*e^2*cos(3*a/b)*Si(3*(a+b*arcsin(c*x))/b)/(b^2*c^5)-5/16*e^2*cos(5*a/b)*Si(5*(a+b*arcsin(c*x))/b)/(b^2*c^5)+d^2*Ci((a+b*arcsin(c*x))/b)*sin(a/b)/(b^2*c)+1/2*d*e*Ci((a+b*arcsin(c*x))/b)*sin(a/b)/(b^2*c^3)+1/8*e^2*Ci((a+b*arcsin(c*x))/b)*sin(a/b)/(b^2*c^5)-3/2*d*e*Ci(3*(a+b*arcsin(c*x))/b)*sin(3*a/b)/(b^2*c^3)-9/16*e^2*Ci(3*(a+b*arcsin(c*x))/b)*sin(3*a/b)/(b^2*c^5)+5/16*e^2*Ci(5*(a+b*arcsin(c*x))/b)*sin(5*a/b)/(b^2*c^5)-d^2*sqrt(1-c^2*x^2)/(b*c*(a+b*arcsin(c*x)))-2*d*e*x^2*sqrt(1-c^2*x^2)/(b*c*(a+b*arcsin(c*x)))-e^2*x^4*sqrt(1-c^2*x^2)/(b*c*(a+b*arcsin(c*x)))],
[(d+e*x^2)/(a+b*arcsin(c*x))^2,x,15,-d*cos(a/b)*Si((a+b*arcsin(c*x))/b)/(b^2*c)-1/4*e*cos(a/b)*Si((a+b*arcsin(c*x))/b)/(b^2*c^3)+3/4*e*cos(3*a/b)*Si(3*(a+b*arcsin(c*x))/b)/(b^2*c^3)+d*Ci((a+b*arcsin(c*x))/b)*sin(a/b)/(b^2*c)+1/4*e*Ci((a+b*arcsin(c*x))/b)*sin(a/b)/(b^2*c^3)-3/4*e*Ci(3*(a+b*arcsin(c*x))/b)*sin(3*a/b)/(b^2*c^3)-d*sqrt(1-c^2*x^2)/(b*c*(a+b*arcsin(c*x)))-e*x^2*sqrt(1-c^2*x^2)/(b*c*(a+b*arcsin(c*x)))],
[1/(a+b*arcsin(c*x))^2,x,5,-cos(a/b)*Si((a+b*arcsin(c*x))/b)/(b^2*c)+Ci((a+b*arcsin(c*x))/b)*sin(a/b)/(b^2*c)-sqrt(1-c^2*x^2)/(b*c*(a+b*arcsin(c*x)))],
[1/((d+e*x^2)*(a+b*arcsin(c*x))^2),x,0,Unintegrable(1/((d+e*x^2)*(a+b*arcsin(c*x))^2),x)],
[1/((d+e*x^2)^2*(a+b*arcsin(c*x))^2),x,0,Unintegrable(1/((d+e*x^2)^2*(a+b*arcsin(c*x))^2),x)],

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

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

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

# n>0
[(d+e*x^2)^2*(a+b*arcsin(c*x))^(1/2),x,42,-1/80*e^2*cos(5*a/b)*FresnelS(sqrt(10/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(b)*sqrt(1/10*Pi)/c^5+1/80*e^2*FresnelC(sqrt(10/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(5*a/b)*sqrt(b)*sqrt(1/10*Pi)/c^5+1/6*d*e*cos(3*a/b)*FresnelS(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(b)*sqrt(1/6*Pi)/c^3+1/16*e^2*cos(3*a/b)*FresnelS(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(b)*sqrt(1/6*Pi)/c^5-1/6*d*e*FresnelC(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(3*a/b)*sqrt(b)*sqrt(1/6*Pi)/c^3-1/16*e^2*FresnelC(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(3*a/b)*sqrt(b)*sqrt(1/6*Pi)/c^5-d^2*cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(b)*sqrt(1/2*Pi)/c-1/2*d*e*cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(b)*sqrt(1/2*Pi)/c^3-1/8*e^2*cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(b)*sqrt(1/2*Pi)/c^5+d^2*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(b)*sqrt(1/2*Pi)/c+1/2*d*e*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(b)*sqrt(1/2*Pi)/c^3+1/8*e^2*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(b)*sqrt(1/2*Pi)/c^5+d^2*x*sqrt(a+b*arcsin(c*x))+2/3*d*e*x^3*sqrt(a+b*arcsin(c*x))+1/5*e^2*x^5*sqrt(a+b*arcsin(c*x))],
[(d+e*x^2)*(a+b*arcsin(c*x))^(1/2),x,23,1/12*e*cos(3*a/b)*FresnelS(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(b)*sqrt(1/6*Pi)/c^3-1/12*e*FresnelC(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(3*a/b)*sqrt(b)*sqrt(1/6*Pi)/c^3-d*cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(b)*sqrt(1/2*Pi)/c-1/4*e*cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(b)*sqrt(1/2*Pi)/c^3+d*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(b)*sqrt(1/2*Pi)/c+1/4*e*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(b)*sqrt(1/2*Pi)/c^3+d*x*sqrt(a+b*arcsin(c*x))+1/3*e*x^3*sqrt(a+b*arcsin(c*x))],
[(a+b*arcsin(c*x))^(1/2),x,7,-cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(b)*sqrt(1/2*Pi)/c+FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(b)*sqrt(1/2*Pi)/c+x*sqrt(a+b*arcsin(c*x))],
[(a+b*arcsin(c*x))^(1/2)/(d+e*x^2),x,0,Unintegrable(sqrt(a+b*arcsin(c*x))/(d+e*x^2),x)],
[(a+b*arcsin(c*x))^(1/2)/(d+e*x^2)^2,x,0,Unintegrable(sqrt(a+b*arcsin(c*x))/(d+e*x^2)^2,x)],
[(d+e*x^2)*(a+b*arcsin(c*x))^(3/2),x,32,d*x*(a+b*arcsin(c*x))^(3/2)+1/3*e*x^3*(a+b*arcsin(c*x))^(3/2)+1/24*b^(3/2)*e*cos(3*a/b)*FresnelC(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/6*Pi)/c^3+1/24*b^(3/2)*e*FresnelS(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(3*a/b)*sqrt(1/6*Pi)/c^3-3/2*b^(3/2)*d*cos(a/b)*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/c-3/8*b^(3/2)*e*cos(a/b)*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/c^3-3/2*b^(3/2)*d*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(1/2*Pi)/c-3/8*b^(3/2)*e*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(1/2*Pi)/c^3+3/2*b*d*sqrt(1-c^2*x^2)*sqrt(a+b*arcsin(c*x))/c+1/3*b*e*sqrt(1-c^2*x^2)*sqrt(a+b*arcsin(c*x))/c^3+1/6*b*e*x^2*sqrt(1-c^2*x^2)*sqrt(a+b*arcsin(c*x))/c],
[(a+b*arcsin(c*x))^(3/2),x,8,x*(a+b*arcsin(c*x))^(3/2)-3/2*b^(3/2)*cos(a/b)*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/c-3/2*b^(3/2)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(1/2*Pi)/c+3/2*b*sqrt(1-c^2*x^2)*sqrt(a+b*arcsin(c*x))/c],
[(a+b*arcsin(c*x))^(3/2)/(d+e*x^2),x,0,Unintegrable((a+b*arcsin(c*x))^(3/2)/(d+e*x^2),x)],
[(a+b*arcsin(c*x))^(3/2)/(d+e*x^2)^2,x,0,Unintegrable((a+b*arcsin(c*x))^(3/2)/(d+e*x^2)^2,x)],

# n<0
[(d+e*x^2)^2/(a+b*arcsin(c*x))^(1/2),x,39,1/8*e^2*cos(5*a/b)*FresnelC(sqrt(10/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/10*Pi)/(c^5*sqrt(b))+1/8*e^2*FresnelS(sqrt(10/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(5*a/b)*sqrt(1/10*Pi)/(c^5*sqrt(b))-d*e*cos(3*a/b)*FresnelC(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/6*Pi)/(c^3*sqrt(b))-d*e*FresnelS(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(3*a/b)*sqrt(1/6*Pi)/(c^3*sqrt(b))+d*e*cos(a/b)*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/(c^3*sqrt(b))+1/4*e^2*cos(a/b)*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/(c^5*sqrt(b))+d*e*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(1/2*Pi)/(c^3*sqrt(b))+1/4*e^2*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(1/2*Pi)/(c^5*sqrt(b))-1/8*e^2*cos(3*a/b)*FresnelC(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(3/2*Pi)/(c^5*sqrt(b))-1/8*e^2*FresnelS(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(3*a/b)*sqrt(3/2*Pi)/(c^5*sqrt(b))+d^2*cos(a/b)*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(2*Pi)/(c*sqrt(b))+d^2*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(2*Pi)/(c*sqrt(b))],
[(d+e*x^2)/(a+b*arcsin(c*x))^(1/2),x,21,-1/2*e*cos(3*a/b)*FresnelC(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/6*Pi)/(c^3*sqrt(b))-1/2*e*FresnelS(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(3*a/b)*sqrt(1/6*Pi)/(c^3*sqrt(b))+1/2*e*cos(a/b)*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/(c^3*sqrt(b))+1/2*e*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(1/2*Pi)/(c^3*sqrt(b))+d*cos(a/b)*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(2*Pi)/(c*sqrt(b))+d*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(2*Pi)/(c*sqrt(b))],
[1/(a+b*arcsin(c*x))^(1/2),x,6,cos(a/b)*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(2*Pi)/(c*sqrt(b))+FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(2*Pi)/(c*sqrt(b))],
[1/((d+e*x^2)*(a+b*arcsin(c*x))^(1/2)),x,0,Unintegrable(1/((d+e*x^2)*sqrt(a+b*arcsin(c*x))),x)],
[1/((d+e*x^2)^2*(a+b*arcsin(c*x))^(1/2)),x,0,Unintegrable(1/((d+e*x^2)^2*sqrt(a+b*arcsin(c*x))),x)],
[(d+e*x^2)/(a+b*arcsin(c*x))^(3/2),x,21,-e*cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(1/2*Pi)/(b^(3/2)*c^3)+e*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(1/2*Pi)/(b^(3/2)*c^3)+e*cos(3*a/b)*FresnelS(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(3/2*Pi)/(b^(3/2)*c^3)-e*FresnelC(sqrt(6/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(3*a/b)*sqrt(3/2*Pi)/(b^(3/2)*c^3)-2*d*cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(2*Pi)/(b^(3/2)*c)+2*d*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(2*Pi)/(b^(3/2)*c)-2*d*sqrt(1-c^2*x^2)/(b*c*sqrt(a+b*arcsin(c*x)))-2*e*x^2*sqrt(1-c^2*x^2)/(b*c*sqrt(a+b*arcsin(c*x)))],
[1/(a+b*arcsin(c*x))^(3/2),x,7,-2*cos(a/b)*FresnelS(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sqrt(2*Pi)/(b^(3/2)*c)+2*FresnelC(sqrt(2/Pi)*sqrt(a+b*arcsin(c*x))/sqrt(b))*sin(a/b)*sqrt(2*Pi)/(b^(3/2)*c)-2*sqrt(1-c^2*x^2)/(b*c*sqrt(a+b*arcsin(c*x)))],
[1/((d+e*x^2)*(a+b*arcsin(c*x))^(3/2)),x,0,Unintegrable(1/((d+e*x^2)*(a+b*arcsin(c*x))^(3/2)),x)],
[1/((d+e*x^2)^2*(a+b*arcsin(c*x))^(3/2)),x,0,Unintegrable(1/((d+e*x^2)^2*(a+b*arcsin(c*x))^(3/2)),x)]]:
