# Maple integration test file: "1 Algebraic functions\1.2 Trinomial products\1.2.1 Quadratic\1.2.1.3 (d+e x)^m (f+g x) (a+b x+c x^2)^p.txt"

lst:=[

# Integrands of the form (e x)^m (f+g x) (a+b x+c x^2)^p

# Integrands of the form (e x)^m (f+g x) (a+b x+c x^2)^p when a=0

# Integrands of the form x^m (A+B x) (b x+c x^2)^p

# p>0
[x^m*(A+B*x)*(b*x+c*x^2),x,2,A*b*x^(2+m)/(2+m)+(b*B+A*c)*x^(3+m)/(3+m)+B*c*x^(4+m)/(4+m)],
[x^3*(A+B*x)*(b*x+c*x^2),x,2,1/5*A*b*x^5+1/6*(b*B+A*c)*x^6+1/7*B*c*x^7],
[x^2*(A+B*x)*(b*x+c*x^2),x,2,1/4*A*b*x^4+1/5*(b*B+A*c)*x^5+1/6*B*c*x^6],
[x*(A+B*x)*(b*x+c*x^2),x,2,1/3*A*b*x^3+1/4*(b*B+A*c)*x^4+1/5*B*c*x^5],
[(A+B*x)*(b*x+c*x^2),x,2,1/2*A*b*x^2+1/3*(b*B+A*c)*x^3+1/4*B*c*x^4],
[(A+B*x)*(b*x+c*x^2)/x,x,2,A*b*x+1/2*(b*B+A*c)*x^2+1/3*B*c*x^3],
[(A+B*x)*(b*x+c*x^2)/x^2,x,2,(b*B+A*c)*x+1/2*B*c*x^2+A*b*log(x)],
[(A+B*x)*(b*x+c*x^2)/x^3,x,2,-A*b/x+B*c*x+(b*B+A*c)*log(x)],
[(A+B*x)*(b*x+c*x^2)/x^4,x,2,-1/2*A*b/x^2+(-b*B-A*c)/x+B*c*log(x)],
[(A+B*x)*(b*x+c*x^2)/x^5,x,2,-1/3*A*b/x^3+1/2*(-b*B-A*c)/x^2-B*c/x],
[(A+B*x)*(b*x+c*x^2)/x^6,x,2,-1/4*A*b/x^4+1/3*(-b*B-A*c)/x^3-1/2*B*c/x^2],
[(A+B*x)*(b*x+c*x^2)/x^7,x,2,-1/5*A*b/x^5+1/4*(-b*B-A*c)/x^4-1/3*B*c/x^3],
[(A+B*x)*(b*x+c*x^2)/x^8,x,2,-1/6*A*b/x^6+1/5*(-b*B-A*c)/x^5-1/4*B*c/x^4],
[x^m*(A+B*x)*(b*x+c*x^2)^2,x,2,A*b^2*x^(3+m)/(3+m)+b*(b*B+2*A*c)*x^(4+m)/(4+m)+c*(2*b*B+A*c)*x^(5+m)/(5+m)+B*c^2*x^(6+m)/(6+m)],
[x^3*(A+B*x)*(b*x+c*x^2)^2,x,2,1/6*A*b^2*x^6+1/7*b*(b*B+2*A*c)*x^7+1/8*c*(2*b*B+A*c)*x^8+1/9*B*c^2*x^9],
[x^2*(A+B*x)*(b*x+c*x^2)^2,x,2,1/5*A*b^2*x^5+1/6*b*(b*B+2*A*c)*x^6+1/7*c*(2*b*B+A*c)*x^7+1/8*B*c^2*x^8],
[x*(A+B*x)*(b*x+c*x^2)^2,x,2,1/4*A*b^2*x^4+1/5*b*(b*B+2*A*c)*x^5+1/6*c*(2*b*B+A*c)*x^6+1/7*B*c^2*x^7],
[(A+B*x)*(b*x+c*x^2)^2,x,2,1/3*A*b^2*x^3+1/4*b*(b*B+2*A*c)*x^4+1/5*c*(2*b*B+A*c)*x^5+1/6*B*c^2*x^6],
[(A+B*x)*(b*x+c*x^2)^2/x,x,2,1/2*A*b^2*x^2+1/3*b*(b*B+2*A*c)*x^3+1/4*c*(2*b*B+A*c)*x^4+1/5*B*c^2*x^5],
[(A+B*x)*(b*x+c*x^2)^2/x^2,x,2,-1/3*(b*B-A*c)*(b+c*x)^3/c^2+1/4*B*(b+c*x)^4/c^2],
[(A+B*x)*(b*x+c*x^2)^2/x^3,x,2,b*(b*B+2*A*c)*x+1/2*c*(2*b*B+A*c)*x^2+1/3*B*c^2*x^3+A*b^2*log(x)],
[(A+B*x)*(b*x+c*x^2)^2/x^4,x,2,-A*b^2/x+c*(2*b*B+A*c)*x+1/2*B*c^2*x^2+b*(b*B+2*A*c)*log(x)],
[(A+B*x)*(b*x+c*x^2)^2/x^5,x,2,-1/2*A*b^2/x^2-b*(b*B+2*A*c)/x+B*c^2*x+c*(2*b*B+A*c)*log(x)],
[(A+B*x)*(b*x+c*x^2)^2/x^6,x,2,-1/3*A*b^2/x^3-1/2*b*(b*B+2*A*c)/x^2-c*(2*b*B+A*c)/x+B*c^2*log(x)],
[(A+B*x)*(b*x+c*x^2)^2/x^7,x,2,-1/4*A*b^2/x^4-1/3*b*(b*B+2*A*c)/x^3-1/2*c*(2*b*B+A*c)/x^2-B*c^2/x],
[(A+B*x)*(b*x+c*x^2)^2/x^8,x,2,-1/5*A*b^2/x^5-1/4*b*(b*B+2*A*c)/x^4-1/3*c*(2*b*B+A*c)/x^3-1/2*B*c^2/x^2],
[x^m*(A+B*x)*(b*x+c*x^2)^3,x,2,A*b^3*x^(4+m)/(4+m)+b^2*(b*B+3*A*c)*x^(5+m)/(5+m)+3*b*c*(b*B+A*c)*x^(6+m)/(6+m)+c^2*(3*b*B+A*c)*x^(7+m)/(7+m)+B*c^3*x^(8+m)/(8+m)],
[x^3*(A+B*x)*(b*x+c*x^2)^3,x,2,1/7*A*b^3*x^7+1/8*b^2*(b*B+3*A*c)*x^8+1/3*b*c*(b*B+A*c)*x^9+1/10*c^2*(3*b*B+A*c)*x^10+1/11*B*c^3*x^11],
[x^2*(A+B*x)*(b*x+c*x^2)^3,x,2,1/6*A*b^3*x^6+1/7*b^2*(b*B+3*A*c)*x^7+3/8*b*c*(b*B+A*c)*x^8+1/9*c^2*(3*b*B+A*c)*x^9+1/10*B*c^3*x^10],
[x*(A+B*x)*(b*x+c*x^2)^3,x,2,1/5*A*b^3*x^5+1/6*b^2*(b*B+3*A*c)*x^6+3/7*b*c*(b*B+A*c)*x^7+1/8*c^2*(3*b*B+A*c)*x^8+1/9*B*c^3*x^9],
[(A+B*x)*(b*x+c*x^2)^3,x,2,1/4*A*b^3*x^4+1/5*b^2*(b*B+3*A*c)*x^5+1/2*b*c*(b*B+A*c)*x^6+1/7*c^2*(3*b*B+A*c)*x^7+1/8*B*c^3*x^8],
[(A+B*x)*(b*x+c*x^2)^3/x,x,2,1/3*A*b^3*x^3+1/4*b^2*(b*B+3*A*c)*x^4+3/5*b*c*(b*B+A*c)*x^5+1/6*c^2*(3*b*B+A*c)*x^6+1/7*B*c^3*x^7],
[(A+B*x)*(b*x+c*x^2)^3/x^2,x,2,1/4*b*(b*B-A*c)*(b+c*x)^4/c^3-1/5*(2*b*B-A*c)*(b+c*x)^5/c^3+1/6*B*(b+c*x)^6/c^3],
[(A+B*x)*(b*x+c*x^2)^3/x^3,x,2,-1/4*(b*B-A*c)*(b+c*x)^4/c^2+1/5*B*(b+c*x)^5/c^2],
[(A+B*x)*(b*x+c*x^2)^3/x^4,x,2,b^2*(b*B+3*A*c)*x+3/2*b*c*(b*B+A*c)*x^2+1/3*c^2*(3*b*B+A*c)*x^3+1/4*B*c^3*x^4+A*b^3*log(x)],
[(A+B*x)*(b*x+c*x^2)^3/x^5,x,2,-A*b^3/x+3*b*c*(b*B+A*c)*x+1/2*c^2*(3*b*B+A*c)*x^2+1/3*B*c^3*x^3+b^2*(b*B+3*A*c)*log(x)],
[(A+B*x)*(b*x+c*x^2)^3/x^6,x,2,-1/2*A*b^3/x^2-b^2*(b*B+3*A*c)/x+c^2*(3*b*B+A*c)*x+1/2*B*c^3*x^2+3*b*c*(b*B+A*c)*log(x)],
[(A+B*x)*(b*x+c*x^2)^3/x^7,x,2,-1/3*A*b^3/x^3-1/2*b^2*(b*B+3*A*c)/x^2-3*b*c*(b*B+A*c)/x+B*c^3*x+c^2*(3*b*B+A*c)*log(x)],
[(A+B*x)*(b*x+c*x^2)^3/x^8,x,2,-1/4*A*b^3/x^4-1/3*b^2*(b*B+3*A*c)/x^3-3/2*b*c*(b*B+A*c)/x^2-c^2*(3*b*B+A*c)/x+B*c^3*log(x)],
[(A+B*x)*(b*x+c*x^2)^3/x^9,x,2,-1/5*A*b^3/x^5-1/4*b^2*(b*B+3*A*c)/x^4-b*c*(b*B+A*c)/x^3-1/2*c^2*(3*b*B+A*c)/x^2-B*c^3/x],
[(A+B*x)*(b*x+c*x^2)^3/x^10,x,2,-1/6*A*b^3/x^6-1/5*b^2*(b*B+3*A*c)/x^5-3/4*b*c*(b*B+A*c)/x^4-1/3*c^2*(3*b*B+A*c)/x^3-1/2*B*c^3/x^2],
[(A+B*x)*(b*x+c*x^2)^3/x^11,x,2,-1/7*A*b^3/x^7-1/6*b^2*(b*B+3*A*c)/x^6-3/5*b*c*(b*B+A*c)/x^5-1/4*c^2*(3*b*B+A*c)/x^4-1/3*B*c^3/x^3],

# p<0
[x^4*(d+e*x)/(b*x+c*x^2),x,2,b^2*(c*d-b*e)*x/c^4-1/2*b*(c*d-b*e)*x^2/c^3+1/3*(c*d-b*e)*x^3/c^2+1/4*e*x^4/c-b^3*(c*d-b*e)*log(b+c*x)/c^5],
[x^3*(d+e*x)/(b*x+c*x^2),x,2,-b*(c*d-b*e)*x/c^3+1/2*(c*d-b*e)*x^2/c^2+1/3*e*x^3/c+b^2*(c*d-b*e)*log(b+c*x)/c^4],
[x^2*(d+e*x)/(b*x+c*x^2),x,2,(c*d-b*e)*x/c^2+1/2*e*x^2/c-b*(c*d-b*e)*log(b+c*x)/c^3],
[x*(d+e*x)/(b*x+c*x^2),x,2,e*x/c+(c*d-b*e)*log(b+c*x)/c^2],
[(d+e*x)/(b*x+c*x^2),x,2,d*log(x)/b-(c*d-b*e)*log(b+c*x)/(b*c)],
[(d+e*x)/(x*(b*x+c*x^2)),x,2,-d/(b*x)-(c*d-b*e)*log(x)/b^2+(c*d-b*e)*log(b+c*x)/b^2],
[(d+e*x)/(x^2*(b*x+c*x^2)),x,2,-1/2*d/(b*x^2)+(c*d-b*e)/(b^2*x)+c*(c*d-b*e)*log(x)/b^3-c*(c*d-b*e)*log(b+c*x)/b^3],
[(d+e*x)/(x^3*(b*x+c*x^2)),x,2,-1/3*d/(b*x^3)+1/2*(c*d-b*e)/(b^2*x^2)-c*(c*d-b*e)/(b^3*x)-c^2*(c*d-b*e)*log(x)/b^4+c^2*(c*d-b*e)*log(b+c*x)/b^4],
[x^5*(d+e*x)/(b*x+c*x^2)^2,x,2,-b*(2*c*d-3*b*e)*x/c^4+1/2*(c*d-2*b*e)*x^2/c^3+1/3*e*x^3/c^2+b^3*(c*d-b*e)/(c^5*(b+c*x))+b^2*(3*c*d-4*b*e)*log(b+c*x)/c^5],
[x^4*(d+e*x)/(b*x+c*x^2)^2,x,2,(c*d-2*b*e)*x/c^3+1/2*e*x^2/c^2-b^2*(c*d-b*e)/(c^4*(b+c*x))-b*(2*c*d-3*b*e)*log(b+c*x)/c^4],
[x^3*(d+e*x)/(b*x+c*x^2)^2,x,2,e*x/c^2+b*(c*d-b*e)/(c^3*(b+c*x))+(c*d-2*b*e)*log(b+c*x)/c^3],
[x^2*(d+e*x)/(b*x+c*x^2)^2,x,2,(-c*d+b*e)/(c^2*(b+c*x))+e*log(b+c*x)/c^2],
[x*(d+e*x)/(b*x+c*x^2)^2,x,2,(c*d-b*e)/(b*c*(b+c*x))+d*log(x)/b^2-d*log(b+c*x)/b^2],
[(d+e*x)/(b*x+c*x^2)^2,x,2,-d/(b^2*x)+(-c*d+b*e)/(b^2*(b+c*x))-(2*c*d-b*e)*log(x)/b^3+(2*c*d-b*e)*log(b+c*x)/b^3],
[(d+e*x)/(x*(b*x+c*x^2)^2),x,2,-1/2*d/(b^2*x^2)+(2*c*d-b*e)/(b^3*x)+c*(c*d-b*e)/(b^3*(b+c*x))+c*(3*c*d-2*b*e)*log(x)/b^4-c*(3*c*d-2*b*e)*log(b+c*x)/b^4],
[(d+e*x)/(x^2*(b*x+c*x^2)^2),x,2,-1/3*d/(b^2*x^3)+1/2*(2*c*d-b*e)/(b^3*x^2)-c*(3*c*d-2*b*e)/(b^4*x)-c^2*(c*d-b*e)/(b^4*(b+c*x))-c^2*(4*c*d-3*b*e)*log(x)/b^5+c^2*(4*c*d-3*b*e)*log(b+c*x)/b^5],
[x^6*(d+e*x)/(b*x+c*x^2)^3,x,2,(c*d-3*b*e)*x/c^4+1/2*e*x^2/c^3+1/2*b^3*(c*d-b*e)/(c^5*(b+c*x)^2)-b^2*(3*c*d-4*b*e)/(c^5*(b+c*x))-3*b*(c*d-2*b*e)*log(b+c*x)/c^5],
[x^5*(d+e*x)/(b*x+c*x^2)^3,x,2,e*x/c^3-1/2*b^2*(c*d-b*e)/(c^4*(b+c*x)^2)+b*(2*c*d-3*b*e)/(c^4*(b+c*x))+(c*d-3*b*e)*log(b+c*x)/c^4],
[x^4*(d+e*x)/(b*x+c*x^2)^3,x,2,1/2*b*(c*d-b*e)/(c^3*(b+c*x)^2)+(-c*d+2*b*e)/(c^3*(b+c*x))+e*log(b+c*x)/c^3],
[x^3*(d+e*x)/(b*x+c*x^2)^3,x,2,1/2*(-c*d+b*e)/(c^2*(b+c*x)^2)-e/(c^2*(b+c*x))],
[x^2*(d+e*x)/(b*x+c*x^2)^3,x,2,1/2*(c*d-b*e)/(b*c*(b+c*x)^2)+d/(b^2*(b+c*x))+d*log(x)/b^3-d*log(b+c*x)/b^3],
[x*(d+e*x)/(b*x+c*x^2)^3,x,2,-d/(b^3*x)+1/2*(-c*d+b*e)/(b^2*(b+c*x)^2)+(-2*c*d+b*e)/(b^3*(b+c*x))-(3*c*d-b*e)*log(x)/b^4+(3*c*d-b*e)*log(b+c*x)/b^4],
[(d+e*x)/(b*x+c*x^2)^3,x,2,-1/2*d/(b^3*x^2)+(3*c*d-b*e)/(b^4*x)+1/2*c*(c*d-b*e)/(b^3*(b+c*x)^2)+c*(3*c*d-2*b*e)/(b^4*(b+c*x))+3*c*(2*c*d-b*e)*log(x)/b^5-3*c*(2*c*d-b*e)*log(b+c*x)/b^5],
[(d+e*x)/(x*(b*x+c*x^2)^3),x,2,-1/3*d/(b^3*x^3)+1/2*(3*c*d-b*e)/(b^4*x^2)-3*c*(2*c*d-b*e)/(b^5*x)-1/2*c^2*(c*d-b*e)/(b^4*(b+c*x)^2)-c^2*(4*c*d-3*b*e)/(b^5*(b+c*x))-2*c^2*(5*c*d-3*b*e)*log(x)/b^6+2*c^2*(5*c*d-3*b*e)*log(b+c*x)/b^6],

# Integrands of the form x^m (A+B x) (b x+c x^2)^(p/2)

# p>0
[x^3*(A+B*x)*sqrt(b*x+c*x^2),x,7,-7/192*b^2*(3*b*B-4*A*c)*(b*x+c*x^2)^(3/2)/c^4+7/160*b*(3*b*B-4*A*c)*x*(b*x+c*x^2)^(3/2)/c^3-1/20*(3*b*B-4*A*c)*x^2*(b*x+c*x^2)^(3/2)/c^2+1/6*B*x^3*(b*x+c*x^2)^(3/2)/c-7/512*b^5*(3*b*B-4*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+7/512*b^3*(3*b*B-4*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^5],
[x^2*(A+B*x)*sqrt(b*x+c*x^2),x,6,1/48*b*(7*b*B-10*A*c)*(b*x+c*x^2)^(3/2)/c^3-1/40*(7*b*B-10*A*c)*x*(b*x+c*x^2)^(3/2)/c^2+1/5*B*x^2*(b*x+c*x^2)^(3/2)/c+1/128*b^4*(7*b*B-10*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-1/128*b^2*(7*b*B-10*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^4],
[x*(A+B*x)*sqrt(b*x+c*x^2),x,4,-1/24*(5*b*B-8*A*c-6*B*c*x)*(b*x+c*x^2)^(3/2)/c^2-1/64*b^3*(5*b*B-8*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/64*b*(5*b*B-8*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^3],
[(A+B*x)*sqrt(b*x+c*x^2),x,4,1/3*B*(b*x+c*x^2)^(3/2)/c+1/8*b^2*(b*B-2*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-1/8*(b*B-2*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^2],
[(A+B*x)*sqrt(b*x+c*x^2)/x,x,4,1/2*B*(b*x+c*x^2)^(3/2)/(c*x)-1/4*b*(b*B-4*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)-1/4*(b*B-4*A*c)*sqrt(b*x+c*x^2)/c],
[(A+B*x)*sqrt(b*x+c*x^2)/x^2,x,4,-2*A*(b*x+c*x^2)^(3/2)/(b*x^2)+(b*B+2*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/sqrt(c)+(b*B+2*A*c)*sqrt(b*x+c*x^2)/b],
[(A+B*x)*sqrt(b*x+c*x^2)/x^3,x,4,-2/3*A*(b*x+c*x^2)^(3/2)/(b*x^3)+2*B*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)-2*B*sqrt(b*x+c*x^2)/x],
[(A+B*x)*sqrt(b*x+c*x^2)/x^4,x,2,-2/5*A*(b*x+c*x^2)^(3/2)/(b*x^4)-2/15*(5*b*B-2*A*c)*(b*x+c*x^2)^(3/2)/(b^2*x^3)],
[(A+B*x)*sqrt(b*x+c*x^2)/x^5,x,3,-2/7*A*(b*x+c*x^2)^(3/2)/(b*x^5)-2/35*(7*b*B-4*A*c)*(b*x+c*x^2)^(3/2)/(b^2*x^4)+4/105*c*(7*b*B-4*A*c)*(b*x+c*x^2)^(3/2)/(b^3*x^3)],
[(A+B*x)*sqrt(b*x+c*x^2)/x^6,x,4,-2/9*A*(b*x+c*x^2)^(3/2)/(b*x^6)-2/21*(3*b*B-2*A*c)*(b*x+c*x^2)^(3/2)/(b^2*x^5)+8/105*c*(3*b*B-2*A*c)*(b*x+c*x^2)^(3/2)/(b^3*x^4)-16/315*c^2*(3*b*B-2*A*c)*(b*x+c*x^2)^(3/2)/(b^4*x^3)],
[(A+B*x)*sqrt(b*x+c*x^2)/x^7,x,5,-2/11*A*(b*x+c*x^2)^(3/2)/(b*x^7)-2/99*(11*b*B-8*A*c)*(b*x+c*x^2)^(3/2)/(b^2*x^6)+4/231*c*(11*b*B-8*A*c)*(b*x+c*x^2)^(3/2)/(b^3*x^5)-16/1155*c^2*(11*b*B-8*A*c)*(b*x+c*x^2)^(3/2)/(b^4*x^4)+32/3465*c^3*(11*b*B-8*A*c)*(b*x+c*x^2)^(3/2)/(b^5*x^3)],
[(A+B*x)*sqrt(b*x+c*x^2)/x^8,x,6,-2/13*A*(b*x+c*x^2)^(3/2)/(b*x^8)-2/143*(13*b*B-10*A*c)*(b*x+c*x^2)^(3/2)/(b^2*x^7)+16/1287*c*(13*b*B-10*A*c)*(b*x+c*x^2)^(3/2)/(b^3*x^6)-32/3003*c^2*(13*b*B-10*A*c)*(b*x+c*x^2)^(3/2)/(b^4*x^5)+128/15015*c^3*(13*b*B-10*A*c)*(b*x+c*x^2)^(3/2)/(b^5*x^4)-256/45045*c^4*(13*b*B-10*A*c)*(b*x+c*x^2)^(3/2)/(b^6*x^3)],
[x^3*(A+B*x)*(b*x+c*x^2)^(3/2),x,8,3/2048*b^3*(11*b*B-16*A*c)*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^5-3/640*b^2*(11*b*B-16*A*c)*(b*x+c*x^2)^(5/2)/c^4+3/448*b*(11*b*B-16*A*c)*x*(b*x+c*x^2)^(5/2)/c^3-1/112*(11*b*B-16*A*c)*x^2*(b*x+c*x^2)^(5/2)/c^2+1/8*B*x^3*(b*x+c*x^2)^(5/2)/c+9/16384*b^7*(11*b*B-16*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(13/2)-9/16384*b^5*(11*b*B-16*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^6],
[x^2*(A+B*x)*(b*x+c*x^2)^(3/2),x,7,-1/384*b^2*(9*b*B-14*A*c)*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^4+1/120*b*(9*b*B-14*A*c)*(b*x+c*x^2)^(5/2)/c^3-1/84*(9*b*B-14*A*c)*x*(b*x+c*x^2)^(5/2)/c^2+1/7*B*x^2*(b*x+c*x^2)^(5/2)/c-1/1024*b^6*(9*b*B-14*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+1/1024*b^4*(9*b*B-14*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^5],
[x*(A+B*x)*(b*x+c*x^2)^(3/2),x,5,1/192*b*(7*b*B-12*A*c)*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^3-1/60*(7*b*B-12*A*c-10*B*c*x)*(b*x+c*x^2)^(5/2)/c^2+1/512*b^5*(7*b*B-12*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-1/512*b^3*(7*b*B-12*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^4],
[(A+B*x)*(b*x+c*x^2)^(3/2),x,5,-1/16*(b*B-2*A*c)*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^2+1/5*B*(b*x+c*x^2)^(5/2)/c-3/128*b^4*(b*B-2*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+3/128*b^2*(b*B-2*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^3],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x,x,5,-1/24*(3*b*B-8*A*c)*(b*x+c*x^2)^(3/2)/c+1/4*B*(b*x+c*x^2)^(5/2)/(c*x)+1/64*b^3*(3*b*B-8*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-1/64*b*(3*b*B-8*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^2],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^2,x,5,1/3*(b*B-6*A*c)*(b*x+c*x^2)^(3/2)/b+2*A*(b*x+c*x^2)^(5/2)/(b*x^2)-1/8*b^2*(b*B-6*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)+1/8*(b*B-6*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^3,x,5,1/2*(b*B+4*A*c)*(b*x+c*x^2)^(3/2)/(b*x)-2*A*(b*x+c*x^2)^(5/2)/(b*x^3)+3/4*b*(b*B+4*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/sqrt(c)+3/4*(b*B+4*A*c)*sqrt(b*x+c*x^2)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^4,x,5,-2/3*(3*b*B+2*A*c)*(b*x+c*x^2)^(3/2)/(b*x^2)-2/3*A*(b*x+c*x^2)^(5/2)/(b*x^4)+(3*b*B+2*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)+c*(3*b*B+2*A*c)*sqrt(b*x+c*x^2)/b],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^5,x,5,-2/3*B*(b*x+c*x^2)^(3/2)/x^3-2/5*A*(b*x+c*x^2)^(5/2)/(b*x^5)+2*B*c^(3/2)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))-2*B*c*sqrt(b*x+c*x^2)/x],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^6,x,2,-2/7*A*(b*x+c*x^2)^(5/2)/(b*x^6)-2/35*(7*b*B-2*A*c)*(b*x+c*x^2)^(5/2)/(b^2*x^5)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^7,x,3,-2/9*A*(b*x+c*x^2)^(5/2)/(b*x^7)-2/63*(9*b*B-4*A*c)*(b*x+c*x^2)^(5/2)/(b^2*x^6)+4/315*c*(9*b*B-4*A*c)*(b*x+c*x^2)^(5/2)/(b^3*x^5)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^8,x,4,-2/11*A*(b*x+c*x^2)^(5/2)/(b*x^8)-2/99*(11*b*B-6*A*c)*(b*x+c*x^2)^(5/2)/(b^2*x^7)+8/693*c*(11*b*B-6*A*c)*(b*x+c*x^2)^(5/2)/(b^3*x^6)-16/3465*c^2*(11*b*B-6*A*c)*(b*x+c*x^2)^(5/2)/(b^4*x^5)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^9,x,5,-2/13*A*(b*x+c*x^2)^(5/2)/(b*x^9)-2/143*(13*b*B-8*A*c)*(b*x+c*x^2)^(5/2)/(b^2*x^8)+4/429*c*(13*b*B-8*A*c)*(b*x+c*x^2)^(5/2)/(b^3*x^7)-16/3003*c^2*(13*b*B-8*A*c)*(b*x+c*x^2)^(5/2)/(b^4*x^6)+32/15015*c^3*(13*b*B-8*A*c)*(b*x+c*x^2)^(5/2)/(b^5*x^5)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^10,x,6,-2/15*A*(b*x+c*x^2)^(5/2)/(b*x^10)-2/39*(3*b*B-2*A*c)*(b*x+c*x^2)^(5/2)/(b^2*x^9)+16/429*c*(3*b*B-2*A*c)*(b*x+c*x^2)^(5/2)/(b^3*x^8)-32/1287*c^2*(3*b*B-2*A*c)*(b*x+c*x^2)^(5/2)/(b^4*x^7)+128/9009*c^3*(3*b*B-2*A*c)*(b*x+c*x^2)^(5/2)/(b^5*x^6)-256/45045*c^4*(3*b*B-2*A*c)*(b*x+c*x^2)^(5/2)/(b^6*x^5)],
[x^3*(A+B*x)*(b*x+c*x^2)^(5/2),x,9,-11/49152*b^5*(13*b*B-20*A*c)*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^6+11/15360*b^3*(13*b*B-20*A*c)*(b+2*c*x)*(b*x+c*x^2)^(5/2)/c^5-11/4480*b^2*(13*b*B-20*A*c)*(b*x+c*x^2)^(7/2)/c^4+11/2880*b*(13*b*B-20*A*c)*x*(b*x+c*x^2)^(7/2)/c^3-1/180*(13*b*B-20*A*c)*x^2*(b*x+c*x^2)^(7/2)/c^2+1/10*B*x^3*(b*x+c*x^2)^(7/2)/c-11/131072*b^9*(13*b*B-20*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(15/2)+11/131072*b^7*(13*b*B-20*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^7],
[x^2*(A+B*x)*(b*x+c*x^2)^(5/2),x,8,5/12288*b^4*(11*b*B-18*A*c)*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^5-1/768*b^2*(11*b*B-18*A*c)*(b+2*c*x)*(b*x+c*x^2)^(5/2)/c^4+1/224*b*(11*b*B-18*A*c)*(b*x+c*x^2)^(7/2)/c^3-1/144*(11*b*B-18*A*c)*x*(b*x+c*x^2)^(7/2)/c^2+1/9*B*x^2*(b*x+c*x^2)^(7/2)/c+5/32768*b^8*(11*b*B-18*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(13/2)-5/32768*b^6*(11*b*B-18*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^6],
[x*(A+B*x)*(b*x+c*x^2)^(5/2),x,6,-5/6144*b^3*(9*b*B-16*A*c)*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^4+1/384*b*(9*b*B-16*A*c)*(b+2*c*x)*(b*x+c*x^2)^(5/2)/c^3-1/112*(9*b*B-16*A*c-14*B*c*x)*(b*x+c*x^2)^(7/2)/c^2-5/16384*b^7*(9*b*B-16*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+5/16384*b^5*(9*b*B-16*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^5],
[(A+B*x)*(b*x+c*x^2)^(5/2),x,6,5/384*b^2*(b*B-2*A*c)*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^3-1/24*(b*B-2*A*c)*(b+2*c*x)*(b*x+c*x^2)^(5/2)/c^2+1/7*B*(b*x+c*x^2)^(7/2)/c+5/1024*b^6*(b*B-2*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-5/1024*b^4*(b*B-2*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^4],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x,x,6,-1/192*b*(5*b*B-12*A*c)*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^2-1/60*(5*b*B-12*A*c)*(b*x+c*x^2)^(5/2)/c+1/6*B*(b*x+c*x^2)^(7/2)/(c*x)-1/512*b^5*(5*b*B-12*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/512*b^3*(5*b*B-12*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^3],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^2,x,6,1/48*(3*b*B-10*A*c)*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c+1/15*(3*b*B-10*A*c)*(b*x+c*x^2)^(5/2)/b+2/3*A*(b*x+c*x^2)^(7/2)/(b*x^2)+1/128*b^4*(3*b*B-10*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-1/128*b^2*(3*b*B-10*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^2],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^3,x,6,5/24*(b*B-8*A*c)*(b*x+c*x^2)^(3/2)+1/4*(b*B-8*A*c)*(b*x+c*x^2)^(5/2)/(b*x)+2*A*(b*x+c*x^2)^(7/2)/(b*x^3)-5/64*b^3*(b*B-8*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)+5/64*b*(b*B-8*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^4,x,6,-5/3*c*(b*B+6*A*c)*(b*x+c*x^2)^(3/2)/b+2*(b*B+6*A*c)*(b*x+c*x^2)^(5/2)/(b*x^2)-2*A*(b*x+c*x^2)^(7/2)/(b*x^4)+5/8*b^2*(b*B+6*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/sqrt(c)-5/8*(b*B+6*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^5,x,6,5/6*c*(3*b*B+4*A*c)*(b*x+c*x^2)^(3/2)/(b*x)-2/3*(3*b*B+4*A*c)*(b*x+c*x^2)^(5/2)/(b*x^3)-2/3*A*(b*x+c*x^2)^(7/2)/(b*x^5)+5/4*b*(3*b*B+4*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)+5/4*c*(3*b*B+4*A*c)*sqrt(b*x+c*x^2)],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^6,x,6,-2/3*c*(5*b*B+2*A*c)*(b*x+c*x^2)^(3/2)/(b*x^2)-2/15*(5*b*B+2*A*c)*(b*x+c*x^2)^(5/2)/(b*x^4)-2/5*A*(b*x+c*x^2)^(7/2)/(b*x^6)+c^(3/2)*(5*b*B+2*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))+c^2*(5*b*B+2*A*c)*sqrt(b*x+c*x^2)/b],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^7,x,6,-2/3*B*c*(b*x+c*x^2)^(3/2)/x^3-2/5*B*(b*x+c*x^2)^(5/2)/x^5-2/7*A*(b*x+c*x^2)^(7/2)/(b*x^7)+2*B*c^(5/2)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))-2*B*c^2*sqrt(b*x+c*x^2)/x],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^8,x,2,-2/9*A*(b*x+c*x^2)^(7/2)/(b*x^8)-2/63*(9*b*B-2*A*c)*(b*x+c*x^2)^(7/2)/(b^2*x^7)],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^9,x,3,-2/11*A*(b*x+c*x^2)^(7/2)/(b*x^9)-2/99*(11*b*B-4*A*c)*(b*x+c*x^2)^(7/2)/(b^2*x^8)+4/693*c*(11*b*B-4*A*c)*(b*x+c*x^2)^(7/2)/(b^3*x^7)],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^10,x,4,-2/13*A*(b*x+c*x^2)^(7/2)/(b*x^10)-2/143*(13*b*B-6*A*c)*(b*x+c*x^2)^(7/2)/(b^2*x^9)+8/1287*c*(13*b*B-6*A*c)*(b*x+c*x^2)^(7/2)/(b^3*x^8)-16/9009*c^2*(13*b*B-6*A*c)*(b*x+c*x^2)^(7/2)/(b^4*x^7)],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^11,x,5,-2/15*A*(b*x+c*x^2)^(7/2)/(b*x^11)-2/195*(15*b*B-8*A*c)*(b*x+c*x^2)^(7/2)/(b^2*x^10)+4/715*c*(15*b*B-8*A*c)*(b*x+c*x^2)^(7/2)/(b^3*x^9)-16/6435*c^2*(15*b*B-8*A*c)*(b*x+c*x^2)^(7/2)/(b^4*x^8)+32/45045*c^3*(15*b*B-8*A*c)*(b*x+c*x^2)^(7/2)/(b^5*x^7)],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^12,x,6,-2/17*A*(b*x+c*x^2)^(7/2)/(b*x^12)-2/255*(17*b*B-10*A*c)*(b*x+c*x^2)^(7/2)/(b^2*x^11)+16/3315*c*(17*b*B-10*A*c)*(b*x+c*x^2)^(7/2)/(b^3*x^10)-32/12155*c^2*(17*b*B-10*A*c)*(b*x+c*x^2)^(7/2)/(b^4*x^9)+128/109395*c^3*(17*b*B-10*A*c)*(b*x+c*x^2)^(7/2)/(b^5*x^8)-256/765765*c^4*(17*b*B-10*A*c)*(b*x+c*x^2)^(7/2)/(b^6*x^7)],

# p<0
[x^4*(A+B*x)/sqrt(b*x+c*x^2),x,7,-7/128*b^4*(9*b*B-10*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+7/128*b^3*(9*b*B-10*A*c)*sqrt(b*x+c*x^2)/c^5-7/192*b^2*(9*b*B-10*A*c)*x*sqrt(b*x+c*x^2)/c^4+7/240*b*(9*b*B-10*A*c)*x^2*sqrt(b*x+c*x^2)/c^3-1/40*(9*b*B-10*A*c)*x^3*sqrt(b*x+c*x^2)/c^2+1/5*B*x^4*sqrt(b*x+c*x^2)/c],
[x^3*(A+B*x)/sqrt(b*x+c*x^2),x,6,5/64*b^3*(7*b*B-8*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-5/64*b^2*(7*b*B-8*A*c)*sqrt(b*x+c*x^2)/c^4+5/96*b*(7*b*B-8*A*c)*x*sqrt(b*x+c*x^2)/c^3-1/24*(7*b*B-8*A*c)*x^2*sqrt(b*x+c*x^2)/c^2+1/4*B*x^3*sqrt(b*x+c*x^2)/c],
[x^2*(A+B*x)/sqrt(b*x+c*x^2),x,5,-1/8*b^2*(5*b*B-6*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/8*b*(5*b*B-6*A*c)*sqrt(b*x+c*x^2)/c^3-1/12*(5*b*B-6*A*c)*x*sqrt(b*x+c*x^2)/c^2+1/3*B*x^2*sqrt(b*x+c*x^2)/c],
[x*(A+B*x)/sqrt(b*x+c*x^2),x,3,1/4*b*(3*b*B-4*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-1/4*(3*b*B-4*A*c-2*B*c*x)*sqrt(b*x+c*x^2)/c^2],
[(A+B*x)/sqrt(b*x+c*x^2),x,3,-(b*B-2*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)+B*sqrt(b*x+c*x^2)/c],
[(A+B*x)/(x*sqrt(b*x+c*x^2)),x,3,2*B*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/sqrt(c)-2*A*sqrt(b*x+c*x^2)/(b*x)],
[(A+B*x)/(x^2*sqrt(b*x+c*x^2)),x,2,-2/3*A*sqrt(b*x+c*x^2)/(b*x^2)-2/3*(3*b*B-2*A*c)*sqrt(b*x+c*x^2)/(b^2*x)],
[(A+B*x)/(x^3*sqrt(b*x+c*x^2)),x,3,-2/5*A*sqrt(b*x+c*x^2)/(b*x^3)-2/15*(5*b*B-4*A*c)*sqrt(b*x+c*x^2)/(b^2*x^2)+4/15*c*(5*b*B-4*A*c)*sqrt(b*x+c*x^2)/(b^3*x)],
[(A+B*x)/(x^4*sqrt(b*x+c*x^2)),x,4,-2/7*A*sqrt(b*x+c*x^2)/(b*x^4)-2/35*(7*b*B-6*A*c)*sqrt(b*x+c*x^2)/(b^2*x^3)+8/105*c*(7*b*B-6*A*c)*sqrt(b*x+c*x^2)/(b^3*x^2)-16/105*c^2*(7*b*B-6*A*c)*sqrt(b*x+c*x^2)/(b^4*x)],
[(A+B*x)/(x^5*sqrt(b*x+c*x^2)),x,5,-2/9*A*sqrt(b*x+c*x^2)/(b*x^5)-2/63*(9*b*B-8*A*c)*sqrt(b*x+c*x^2)/(b^2*x^4)+4/105*c*(9*b*B-8*A*c)*sqrt(b*x+c*x^2)/(b^3*x^3)-16/315*c^2*(9*b*B-8*A*c)*sqrt(b*x+c*x^2)/(b^4*x^2)+32/315*c^3*(9*b*B-8*A*c)*sqrt(b*x+c*x^2)/(b^5*x)],
[(A+B*x)/(x^6*sqrt(b*x+c*x^2)),x,6,-2/11*A*sqrt(b*x+c*x^2)/(b*x^6)-2/99*(11*b*B-10*A*c)*sqrt(b*x+c*x^2)/(b^2*x^5)+16/693*c*(11*b*B-10*A*c)*sqrt(b*x+c*x^2)/(b^3*x^4)-32/1155*c^2*(11*b*B-10*A*c)*sqrt(b*x+c*x^2)/(b^4*x^3)+128/3465*c^3*(11*b*B-10*A*c)*sqrt(b*x+c*x^2)/(b^5*x^2)-256/3465*c^4*(11*b*B-10*A*c)*sqrt(b*x+c*x^2)/(b^6*x)],
[x^4*(A+B*x)/(b*x+c*x^2)^(3/2),x,6,-5/8*b^2*(7*b*B-6*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-2*(b*B-A*c)*x^4/(b*c*sqrt(b*x+c*x^2))+5/8*b*(7*b*B-6*A*c)*sqrt(b*x+c*x^2)/c^4-5/12*(7*b*B-6*A*c)*x*sqrt(b*x+c*x^2)/c^3+1/3*(7*b*B-6*A*c)*x^2*sqrt(b*x+c*x^2)/(b*c^2)],
[x^3*(A+B*x)/(b*x+c*x^2)^(3/2),x,5,3/4*b*(5*b*B-4*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-2*(b*B-A*c)*x^3/(b*c*sqrt(b*x+c*x^2))-3/4*(5*b*B-4*A*c)*sqrt(b*x+c*x^2)/c^3+1/2*(5*b*B-4*A*c)*x*sqrt(b*x+c*x^2)/(b*c^2)],
[x^2*(A+B*x)/(b*x+c*x^2)^(3/2),x,4,-(3*b*B-2*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-2*(b*B-A*c)*x^2/(b*c*sqrt(b*x+c*x^2))+(3*b*B-2*A*c)*sqrt(b*x+c*x^2)/(b*c^2)],
[x*(A+B*x)/(b*x+c*x^2)^(3/2),x,3,2*B*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)-2*(b*B-A*c)*x/(b*c*sqrt(b*x+c*x^2))],
[(A+B*x)/(b*x+c*x^2)^(3/2),x,1,-2*(A*b-(b*B-2*A*c)*x)/(b^2*sqrt(b*x+c*x^2))],
[(A+B*x)/(x*(b*x+c*x^2)^(3/2)),x,2,-2/3*A/(b*x*sqrt(b*x+c*x^2))-2/3*(3*b*B-4*A*c)*(b+2*c*x)/(b^3*sqrt(b*x+c*x^2))],
[(A+B*x)/(x^2*(b*x+c*x^2)^(3/2)),x,3,-2/5*A/(b*x^2*sqrt(b*x+c*x^2))-2/15*(5*b*B-6*A*c)/(b^2*x*sqrt(b*x+c*x^2))+8/15*c*(5*b*B-6*A*c)*(b+2*c*x)/(b^4*sqrt(b*x+c*x^2))],
[(A+B*x)/(x^3*(b*x+c*x^2)^(3/2)),x,4,-2/7*A/(b*x^3*sqrt(b*x+c*x^2))-2/35*(7*b*B-8*A*c)/(b^2*x^2*sqrt(b*x+c*x^2))+4/35*c*(7*b*B-8*A*c)/(b^3*x*sqrt(b*x+c*x^2))-16/35*c^2*(7*b*B-8*A*c)*(b+2*c*x)/(b^5*sqrt(b*x+c*x^2))],
[(A+B*x)/(x^4*(b*x+c*x^2)^(3/2)),x,5,-2/9*A/(b*x^4*sqrt(b*x+c*x^2))-2/63*(9*b*B-10*A*c)/(b^2*x^3*sqrt(b*x+c*x^2))+16/315*c*(9*b*B-10*A*c)/(b^3*x^2*sqrt(b*x+c*x^2))-32/315*c^2*(9*b*B-10*A*c)/(b^4*x*sqrt(b*x+c*x^2))+128/315*c^3*(9*b*B-10*A*c)*(b+2*c*x)/(b^6*sqrt(b*x+c*x^2))],
[x^5*(A+B*x)/(b*x+c*x^2)^(5/2),x,6,-2/3*(b*B-A*c)*x^5/(b*c*(b*x+c*x^2)^(3/2))+5/4*b*(7*b*B-4*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-2/3*(7*b*B-4*A*c)*x^3/(b*c^2*sqrt(b*x+c*x^2))-5/4*(7*b*B-4*A*c)*sqrt(b*x+c*x^2)/c^4+5/6*(7*b*B-4*A*c)*x*sqrt(b*x+c*x^2)/(b*c^3)],
[x^4*(A+B*x)/(b*x+c*x^2)^(5/2),x,5,-2/3*(b*B-A*c)*x^4/(b*c*(b*x+c*x^2)^(3/2))-(5*b*B-2*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-2/3*(5*b*B-2*A*c)*x^2/(b*c^2*sqrt(b*x+c*x^2))+(5*b*B-2*A*c)*sqrt(b*x+c*x^2)/(b*c^3)],
[x^3*(A+B*x)/(b*x+c*x^2)^(5/2),x,4,-2/3*(b*B-A*c)*x^3/(b*c*(b*x+c*x^2)^(3/2))+2*B*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-2*B*x/(c^2*sqrt(b*x+c*x^2))],
[x^2*(A+B*x)/(b*x+c*x^2)^(5/2),x,2,-2/3*(b*B-A*c)*x^2/(b*c*(b*x+c*x^2)^(3/2))+2/3*(b*B+2*A*c)*x/(b^2*c*sqrt(b*x+c*x^2))],
[x*(A+B*x)/(b*x+c*x^2)^(5/2),x,2,-2/3*(b*B-A*c)*x/(b*c*(b*x+c*x^2)^(3/2))+2/3*(b*B-4*A*c)*(b+2*c*x)/(b^3*c*sqrt(b*x+c*x^2))],
[(A+B*x)/(b*x+c*x^2)^(5/2),x,2,-2/3*(A*b-(b*B-2*A*c)*x)/(b^2*(b*x+c*x^2)^(3/2))-8/3*(b*B-2*A*c)*(b+2*c*x)/(b^4*sqrt(b*x+c*x^2))],
[(A+B*x)/(x*(b*x+c*x^2)^(5/2)),x,3,-2/5*A/(b*x*(b*x+c*x^2)^(3/2))-2/15*(5*b*B-8*A*c)*(b+2*c*x)/(b^3*(b*x+c*x^2)^(3/2))+16/15*c*(5*b*B-8*A*c)*(b+2*c*x)/(b^5*sqrt(b*x+c*x^2))],
[(A+B*x)/(x^2*(b*x+c*x^2)^(5/2)),x,4,-2/7*A/(b*x^2*(b*x+c*x^2)^(3/2))-2/35*(7*b*B-10*A*c)/(b^2*x*(b*x+c*x^2)^(3/2))+16/105*c*(7*b*B-10*A*c)*(b+2*c*x)/(b^4*(b*x+c*x^2)^(3/2))-128/105*c^2*(7*b*B-10*A*c)*(b+2*c*x)/(b^6*sqrt(b*x+c*x^2))],
[(A+B*x)/(x^3*(b*x+c*x^2)^(5/2)),x,5,-2/9*A/(b*x^3*(b*x+c*x^2)^(3/2))-2/21*(3*b*B-4*A*c)/(b^2*x^2*(b*x+c*x^2)^(3/2))+4/21*c*(3*b*B-4*A*c)/(b^3*x*(b*x+c*x^2)^(3/2))-32/63*c^2*(3*b*B-4*A*c)*(b+2*c*x)/(b^5*(b*x+c*x^2)^(3/2))+256/63*c^3*(3*b*B-4*A*c)*(b+2*c*x)/(b^7*sqrt(b*x+c*x^2))],
[(d+e*x)/(b*x+c*x^2)^(7/2),x,3,-2/5*(b*d+(2*c*d-b*e)*x)/(b^2*(b*x+c*x^2)^(5/2))+16/15*(2*c*d-b*e)*(b+2*c*x)/(b^4*(b*x+c*x^2)^(3/2))-128/15*c*(2*c*d-b*e)*(b+2*c*x)/(b^6*sqrt(b*x+c*x^2))],
[(d+e*x)/(b*x+c*x^2)^(9/2),x,4,-2/7*(b*d+(2*c*d-b*e)*x)/(b^2*(b*x+c*x^2)^(7/2))+24/35*(2*c*d-b*e)*(b+2*c*x)/(b^4*(b*x+c*x^2)^(5/2))-128/35*c*(2*c*d-b*e)*(b+2*c*x)/(b^6*(b*x+c*x^2)^(3/2))+1024/35*c^2*(2*c*d-b*e)*(b+2*c*x)/(b^8*sqrt(b*x+c*x^2))],

# Integrands of the form (e x)^(m/2) (A+B x) (b x+c x^2)^p

# p>0
[x^(7/2)*(A+B*x)*(b*x+c*x^2),x,2,2/11*A*b*x^(11/2)+2/13*(b*B+A*c)*x^(13/2)+2/15*B*c*x^(15/2)],
[x^(5/2)*(A+B*x)*(b*x+c*x^2),x,2,2/9*A*b*x^(9/2)+2/11*(b*B+A*c)*x^(11/2)+2/13*B*c*x^(13/2)],
[x^(3/2)*(A+B*x)*(b*x+c*x^2),x,2,2/7*A*b*x^(7/2)+2/9*(b*B+A*c)*x^(9/2)+2/11*B*c*x^(11/2)],
[(A+B*x)*(b*x+c*x^2)*sqrt(x),x,2,2/5*A*b*x^(5/2)+2/7*(b*B+A*c)*x^(7/2)+2/9*B*c*x^(9/2)],
[(A+B*x)*(b*x+c*x^2)/sqrt(x),x,2,2/3*A*b*x^(3/2)+2/5*(b*B+A*c)*x^(5/2)+2/7*B*c*x^(7/2)],
[(A+B*x)*(b*x+c*x^2)/x^(3/2),x,2,2/3*(b*B+A*c)*x^(3/2)+2/5*B*c*x^(5/2)+2*A*b*sqrt(x)],
[(A+B*x)*(b*x+c*x^2)/x^(5/2),x,2,2/3*B*c*x^(3/2)-2*A*b/sqrt(x)+2*(b*B+A*c)*sqrt(x)],
[(A+B*x)*(b*x+c*x^2)/x^(7/2),x,2,-2/3*A*b/x^(3/2)-2*(b*B+A*c)/sqrt(x)+2*B*c*sqrt(x)],
[(A+B*x)*(b*x+c*x^2)/x^(9/2),x,2,-2/5*A*b/x^(5/2)-2/3*(b*B+A*c)/x^(3/2)-2*B*c/sqrt(x)],
[x^(7/2)*(A+B*x)*(b*x+c*x^2)^2,x,2,2/13*A*b^2*x^(13/2)+2/15*b*(b*B+2*A*c)*x^(15/2)+2/17*c*(2*b*B+A*c)*x^(17/2)+2/19*B*c^2*x^(19/2)],
[x^(5/2)*(A+B*x)*(b*x+c*x^2)^2,x,2,2/11*A*b^2*x^(11/2)+2/13*b*(b*B+2*A*c)*x^(13/2)+2/15*c*(2*b*B+A*c)*x^(15/2)+2/17*B*c^2*x^(17/2)],
[x^(3/2)*(A+B*x)*(b*x+c*x^2)^2,x,2,2/9*A*b^2*x^(9/2)+2/11*b*(b*B+2*A*c)*x^(11/2)+2/13*c*(2*b*B+A*c)*x^(13/2)+2/15*B*c^2*x^(15/2)],
[(A+B*x)*(b*x+c*x^2)^2*sqrt(x),x,2,2/7*A*b^2*x^(7/2)+2/9*b*(b*B+2*A*c)*x^(9/2)+2/11*c*(2*b*B+A*c)*x^(11/2)+2/13*B*c^2*x^(13/2)],
[(A+B*x)*(b*x+c*x^2)^2/sqrt(x),x,2,2/5*A*b^2*x^(5/2)+2/7*b*(b*B+2*A*c)*x^(7/2)+2/9*c*(2*b*B+A*c)*x^(9/2)+2/11*B*c^2*x^(11/2)],
[(A+B*x)*(b*x+c*x^2)^2/x^(3/2),x,2,2/3*A*b^2*x^(3/2)+2/5*b*(b*B+2*A*c)*x^(5/2)+2/7*c*(2*b*B+A*c)*x^(7/2)+2/9*B*c^2*x^(9/2)],
[(A+B*x)*(b*x+c*x^2)^2/x^(5/2),x,2,2/3*b*(b*B+2*A*c)*x^(3/2)+2/5*c*(2*b*B+A*c)*x^(5/2)+2/7*B*c^2*x^(7/2)+2*A*b^2*sqrt(x)],
[(A+B*x)*(b*x+c*x^2)^2/x^(7/2),x,2,2/3*c*(2*b*B+A*c)*x^(3/2)+2/5*B*c^2*x^(5/2)-2*A*b^2/sqrt(x)+2*b*(b*B+2*A*c)*sqrt(x)],
[(A+B*x)*(b*x+c*x^2)^2/x^(9/2),x,2,-2/3*A*b^2/x^(3/2)+2/3*B*c^2*x^(3/2)-2*b*(b*B+2*A*c)/sqrt(x)+2*c*(2*b*B+A*c)*sqrt(x)],
[x^(7/2)*(A+B*x)*(b*x+c*x^2)^3,x,2,2/15*A*b^3*x^(15/2)+2/17*b^2*(b*B+3*A*c)*x^(17/2)+6/19*b*c*(b*B+A*c)*x^(19/2)+2/21*c^2*(3*b*B+A*c)*x^(21/2)+2/23*B*c^3*x^(23/2)],
[x^(5/2)*(A+B*x)*(b*x+c*x^2)^3,x,2,2/13*A*b^3*x^(13/2)+2/15*b^2*(b*B+3*A*c)*x^(15/2)+6/17*b*c*(b*B+A*c)*x^(17/2)+2/19*c^2*(3*b*B+A*c)*x^(19/2)+2/21*B*c^3*x^(21/2)],
[x^(3/2)*(A+B*x)*(b*x+c*x^2)^3,x,2,2/11*A*b^3*x^(11/2)+2/13*b^2*(b*B+3*A*c)*x^(13/2)+2/5*b*c*(b*B+A*c)*x^(15/2)+2/17*c^2*(3*b*B+A*c)*x^(17/2)+2/19*B*c^3*x^(19/2)],
[(A+B*x)*(b*x+c*x^2)^3*sqrt(x),x,2,2/9*A*b^3*x^(9/2)+2/11*b^2*(b*B+3*A*c)*x^(11/2)+6/13*b*c*(b*B+A*c)*x^(13/2)+2/15*c^2*(3*b*B+A*c)*x^(15/2)+2/17*B*c^3*x^(17/2)],
[(A+B*x)*(b*x+c*x^2)^3/sqrt(x),x,2,2/7*A*b^3*x^(7/2)+2/9*b^2*(b*B+3*A*c)*x^(9/2)+6/11*b*c*(b*B+A*c)*x^(11/2)+2/13*c^2*(3*b*B+A*c)*x^(13/2)+2/15*B*c^3*x^(15/2)],
[(A+B*x)*(b*x+c*x^2)^3/x^(3/2),x,2,2/5*A*b^3*x^(5/2)+2/7*b^2*(b*B+3*A*c)*x^(7/2)+2/3*b*c*(b*B+A*c)*x^(9/2)+2/11*c^2*(3*b*B+A*c)*x^(11/2)+2/13*B*c^3*x^(13/2)],
[(A+B*x)*(b*x+c*x^2)^3/x^(5/2),x,2,2/3*A*b^3*x^(3/2)+2/5*b^2*(b*B+3*A*c)*x^(5/2)+6/7*b*c*(b*B+A*c)*x^(7/2)+2/9*c^2*(3*b*B+A*c)*x^(9/2)+2/11*B*c^3*x^(11/2)],
[(A+B*x)*(b*x+c*x^2)^3/x^(7/2),x,2,2/3*b^2*(b*B+3*A*c)*x^(3/2)+6/5*b*c*(b*B+A*c)*x^(5/2)+2/7*c^2*(3*b*B+A*c)*x^(7/2)+2/9*B*c^3*x^(9/2)+2*A*b^3*sqrt(x)],
[(A+B*x)*(b*x+c*x^2)^3/x^(9/2),x,2,2*b*c*(b*B+A*c)*x^(3/2)+2/5*c^2*(3*b*B+A*c)*x^(5/2)+2/7*B*c^3*x^(7/2)-2*A*b^3/sqrt(x)+2*b^2*(b*B+3*A*c)*sqrt(x)],
[(A+B*x)*(b*x+c*x^2)^3/x^(11/2),x,2,-2/3*A*b^3/x^(3/2)+2/3*c^2*(3*b*B+A*c)*x^(3/2)+2/5*B*c^3*x^(5/2)-2*b^2*(b*B+3*A*c)/sqrt(x)+6*b*c*(b*B+A*c)*sqrt(x)],

# p<0
[x^(7/2)*(A+B*x)/(b*x+c*x^2),x,7,2/3*b*(b*B-A*c)*x^(3/2)/c^3-2/5*(b*B-A*c)*x^(5/2)/c^2+2/7*B*x^(7/2)/c+2*b^(5/2)*(b*B-A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/c^(9/2)-2*b^2*(b*B-A*c)*sqrt(x)/c^4],
[x^(5/2)*(A+B*x)/(b*x+c*x^2),x,6,-2/3*(b*B-A*c)*x^(3/2)/c^2+2/5*B*x^(5/2)/c-2*b^(3/2)*(b*B-A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/c^(7/2)+2*b*(b*B-A*c)*sqrt(x)/c^3],
[x^(3/2)*(A+B*x)/(b*x+c*x^2),x,5,2/3*B*x^(3/2)/c+2*(b*B-A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))*sqrt(b)/c^(5/2)-2*(b*B-A*c)*sqrt(x)/c^2],
[(A+B*x)*sqrt(x)/(b*x+c*x^2),x,4,-2*(b*B-A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/(c^(3/2)*sqrt(b))+2*B*sqrt(x)/c],
[(A+B*x)/((b*x+c*x^2)*sqrt(x)),x,4,2*(b*B-A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/(b^(3/2)*sqrt(c))-2*A/(b*sqrt(x))],
[(A+B*x)/(x^(3/2)*(b*x+c*x^2)),x,5,-2/3*A/(b*x^(3/2))-2*(b*B-A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))*sqrt(c)/b^(5/2)-2*(b*B-A*c)/(b^2*sqrt(x))],
[(A+B*x)/(x^(5/2)*(b*x+c*x^2)),x,6,-2/5*A/(b*x^(5/2))-2/3*(b*B-A*c)/(b^2*x^(3/2))+2*c^(3/2)*(b*B-A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/b^(7/2)+2*c*(b*B-A*c)/(b^3*sqrt(x))],
[(A+B*x)/(x^(7/2)*(b*x+c*x^2)),x,7,-2/7*A/(b*x^(7/2))-2/5*(b*B-A*c)/(b^2*x^(5/2))+2/3*c*(b*B-A*c)/(b^3*x^(3/2))-2*c^(5/2)*(b*B-A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/b^(9/2)-2*c^2*(b*B-A*c)/(b^4*sqrt(x))],
[(A+B*x)/(x^(9/2)*(b*x+c*x^2)),x,8,-2/9*A/(b*x^(9/2))-2/7*(b*B-A*c)/(b^2*x^(7/2))+2/5*c*(b*B-A*c)/(b^3*x^(5/2))-2/3*c^2*(b*B-A*c)/(b^4*x^(3/2))+2*c^(7/2)*(b*B-A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/b^(11/2)+2*c^3*(b*B-A*c)/(b^5*sqrt(x))],
[x^(9/2)*(A+B*x)/(b*x+c*x^2)^2,x,7,-1/3*(7*b*B-5*A*c)*x^(3/2)/c^3+1/5*(7*b*B-5*A*c)*x^(5/2)/(b*c^2)-(b*B-A*c)*x^(7/2)/(b*c*(b+c*x))-b^(3/2)*(7*b*B-5*A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/c^(9/2)+b*(7*b*B-5*A*c)*sqrt(x)/c^4],
[x^(7/2)*(A+B*x)/(b*x+c*x^2)^2,x,6,1/3*(5*b*B-3*A*c)*x^(3/2)/(b*c^2)-(b*B-A*c)*x^(5/2)/(b*c*(b+c*x))+(5*b*B-3*A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))*sqrt(b)/c^(7/2)-(5*b*B-3*A*c)*sqrt(x)/c^3],
[x^(5/2)*(A+B*x)/(b*x+c*x^2)^2,x,5,-(b*B-A*c)*x^(3/2)/(b*c*(b+c*x))-(3*b*B-A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/(c^(5/2)*sqrt(b))+(3*b*B-A*c)*sqrt(x)/(b*c^2)],
[x^(3/2)*(A+B*x)/(b*x+c*x^2)^2,x,4,(b*B+A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/(b^(3/2)*c^(3/2))-(b*B-A*c)*sqrt(x)/(b*c*(b+c*x))],
[(A+B*x)*sqrt(x)/(b*x+c*x^2)^2,x,5,(b*B-3*A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/(b^(5/2)*sqrt(c))+(b*B-3*A*c)/(b^2*c*sqrt(x))+(-b*B+A*c)/(b*c*(b+c*x)*sqrt(x))],
[(A+B*x)/((b*x+c*x^2)^2*sqrt(x)),x,6,1/3*(3*b*B-5*A*c)/(b^2*c*x^(3/2))+(-b*B+A*c)/(b*c*x^(3/2)*(b+c*x))-(3*b*B-5*A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))*sqrt(c)/b^(7/2)+(-3*b*B+5*A*c)/(b^3*sqrt(x))],
[(A+B*x)/(x^(3/2)*(b*x+c*x^2)^2),x,7,1/5*(5*b*B-7*A*c)/(b^2*c*x^(5/2))+1/3*(-5*b*B+7*A*c)/(b^3*x^(3/2))+(-b*B+A*c)/(b*c*x^(5/2)*(b+c*x))+c^(3/2)*(5*b*B-7*A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/b^(9/2)+c*(5*b*B-7*A*c)/(b^4*sqrt(x))],
[(A+B*x)/(x^(5/2)*(b*x+c*x^2)^2),x,8,1/7*(7*b*B-9*A*c)/(b^2*c*x^(7/2))+1/5*(-7*b*B+9*A*c)/(b^3*x^(5/2))+1/3*c*(7*b*B-9*A*c)/(b^4*x^(3/2))+(-b*B+A*c)/(b*c*x^(7/2)*(b+c*x))-c^(5/2)*(7*b*B-9*A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/b^(11/2)-c^2*(7*b*B-9*A*c)/(b^5*sqrt(x))],
[x^(13/2)*(A+B*x)/(b*x+c*x^2)^3,x,8,-7/12*(9*b*B-5*A*c)*x^(3/2)/c^4+7/20*(9*b*B-5*A*c)*x^(5/2)/(b*c^3)-1/2*(b*B-A*c)*x^(9/2)/(b*c*(b+c*x)^2)-1/4*(9*b*B-5*A*c)*x^(7/2)/(b*c^2*(b+c*x))-7/4*b^(3/2)*(9*b*B-5*A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/c^(11/2)+7/4*b*(9*b*B-5*A*c)*sqrt(x)/c^5],
[x^(11/2)*(A+B*x)/(b*x+c*x^2)^3,x,7,5/12*(7*b*B-3*A*c)*x^(3/2)/(b*c^3)-1/2*(b*B-A*c)*x^(7/2)/(b*c*(b+c*x)^2)-1/4*(7*b*B-3*A*c)*x^(5/2)/(b*c^2*(b+c*x))+5/4*(7*b*B-3*A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))*sqrt(b)/c^(9/2)-5/4*(7*b*B-3*A*c)*sqrt(x)/c^4],
[x^(9/2)*(A+B*x)/(b*x+c*x^2)^3,x,6,-1/2*(b*B-A*c)*x^(5/2)/(b*c*(b+c*x)^2)-1/4*(5*b*B-A*c)*x^(3/2)/(b*c^2*(b+c*x))-3/4*(5*b*B-A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/(c^(7/2)*sqrt(b))+3/4*(5*b*B-A*c)*sqrt(x)/(b*c^3)],
[x^(7/2)*(A+B*x)/(b*x+c*x^2)^3,x,5,-1/2*(b*B-A*c)*x^(3/2)/(b*c*(b+c*x)^2)+1/4*(3*b*B+A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/(b^(3/2)*c^(5/2))-1/4*(3*b*B+A*c)*sqrt(x)/(b*c^2*(b+c*x))],
[x^(5/2)*(A+B*x)/(b*x+c*x^2)^3,x,5,1/4*(b*B+3*A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/(b^(5/2)*c^(3/2))-1/2*(b*B-A*c)*sqrt(x)/(b*c*(b+c*x)^2)+1/4*(b*B+3*A*c)*sqrt(x)/(b^2*c*(b+c*x))],
[x^(3/2)*(A+B*x)/(b*x+c*x^2)^3,x,6,3/4*(b*B-5*A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/(b^(7/2)*sqrt(c))+3/4*(b*B-5*A*c)/(b^3*c*sqrt(x))+1/2*(-b*B+A*c)/(b*c*(b+c*x)^2*sqrt(x))+1/4*(-b*B+5*A*c)/(b^2*c*(b+c*x)*sqrt(x))],
[(A+B*x)*sqrt(x)/(b*x+c*x^2)^3,x,7,5/12*(3*b*B-7*A*c)/(b^3*c*x^(3/2))+1/2*(-b*B+A*c)/(b*c*x^(3/2)*(b+c*x)^2)+1/4*(-3*b*B+7*A*c)/(b^2*c*x^(3/2)*(b+c*x))-5/4*(3*b*B-7*A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))*sqrt(c)/b^(9/2)-5/4*(3*b*B-7*A*c)/(b^4*sqrt(x))],
[(A+B*x)/((b*x+c*x^2)^3*sqrt(x)),x,8,7/20*(5*b*B-9*A*c)/(b^3*c*x^(5/2))-7/12*(5*b*B-9*A*c)/(b^4*x^(3/2))+1/2*(-b*B+A*c)/(b*c*x^(5/2)*(b+c*x)^2)+1/4*(-5*b*B+9*A*c)/(b^2*c*x^(5/2)*(b+c*x))+7/4*c^(3/2)*(5*b*B-9*A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/b^(11/2)+7/4*c*(5*b*B-9*A*c)/(b^5*sqrt(x))],
[(A+B*x)/(x^(3/2)*(b*x+c*x^2)^3),x,9,9/28*(7*b*B-11*A*c)/(b^3*c*x^(7/2))-9/20*(7*b*B-11*A*c)/(b^4*x^(5/2))+3/4*c*(7*b*B-11*A*c)/(b^5*x^(3/2))+1/2*(-b*B+A*c)/(b*c*x^(7/2)*(b+c*x)^2)+1/4*(-7*b*B+11*A*c)/(b^2*c*x^(7/2)*(b+c*x))-9/4*c^(5/2)*(7*b*B-11*A*c)*arctan(sqrt(c)*sqrt(x)/sqrt(b))/b^(13/2)-9/4*c^2*(7*b*B-11*A*c)/(b^6*sqrt(x))],

# Integrands of the form (e x)^(m/2) (A+B x) (b x+c x^2)^(p/2)

# p>0
[x^(7/2)*(A+B*x)*sqrt(b*x+c*x^2),x,6,-256/45045*b^4*(10*b*B-13*A*c)*(b*x+c*x^2)^(3/2)/(c^6*x^(3/2))+16/1287*b*(10*b*B-13*A*c)*x^(3/2)*(b*x+c*x^2)^(3/2)/c^3-2/143*(10*b*B-13*A*c)*x^(5/2)*(b*x+c*x^2)^(3/2)/c^2+2/13*B*x^(7/2)*(b*x+c*x^2)^(3/2)/c+128/15015*b^3*(10*b*B-13*A*c)*(b*x+c*x^2)^(3/2)/(c^5*sqrt(x))-32/3003*b^2*(10*b*B-13*A*c)*(b*x+c*x^2)^(3/2)*sqrt(x)/c^4],
[x^(5/2)*(A+B*x)*sqrt(b*x+c*x^2),x,5,32/3465*b^3*(8*b*B-11*A*c)*(b*x+c*x^2)^(3/2)/(c^5*x^(3/2))-2/99*(8*b*B-11*A*c)*x^(3/2)*(b*x+c*x^2)^(3/2)/c^2+2/11*B*x^(5/2)*(b*x+c*x^2)^(3/2)/c-16/1155*b^2*(8*b*B-11*A*c)*(b*x+c*x^2)^(3/2)/(c^4*sqrt(x))+4/231*b*(8*b*B-11*A*c)*(b*x+c*x^2)^(3/2)*sqrt(x)/c^3],
[x^(3/2)*(A+B*x)*sqrt(b*x+c*x^2),x,4,-16/315*b^2*(2*b*B-3*A*c)*(b*x+c*x^2)^(3/2)/(c^4*x^(3/2))+2/9*B*x^(3/2)*(b*x+c*x^2)^(3/2)/c+8/105*b*(2*b*B-3*A*c)*(b*x+c*x^2)^(3/2)/(c^3*sqrt(x))-2/21*(2*b*B-3*A*c)*(b*x+c*x^2)^(3/2)*sqrt(x)/c^2],
[(A+B*x)*sqrt(x)*sqrt(b*x+c*x^2),x,3,4/105*b*(4*b*B-7*A*c)*(b*x+c*x^2)^(3/2)/(c^3*x^(3/2))-2/35*(4*b*B-7*A*c)*(b*x+c*x^2)^(3/2)/(c^2*sqrt(x))+2/7*B*(b*x+c*x^2)^(3/2)*sqrt(x)/c],
[(A+B*x)*sqrt(b*x+c*x^2)/sqrt(x),x,2,-2/15*(2*b*B-5*A*c)*(b*x+c*x^2)^(3/2)/(c^2*x^(3/2))+2/5*B*(b*x+c*x^2)^(3/2)/(c*sqrt(x))],
[(A+B*x)*sqrt(b*x+c*x^2)/x^(3/2),x,4,2/3*B*(b*x+c*x^2)^(3/2)/(c*x^(3/2))-2*A*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))*sqrt(b)+2*A*sqrt(b*x+c*x^2)/sqrt(x)],
[(A+B*x)*sqrt(b*x+c*x^2)/x^(5/2),x,4,-A*(b*x+c*x^2)^(3/2)/(b*x^(5/2))-(2*b*B+A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/sqrt(b)+(2*b*B+A*c)*sqrt(b*x+c*x^2)/(b*sqrt(x))],
[(A+B*x)*sqrt(b*x+c*x^2)/x^(7/2),x,4,-1/2*A*(b*x+c*x^2)^(3/2)/(b*x^(7/2))-1/4*c*(4*b*B-A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(3/2)-1/4*(4*b*B-A*c)*sqrt(b*x+c*x^2)/(b*x^(3/2))],
[(A+B*x)*sqrt(b*x+c*x^2)/x^(9/2),x,5,-1/3*A*(b*x+c*x^2)^(3/2)/(b*x^(9/2))+1/8*c^2*(2*b*B-A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(5/2)-1/4*(2*b*B-A*c)*sqrt(b*x+c*x^2)/(b*x^(5/2))-1/8*c*(2*b*B-A*c)*sqrt(b*x+c*x^2)/(b^2*x^(3/2))],
[x^(5/2)*(A+B*x)*(b*x+c*x^2)^(3/2),x,6,-256/45045*b^4*(2*b*B-3*A*c)*(b*x+c*x^2)^(5/2)/(c^6*x^(5/2))+128/9009*b^3*(2*b*B-3*A*c)*(b*x+c*x^2)^(5/2)/(c^5*x^(3/2))-2/39*(2*b*B-3*A*c)*x^(3/2)*(b*x+c*x^2)^(5/2)/c^2+2/15*B*x^(5/2)*(b*x+c*x^2)^(5/2)/c-32/1287*b^2*(2*b*B-3*A*c)*(b*x+c*x^2)^(5/2)/(c^4*sqrt(x))+16/429*b*(2*b*B-3*A*c)*(b*x+c*x^2)^(5/2)*sqrt(x)/c^3],
[x^(3/2)*(A+B*x)*(b*x+c*x^2)^(3/2),x,5,32/15015*b^3*(8*b*B-13*A*c)*(b*x+c*x^2)^(5/2)/(c^5*x^(5/2))-16/3003*b^2*(8*b*B-13*A*c)*(b*x+c*x^2)^(5/2)/(c^4*x^(3/2))+2/13*B*x^(3/2)*(b*x+c*x^2)^(5/2)/c+4/429*b*(8*b*B-13*A*c)*(b*x+c*x^2)^(5/2)/(c^3*sqrt(x))-2/143*(8*b*B-13*A*c)*(b*x+c*x^2)^(5/2)*sqrt(x)/c^2],
[(A+B*x)*(b*x+c*x^2)^(3/2)*sqrt(x),x,4,-16/3465*b^2*(6*b*B-11*A*c)*(b*x+c*x^2)^(5/2)/(c^4*x^(5/2))+8/693*b*(6*b*B-11*A*c)*(b*x+c*x^2)^(5/2)/(c^3*x^(3/2))-2/99*(6*b*B-11*A*c)*(b*x+c*x^2)^(5/2)/(c^2*sqrt(x))+2/11*B*(b*x+c*x^2)^(5/2)*sqrt(x)/c],
[(A+B*x)*(b*x+c*x^2)^(3/2)/sqrt(x),x,3,4/315*b*(4*b*B-9*A*c)*(b*x+c*x^2)^(5/2)/(c^3*x^(5/2))-2/63*(4*b*B-9*A*c)*(b*x+c*x^2)^(5/2)/(c^2*x^(3/2))+2/9*B*(b*x+c*x^2)^(5/2)/(c*sqrt(x))],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^(3/2),x,2,-2/35*(2*b*B-7*A*c)*(b*x+c*x^2)^(5/2)/(c^2*x^(5/2))+2/7*B*(b*x+c*x^2)^(5/2)/(c*x^(3/2))],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^(5/2),x,5,2/3*A*(b*x+c*x^2)^(3/2)/x^(3/2)+2/5*B*(b*x+c*x^2)^(5/2)/(c*x^(5/2))-2*A*b^(3/2)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))+2*A*b*sqrt(b*x+c*x^2)/sqrt(x)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^(7/2),x,5,1/3*(2*b*B+3*A*c)*(b*x+c*x^2)^(3/2)/(b*x^(3/2))-A*(b*x+c*x^2)^(5/2)/(b*x^(7/2))-(2*b*B+3*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))*sqrt(b)+(2*b*B+3*A*c)*sqrt(b*x+c*x^2)/sqrt(x)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^(9/2),x,5,-1/4*(4*b*B+A*c)*(b*x+c*x^2)^(3/2)/(b*x^(5/2))-1/2*A*(b*x+c*x^2)^(5/2)/(b*x^(9/2))-3/4*c*(4*b*B+A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/sqrt(b)+3/4*c*(4*b*B+A*c)*sqrt(b*x+c*x^2)/(b*sqrt(x))],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^(11/2),x,5,-1/12*(6*b*B-A*c)*(b*x+c*x^2)^(3/2)/(b*x^(7/2))-1/3*A*(b*x+c*x^2)^(5/2)/(b*x^(11/2))-1/8*c^2*(6*b*B-A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(3/2)-1/8*c*(6*b*B-A*c)*sqrt(b*x+c*x^2)/(b*x^(3/2))],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^(13/2),x,6,-1/24*(8*b*B-3*A*c)*(b*x+c*x^2)^(3/2)/(b*x^(9/2))-1/4*A*(b*x+c*x^2)^(5/2)/(b*x^(13/2))+1/64*c^3*(8*b*B-3*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(5/2)-1/32*c*(8*b*B-3*A*c)*sqrt(b*x+c*x^2)/(b*x^(5/2))-1/64*c^2*(8*b*B-3*A*c)*sqrt(b*x+c*x^2)/(b^2*x^(3/2))],
[(A+B*x)*(b*x+c*x^2)^(3/2)/x^(15/2),x,7,-1/8*(2*b*B-A*c)*(b*x+c*x^2)^(3/2)/(b*x^(11/2))-1/5*A*(b*x+c*x^2)^(5/2)/(b*x^(15/2))-3/128*c^4*(2*b*B-A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(7/2)-1/16*c*(2*b*B-A*c)*sqrt(b*x+c*x^2)/(b*x^(7/2))-1/64*c^2*(2*b*B-A*c)*sqrt(b*x+c*x^2)/(b^2*x^(5/2))+3/128*c^3*(2*b*B-A*c)*sqrt(b*x+c*x^2)/(b^3*x^(3/2))],
[x^(3/2)*(A+B*x)*(b*x+c*x^2)^(5/2),x,6,-256/765765*b^4*(10*b*B-17*A*c)*(b*x+c*x^2)^(7/2)/(c^6*x^(7/2))+128/109395*b^3*(10*b*B-17*A*c)*(b*x+c*x^2)^(7/2)/(c^5*x^(5/2))-32/12155*b^2*(10*b*B-17*A*c)*(b*x+c*x^2)^(7/2)/(c^4*x^(3/2))+2/17*B*x^(3/2)*(b*x+c*x^2)^(7/2)/c+16/3315*b*(10*b*B-17*A*c)*(b*x+c*x^2)^(7/2)/(c^3*sqrt(x))-2/255*(10*b*B-17*A*c)*(b*x+c*x^2)^(7/2)*sqrt(x)/c^2],
[(A+B*x)*(b*x+c*x^2)^(5/2)*sqrt(x),x,5,32/45045*b^3*(8*b*B-15*A*c)*(b*x+c*x^2)^(7/2)/(c^5*x^(7/2))-16/6435*b^2*(8*b*B-15*A*c)*(b*x+c*x^2)^(7/2)/(c^4*x^(5/2))+4/715*b*(8*b*B-15*A*c)*(b*x+c*x^2)^(7/2)/(c^3*x^(3/2))-2/195*(8*b*B-15*A*c)*(b*x+c*x^2)^(7/2)/(c^2*sqrt(x))+2/15*B*(b*x+c*x^2)^(7/2)*sqrt(x)/c],
[(A+B*x)*(b*x+c*x^2)^(5/2)/sqrt(x),x,4,-16/9009*b^2*(6*b*B-13*A*c)*(b*x+c*x^2)^(7/2)/(c^4*x^(7/2))+8/1287*b*(6*b*B-13*A*c)*(b*x+c*x^2)^(7/2)/(c^3*x^(5/2))-2/143*(6*b*B-13*A*c)*(b*x+c*x^2)^(7/2)/(c^2*x^(3/2))+2/13*B*(b*x+c*x^2)^(7/2)/(c*sqrt(x))],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^(3/2),x,3,4/693*b*(4*b*B-11*A*c)*(b*x+c*x^2)^(7/2)/(c^3*x^(7/2))-2/99*(4*b*B-11*A*c)*(b*x+c*x^2)^(7/2)/(c^2*x^(5/2))+2/11*B*(b*x+c*x^2)^(7/2)/(c*x^(3/2))],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^(5/2),x,2,-2/63*(2*b*B-9*A*c)*(b*x+c*x^2)^(7/2)/(c^2*x^(7/2))+2/9*B*(b*x+c*x^2)^(7/2)/(c*x^(5/2))],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^(7/2),x,6,2/3*A*b*(b*x+c*x^2)^(3/2)/x^(3/2)+2/5*A*(b*x+c*x^2)^(5/2)/x^(5/2)+2/7*B*(b*x+c*x^2)^(7/2)/(c*x^(7/2))-2*A*b^(5/2)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))+2*A*b^2*sqrt(b*x+c*x^2)/sqrt(x)],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^(9/2),x,6,1/3*(2*b*B+5*A*c)*(b*x+c*x^2)^(3/2)/x^(3/2)+1/5*(2*b*B+5*A*c)*(b*x+c*x^2)^(5/2)/(b*x^(5/2))-A*(b*x+c*x^2)^(7/2)/(b*x^(9/2))-b^(3/2)*(2*b*B+5*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))+b*(2*b*B+5*A*c)*sqrt(b*x+c*x^2)/sqrt(x)],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^(11/2),x,6,5/12*c*(4*b*B+3*A*c)*(b*x+c*x^2)^(3/2)/(b*x^(3/2))-1/4*(4*b*B+3*A*c)*(b*x+c*x^2)^(5/2)/(b*x^(7/2))-1/2*A*(b*x+c*x^2)^(7/2)/(b*x^(11/2))-5/4*c*(4*b*B+3*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))*sqrt(b)+5/4*c*(4*b*B+3*A*c)*sqrt(b*x+c*x^2)/sqrt(x)],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^(13/2),x,6,-5/24*c*(6*b*B+A*c)*(b*x+c*x^2)^(3/2)/(b*x^(5/2))-1/12*(6*b*B+A*c)*(b*x+c*x^2)^(5/2)/(b*x^(9/2))-1/3*A*(b*x+c*x^2)^(7/2)/(b*x^(13/2))-5/8*c^2*(6*b*B+A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/sqrt(b)+5/8*c^2*(6*b*B+A*c)*sqrt(b*x+c*x^2)/(b*sqrt(x))],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^(15/2),x,6,-5/96*c*(8*b*B-A*c)*(b*x+c*x^2)^(3/2)/(b*x^(7/2))-1/24*(8*b*B-A*c)*(b*x+c*x^2)^(5/2)/(b*x^(11/2))-1/4*A*(b*x+c*x^2)^(7/2)/(b*x^(15/2))-5/64*c^3*(8*b*B-A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(3/2)-5/64*c^2*(8*b*B-A*c)*sqrt(b*x+c*x^2)/(b*x^(3/2))],
[(A+B*x)*(b*x+c*x^2)^(5/2)/x^(17/2),x,7,-1/48*c*(10*b*B-3*A*c)*(b*x+c*x^2)^(3/2)/(b*x^(9/2))-1/40*(10*b*B-3*A*c)*(b*x+c*x^2)^(5/2)/(b*x^(13/2))-1/5*A*(b*x+c*x^2)^(7/2)/(b*x^(17/2))+1/128*c^4*(10*b*B-3*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(5/2)-1/64*c^2*(10*b*B-3*A*c)*sqrt(b*x+c*x^2)/(b*x^(5/2))-1/128*c^3*(10*b*B-3*A*c)*sqrt(b*x+c*x^2)/(b^2*x^(3/2))],

# p<0
[x^(7/2)*(A+B*x)/sqrt(b*x+c*x^2),x,5,4/105*b*(8*b*B-9*A*c)*x^(3/2)*sqrt(b*x+c*x^2)/c^3-2/63*(8*b*B-9*A*c)*x^(5/2)*sqrt(b*x+c*x^2)/c^2+2/9*B*x^(7/2)*sqrt(b*x+c*x^2)/c+32/315*b^3*(8*b*B-9*A*c)*sqrt(b*x+c*x^2)/(c^5*sqrt(x))-16/315*b^2*(8*b*B-9*A*c)*sqrt(x)*sqrt(b*x+c*x^2)/c^4],
[x^(5/2)*(A+B*x)/sqrt(b*x+c*x^2),x,4,-2/35*(6*b*B-7*A*c)*x^(3/2)*sqrt(b*x+c*x^2)/c^2+2/7*B*x^(5/2)*sqrt(b*x+c*x^2)/c-16/105*b^2*(6*b*B-7*A*c)*sqrt(b*x+c*x^2)/(c^4*sqrt(x))+8/105*b*(6*b*B-7*A*c)*sqrt(x)*sqrt(b*x+c*x^2)/c^3],
[x^(3/2)*(A+B*x)/sqrt(b*x+c*x^2),x,3,2/5*B*x^(3/2)*sqrt(b*x+c*x^2)/c+4/15*b*(4*b*B-5*A*c)*sqrt(b*x+c*x^2)/(c^3*sqrt(x))-2/15*(4*b*B-5*A*c)*sqrt(x)*sqrt(b*x+c*x^2)/c^2],
[(A+B*x)*sqrt(x)/sqrt(b*x+c*x^2),x,2,-2/3*(2*b*B-3*A*c)*sqrt(b*x+c*x^2)/(c^2*sqrt(x))+2/3*B*sqrt(x)*sqrt(b*x+c*x^2)/c],
[(A+B*x)/(sqrt(e*x)*sqrt(b*x+c*x^2)),x,3,-2*A*arctanh(sqrt(e)*sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(e*x)))/(sqrt(b)*sqrt(e))+2*B*sqrt(b*x+c*x^2)/(c*sqrt(e*x))],
[(A+B*x)/(x^(3/2)*sqrt(b*x+c*x^2)),x,3,-(2*b*B-A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(3/2)-A*sqrt(b*x+c*x^2)/(b*x^(3/2))],
[(A+B*x)/(x^(5/2)*sqrt(b*x+c*x^2)),x,4,1/4*c*(4*b*B-3*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(5/2)-1/2*A*sqrt(b*x+c*x^2)/(b*x^(5/2))-1/4*(4*b*B-3*A*c)*sqrt(b*x+c*x^2)/(b^2*x^(3/2))],
[(A+B*x)/(x^(7/2)*sqrt(b*x+c*x^2)),x,5,-1/8*c^2*(6*b*B-5*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(7/2)-1/3*A*sqrt(b*x+c*x^2)/(b*x^(7/2))-1/12*(6*b*B-5*A*c)*sqrt(b*x+c*x^2)/(b^2*x^(5/2))+1/8*c*(6*b*B-5*A*c)*sqrt(b*x+c*x^2)/(b^3*x^(3/2))],
[x^(9/2)*(A+B*x)/(b*x+c*x^2)^(3/2),x,5,-2*(b*B-A*c)*x^(9/2)/(b*c*sqrt(b*x+c*x^2))-12/35*(8*b*B-7*A*c)*x^(3/2)*sqrt(b*x+c*x^2)/c^3+2/7*(8*b*B-7*A*c)*x^(5/2)*sqrt(b*x+c*x^2)/(b*c^2)-32/35*b^2*(8*b*B-7*A*c)*sqrt(b*x+c*x^2)/(c^5*sqrt(x))+16/35*b*(8*b*B-7*A*c)*sqrt(x)*sqrt(b*x+c*x^2)/c^4],
[x^(7/2)*(A+B*x)/(b*x+c*x^2)^(3/2),x,4,-2*(b*B-A*c)*x^(7/2)/(b*c*sqrt(b*x+c*x^2))+2/5*(6*b*B-5*A*c)*x^(3/2)*sqrt(b*x+c*x^2)/(b*c^2)+16/15*b*(6*b*B-5*A*c)*sqrt(b*x+c*x^2)/(c^4*sqrt(x))-8/15*(6*b*B-5*A*c)*sqrt(x)*sqrt(b*x+c*x^2)/c^3],
[x^(5/2)*(A+B*x)/(b*x+c*x^2)^(3/2),x,3,-2*(b*B-A*c)*x^(5/2)/(b*c*sqrt(b*x+c*x^2))-4/3*(4*b*B-3*A*c)*sqrt(b*x+c*x^2)/(c^3*sqrt(x))+2/3*(4*b*B-3*A*c)*sqrt(x)*sqrt(b*x+c*x^2)/(b*c^2)],
[x^(3/2)*(A+B*x)/(b*x+c*x^2)^(3/2),x,2,-2*(b*B-A*c)*x^(3/2)/(b*c*sqrt(b*x+c*x^2))+2*(2*b*B-A*c)*sqrt(b*x+c*x^2)/(b*c^2*sqrt(x))],
[(A+B*x)*sqrt(x)/(b*x+c*x^2)^(3/2),x,3,-2*A*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(3/2)-2*(b*B-A*c)*sqrt(x)/(b*c*sqrt(b*x+c*x^2))],
[(A+B*x)/((b*x+c*x^2)^(3/2)*sqrt(x)),x,4,-(2*b*B-3*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(5/2)-A/(b*sqrt(x)*sqrt(b*x+c*x^2))+(2*b*B-3*A*c)*sqrt(x)/(b^2*sqrt(b*x+c*x^2))],
[(A+B*x)/(x^(3/2)*(b*x+c*x^2)^(3/2)),x,5,3/4*c*(4*b*B-5*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(7/2)-1/2*A/(b*x^(3/2)*sqrt(b*x+c*x^2))+1/4*(-4*b*B+5*A*c)/(b^2*sqrt(x)*sqrt(b*x+c*x^2))-3/4*c*(4*b*B-5*A*c)*sqrt(x)/(b^3*sqrt(b*x+c*x^2))],
[(A+B*x)/(x^(5/2)*(b*x+c*x^2)^(3/2)),x,6,-5/8*c^2*(6*b*B-7*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(9/2)-1/3*A/(b*x^(5/2)*sqrt(b*x+c*x^2))+1/12*(-6*b*B+7*A*c)/(b^2*x^(3/2)*sqrt(b*x+c*x^2))+5/24*c*(6*b*B-7*A*c)/(b^3*sqrt(x)*sqrt(b*x+c*x^2))+5/8*c^2*(6*b*B-7*A*c)*sqrt(x)/(b^4*sqrt(b*x+c*x^2))],
[(A+B*x)/(x^(7/2)*(b*x+c*x^2)^(3/2)),x,7,35/64*c^3*(8*b*B-9*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(11/2)-1/4*A/(b*x^(7/2)*sqrt(b*x+c*x^2))+1/24*(-8*b*B+9*A*c)/(b^2*x^(5/2)*sqrt(b*x+c*x^2))+7/96*c*(8*b*B-9*A*c)/(b^3*x^(3/2)*sqrt(b*x+c*x^2))-35/192*c^2*(8*b*B-9*A*c)/(b^4*sqrt(x)*sqrt(b*x+c*x^2))-35/64*c^3*(8*b*B-9*A*c)*sqrt(x)/(b^5*sqrt(b*x+c*x^2))],
[x^(11/2)*(A+B*x)/(b*x+c*x^2)^(5/2),x,5,-2/3*(b*B-A*c)*x^(11/2)/(b*c*(b*x+c*x^2)^(3/2))+16/15*b*(8*b*B-5*A*c)*x^(3/2)/(c^4*sqrt(b*x+c*x^2))-4/15*(8*b*B-5*A*c)*x^(5/2)/(c^3*sqrt(b*x+c*x^2))+2/15*(8*b*B-5*A*c)*x^(7/2)/(b*c^2*sqrt(b*x+c*x^2))+32/15*b^2*(8*b*B-5*A*c)*sqrt(x)/(c^5*sqrt(b*x+c*x^2))],
[x^(9/2)*(A+B*x)/(b*x+c*x^2)^(5/2),x,4,-2/3*(b*B-A*c)*x^(9/2)/(b*c*(b*x+c*x^2)^(3/2))-8/3*(2*b*B-A*c)*x^(3/2)/(c^3*sqrt(b*x+c*x^2))+2/3*(2*b*B-A*c)*x^(5/2)/(b*c^2*sqrt(b*x+c*x^2))-16/3*b*(2*b*B-A*c)*sqrt(x)/(c^4*sqrt(b*x+c*x^2))],
[x^(7/2)*(A+B*x)/(b*x+c*x^2)^(5/2),x,3,-2/3*(b*B-A*c)*x^(7/2)/(b*c*(b*x+c*x^2)^(3/2))+2/3*(4*b*B-A*c)*x^(3/2)/(b*c^2*sqrt(b*x+c*x^2))+4/3*(4*b*B-A*c)*sqrt(x)/(c^3*sqrt(b*x+c*x^2))],
[x^(5/2)*(A+B*x)/(b*x+c*x^2)^(5/2),x,2,-2/3*(b*B-A*c)*x^(5/2)/(b*c*(b*x+c*x^2)^(3/2))-2/3*(2*b*B+A*c)*sqrt(x)/(b*c^2*sqrt(b*x+c*x^2))],
[x^(3/2)*(A+B*x)/(b*x+c*x^2)^(5/2),x,4,-2/3*(b*B-A*c)*x^(3/2)/(b*c*(b*x+c*x^2)^(3/2))-2*A*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(5/2)+2*A*sqrt(x)/(b^2*sqrt(b*x+c*x^2))],
[(A+B*x)*sqrt(x)/(b*x+c*x^2)^(5/2),x,5,-(2*b*B-5*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(7/2)-2/3*(b*B-A*c)*sqrt(x)/(b*c*(b*x+c*x^2)^(3/2))+1/3*(2*b*B-5*A*c)/(b^2*c*sqrt(x)*sqrt(b*x+c*x^2))+(2*b*B-5*A*c)*sqrt(x)/(b^3*sqrt(b*x+c*x^2))],
[(A+B*x)/((b*x+c*x^2)^(5/2)*sqrt(x)),x,6,5/4*c*(4*b*B-7*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(9/2)-1/2*A/(b*(b*x+c*x^2)^(3/2)*sqrt(x))+1/6*(4*b*B-7*A*c)*sqrt(x)/(b^2*(b*x+c*x^2)^(3/2))-5/12*(4*b*B-7*A*c)/(b^3*sqrt(x)*sqrt(b*x+c*x^2))-5/4*c*(4*b*B-7*A*c)*sqrt(x)/(b^4*sqrt(b*x+c*x^2))],
[(A+B*x)/(x^(3/2)*(b*x+c*x^2)^(5/2)),x,7,-1/3*A/(b*x^(3/2)*(b*x+c*x^2)^(3/2))-35/8*c^2*(2*b*B-3*A*c)*arctanh(sqrt(b*x+c*x^2)/(sqrt(b)*sqrt(x)))/b^(11/2)+1/4*(-2*b*B+3*A*c)/(b^2*(b*x+c*x^2)^(3/2)*sqrt(x))-7/12*c*(2*b*B-3*A*c)*sqrt(x)/(b^3*(b*x+c*x^2)^(3/2))+35/24*c*(2*b*B-3*A*c)/(b^4*sqrt(x)*sqrt(b*x+c*x^2))+35/8*c^2*(2*b*B-3*A*c)*sqrt(x)/(b^5*sqrt(b*x+c*x^2))],

# Integrands of the form (e x)^m (A+B x) (b x+c x^2)^p when p is symbolic
[x^(1+p)*(2*b+3*c*x)*(b*x+c*x^2)^p,x,1,x^(1+p)*(b*x+c*x^2)^(1+p)/(1+p)],

# Integrands of the form (e x)^m (f+g x) (a+b x+c x^2)^p when b=0

# Integrands of the form x^m (A+B x) (a+c x^2)^p

# p>0
[x^3*(A+B*x)*(a+c*x^2),x,2,1/4*a*A*x^4+1/5*a*B*x^5+1/6*A*c*x^6+1/7*B*c*x^7],
[x^2*(A+B*x)*(a+c*x^2),x,2,1/3*a*A*x^3+1/4*a*B*x^4+1/5*A*c*x^5+1/6*B*c*x^6],
[x*(A+B*x)*(a+c*x^2),x,2,1/2*a*A*x^2+1/3*a*B*x^3+1/4*A*c*x^4+1/5*B*c*x^5],
[(A+B*x)*(a+c*x^2),x,2,a*A*x+1/3*A*c*x^3+1/4*B*(a+c*x^2)^2/c],
[(A+B*x)*(a+c*x^2)/x,x,2,a*B*x+1/2*A*c*x^2+1/3*B*c*x^3+a*A*log(x)],
[(A+B*x)*(a+c*x^2)/x^2,x,2,-a*A/x+A*c*x+1/2*B*c*x^2+a*B*log(x)],
[(A+B*x)*(a+c*x^2)/x^3,x,2,-1/2*a*A/x^2-a*B/x+B*c*x+A*c*log(x)],
[x^3*(A+B*x)*(a+c*x^2)^2,x,2,1/4*a^2*A*x^4+1/5*a^2*B*x^5+1/3*a*A*c*x^6+2/7*a*B*c*x^7+1/8*A*c^2*x^8+1/9*B*c^2*x^9],
[x^2*(A+B*x)*(a+c*x^2)^2,x,2,1/3*a^2*A*x^3+1/4*a^2*B*x^4+2/5*a*A*c*x^5+1/3*a*B*c*x^6+1/7*A*c^2*x^7+1/8*B*c^2*x^8],
[x*(A+B*x)*(a+c*x^2)^2,x,2,1/2*a^2*A*x^2+1/3*a^2*B*x^3+1/2*a*A*c*x^4+2/5*a*B*c*x^5+1/6*A*c^2*x^6+1/7*B*c^2*x^7],
[(A+B*x)*(a+c*x^2)^2,x,3,a^2*A*x+2/3*a*A*c*x^3+1/5*A*c^2*x^5+1/6*B*(a+c*x^2)^3/c],
[(A+B*x)*(a+c*x^2)^2/x,x,2,a^2*B*x+a*A*c*x^2+2/3*a*B*c*x^3+1/4*A*c^2*x^4+1/5*B*c^2*x^5+a^2*A*log(x)],
[(A+B*x)*(a+c*x^2)^2/x^2,x,2,-a^2*A/x+2*a*A*c*x+a*B*c*x^2+1/3*A*c^2*x^3+1/4*B*c^2*x^4+a^2*B*log(x)],
[(A+B*x)*(a+c*x^2)^2/x^3,x,2,-1/2*a^2*A/x^2-a^2*B/x+2*a*B*c*x+1/2*A*c^2*x^2+1/3*B*c^2*x^3+2*a*A*c*log(x)],
[x^3*(A+B*x)*(a+c*x^2)^3,x,2,1/4*a^3*A*x^4+1/5*a^3*B*x^5+1/2*a^2*A*c*x^6+3/7*a^2*B*c*x^7+3/8*a*A*c^2*x^8+1/3*a*B*c^2*x^9+1/10*A*c^3*x^10+1/11*B*c^3*x^11],
[x^2*(A+B*x)*(a+c*x^2)^3,x,2,1/3*a^3*A*x^3+1/4*a^3*B*x^4+3/5*a^2*A*c*x^5+1/2*a^2*B*c*x^6+3/7*a*A*c^2*x^7+3/8*a*B*c^2*x^8+1/9*A*c^3*x^9+1/10*B*c^3*x^10],
[x*(A+B*x)*(a+c*x^2)^3,x,2,1/2*a^3*A*x^2+1/3*a^3*B*x^3+3/4*a^2*A*c*x^4+3/5*a^2*B*c*x^5+1/2*a*A*c^2*x^6+3/7*a*B*c^2*x^7+1/8*A*c^3*x^8+1/9*B*c^3*x^9],
[(A+B*x)*(a+c*x^2)^3,x,3,a^3*A*x+a^2*A*c*x^3+3/5*a*A*c^2*x^5+1/7*A*c^3*x^7+1/8*B*(a+c*x^2)^4/c],
[(A+B*x)*(a+c*x^2)^3/x,x,2,a^3*B*x+3/2*a^2*A*c*x^2+a^2*B*c*x^3+3/4*a*A*c^2*x^4+3/5*a*B*c^2*x^5+1/6*A*c^3*x^6+1/7*B*c^3*x^7+a^3*A*log(x)],
[(A+B*x)*(a+c*x^2)^3/x^2,x,2,-a^3*A/x+3*a^2*A*c*x+3/2*a^2*B*c*x^2+a*A*c^2*x^3+3/4*a*B*c^2*x^4+1/5*A*c^3*x^5+1/6*B*c^3*x^6+a^3*B*log(x)],
[(A+B*x)*(a+c*x^2)^3/x^3,x,2,-1/2*a^3*A/x^2-a^3*B/x+3*a^2*B*c*x+3/2*a*A*c^2*x^2+a*B*c^2*x^3+1/4*A*c^3*x^4+1/5*B*c^3*x^5+3*a^2*A*c*log(x)],
[x^3*(A+B*x)*(a+c*x^2)^4,x,2,1/4*a^4*A*x^4+1/5*a^4*B*x^5+2/3*a^3*A*c*x^6+4/7*a^3*B*c*x^7+3/4*a^2*A*c^2*x^8+2/3*a^2*B*c^2*x^9+2/5*a*A*c^3*x^10+4/11*a*B*c^3*x^11+1/12*A*c^4*x^12+1/13*B*c^4*x^13],
[x^2*(A+B*x)*(a+c*x^2)^4,x,2,1/3*a^4*A*x^3+1/4*a^4*B*x^4+4/5*a^3*A*c*x^5+2/3*a^3*B*c*x^6+6/7*a^2*A*c^2*x^7+3/4*a^2*B*c^2*x^8+4/9*a*A*c^3*x^9+2/5*a*B*c^3*x^10+1/11*A*c^4*x^11+1/12*B*c^4*x^12],
[x*(A+B*x)*(a+c*x^2)^4,x,2,1/2*a^4*A*x^2+1/3*a^4*B*x^3+a^3*A*c*x^4+4/5*a^3*B*c*x^5+a^2*A*c^2*x^6+6/7*a^2*B*c^2*x^7+1/2*a*A*c^3*x^8+4/9*a*B*c^3*x^9+1/10*A*c^4*x^10+1/11*B*c^4*x^11],
[(A+B*x)*(a+c*x^2)^4,x,3,a^4*A*x+4/3*a^3*A*c*x^3+6/5*a^2*A*c^2*x^5+4/7*a*A*c^3*x^7+1/9*A*c^4*x^9+1/10*B*(a+c*x^2)^5/c],
[(A+B*x)*(a+c*x^2)^4/x,x,2,a^4*B*x+2*a^3*A*c*x^2+4/3*a^3*B*c*x^3+3/2*a^2*A*c^2*x^4+6/5*a^2*B*c^2*x^5+2/3*a*A*c^3*x^6+4/7*a*B*c^3*x^7+1/8*A*c^4*x^8+1/9*B*c^4*x^9+a^4*A*log(x)],
[(A+B*x)*(a+c*x^2)^4/x^2,x,2,-a^4*A/x+4*a^3*A*c*x+2*a^3*B*c*x^2+2*a^2*A*c^2*x^3+3/2*a^2*B*c^2*x^4+4/5*a*A*c^3*x^5+2/3*a*B*c^3*x^6+1/7*A*c^4*x^7+1/8*B*c^4*x^8+a^4*B*log(x)],
[(A+B*x)*(a+c*x^2)^4/x^3,x,2,-1/2*a^4*A/x^2-a^4*B/x+4*a^3*B*c*x+3*a^2*A*c^2*x^2+2*a^2*B*c^2*x^3+a*A*c^3*x^4+4/5*a*B*c^3*x^5+1/6*A*c^4*x^6+1/7*B*c^4*x^7+4*a^3*A*c*log(x)],

# p<0
[x^4*(d+e*x)/(a+c*x^2),x,5,-a*d*x/c^2-1/2*a*e*x^2/c^2+1/3*d*x^3/c+1/4*e*x^4/c+a^(3/2)*d*arctan(x*sqrt(c)/sqrt(a))/c^(5/2)+1/2*a^2*e*log(a+c*x^2)/c^3],
[x^3*(d+e*x)/(a+c*x^2),x,5,-a*e*x/c^2+1/2*d*x^2/c+1/3*e*x^3/c+a^(3/2)*e*arctan(x*sqrt(c)/sqrt(a))/c^(5/2)-1/2*a*d*log(a+c*x^2)/c^2],
[x^2*(d+e*x)/(a+c*x^2),x,5,d*x/c+1/2*e*x^2/c-1/2*a*e*log(a+c*x^2)/c^2-d*arctan(x*sqrt(c)/sqrt(a))*sqrt(a)/c^(3/2)],
[x*(d+e*x)/(a+c*x^2),x,4,e*x/c+1/2*d*log(a+c*x^2)/c-e*arctan(x*sqrt(c)/sqrt(a))*sqrt(a)/c^(3/2)],
[(d+e*x)/(a+c*x^2),x,3,1/2*e*log(a+c*x^2)/c+d*arctan(x*sqrt(c)/sqrt(a))/(sqrt(a)*sqrt(c))],
[(d+e*x)/(x*(a+c*x^2)),x,5,d*log(x)/a-1/2*d*log(a+c*x^2)/a+e*arctan(x*sqrt(c)/sqrt(a))/(sqrt(a)*sqrt(c))],
[(d+e*x)/(x^2*(a+c*x^2)),x,5,-d/(a*x)+e*log(x)/a-1/2*e*log(a+c*x^2)/a-d*arctan(x*sqrt(c)/sqrt(a))*sqrt(c)/a^(3/2)],
[(d+e*x)/(x^3*(a+c*x^2)),x,5,-1/2*d/(a*x^2)-e/(a*x)-c*d*log(x)/a^2+1/2*c*d*log(a+c*x^2)/a^2-e*arctan(x*sqrt(c)/sqrt(a))*sqrt(c)/a^(3/2)],
[(d+e*x)/(x^4*(a+c*x^2)),x,5,-1/3*d/(a*x^3)-1/2*e/(a*x^2)+c*d/(a^2*x)+c^(3/2)*d*arctan(x*sqrt(c)/sqrt(a))/a^(5/2)-c*e*log(x)/a^2+1/2*c*e*log(a+c*x^2)/a^2],
[(d+e*x)/(a-c*x^2),x,3,-1/2*e*log(a-c*x^2)/c+d*arctanh(x*sqrt(c)/sqrt(a))/(sqrt(a)*sqrt(c))],
[x^4*(d+e*x)/(a+c*x^2)^2,x,6,3/2*d*x/c^2+e*x^2/c^2-1/2*x^3*(d+e*x)/(c*(a+c*x^2))-a*e*log(a+c*x^2)/c^3-3/2*d*arctan(x*sqrt(c)/sqrt(a))*sqrt(a)/c^(5/2)],
[x^3*(d+e*x)/(a+c*x^2)^2,x,5,3/2*e*x/c^2-1/2*x^2*(d+e*x)/(c*(a+c*x^2))+1/2*d*log(a+c*x^2)/c^2-3/2*e*arctan(x*sqrt(c)/sqrt(a))*sqrt(a)/c^(5/2)],
[x^2*(d+e*x)/(a+c*x^2)^2,x,4,-1/2*x*(d+e*x)/(c*(a+c*x^2))+1/2*e*log(a+c*x^2)/c^2+1/2*d*arctan(x*sqrt(c)/sqrt(a))/(c^(3/2)*sqrt(a))],
[x*(d+e*x)/(a+c*x^2)^2,x,2,1/2*(-d-e*x)/(c*(a+c*x^2))+1/2*e*arctan(x*sqrt(c)/sqrt(a))/(c^(3/2)*sqrt(a))],
[(d+e*x)/(a+c*x^2)^2,x,2,1/2*(-a*e+c*d*x)/(a*c*(a+c*x^2))+1/2*d*arctan(x*sqrt(c)/sqrt(a))/(a^(3/2)*sqrt(c))],
[(d+e*x)/(x*(a+c*x^2)^2),x,6,1/2*(d+e*x)/(a*(a+c*x^2))+d*log(x)/a^2-1/2*d*log(a+c*x^2)/a^2+1/2*e*arctan(x*sqrt(c)/sqrt(a))/(a^(3/2)*sqrt(c))],
[(d+e*x)/(x^2*(a+c*x^2)^2),x,6,-3/2*d/(a^2*x)+1/2*(d+e*x)/(a*x*(a+c*x^2))+e*log(x)/a^2-1/2*e*log(a+c*x^2)/a^2-3/2*d*arctan(x*sqrt(c)/sqrt(a))*sqrt(c)/a^(5/2)],
[(d+e*x)/(x^3*(a+c*x^2)^2),x,6,-d/(a^2*x^2)-3/2*e/(a^2*x)+1/2*(d+e*x)/(a*x^2*(a+c*x^2))-2*c*d*log(x)/a^3+c*d*log(a+c*x^2)/a^3-3/2*e*arctan(x*sqrt(c)/sqrt(a))*sqrt(c)/a^(5/2)],
[x^4*(d+e*x)/(a^2-c^2*x^2),x,5,-a^2*d*x/c^4-1/2*a^2*e*x^2/c^4-1/3*d*x^3/c^2-1/4*e*x^4/c^2-1/2*a^3*(c*d+a*e)*log(a-c*x)/c^6+1/2*a^3*(c*d-a*e)*log(a+c*x)/c^6],
[x^3*(d+e*x)/(a^2-c^2*x^2),x,5,-a^2*e*x/c^4-1/2*d*x^2/c^2-1/3*e*x^3/c^2-1/2*a^2*(c*d+a*e)*log(a-c*x)/c^5-1/2*a^2*(c*d-a*e)*log(a+c*x)/c^5],
[x^2*(d+e*x)/(a^2-c^2*x^2),x,5,-d*x/c^2-1/2*e*x^2/c^2-1/2*a*(c*d+a*e)*log(a-c*x)/c^4+1/2*a*(c*d-a*e)*log(a+c*x)/c^4],
[x*(d+e*x)/(a^2-c^2*x^2),x,4,-e*x/c^2-1/2*(c*d+a*e)*log(a-c*x)/c^3-1/2*(c*d-a*e)*log(a+c*x)/c^3],
[(d+e*x)/(a^2-c^2*x^2),x,3,-1/2*(c*d/a+e)*log(a-c*x)/c^2+1/2*(c*d/a-e)*log(a+c*x)/c^2],
[(d+e*x)/(x*(a^2-c^2*x^2)),x,2,d*log(x)/a^2-1/2*(c*d+a*e)*log(a-c*x)/(a^2*c)-1/2*(c*d-a*e)*log(a+c*x)/(a^2*c)],
[(d+e*x)/(x^2*(a^2-c^2*x^2)),x,2,-d/(a^2*x)+e*log(x)/a^2-1/2*(c*d+a*e)*log(a-c*x)/a^3+1/2*(c*d-a*e)*log(a+c*x)/a^3],
[(d+e*x)/(x^3*(a^2-c^2*x^2)),x,2,-1/2*d/(a^2*x^2)-e/(a^2*x)+c^2*d*log(x)/a^4-1/2*c*(c*d+a*e)*log(a-c*x)/a^4-1/2*c*(c*d-a*e)*log(a+c*x)/a^4],
[(d+e*x)/(x^4*(a^2-c^2*x^2)),x,2,-1/3*d/(a^2*x^3)-1/2*e/(a^2*x^2)-c^2*d/(a^4*x)+c^2*e*log(x)/a^4-1/2*c^2*(c*d+a*e)*log(a-c*x)/a^5+1/2*c^2*(c*d-a*e)*log(a+c*x)/a^5],
[x^4*(d+e*x)/(a^2-c^2*x^2)^2,x,6,3/2*d*x/c^4+e*x^2/c^4+1/2*x^3*(d+e*x)/(c^2*(a^2-c^2*x^2))+1/4*a*(3*c*d+4*a*e)*log(a-c*x)/c^6-1/4*a*(3*c*d-4*a*e)*log(a+c*x)/c^6],
[x^3*(d+e*x)/(a^2-c^2*x^2)^2,x,5,3/2*e*x/c^4+1/2*x^2*(d+e*x)/(c^2*(a^2-c^2*x^2))+1/4*(2*c*d+3*a*e)*log(a-c*x)/c^5+1/4*(2*c*d-3*a*e)*log(a+c*x)/c^5],
[x^2*(d+e*x)/(a^2-c^2*x^2)^2,x,4,1/2*x*(d+e*x)/(c^2*(a^2-c^2*x^2))+1/4*(c*d+2*a*e)*log(a-c*x)/(a*c^4)-1/4*(c*d-2*a*e)*log(a+c*x)/(a*c^4)],
[x*(d+e*x)/(a^2-c^2*x^2)^2,x,2,1/2*(d+e*x)/(c^2*(a^2-c^2*x^2))-1/2*e*arctanh(c*x/a)/(a*c^3)],
[(d+e*x)/(a^2-c^2*x^2)^2,x,2,1/2*(a^2*e+c^2*d*x)/(a^2*c^2*(a^2-c^2*x^2))+1/2*d*arctanh(c*x/a)/(a^3*c)],
[(d+e*x)/(x*(a^2-c^2*x^2)^2),x,3,1/2*(d+e*x)/(a^2*(a^2-c^2*x^2))+d*log(x)/a^4-1/4*(2*c*d+a*e)*log(a-c*x)/(a^4*c)-1/4*(2*c*d-a*e)*log(a+c*x)/(a^4*c)],
[(d+e*x)/(x^2*(a^2-c^2*x^2)^2),x,3,-3/2*d/(a^4*x)+1/2*(d+e*x)/(a^2*x*(a^2-c^2*x^2))+e*log(x)/a^4-1/4*(3*c*d+2*a*e)*log(a-c*x)/a^5+1/4*(3*c*d-2*a*e)*log(a+c*x)/a^5],
[(d+e*x)/(x^3*(a^2-c^2*x^2)^2),x,3,-d/(a^4*x^2)-3/2*e/(a^4*x)+1/2*(d+e*x)/(a^2*x^2*(a^2-c^2*x^2))+2*c^2*d*log(x)/a^6-1/4*c*(4*c*d+3*a*e)*log(a-c*x)/a^6-1/4*c*(4*c*d-3*a*e)*log(a+c*x)/a^6],

# Integrands of the form x^m (A+B x) (a+c x^2)^(p/2)

# p>0
[x^4*(A+B*x)*sqrt(a+c*x^2),x,7,-4/35*a*B*x^2*(a+c*x^2)^(3/2)/c^2+1/6*A*x^3*(a+c*x^2)^(3/2)/c+1/7*B*x^4*(a+c*x^2)^(3/2)/c+1/840*a*(64*a*B-105*A*c*x)*(a+c*x^2)^(3/2)/c^3+1/16*a^3*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(5/2)+1/16*a^2*A*x*sqrt(a+c*x^2)/c^2],
[x^3*(A+B*x)*sqrt(a+c*x^2),x,6,1/5*A*x^2*(a+c*x^2)^(3/2)/c+1/6*B*x^3*(a+c*x^2)^(3/2)/c-1/120*a*(16*A+15*B*x)*(a+c*x^2)^(3/2)/c^2+1/16*a^3*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(5/2)+1/16*a^2*B*x*sqrt(a+c*x^2)/c^2],
[x^2*(A+B*x)*sqrt(a+c*x^2),x,5,1/5*B*x^2*(a+c*x^2)^(3/2)/c-1/60*(8*a*B-15*A*c*x)*(a+c*x^2)^(3/2)/c^2-1/8*a^2*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(3/2)-1/8*a*A*x*sqrt(a+c*x^2)/c],
[x*(A+B*x)*sqrt(a+c*x^2),x,4,1/12*(4*A+3*B*x)*(a+c*x^2)^(3/2)/c-1/8*a^2*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(3/2)-1/8*a*B*x*sqrt(a+c*x^2)/c],
[(A+B*x)*sqrt(a+c*x^2),x,4,1/3*B*(a+c*x^2)^(3/2)/c+1/2*a*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/sqrt(c)+1/2*A*x*sqrt(a+c*x^2)],
[(A+B*x)*sqrt(a+c*x^2)/x,x,7,-A*arctanh(sqrt(a+c*x^2)/sqrt(a))*sqrt(a)+1/2*a*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/sqrt(c)+1/2*(2*A+B*x)*sqrt(a+c*x^2)],
[(A+B*x)*sqrt(a+c*x^2)/x^2,x,7,-B*arctanh(sqrt(a+c*x^2)/sqrt(a))*sqrt(a)+A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))*sqrt(c)-(A-B*x)*sqrt(a+c*x^2)/x],
[(A+B*x)*sqrt(a+c*x^2)/x^3,x,7,-1/2*A*c*arctanh(sqrt(a+c*x^2)/sqrt(a))/sqrt(a)+B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))*sqrt(c)-1/2*(A+2*B*x)*sqrt(a+c*x^2)/x^2],
[(A+B*x)*sqrt(a+c*x^2)/x^4,x,5,-1/3*A*(a+c*x^2)^(3/2)/(a*x^3)-1/2*B*c*arctanh(sqrt(a+c*x^2)/sqrt(a))/sqrt(a)-1/2*B*sqrt(a+c*x^2)/x^2],
[(A+B*x)*sqrt(a+c*x^2)/x^5,x,6,-1/4*A*(a+c*x^2)^(3/2)/(a*x^4)-1/3*B*(a+c*x^2)^(3/2)/(a*x^3)+1/8*A*c^2*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(3/2)+1/8*A*c*sqrt(a+c*x^2)/(a*x^2)],
[(A+B*x)*sqrt(a+c*x^2)/x^6,x,7,-1/5*A*(a+c*x^2)^(3/2)/(a*x^5)-1/4*B*(a+c*x^2)^(3/2)/(a*x^4)+2/15*A*c*(a+c*x^2)^(3/2)/(a^2*x^3)+1/8*B*c^2*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(3/2)+1/8*B*c*sqrt(a+c*x^2)/(a*x^2)],
[(A+B*x)*sqrt(a+c*x^2)/x^7,x,8,-1/6*A*(a+c*x^2)^(3/2)/(a*x^6)-1/5*B*(a+c*x^2)^(3/2)/(a*x^5)+1/8*A*c*(a+c*x^2)^(3/2)/(a^2*x^4)+2/15*B*c*(a+c*x^2)^(3/2)/(a^2*x^3)-1/16*A*c^3*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(5/2)-1/16*A*c^2*sqrt(a+c*x^2)/(a^2*x^2)],
[x^4*(A+B*x)*(a+c*x^2)^(3/2),x,8,1/64*a^2*A*x*(a+c*x^2)^(3/2)/c^2-4/63*a*B*x^2*(a+c*x^2)^(5/2)/c^2+1/8*A*x^3*(a+c*x^2)^(5/2)/c+1/9*B*x^4*(a+c*x^2)^(5/2)/c+1/5040*a*(128*a*B-315*A*c*x)*(a+c*x^2)^(5/2)/c^3+3/128*a^4*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(5/2)+3/128*a^3*A*x*sqrt(a+c*x^2)/c^2],
[x^3*(A+B*x)*(a+c*x^2)^(3/2),x,7,1/64*a^2*B*x*(a+c*x^2)^(3/2)/c^2+1/7*A*x^2*(a+c*x^2)^(5/2)/c+1/8*B*x^3*(a+c*x^2)^(5/2)/c-1/560*a*(32*A+35*B*x)*(a+c*x^2)^(5/2)/c^2+3/128*a^4*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(5/2)+3/128*a^3*B*x*sqrt(a+c*x^2)/c^2],
[x^2*(A+B*x)*(a+c*x^2)^(3/2),x,6,-1/24*a*A*x*(a+c*x^2)^(3/2)/c+1/7*B*x^2*(a+c*x^2)^(5/2)/c-1/210*(12*a*B-35*A*c*x)*(a+c*x^2)^(5/2)/c^2-1/16*a^3*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(3/2)-1/16*a^2*A*x*sqrt(a+c*x^2)/c],
[x*(A+B*x)*(a+c*x^2)^(3/2),x,5,-1/24*a*B*x*(a+c*x^2)^(3/2)/c+1/30*(6*A+5*B*x)*(a+c*x^2)^(5/2)/c-1/16*a^3*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(3/2)-1/16*a^2*B*x*sqrt(a+c*x^2)/c],
[(A+B*x)*(a+c*x^2)^(3/2),x,5,1/4*A*x*(a+c*x^2)^(3/2)+1/5*B*(a+c*x^2)^(5/2)/c+3/8*a^2*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/sqrt(c)+3/8*a*A*x*sqrt(a+c*x^2)],
[(A+B*x)*(a+c*x^2)^(3/2)/x,x,8,1/12*(4*A+3*B*x)*(a+c*x^2)^(3/2)-a^(3/2)*A*arctanh(sqrt(a+c*x^2)/sqrt(a))+3/8*a^2*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/sqrt(c)+1/8*a*(8*A+3*B*x)*sqrt(a+c*x^2)],
[(A+B*x)*(a+c*x^2)^(3/2)/x^2,x,8,-1/3*(3*A-B*x)*(a+c*x^2)^(3/2)/x-a^(3/2)*B*arctanh(sqrt(a+c*x^2)/sqrt(a))+3/2*a*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))*sqrt(c)+1/2*(2*a*B+3*A*c*x)*sqrt(a+c*x^2)],
[(A+B*x)*(a+c*x^2)^(3/2)/x^3,x,8,-1/2*(A-B*x)*(a+c*x^2)^(3/2)/x^2-3/2*A*c*arctanh(sqrt(a+c*x^2)/sqrt(a))*sqrt(a)+3/2*a*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))*sqrt(c)-3/2*(a*B-A*c*x)*sqrt(a+c*x^2)/x],
[(A+B*x)*(a+c*x^2)^(3/2)/x^4,x,8,-1/6*(2*A+3*B*x)*(a+c*x^2)^(3/2)/x^3+A*c^(3/2)*arctanh(x*sqrt(c)/sqrt(a+c*x^2))-3/2*B*c*arctanh(sqrt(a+c*x^2)/sqrt(a))*sqrt(a)-1/2*c*(2*A-3*B*x)*sqrt(a+c*x^2)/x],
[(A+B*x)*(a+c*x^2)^(3/2)/x^5,x,8,-1/12*(3*A+4*B*x)*(a+c*x^2)^(3/2)/x^4+B*c^(3/2)*arctanh(x*sqrt(c)/sqrt(a+c*x^2))-3/8*A*c^2*arctanh(sqrt(a+c*x^2)/sqrt(a))/sqrt(a)-1/8*c*(3*A+8*B*x)*sqrt(a+c*x^2)/x^2],
[(A+B*x)*(a+c*x^2)^(3/2)/x^6,x,6,-1/4*B*(a+c*x^2)^(3/2)/x^4-1/5*A*(a+c*x^2)^(5/2)/(a*x^5)-3/8*B*c^2*arctanh(sqrt(a+c*x^2)/sqrt(a))/sqrt(a)-3/8*B*c*sqrt(a+c*x^2)/x^2],
[(A+B*x)*(a+c*x^2)^(3/2)/x^7,x,7,1/24*A*c*(a+c*x^2)^(3/2)/(a*x^4)-1/6*A*(a+c*x^2)^(5/2)/(a*x^6)-1/5*B*(a+c*x^2)^(5/2)/(a*x^5)+1/16*A*c^3*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(3/2)+1/16*A*c^2*sqrt(a+c*x^2)/(a*x^2)],
[(A+B*x)*(a+c*x^2)^(3/2)/x^8,x,8,1/24*B*c*(a+c*x^2)^(3/2)/(a*x^4)-1/7*A*(a+c*x^2)^(5/2)/(a*x^7)-1/6*B*(a+c*x^2)^(5/2)/(a*x^6)+2/35*A*c*(a+c*x^2)^(5/2)/(a^2*x^5)+1/16*B*c^3*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(3/2)+1/16*B*c^2*sqrt(a+c*x^2)/(a*x^2)],
[x^4*(A+B*x)*(a+c*x^2)^(5/2),x,9,1/128*a^3*A*x*(a+c*x^2)^(3/2)/c^2+1/160*a^2*A*x*(a+c*x^2)^(5/2)/c^2-4/99*a*B*x^2*(a+c*x^2)^(7/2)/c^2+1/10*A*x^3*(a+c*x^2)^(7/2)/c+1/11*B*x^4*(a+c*x^2)^(7/2)/c+1/55440*a*(640*a*B-2079*A*c*x)*(a+c*x^2)^(7/2)/c^3+3/256*a^5*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(5/2)+3/256*a^4*A*x*sqrt(a+c*x^2)/c^2],
[x^3*(A+B*x)*(a+c*x^2)^(5/2),x,8,1/128*a^3*B*x*(a+c*x^2)^(3/2)/c^2+1/160*a^2*B*x*(a+c*x^2)^(5/2)/c^2+1/9*A*x^2*(a+c*x^2)^(7/2)/c+1/10*B*x^3*(a+c*x^2)^(7/2)/c-1/5040*a*(160*A+189*B*x)*(a+c*x^2)^(7/2)/c^2+3/256*a^5*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(5/2)+3/256*a^4*B*x*sqrt(a+c*x^2)/c^2],
[x^2*(A+B*x)*(a+c*x^2)^(5/2),x,7,-5/192*a^2*A*x*(a+c*x^2)^(3/2)/c-1/48*a*A*x*(a+c*x^2)^(5/2)/c+1/9*B*x^2*(a+c*x^2)^(7/2)/c-1/504*(16*a*B-63*A*c*x)*(a+c*x^2)^(7/2)/c^2-5/128*a^4*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(3/2)-5/128*a^3*A*x*sqrt(a+c*x^2)/c],
[x*(A+B*x)*(a+c*x^2)^(5/2),x,6,-5/192*a^2*B*x*(a+c*x^2)^(3/2)/c-1/48*a*B*x*(a+c*x^2)^(5/2)/c+1/56*(8*A+7*B*x)*(a+c*x^2)^(7/2)/c-5/128*a^4*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(3/2)-5/128*a^3*B*x*sqrt(a+c*x^2)/c],
[(A+B*x)*(a+c*x^2)^(5/2),x,6,5/24*a*A*x*(a+c*x^2)^(3/2)+1/6*A*x*(a+c*x^2)^(5/2)+1/7*B*(a+c*x^2)^(7/2)/c+5/16*a^3*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/sqrt(c)+5/16*a^2*A*x*sqrt(a+c*x^2)],
[(A+B*x)*(a+c*x^2)^(5/2)/x,x,9,1/24*a*(8*A+5*B*x)*(a+c*x^2)^(3/2)+1/30*(6*A+5*B*x)*(a+c*x^2)^(5/2)-a^(5/2)*A*arctanh(sqrt(a+c*x^2)/sqrt(a))+5/16*a^3*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/sqrt(c)+1/16*a^2*(16*A+5*B*x)*sqrt(a+c*x^2)],
[(A+B*x)*(a+c*x^2)^(5/2)/x^2,x,9,1/12*(4*a*B+15*A*c*x)*(a+c*x^2)^(3/2)-1/5*(5*A-B*x)*(a+c*x^2)^(5/2)/x-a^(5/2)*B*arctanh(sqrt(a+c*x^2)/sqrt(a))+15/8*a^2*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))*sqrt(c)+1/8*a*(8*a*B+15*A*c*x)*sqrt(a+c*x^2)],
[(A+B*x)*(a+c*x^2)^(5/2)/x^3,x,9,-5/12*(3*a*B-2*A*c*x)*(a+c*x^2)^(3/2)/x-1/4*(2*A-B*x)*(a+c*x^2)^(5/2)/x^2-5/2*a^(3/2)*A*c*arctanh(sqrt(a+c*x^2)/sqrt(a))+15/8*a^2*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))*sqrt(c)+5/8*a*c*(4*A+3*B*x)*sqrt(a+c*x^2)],
[(A+B*x)*(a+c*x^2)^(5/2)/x^4,x,9,-5/6*(a*B-A*c*x)*(a+c*x^2)^(3/2)/x^2-1/3*(A-B*x)*(a+c*x^2)^(5/2)/x^3+5/2*a*A*c^(3/2)*arctanh(x*sqrt(c)/sqrt(a+c*x^2))-5/2*a^(3/2)*B*c*arctanh(sqrt(a+c*x^2)/sqrt(a))-5/2*a*c*(A-B*x)*sqrt(a+c*x^2)/x],
[(A+B*x)*(a+c*x^2)^(5/2)/x^5,x,9,-5/24*(4*a*B+3*A*c*x)*(a+c*x^2)^(3/2)/x^3-1/4*(A-2*B*x)*(a+c*x^2)^(5/2)/x^4+5/2*a*B*c^(3/2)*arctanh(x*sqrt(c)/sqrt(a+c*x^2))-15/8*A*c^2*arctanh(sqrt(a+c*x^2)/sqrt(a))*sqrt(a)-5/8*c*(4*a*B-3*A*c*x)*sqrt(a+c*x^2)/x],
[(A+B*x)*(a+c*x^2)^(5/2)/x^6,x,9,-1/24*c*(8*A+15*B*x)*(a+c*x^2)^(3/2)/x^3-1/20*(4*A+5*B*x)*(a+c*x^2)^(5/2)/x^5+A*c^(5/2)*arctanh(x*sqrt(c)/sqrt(a+c*x^2))-15/8*B*c^2*arctanh(sqrt(a+c*x^2)/sqrt(a))*sqrt(a)-1/8*c^2*(8*A-15*B*x)*sqrt(a+c*x^2)/x],
[(A+B*x)*(a+c*x^2)^(5/2)/x^7,x,9,-1/24*c*(5*A+8*B*x)*(a+c*x^2)^(3/2)/x^4-1/30*(5*A+6*B*x)*(a+c*x^2)^(5/2)/x^6+B*c^(5/2)*arctanh(x*sqrt(c)/sqrt(a+c*x^2))-5/16*A*c^3*arctanh(sqrt(a+c*x^2)/sqrt(a))/sqrt(a)-1/16*c^2*(5*A+16*B*x)*sqrt(a+c*x^2)/x^2],
[(A+B*x)*(a+c*x^2)^(5/2)/x^8,x,7,-5/24*B*c*(a+c*x^2)^(3/2)/x^4-1/6*B*(a+c*x^2)^(5/2)/x^6-1/7*A*(a+c*x^2)^(7/2)/(a*x^7)-5/16*B*c^3*arctanh(sqrt(a+c*x^2)/sqrt(a))/sqrt(a)-5/16*B*c^2*sqrt(a+c*x^2)/x^2],
[(A+B*x)*(a+c*x^2)^(5/2)/x^9,x,8,5/192*A*c^2*(a+c*x^2)^(3/2)/(a*x^4)+1/48*A*c*(a+c*x^2)^(5/2)/(a*x^6)-1/8*A*(a+c*x^2)^(7/2)/(a*x^8)-1/7*B*(a+c*x^2)^(7/2)/(a*x^7)+5/128*A*c^4*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(3/2)+5/128*A*c^3*sqrt(a+c*x^2)/(a*x^2)],
[(A+B*x)*(a+c*x^2)^(5/2)/x^10,x,9,5/192*B*c^2*(a+c*x^2)^(3/2)/(a*x^4)+1/48*B*c*(a+c*x^2)^(5/2)/(a*x^6)-1/9*A*(a+c*x^2)^(7/2)/(a*x^9)-1/8*B*(a+c*x^2)^(7/2)/(a*x^8)+2/63*A*c*(a+c*x^2)^(7/2)/(a^2*x^7)+5/128*B*c^4*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(3/2)+5/128*B*c^3*sqrt(a+c*x^2)/(a*x^2)],

# p<0
[x^4*(A+B*x)/sqrt(a+c*x^2),x,6,3/8*a^2*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(5/2)-4/15*a*B*x^2*sqrt(a+c*x^2)/c^2+1/4*A*x^3*sqrt(a+c*x^2)/c+1/5*B*x^4*sqrt(a+c*x^2)/c+1/120*a*(64*a*B-45*A*c*x)*sqrt(a+c*x^2)/c^3],
[x^3*(A+B*x)/sqrt(a+c*x^2),x,5,3/8*a^2*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(5/2)+1/3*A*x^2*sqrt(a+c*x^2)/c+1/4*B*x^3*sqrt(a+c*x^2)/c-1/24*a*(16*A+9*B*x)*sqrt(a+c*x^2)/c^2],
[x^2*(A+B*x)/sqrt(a+c*x^2),x,4,-1/2*a*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(3/2)+1/3*B*x^2*sqrt(a+c*x^2)/c-1/6*(4*a*B-3*A*c*x)*sqrt(a+c*x^2)/c^2],
[x*(A+B*x)/sqrt(a+c*x^2),x,3,-1/2*a*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(3/2)+1/2*(2*A+B*x)*sqrt(a+c*x^2)/c],
[(A+B*x)/sqrt(a+c*x^2),x,3,A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/sqrt(c)+B*sqrt(a+c*x^2)/c],
[(A+B*x)/(x*sqrt(a+c*x^2)),x,6,-A*arctanh(sqrt(a+c*x^2)/sqrt(a))/sqrt(a)+B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/sqrt(c)],
[(A+B*x)/(x^2*sqrt(a+c*x^2)),x,4,-B*arctanh(sqrt(a+c*x^2)/sqrt(a))/sqrt(a)-A*sqrt(a+c*x^2)/(a*x)],
[(A+B*x)/(x^3*sqrt(a+c*x^2)),x,5,1/2*A*c*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(3/2)-1/2*A*sqrt(a+c*x^2)/(a*x^2)-B*sqrt(a+c*x^2)/(a*x)],
[(A+B*x)/(x^4*sqrt(a+c*x^2)),x,6,1/2*B*c*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(3/2)-1/3*A*sqrt(a+c*x^2)/(a*x^3)-1/2*B*sqrt(a+c*x^2)/(a*x^2)+2/3*A*c*sqrt(a+c*x^2)/(a^2*x)],
[(A+B*x)/(x^5*sqrt(a+c*x^2)),x,7,-3/8*A*c^2*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(5/2)-1/4*A*sqrt(a+c*x^2)/(a*x^4)-1/3*B*sqrt(a+c*x^2)/(a*x^3)+3/8*A*c*sqrt(a+c*x^2)/(a^2*x^2)+2/3*B*c*sqrt(a+c*x^2)/(a^2*x)],
[(A+B*x)/(x^6*sqrt(a+c*x^2)),x,8,-3/8*B*c^2*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(5/2)-1/5*A*sqrt(a+c*x^2)/(a*x^5)-1/4*B*sqrt(a+c*x^2)/(a*x^4)+4/15*A*c*sqrt(a+c*x^2)/(a^2*x^3)+3/8*B*c*sqrt(a+c*x^2)/(a^2*x^2)-8/15*A*c^2*sqrt(a+c*x^2)/(a^3*x)],
[x^4*(A+B*x)/(a+c*x^2)^(3/2),x,5,-3/2*a*A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(5/2)-x^3*(A+B*x)/(c*sqrt(a+c*x^2))+4/3*B*x^2*sqrt(a+c*x^2)/c^2-1/6*(16*a*B-9*A*c*x)*sqrt(a+c*x^2)/c^3],
[x^3*(A+B*x)/(a+c*x^2)^(3/2),x,4,-3/2*a*B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(5/2)-x^2*(A+B*x)/(c*sqrt(a+c*x^2))+1/2*(4*A+3*B*x)*sqrt(a+c*x^2)/c^2],
[x^2*(A+B*x)/(a+c*x^2)^(3/2),x,4,A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(3/2)-x*(A+B*x)/(c*sqrt(a+c*x^2))+2*B*sqrt(a+c*x^2)/c^2],
[x*(A+B*x)/(a+c*x^2)^(3/2),x,3,B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(3/2)+(-A-B*x)/(c*sqrt(a+c*x^2))],
[(A+B*x)/(a+c*x^2)^(3/2),x,1,(-a*B+A*c*x)/(a*c*sqrt(a+c*x^2))],
[(A+B*x)/(x*(a+c*x^2)^(3/2)),x,5,-A*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(3/2)+(A+B*x)/(a*sqrt(a+c*x^2))],
[(A+B*x)/(x^2*(a+c*x^2)^(3/2)),x,5,-B*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(3/2)+(A+B*x)/(a*x*sqrt(a+c*x^2))-2*A*sqrt(a+c*x^2)/(a^2*x)],
[(A+B*x)/(x^3*(a+c*x^2)^(3/2)),x,6,3/2*A*c*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(5/2)+(A+B*x)/(a*x^2*sqrt(a+c*x^2))-3/2*A*sqrt(a+c*x^2)/(a^2*x^2)-2*B*sqrt(a+c*x^2)/(a^2*x)],
[(A+B*x)/(x^4*(a+c*x^2)^(3/2)),x,7,3/2*B*c*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(5/2)+(A+B*x)/(a*x^3*sqrt(a+c*x^2))-4/3*A*sqrt(a+c*x^2)/(a^2*x^3)-3/2*B*sqrt(a+c*x^2)/(a^2*x^2)+8/3*A*c*sqrt(a+c*x^2)/(a^3*x)],
[x^4*(A+B*x)/(a+c*x^2)^(5/2),x,5,-1/3*x^3*(A+B*x)/(c*(a+c*x^2)^(3/2))+A*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(5/2)-1/3*x*(3*A+4*B*x)/(c^2*sqrt(a+c*x^2))+8/3*B*sqrt(a+c*x^2)/c^3],
[x^3*(A+B*x)/(a+c*x^2)^(5/2),x,4,-1/3*x^2*(A+B*x)/(c*(a+c*x^2)^(3/2))+B*arctanh(x*sqrt(c)/sqrt(a+c*x^2))/c^(5/2)+1/3*(-2*A-3*B*x)/(c^2*sqrt(a+c*x^2))],
[x^2*(A+B*x)/(a+c*x^2)^(5/2),x,2,-1/3*x^2*(a*B-A*c*x)/(a*c*(a+c*x^2)^(3/2))-2/3*B/(c^2*sqrt(a+c*x^2))],
[x*(A+B*x)/(a+c*x^2)^(5/2),x,2,1/3*(-A-B*x)/(c*(a+c*x^2)^(3/2))+1/3*B*x/(a*c*sqrt(a+c*x^2))],
[(A+B*x)/(a+c*x^2)^(5/2),x,2,1/3*(-a*B+A*c*x)/(a*c*(a+c*x^2)^(3/2))+2/3*A*x/(a^2*sqrt(a+c*x^2))],
[(A+B*x)/(x*(a+c*x^2)^(5/2)),x,6,1/3*(A+B*x)/(a*(a+c*x^2)^(3/2))-A*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(5/2)+1/3*(3*A+2*B*x)/(a^2*sqrt(a+c*x^2))],
[(A+B*x)/(x^2*(a+c*x^2)^(5/2)),x,6,1/3*(A+B*x)/(a*x*(a+c*x^2)^(3/2))-B*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(5/2)+1/3*(4*A+3*B*x)/(a^2*x*sqrt(a+c*x^2))-8/3*A*sqrt(a+c*x^2)/(a^3*x)],
[(A+B*x)/(x^3*(a+c*x^2)^(5/2)),x,7,1/3*(A+B*x)/(a*x^2*(a+c*x^2)^(3/2))+5/2*A*c*arctanh(sqrt(a+c*x^2)/sqrt(a))/a^(7/2)+1/3*(5*A+4*B*x)/(a^2*x^2*sqrt(a+c*x^2))-5/2*A*sqrt(a+c*x^2)/(a^3*x^2)-8/3*B*sqrt(a+c*x^2)/(a^3*x)],
[(d+e*x)/(a+c*x^2)^(7/2),x,3,1/5*(-a*e+c*d*x)/(a*c*(a+c*x^2)^(5/2))+4/15*d*x/(a^2*(a+c*x^2)^(3/2))+8/15*d*x/(a^3*sqrt(a+c*x^2))],
[(d+e*x)/(a+c*x^2)^(9/2),x,4,1/7*(-a*e+c*d*x)/(a*c*(a+c*x^2)^(7/2))+6/35*d*x/(a^2*(a+c*x^2)^(5/2))+8/35*d*x/(a^3*(a+c*x^2)^(3/2))+16/35*d*x/(a^4*sqrt(a+c*x^2))],

# Integrands of the form (e x)^(m/2) (A+B x) (a+c x^2)^p

# p>0
[x^(7/2)*(A+B*x)*(a+c*x^2),x,2,2/9*a*A*x^(9/2)+2/11*a*B*x^(11/2)+2/13*A*c*x^(13/2)+2/15*B*c*x^(15/2)],
[x^(5/2)*(A+B*x)*(a+c*x^2),x,2,2/7*a*A*x^(7/2)+2/9*a*B*x^(9/2)+2/11*A*c*x^(11/2)+2/13*B*c*x^(13/2)],
[x^(3/2)*(A+B*x)*(a+c*x^2),x,2,2/5*a*A*x^(5/2)+2/7*a*B*x^(7/2)+2/9*A*c*x^(9/2)+2/11*B*c*x^(11/2)],
[(A+B*x)*(a+c*x^2)*sqrt(x),x,2,2/3*a*A*x^(3/2)+2/5*a*B*x^(5/2)+2/7*A*c*x^(7/2)+2/9*B*c*x^(9/2)],
[(A+B*x)*(a+c*x^2)/sqrt(x),x,2,2/3*a*B*x^(3/2)+2/5*A*c*x^(5/2)+2/7*B*c*x^(7/2)+2*a*A*sqrt(x)],
[(A+B*x)*(a+c*x^2)/x^(3/2),x,2,2/3*A*c*x^(3/2)+2/5*B*c*x^(5/2)-2*a*A/sqrt(x)+2*a*B*sqrt(x)],
[(A+B*x)*(a+c*x^2)/x^(5/2),x,2,-2/3*a*A/x^(3/2)+2/3*B*c*x^(3/2)-2*a*B/sqrt(x)+2*A*c*sqrt(x)],
[(A+B*x)*(a+c*x^2)/x^(7/2),x,2,-2/5*a*A/x^(5/2)-2/3*a*B/x^(3/2)-2*A*c/sqrt(x)+2*B*c*sqrt(x)],
[(A+B*x)*(a+c*x^2)/x^(9/2),x,2,-2/7*a*A/x^(7/2)-2/5*a*B/x^(5/2)-2/3*A*c/x^(3/2)-2*B*c/sqrt(x)],
[x^(7/2)*(A+B*x)*(a+c*x^2)^2,x,2,2/9*a^2*A*x^(9/2)+2/11*a^2*B*x^(11/2)+4/13*a*A*c*x^(13/2)+4/15*a*B*c*x^(15/2)+2/17*A*c^2*x^(17/2)+2/19*B*c^2*x^(19/2)],
[x^(5/2)*(A+B*x)*(a+c*x^2)^2,x,2,2/7*a^2*A*x^(7/2)+2/9*a^2*B*x^(9/2)+4/11*a*A*c*x^(11/2)+4/13*a*B*c*x^(13/2)+2/15*A*c^2*x^(15/2)+2/17*B*c^2*x^(17/2)],
[x^(3/2)*(A+B*x)*(a+c*x^2)^2,x,2,2/5*a^2*A*x^(5/2)+2/7*a^2*B*x^(7/2)+4/9*a*A*c*x^(9/2)+4/11*a*B*c*x^(11/2)+2/13*A*c^2*x^(13/2)+2/15*B*c^2*x^(15/2)],
[(A+B*x)*(a+c*x^2)^2*sqrt(x),x,2,2/3*a^2*A*x^(3/2)+2/5*a^2*B*x^(5/2)+4/7*a*A*c*x^(7/2)+4/9*a*B*c*x^(9/2)+2/11*A*c^2*x^(11/2)+2/13*B*c^2*x^(13/2)],
[(A+B*x)*(a+c*x^2)^2/sqrt(x),x,2,2/3*a^2*B*x^(3/2)+4/5*a*A*c*x^(5/2)+4/7*a*B*c*x^(7/2)+2/9*A*c^2*x^(9/2)+2/11*B*c^2*x^(11/2)+2*a^2*A*sqrt(x)],
[(A+B*x)*(a+c*x^2)^2/x^(3/2),x,2,4/3*a*A*c*x^(3/2)+4/5*a*B*c*x^(5/2)+2/7*A*c^2*x^(7/2)+2/9*B*c^2*x^(9/2)-2*a^2*A/sqrt(x)+2*a^2*B*sqrt(x)],
[(A+B*x)*(a+c*x^2)^2/x^(5/2),x,2,-2/3*a^2*A/x^(3/2)+4/3*a*B*c*x^(3/2)+2/5*A*c^2*x^(5/2)+2/7*B*c^2*x^(7/2)-2*a^2*B/sqrt(x)+4*a*A*c*sqrt(x)],
[(A+B*x)*(a+c*x^2)^2/x^(7/2),x,2,-2/5*a^2*A/x^(5/2)-2/3*a^2*B/x^(3/2)+2/3*A*c^2*x^(3/2)+2/5*B*c^2*x^(5/2)-4*a*A*c/sqrt(x)+4*a*B*c*sqrt(x)],
[(A+B*x)*(a+c*x^2)^2/x^(9/2),x,2,-2/7*a^2*A/x^(7/2)-2/5*a^2*B/x^(5/2)-4/3*a*A*c/x^(3/2)+2/3*B*c^2*x^(3/2)-4*a*B*c/sqrt(x)+2*A*c^2*sqrt(x)],
[x^(7/2)*(A+B*x)*(a+c*x^2)^3,x,2,2/9*a^3*A*x^(9/2)+2/11*a^3*B*x^(11/2)+6/13*a^2*A*c*x^(13/2)+2/5*a^2*B*c*x^(15/2)+6/17*a*A*c^2*x^(17/2)+6/19*a*B*c^2*x^(19/2)+2/21*A*c^3*x^(21/2)+2/23*B*c^3*x^(23/2)],
[x^(5/2)*(A+B*x)*(a+c*x^2)^3,x,2,2/7*a^3*A*x^(7/2)+2/9*a^3*B*x^(9/2)+6/11*a^2*A*c*x^(11/2)+6/13*a^2*B*c*x^(13/2)+2/5*a*A*c^2*x^(15/2)+6/17*a*B*c^2*x^(17/2)+2/19*A*c^3*x^(19/2)+2/21*B*c^3*x^(21/2)],
[x^(3/2)*(A+B*x)*(a+c*x^2)^3,x,2,2/5*a^3*A*x^(5/2)+2/7*a^3*B*x^(7/2)+2/3*a^2*A*c*x^(9/2)+6/11*a^2*B*c*x^(11/2)+6/13*a*A*c^2*x^(13/2)+2/5*a*B*c^2*x^(15/2)+2/17*A*c^3*x^(17/2)+2/19*B*c^3*x^(19/2)],
[(A+B*x)*(a+c*x^2)^3*sqrt(x),x,2,2/3*a^3*A*x^(3/2)+2/5*a^3*B*x^(5/2)+6/7*a^2*A*c*x^(7/2)+2/3*a^2*B*c*x^(9/2)+6/11*a*A*c^2*x^(11/2)+6/13*a*B*c^2*x^(13/2)+2/15*A*c^3*x^(15/2)+2/17*B*c^3*x^(17/2)],
[(A+B*x)*(a+c*x^2)^3/sqrt(x),x,2,2/3*a^3*B*x^(3/2)+6/5*a^2*A*c*x^(5/2)+6/7*a^2*B*c*x^(7/2)+2/3*a*A*c^2*x^(9/2)+6/11*a*B*c^2*x^(11/2)+2/13*A*c^3*x^(13/2)+2/15*B*c^3*x^(15/2)+2*a^3*A*sqrt(x)],
[(A+B*x)*(a+c*x^2)^3/x^(3/2),x,2,2*a^2*A*c*x^(3/2)+6/5*a^2*B*c*x^(5/2)+6/7*a*A*c^2*x^(7/2)+2/3*a*B*c^2*x^(9/2)+2/11*A*c^3*x^(11/2)+2/13*B*c^3*x^(13/2)-2*a^3*A/sqrt(x)+2*a^3*B*sqrt(x)],
[(A+B*x)*(a+c*x^2)^3/x^(5/2),x,2,-2/3*a^3*A/x^(3/2)+2*a^2*B*c*x^(3/2)+6/5*a*A*c^2*x^(5/2)+6/7*a*B*c^2*x^(7/2)+2/9*A*c^3*x^(9/2)+2/11*B*c^3*x^(11/2)-2*a^3*B/sqrt(x)+6*a^2*A*c*sqrt(x)],
[(A+B*x)*(a+c*x^2)^3/x^(7/2),x,2,-2/5*a^3*A/x^(5/2)-2/3*a^3*B/x^(3/2)+2*a*A*c^2*x^(3/2)+6/5*a*B*c^2*x^(5/2)+2/7*A*c^3*x^(7/2)+2/9*B*c^3*x^(9/2)-6*a^2*A*c/sqrt(x)+6*a^2*B*c*sqrt(x)],
[(A+B*x)*(a+c*x^2)^3/x^(9/2),x,2,-2/7*a^3*A/x^(7/2)-2/5*a^3*B/x^(5/2)-2*a^2*A*c/x^(3/2)+2*a*B*c^2*x^(3/2)+2/5*A*c^3*x^(5/2)+2/7*B*c^3*x^(7/2)-6*a^2*B*c/sqrt(x)+6*a*A*c^2*sqrt(x)],
[(A+B*x)*(a+c*x^2)^3/x^(11/2),x,2,-2/9*a^3*A/x^(9/2)-2/7*a^3*B/x^(7/2)-6/5*a^2*A*c/x^(5/2)-2*a^2*B*c/x^(3/2)+2/3*A*c^3*x^(3/2)+2/5*B*c^3*x^(5/2)-6*a*A*c^2/sqrt(x)+6*a*B*c^2*sqrt(x)],

# p<0
[x^(5/2)*(A+B*x)/(a+c*x^2),x,13,2/3*A*x^(3/2)/c+2/5*B*x^(5/2)/c-a^(3/4)*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)-A*sqrt(c))/(c^(9/4)*sqrt(2))+a^(3/4)*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)-A*sqrt(c))/(c^(9/4)*sqrt(2))-1/2*a^(3/4)*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)+A*sqrt(c))/(c^(9/4)*sqrt(2))+1/2*a^(3/4)*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)+A*sqrt(c))/(c^(9/4)*sqrt(2))-2*a*B*sqrt(x)/c^2],
[x^(3/2)*(A+B*x)/(a+c*x^2),x,12,2/3*B*x^(3/2)/c-1/2*a^(1/4)*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-A*sqrt(c))/(c^(7/4)*sqrt(2))+1/2*a^(1/4)*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-A*sqrt(c))/(c^(7/4)*sqrt(2))+a^(1/4)*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+A*sqrt(c))/(c^(7/4)*sqrt(2))-a^(1/4)*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+A*sqrt(c))/(c^(7/4)*sqrt(2))+2*A*sqrt(x)/c],
[x^(1/2)*(A+B*x)/(a+c*x^2),x,11,arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)-A*sqrt(c))/(a^(1/4)*c^(5/4)*sqrt(2))-arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)-A*sqrt(c))/(a^(1/4)*c^(5/4)*sqrt(2))+1/2*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)+A*sqrt(c))/(a^(1/4)*c^(5/4)*sqrt(2))-1/2*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)+A*sqrt(c))/(a^(1/4)*c^(5/4)*sqrt(2))+2*B*sqrt(x)/c],
[(A+B*x)/(x^(1/2)*(a+c*x^2)),x,10,1/2*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-A*sqrt(c))/(a^(3/4)*c^(3/4)*sqrt(2))-1/2*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-A*sqrt(c))/(a^(3/4)*c^(3/4)*sqrt(2))-arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+A*sqrt(c))/(a^(3/4)*c^(3/4)*sqrt(2))+arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+A*sqrt(c))/(a^(3/4)*c^(3/4)*sqrt(2))],
[(A+B*x)/(x^(3/2)*(a+c*x^2)),x,11,-arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)-A*sqrt(c))/(a^(5/4)*c^(1/4)*sqrt(2))+arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)-A*sqrt(c))/(a^(5/4)*c^(1/4)*sqrt(2))-1/2*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)+A*sqrt(c))/(a^(5/4)*c^(1/4)*sqrt(2))+1/2*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)+A*sqrt(c))/(a^(5/4)*c^(1/4)*sqrt(2))-2*A/(a*sqrt(x))],
[(A+B*x)/(x^(5/2)*(a+c*x^2)),x,12,-2/3*A/(a*x^(3/2))-1/2*c^(1/4)*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-A*sqrt(c))/(a^(7/4)*sqrt(2))+1/2*c^(1/4)*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-A*sqrt(c))/(a^(7/4)*sqrt(2))+c^(1/4)*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+A*sqrt(c))/(a^(7/4)*sqrt(2))-c^(1/4)*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+A*sqrt(c))/(a^(7/4)*sqrt(2))-2*B/(a*sqrt(x))],
[(A+B*x)/(x^(7/2)*(a+c*x^2)),x,13,-2/5*A/(a*x^(5/2))-2/3*B/(a*x^(3/2))+c^(3/4)*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)-A*sqrt(c))/(a^(9/4)*sqrt(2))-c^(3/4)*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)-A*sqrt(c))/(a^(9/4)*sqrt(2))+1/2*c^(3/4)*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)+A*sqrt(c))/(a^(9/4)*sqrt(2))-1/2*c^(3/4)*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)+A*sqrt(c))/(a^(9/4)*sqrt(2))+2*A*c/(a^2*sqrt(x))],
[(A+B*x)/(x^(9/2)*(a+c*x^2)),x,14,-2/7*A/(a*x^(7/2))-2/5*B/(a*x^(5/2))+2/3*A*c/(a^2*x^(3/2))+1/2*c^(5/4)*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-A*sqrt(c))/(a^(11/4)*sqrt(2))-1/2*c^(5/4)*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-A*sqrt(c))/(a^(11/4)*sqrt(2))-c^(5/4)*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+A*sqrt(c))/(a^(11/4)*sqrt(2))+c^(5/4)*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+A*sqrt(c))/(a^(11/4)*sqrt(2))+2*B*c/(a^2*sqrt(x))],
[x^(5/2)*(A+B*x)/(a+c*x^2)^2,x,12,-1/2*x^(3/2)*(A+B*x)/(c*(a+c*x^2))+1/4*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(5*B*sqrt(a)-3*A*sqrt(c))/(a^(1/4)*c^(9/4)*sqrt(2))-1/4*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(5*B*sqrt(a)-3*A*sqrt(c))/(a^(1/4)*c^(9/4)*sqrt(2))+1/8*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(5*B*sqrt(a)+3*A*sqrt(c))/(a^(1/4)*c^(9/4)*sqrt(2))-1/8*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(5*B*sqrt(a)+3*A*sqrt(c))/(a^(1/4)*c^(9/4)*sqrt(2))+5/2*B*sqrt(x)/c^2],
[x^(3/2)*(A+B*x)/(a+c*x^2)^2,x,11,1/8*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(3*B*sqrt(a)-A*sqrt(c))/(a^(3/4)*c^(7/4)*sqrt(2))-1/8*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(3*B*sqrt(a)-A*sqrt(c))/(a^(3/4)*c^(7/4)*sqrt(2))-1/4*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(3*B*sqrt(a)+A*sqrt(c))/(a^(3/4)*c^(7/4)*sqrt(2))+1/4*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(3*B*sqrt(a)+A*sqrt(c))/(a^(3/4)*c^(7/4)*sqrt(2))-1/2*(A+B*x)*sqrt(x)/(c*(a+c*x^2))],
[x^(1/2)*(A+B*x)/(a+c*x^2)^2,x,11,-1/8*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-A*sqrt(c))/(a^(5/4)*c^(5/4)*sqrt(2))+1/8*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-A*sqrt(c))/(a^(5/4)*c^(5/4)*sqrt(2))-1/4*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+A*sqrt(c))/(a^(5/4)*c^(5/4)*sqrt(2))+1/4*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+A*sqrt(c))/(a^(5/4)*c^(5/4)*sqrt(2))-1/2*(a*B-A*c*x)*sqrt(x)/(a*c*(a+c*x^2))],
[(A+B*x)/(x^(1/2)*(a+c*x^2)^2),x,11,1/8*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-3*A*sqrt(c))/(a^(7/4)*c^(3/4)*sqrt(2))-1/8*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-3*A*sqrt(c))/(a^(7/4)*c^(3/4)*sqrt(2))-1/4*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+3*A*sqrt(c))/(a^(7/4)*c^(3/4)*sqrt(2))+1/4*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+3*A*sqrt(c))/(a^(7/4)*c^(3/4)*sqrt(2))+1/2*(A+B*x)*sqrt(x)/(a*(a+c*x^2))],
[(A+B*x)/(x^(3/2)*(a+c*x^2)^2),x,12,-1/4*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(3*B*sqrt(a)-5*A*sqrt(c))/(a^(9/4)*c^(1/4)*sqrt(2))+1/4*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(3*B*sqrt(a)-5*A*sqrt(c))/(a^(9/4)*c^(1/4)*sqrt(2))-1/8*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(3*B*sqrt(a)+5*A*sqrt(c))/(a^(9/4)*c^(1/4)*sqrt(2))+1/8*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(3*B*sqrt(a)+5*A*sqrt(c))/(a^(9/4)*c^(1/4)*sqrt(2))-5/2*A/(a^2*sqrt(x))+1/2*(A+B*x)/(a*(a+c*x^2)*sqrt(x))],
[(A+B*x)/(x^(5/2)*(a+c*x^2)^2),x,13,-7/6*A/(a^2*x^(3/2))+1/2*(A+B*x)/(a*x^(3/2)*(a+c*x^2))-1/8*c^(1/4)*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(5*B*sqrt(a)-7*A*sqrt(c))/(a^(11/4)*sqrt(2))+1/8*c^(1/4)*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(5*B*sqrt(a)-7*A*sqrt(c))/(a^(11/4)*sqrt(2))+1/4*c^(1/4)*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(5*B*sqrt(a)+7*A*sqrt(c))/(a^(11/4)*sqrt(2))-1/4*c^(1/4)*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(5*B*sqrt(a)+7*A*sqrt(c))/(a^(11/4)*sqrt(2))-5/2*B/(a^2*sqrt(x))],
[x^(7/2)*(A+B*x)/(a+c*x^2)^3,x,12,-1/4*x^(5/2)*(A+B*x)/(c*(a+c*x^2)^2)+1/64*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(21*B*sqrt(a)-5*A*sqrt(c))/(a^(3/4)*c^(11/4)*sqrt(2))-1/64*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(21*B*sqrt(a)-5*A*sqrt(c))/(a^(3/4)*c^(11/4)*sqrt(2))-1/32*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(21*B*sqrt(a)+5*A*sqrt(c))/(a^(3/4)*c^(11/4)*sqrt(2))+1/32*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(21*B*sqrt(a)+5*A*sqrt(c))/(a^(3/4)*c^(11/4)*sqrt(2))-1/16*(5*A+7*B*x)*sqrt(x)/(c^2*(a+c*x^2))],
[x^(5/2)*(A+B*x)/(a+c*x^2)^3,x,12,-1/4*x^(3/2)*(A+B*x)/(c*(a+c*x^2)^2)-1/64*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(5*B*sqrt(a)-3*A*sqrt(c))/(a^(5/4)*c^(9/4)*sqrt(2))+1/64*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(5*B*sqrt(a)-3*A*sqrt(c))/(a^(5/4)*c^(9/4)*sqrt(2))-1/32*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(5*B*sqrt(a)+3*A*sqrt(c))/(a^(5/4)*c^(9/4)*sqrt(2))+1/32*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(5*B*sqrt(a)+3*A*sqrt(c))/(a^(5/4)*c^(9/4)*sqrt(2))-1/16*(5*a*B-3*A*c*x)*sqrt(x)/(a*c^2*(a+c*x^2))],
[x^(3/2)*(A+B*x)/(a+c*x^2)^3,x,12,3/64*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-A*sqrt(c))/(a^(7/4)*c^(7/4)*sqrt(2))-3/64*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(B*sqrt(a)-A*sqrt(c))/(a^(7/4)*c^(7/4)*sqrt(2))-3/32*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+A*sqrt(c))/(a^(7/4)*c^(7/4)*sqrt(2))+3/32*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(B*sqrt(a)+A*sqrt(c))/(a^(7/4)*c^(7/4)*sqrt(2))-1/4*(A+B*x)*sqrt(x)/(c*(a+c*x^2)^2)+1/16*(A+3*B*x)*sqrt(x)/(a*c*(a+c*x^2))],
[x^(1/2)*(A+B*x)/(a+c*x^2)^3,x,12,-1/64*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(3*B*sqrt(a)-5*A*sqrt(c))/(a^(9/4)*c^(5/4)*sqrt(2))+1/64*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(3*B*sqrt(a)-5*A*sqrt(c))/(a^(9/4)*c^(5/4)*sqrt(2))-1/32*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(3*B*sqrt(a)+5*A*sqrt(c))/(a^(9/4)*c^(5/4)*sqrt(2))+1/32*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(3*B*sqrt(a)+5*A*sqrt(c))/(a^(9/4)*c^(5/4)*sqrt(2))-1/4*(a*B-A*c*x)*sqrt(x)/(a*c*(a+c*x^2)^2)+1/16*(a*B+5*A*c*x)*sqrt(x)/(a^2*c*(a+c*x^2))],
[(A+B*x)/(x^(1/2)*(a+c*x^2)^3),x,12,1/64*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(5*B*sqrt(a)-21*A*sqrt(c))/(a^(11/4)*c^(3/4)*sqrt(2))-1/64*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(5*B*sqrt(a)-21*A*sqrt(c))/(a^(11/4)*c^(3/4)*sqrt(2))-1/32*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(5*B*sqrt(a)+21*A*sqrt(c))/(a^(11/4)*c^(3/4)*sqrt(2))+1/32*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(5*B*sqrt(a)+21*A*sqrt(c))/(a^(11/4)*c^(3/4)*sqrt(2))+1/4*(A+B*x)*sqrt(x)/(a*(a+c*x^2)^2)+1/16*(7*A+5*B*x)*sqrt(x)/(a^2*(a+c*x^2))],
[(A+B*x)/(x^(3/2)*(a+c*x^2)^3),x,13,-3/32*arctan(1-c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(7*B*sqrt(a)-15*A*sqrt(c))/(a^(13/4)*c^(1/4)*sqrt(2))+3/32*arctan(1+c^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))*(7*B*sqrt(a)-15*A*sqrt(c))/(a^(13/4)*c^(1/4)*sqrt(2))-3/64*log(sqrt(a)+x*sqrt(c)-a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(7*B*sqrt(a)+15*A*sqrt(c))/(a^(13/4)*c^(1/4)*sqrt(2))+3/64*log(sqrt(a)+x*sqrt(c)+a^(1/4)*c^(1/4)*sqrt(2)*sqrt(x))*(7*B*sqrt(a)+15*A*sqrt(c))/(a^(13/4)*c^(1/4)*sqrt(2))-45/16*A/(a^3*sqrt(x))+1/4*(A+B*x)/(a*(a+c*x^2)^2*sqrt(x))+1/16*(9*A+7*B*x)/(a^2*(a+c*x^2)*sqrt(x))],
[(1-x)/((1+x^2)*sqrt(x)),x,4,-log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+log(1+x+sqrt(2)*sqrt(x))/sqrt(2)],

# Integrands of the form (e x)^(m/2) (A+B x) (a+c x^2)^(p/2)

# p>0
[(e*x)^(7/2)*(A+B*x)*sqrt(a+c*x^2),x,10,-14/117*a*B*e^2*(e*x)^(3/2)*(a+c*x^2)^(3/2)/c^2+2/11*A*e*(e*x)^(5/2)*(a+c*x^2)^(3/2)/c+2/13*B*(e*x)^(7/2)*(a+c*x^2)^(3/2)/c-10/77*a*A*e^3*(a+c*x^2)^(3/2)*sqrt(e*x)/c^2+28/195*a^3*B*e^4*x*sqrt(a+c*x^2)/(c^(5/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+2/15015*a^2*e^3*(325*A+539*B*x)*sqrt(e*x)*sqrt(a+c*x^2)/c^2-28/195*a^(13/4)*B*e^4*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(11/4)*sqrt(e*x)*sqrt(a+c*x^2))+2/15015*a^(11/4)*e^4*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(539*B*sqrt(a)+325*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(11/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(5/2)*(A+B*x)*sqrt(a+c*x^2),x,9,2/9*A*e*(e*x)^(3/2)*(a+c*x^2)^(3/2)/c+2/11*B*(e*x)^(5/2)*(a+c*x^2)^(3/2)/c-10/77*a*B*e^2*(a+c*x^2)^(3/2)*sqrt(e*x)/c^2-4/15*a^2*A*e^3*x*sqrt(a+c*x^2)/(c^(3/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+2/1155*a*e^2*(25*a*B-77*A*c*x)*sqrt(e*x)*sqrt(a+c*x^2)/c^2+4/15*a^(9/4)*A*e^3*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))+2/1155*a^(9/4)*e^3*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(25*B*sqrt(a)-77*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(9/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(3/2)*(A+B*x)*sqrt(a+c*x^2),x,8,2/9*B*(e*x)^(3/2)*(a+c*x^2)^(3/2)/c+2/7*A*e*(a+c*x^2)^(3/2)*sqrt(e*x)/c-4/15*a^2*B*e^2*x*sqrt(a+c*x^2)/(c^(3/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-2/105*a*e*(5*A+7*B*x)*sqrt(e*x)*sqrt(a+c*x^2)/c+4/15*a^(9/4)*B*e^2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))-2/105*a^(7/4)*e^2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(7*B*sqrt(a)+5*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(1/2)*(A+B*x)*sqrt(a+c*x^2),x,7,2/7*B*(a+c*x^2)^(3/2)*sqrt(e*x)/c+4/5*a*A*e*x*sqrt(a+c*x^2)/(sqrt(c)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-2/105*(5*a*B-21*A*c*x)*sqrt(e*x)*sqrt(a+c*x^2)/c-4/5*a^(5/4)*A*e*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))-2/105*a^(5/4)*e*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(5*B*sqrt(a)-21*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(5/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*sqrt(a+c*x^2)/(e*x)^(1/2),x,6,4/5*a*B*x*sqrt(a+c*x^2)/(sqrt(c)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+2/15*(5*A+3*B*x)*sqrt(e*x)*sqrt(a+c*x^2)/e-4/5*a^(5/4)*B*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))+2/15*a^(3/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(3*B*sqrt(a)+5*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*sqrt(a+c*x^2)/(e*x)^(3/2),x,6,-2/3*(3*A-B*x)*sqrt(a+c*x^2)/(e*sqrt(e*x))+4*A*x*sqrt(c)*sqrt(a+c*x^2)/(e*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-4*a^(1/4)*A*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e*sqrt(e*x)*sqrt(a+c*x^2))+2/3*a^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(B*sqrt(a)+3*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(1/4)*e*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*sqrt(a+c*x^2)/(e*x)^(5/2),x,6,-2/3*(A+3*B*x)*sqrt(a+c*x^2)/(e*(e*x)^(3/2))+4*B*x*sqrt(c)*sqrt(a+c*x^2)/(e^2*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-4*a^(1/4)*B*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^2*sqrt(e*x)*sqrt(a+c*x^2))+2/3*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(3*B*sqrt(a)+A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(1/4)*e^2*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*sqrt(a+c*x^2)/(e*x)^(7/2),x,7,-2/15*(3*A+5*B*x)*sqrt(a+c*x^2)/(e*(e*x)^(5/2))-4/5*A*c*sqrt(a+c*x^2)/(a*e^3*sqrt(e*x))+4/5*A*c^(3/2)*x*sqrt(a+c*x^2)/(a*e^3*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-4/5*A*c^(5/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*e^3*sqrt(e*x)*sqrt(a+c*x^2))+2/15*c^(3/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(5*B*sqrt(a)+3*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*e^3*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*sqrt(a+c*x^2)/(e*x)^(9/2),x,8,-4/21*A*c*sqrt(a+c*x^2)/(a*e^3*(e*x)^(3/2))-2/35*(5*A+7*B*x)*sqrt(a+c*x^2)/(e*(e*x)^(7/2))-4/5*B*c*sqrt(a+c*x^2)/(a*e^4*sqrt(e*x))+4/5*B*c^(3/2)*x*sqrt(a+c*x^2)/(a*e^4*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-4/5*B*c^(5/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*e^4*sqrt(e*x)*sqrt(a+c*x^2))+2/105*c^(5/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(21*B*sqrt(a)-5*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(5/4)*e^4*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(5/2)*(A+B*x)*(a+c*x^2)^(3/2),x,10,2/13*A*e*(e*x)^(3/2)*(a+c*x^2)^(5/2)/c+2/15*B*(e*x)^(5/2)*(a+c*x^2)^(5/2)/c+2/3003*a*e^2*(13*a*B-77*A*c*x)*(a+c*x^2)^(3/2)*sqrt(e*x)/c^2-2/33*a*B*e^2*(a+c*x^2)^(5/2)*sqrt(e*x)/c^2-8/65*a^3*A*e^3*x*sqrt(a+c*x^2)/(c^(3/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+4/15015*a^2*e^2*(65*a*B-231*A*c*x)*sqrt(e*x)*sqrt(a+c*x^2)/c^2+8/65*a^(13/4)*A*e^3*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))+4/15015*a^(13/4)*e^3*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(65*B*sqrt(a)-231*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(9/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(3/2)*(A+B*x)*(a+c*x^2)^(3/2),x,9,2/13*B*(e*x)^(3/2)*(a+c*x^2)^(5/2)/c-2/3003*a*e*(39*A+77*B*x)*(a+c*x^2)^(3/2)*sqrt(e*x)/c+2/11*A*e*(a+c*x^2)^(5/2)*sqrt(e*x)/c-8/65*a^3*B*e^2*x*sqrt(a+c*x^2)/(c^(3/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-4/5005*a^2*e*(65*A+77*B*x)*sqrt(e*x)*sqrt(a+c*x^2)/c+8/65*a^(13/4)*B*e^2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))-4/5005*a^(11/4)*e^2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(77*B*sqrt(a)+65*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(1/2)*(A+B*x)*(a+c*x^2)^(3/2),x,8,-2/693*(9*a*B-77*A*c*x)*(a+c*x^2)^(3/2)*sqrt(e*x)/c+2/11*B*(a+c*x^2)^(5/2)*sqrt(e*x)/c+8/15*a^2*A*e*x*sqrt(a+c*x^2)/(sqrt(c)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-4/1155*a*(15*a*B-77*A*c*x)*sqrt(e*x)*sqrt(a+c*x^2)/c-8/15*a^(9/4)*A*e*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))-4/1155*a^(9/4)*e*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(15*B*sqrt(a)-77*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(5/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(3/2)/(e*x)^(1/2),x,7,2/63*(9*A+7*B*x)*(a+c*x^2)^(3/2)*sqrt(e*x)/e+8/15*a^2*B*x*sqrt(a+c*x^2)/(sqrt(c)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+4/105*a*(15*A+7*B*x)*sqrt(e*x)*sqrt(a+c*x^2)/e-8/15*a^(9/4)*B*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))+4/105*a^(7/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(7*B*sqrt(a)+15*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(3/2)/(e*x)^(3/2),x,7,-2/7*(7*A-B*x)*(a+c*x^2)^(3/2)/(e*sqrt(e*x))+24/5*a*A*x*sqrt(c)*sqrt(a+c*x^2)/(e*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+4/35*(5*a*B+21*A*c*x)*sqrt(e*x)*sqrt(a+c*x^2)/e^2-24/5*a^(5/4)*A*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e*sqrt(e*x)*sqrt(a+c*x^2))+4/35*a^(5/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(5*B*sqrt(a)+21*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(1/4)*e*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(3/2)/(e*x)^(5/2),x,7,-2/15*(5*A-3*B*x)*(a+c*x^2)^(3/2)/(e*(e*x)^(3/2))-4/15*(9*a*B-5*A*c*x)*sqrt(a+c*x^2)/(e^2*sqrt(e*x))+24/5*a*B*x*sqrt(c)*sqrt(a+c*x^2)/(e^2*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-24/5*a^(5/4)*B*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^2*sqrt(e*x)*sqrt(a+c*x^2))+4/15*a^(3/4)*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(9*B*sqrt(a)+5*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^2*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(3/2)/(e*x)^(7/2),x,7,-2/15*(3*A+5*B*x)*(a+c*x^2)^(3/2)/(e*(e*x)^(5/2))-4/15*c*(9*A-5*B*x)*sqrt(a+c*x^2)/(e^3*sqrt(e*x))+24/5*A*c^(3/2)*x*sqrt(a+c*x^2)/(e^3*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-24/5*a^(1/4)*A*c^(5/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^3*sqrt(e*x)*sqrt(a+c*x^2))+4/15*a^(1/4)*c^(3/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(5*B*sqrt(a)+9*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^3*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(3/2)/(e*x)^(9/2),x,7,-2/35*(5*A+7*B*x)*(a+c*x^2)^(3/2)/(e*(e*x)^(7/2))-4/35*c*(5*A+21*B*x)*sqrt(a+c*x^2)/(e^3*(e*x)^(3/2))+24/5*B*c^(3/2)*x*sqrt(a+c*x^2)/(e^4*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-24/5*a^(1/4)*B*c^(5/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^4*sqrt(e*x)*sqrt(a+c*x^2))+4/35*c^(5/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(21*B*sqrt(a)+5*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(1/4)*e^4*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(3/2)*(A+B*x)*(a+c*x^2)^(5/2),x,10,2/17*B*(e*x)^(3/2)*(a+c*x^2)^(7/2)/c-4/51051*a^2*e*(221*A+385*B*x)*(a+c*x^2)^(3/2)*sqrt(e*x)/c-2/36465*a*e*(221*A+495*B*x)*(a+c*x^2)^(5/2)*sqrt(e*x)/c+2/15*A*e*(a+c*x^2)^(7/2)*sqrt(e*x)/c-16/221*a^4*B*e^2*x*sqrt(a+c*x^2)/(c^(3/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-8/51051*a^3*e*(221*A+231*B*x)*sqrt(e*x)*sqrt(a+c*x^2)/c+16/221*a^(17/4)*B*e^2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))-8/51051*a^(15/4)*e^2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(231*B*sqrt(a)+221*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(1/2)*(A+B*x)*(a+c*x^2)^(5/2),x,9,-4/9009*a*(39*a*B-385*A*c*x)*(a+c*x^2)^(3/2)*sqrt(e*x)/c-2/2145*(13*a*B-165*A*c*x)*(a+c*x^2)^(5/2)*sqrt(e*x)/c+2/15*B*(a+c*x^2)^(7/2)*sqrt(e*x)/c+16/39*a^3*A*e*x*sqrt(a+c*x^2)/(sqrt(c)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-8/3003*a^2*(13*a*B-77*A*c*x)*sqrt(e*x)*sqrt(a+c*x^2)/c-16/39*a^(13/4)*A*e*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))-8/3003*a^(13/4)*e*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(13*B*sqrt(a)-77*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(5/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(5/2)/(e*x)^(1/2),x,8,20/9009*a*(117*A+77*B*x)*(a+c*x^2)^(3/2)*sqrt(e*x)/e+2/143*(13*A+11*B*x)*(a+c*x^2)^(5/2)*sqrt(e*x)/e+16/39*a^3*B*x*sqrt(a+c*x^2)/(sqrt(c)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+8/3003*a^2*(195*A+77*B*x)*sqrt(e*x)*sqrt(a+c*x^2)/e-16/39*a^(13/4)*B*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))+8/3003*a^(11/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(77*B*sqrt(a)+195*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(5/2)/(e*x)^(3/2),x,8,-2/11*(11*A-B*x)*(a+c*x^2)^(5/2)/(e*sqrt(e*x))+20/693*(9*a*B+77*A*c*x)*(a+c*x^2)^(3/2)*sqrt(e*x)/e^2+16/3*a^2*A*x*sqrt(c)*sqrt(a+c*x^2)/(e*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+8/231*a*(15*a*B+77*A*c*x)*sqrt(e*x)*sqrt(a+c*x^2)/e^2-16/3*a^(9/4)*A*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e*sqrt(e*x)*sqrt(a+c*x^2))+8/231*a^(9/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(15*B*sqrt(a)+77*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(1/4)*e*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(5/2)/(e*x)^(5/2),x,8,-2/9*(3*A-B*x)*(a+c*x^2)^(5/2)/(e*(e*x)^(3/2))-20/63*(7*a*B-3*A*c*x)*(a+c*x^2)^(3/2)/(e^2*sqrt(e*x))+16/3*a^2*B*x*sqrt(c)*sqrt(a+c*x^2)/(e^2*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+8/21*a*c*(5*A+7*B*x)*sqrt(e*x)*sqrt(a+c*x^2)/e^3-16/3*a^(9/4)*B*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^2*sqrt(e*x)*sqrt(a+c*x^2))+8/21*a^(7/4)*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(7*B*sqrt(a)+5*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^2*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(5/2)/(e*x)^(7/2),x,8,-4/105*(25*a*B-21*A*c*x)*(a+c*x^2)^(3/2)/(e^2*(e*x)^(3/2))-2/35*(7*A-5*B*x)*(a+c*x^2)^(5/2)/(e*(e*x)^(5/2))-8/105*a*c*(63*A-25*B*x)*sqrt(a+c*x^2)/(e^3*sqrt(e*x))+48/5*a*A*c^(3/2)*x*sqrt(a+c*x^2)/(e^3*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-48/5*a^(5/4)*A*c^(5/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^3*sqrt(e*x)*sqrt(a+c*x^2))+8/105*a^(5/4)*c^(3/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(25*B*sqrt(a)+63*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^3*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(5/2)/(e*x)^(9/2),x,8,-4/105*(21*a*B+25*A*c*x)*(a+c*x^2)^(3/2)/(e^2*(e*x)^(5/2))-2/35*(5*A-7*B*x)*(a+c*x^2)^(5/2)/(e*(e*x)^(7/2))-8/105*c*(63*a*B-25*A*c*x)*sqrt(a+c*x^2)/(e^4*sqrt(e*x))+48/5*a*B*c^(3/2)*x*sqrt(a+c*x^2)/(e^4*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-48/5*a^(5/4)*B*c^(5/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^4*sqrt(e*x)*sqrt(a+c*x^2))+8/105*a^(3/4)*c^(5/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(63*B*sqrt(a)+25*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^4*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(5/2)/(e*x)^(11/2),x,8,-4/63*c*(7*A+15*B*x)*(a+c*x^2)^(3/2)/(e^3*(e*x)^(5/2))-2/63*(7*A+9*B*x)*(a+c*x^2)^(5/2)/(e*(e*x)^(9/2))-8/21*c^2*(7*A-5*B*x)*sqrt(a+c*x^2)/(e^5*sqrt(e*x))+16/3*A*c^(5/2)*x*sqrt(a+c*x^2)/(e^5*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-16/3*a^(1/4)*A*c^(9/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^5*sqrt(e*x)*sqrt(a+c*x^2))+8/21*a^(1/4)*c^(7/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(5*B*sqrt(a)+7*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(e^5*sqrt(e*x)*sqrt(a+c*x^2))],

# p<0
[(e*x)^(7/2)*(A+B*x)/sqrt(a+c*x^2),x,9,-14/45*a*B*e^2*(e*x)^(3/2)*sqrt(a+c*x^2)/c^2+2/7*A*e*(e*x)^(5/2)*sqrt(a+c*x^2)/c+2/9*B*(e*x)^(7/2)*sqrt(a+c*x^2)/c+14/15*a^2*B*e^4*x*sqrt(a+c*x^2)/(c^(5/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-10/21*a*A*e^3*sqrt(e*x)*sqrt(a+c*x^2)/c^2-14/15*a^(9/4)*B*e^4*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(11/4)*sqrt(e*x)*sqrt(a+c*x^2))+1/105*a^(7/4)*e^4*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(49*B*sqrt(a)+25*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(11/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(5/2)*(A+B*x)/sqrt(a+c*x^2),x,8,2/5*A*e*(e*x)^(3/2)*sqrt(a+c*x^2)/c+2/7*B*(e*x)^(5/2)*sqrt(a+c*x^2)/c-6/5*a*A*e^3*x*sqrt(a+c*x^2)/(c^(3/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-10/21*a*B*e^2*sqrt(e*x)*sqrt(a+c*x^2)/c^2+6/5*a^(5/4)*A*e^3*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))+1/105*a^(5/4)*e^3*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(25*B*sqrt(a)-63*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(9/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(3/2)*(A+B*x)/sqrt(a+c*x^2),x,7,2/5*B*(e*x)^(3/2)*sqrt(a+c*x^2)/c-6/5*a*B*e^2*x*sqrt(a+c*x^2)/(c^(3/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+2/3*A*e*sqrt(e*x)*sqrt(a+c*x^2)/c+6/5*a^(5/4)*B*e^2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))-1/15*a^(3/4)*e^2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(9*B*sqrt(a)+5*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(1/2)*(A+B*x)/sqrt(a+c*x^2),x,6,2*A*e*x*sqrt(a+c*x^2)/(sqrt(c)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+2/3*B*sqrt(e*x)*sqrt(a+c*x^2)/c-2*a^(1/4)*A*e*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))-1/3*a^(1/4)*e*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(B*sqrt(a)-3*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(5/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((e*x)^(1/2)*sqrt(a+c*x^2)),x,5,2*B*x*sqrt(a+c*x^2)/(sqrt(c)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-2*a^(1/4)*B*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))+a^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*(B+A*sqrt(c)/sqrt(a))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((e*x)^(3/2)*sqrt(a+c*x^2)),x,6,-2*A*sqrt(a+c*x^2)/(a*e*sqrt(e*x))+2*A*x*sqrt(c)*sqrt(a+c*x^2)/(a*e*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-2*A*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*e*sqrt(e*x)*sqrt(a+c*x^2))+sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(B*sqrt(a)+A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*c^(1/4)*e*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((e*x)^(5/2)*sqrt(a+c*x^2)),x,7,-2/3*A*sqrt(a+c*x^2)/(a*e*(e*x)^(3/2))-2*B*sqrt(a+c*x^2)/(a*e^2*sqrt(e*x))+2*B*x*sqrt(c)*sqrt(a+c*x^2)/(a*e^2*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-2*B*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*e^2*sqrt(e*x)*sqrt(a+c*x^2))+1/3*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(3*B*sqrt(a)-A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(5/4)*e^2*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((e*x)^(7/2)*sqrt(a+c*x^2)),x,8,-2/5*A*sqrt(a+c*x^2)/(a*e*(e*x)^(5/2))-2/3*B*sqrt(a+c*x^2)/(a*e^2*(e*x)^(3/2))+6/5*A*c*sqrt(a+c*x^2)/(a^2*e^3*sqrt(e*x))-6/5*A*c^(3/2)*x*sqrt(a+c*x^2)/(a^2*e^3*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+6/5*A*c^(5/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(7/4)*e^3*sqrt(e*x)*sqrt(a+c*x^2))-1/15*c^(3/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(5*B*sqrt(a)+9*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(7/4)*e^3*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(7/2)*(A+B*x)/(a+c*x^2)^(3/2),x,8,-e*(e*x)^(5/2)*(A+B*x)/(c*sqrt(a+c*x^2))+7/5*B*e^2*(e*x)^(3/2)*sqrt(a+c*x^2)/c^2-21/5*a*B*e^4*x*sqrt(a+c*x^2)/(c^(5/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+5/3*A*e^3*sqrt(e*x)*sqrt(a+c*x^2)/c^2+21/5*a^(5/4)*B*e^4*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(11/4)*sqrt(e*x)*sqrt(a+c*x^2))-1/30*a^(3/4)*e^4*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(63*B*sqrt(a)+25*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(11/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(5/2)*(A+B*x)/(a+c*x^2)^(3/2),x,7,-e*(e*x)^(3/2)*(A+B*x)/(c*sqrt(a+c*x^2))+3*A*e^3*x*sqrt(a+c*x^2)/(c^(3/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+5/3*B*e^2*sqrt(e*x)*sqrt(a+c*x^2)/c^2-3*a^(1/4)*A*e^3*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))-1/6*a^(1/4)*e^3*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(5*B*sqrt(a)-9*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(9/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(3/2)*(A+B*x)/(a+c*x^2)^(3/2),x,6,-e*(A+B*x)*sqrt(e*x)/(c*sqrt(a+c*x^2))+3*B*e^2*x*sqrt(a+c*x^2)/(c^(3/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-3*a^(1/4)*B*e^2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))+1/2*e^2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(3*B*sqrt(a)+A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(1/4)*c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(1/2)*(A+B*x)/(a+c*x^2)^(3/2),x,6,-(a*B-A*c*x)*sqrt(e*x)/(a*c*sqrt(a+c*x^2))-A*e*x*sqrt(a+c*x^2)/(a*sqrt(c)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+A*e*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))+1/2*e*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(B*sqrt(a)-A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*c^(5/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((e*x)^(1/2)*(a+c*x^2)^(3/2)),x,6,(A+B*x)*sqrt(e*x)/(a*e*sqrt(a+c*x^2))-B*x*sqrt(a+c*x^2)/(a*sqrt(c)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+B*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))-1/2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(B*sqrt(a)-A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(5/4)*c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((e*x)^(3/2)*(a+c*x^2)^(3/2)),x,7,(A+B*x)/(a*e*sqrt(e*x)*sqrt(a+c*x^2))-3*A*sqrt(a+c*x^2)/(a^2*e*sqrt(e*x))+3*A*x*sqrt(c)*sqrt(a+c*x^2)/(a^2*e*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-3*A*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(7/4)*e*sqrt(e*x)*sqrt(a+c*x^2))+1/2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(B*sqrt(a)+3*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(7/4)*c^(1/4)*e*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((e*x)^(5/2)*(a+c*x^2)^(3/2)),x,8,(A+B*x)/(a*e*(e*x)^(3/2)*sqrt(a+c*x^2))-5/3*A*sqrt(a+c*x^2)/(a^2*e*(e*x)^(3/2))-3*B*sqrt(a+c*x^2)/(a^2*e^2*sqrt(e*x))+3*B*x*sqrt(c)*sqrt(a+c*x^2)/(a^2*e^2*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-3*B*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(7/4)*e^2*sqrt(e*x)*sqrt(a+c*x^2))+1/6*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(9*B*sqrt(a)-5*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(9/4)*e^2*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((e*x)^(7/2)*(a+c*x^2)^(3/2)),x,9,(A+B*x)/(a*e*(e*x)^(5/2)*sqrt(a+c*x^2))-7/5*A*sqrt(a+c*x^2)/(a^2*e*(e*x)^(5/2))-5/3*B*sqrt(a+c*x^2)/(a^2*e^2*(e*x)^(3/2))+21/5*A*c*sqrt(a+c*x^2)/(a^3*e^3*sqrt(e*x))-21/5*A*c^(3/2)*x*sqrt(a+c*x^2)/(a^3*e^3*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+21/5*A*c^(5/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(11/4)*e^3*sqrt(e*x)*sqrt(a+c*x^2))-1/30*c^(3/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(25*B*sqrt(a)+63*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(11/4)*e^3*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(13/2)*(A+B*x)/(a+c*x^2)^(5/2),x,10,-1/3*e*(e*x)^(11/2)*(A+B*x)/(c*(a+c*x^2)^(3/2))-1/6*e^3*(e*x)^(7/2)*(11*A+13*B*x)/(c^2*sqrt(a+c*x^2))+77/30*A*e^5*(e*x)^(3/2)*sqrt(a+c*x^2)/c^3+39/14*B*e^4*(e*x)^(5/2)*sqrt(a+c*x^2)/c^3-77/10*a*A*e^7*x*sqrt(a+c*x^2)/(c^(7/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-65/14*a*B*e^6*sqrt(e*x)*sqrt(a+c*x^2)/c^4+77/10*a^(5/4)*A*e^7*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(15/4)*sqrt(e*x)*sqrt(a+c*x^2))+1/140*a^(5/4)*e^7*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(325*B*sqrt(a)-539*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(17/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(11/2)*(A+B*x)/(a+c*x^2)^(5/2),x,9,-1/3*e*(e*x)^(9/2)*(A+B*x)/(c*(a+c*x^2)^(3/2))-1/6*e^3*(e*x)^(5/2)*(9*A+11*B*x)/(c^2*sqrt(a+c*x^2))+77/30*B*e^4*(e*x)^(3/2)*sqrt(a+c*x^2)/c^3-77/10*a*B*e^6*x*sqrt(a+c*x^2)/(c^(7/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+5/2*A*e^5*sqrt(e*x)*sqrt(a+c*x^2)/c^3+77/10*a^(5/4)*B*e^6*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(15/4)*sqrt(e*x)*sqrt(a+c*x^2))-1/20*a^(3/4)*e^6*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(77*B*sqrt(a)+25*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(15/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(9/2)*(A+B*x)/(a+c*x^2)^(5/2),x,8,-1/3*e*(e*x)^(7/2)*(A+B*x)/(c*(a+c*x^2)^(3/2))-1/6*e^3*(e*x)^(3/2)*(7*A+9*B*x)/(c^2*sqrt(a+c*x^2))+7/2*A*e^5*x*sqrt(a+c*x^2)/(c^(5/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+5/2*B*e^4*sqrt(e*x)*sqrt(a+c*x^2)/c^3-7/2*a^(1/4)*A*e^5*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(11/4)*sqrt(e*x)*sqrt(a+c*x^2))-1/4*a^(1/4)*e^5*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(5*B*sqrt(a)-7*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(13/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(7/2)*(A+B*x)/(a+c*x^2)^(5/2),x,7,-1/3*e*(e*x)^(5/2)*(A+B*x)/(c*(a+c*x^2)^(3/2))-1/6*e^3*(5*A+7*B*x)*sqrt(e*x)/(c^2*sqrt(a+c*x^2))+7/2*B*e^4*x*sqrt(a+c*x^2)/(c^(5/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-7/2*a^(1/4)*B*e^4*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(11/4)*sqrt(e*x)*sqrt(a+c*x^2))+1/12*e^4*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(21*B*sqrt(a)+5*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(1/4)*c^(11/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(5/2)*(A+B*x)/(a+c*x^2)^(5/2),x,7,-1/3*e*(e*x)^(3/2)*(A+B*x)/(c*(a+c*x^2)^(3/2))-1/6*e^2*(5*a*B-3*A*c*x)*sqrt(e*x)/(a*c^2*sqrt(a+c*x^2))-1/2*A*e^3*x*sqrt(a+c*x^2)/(a*c^(3/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+1/2*A*e^3*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))+1/12*e^3*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(5*B*sqrt(a)-3*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*c^(9/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(3/2)*(A+B*x)/(a+c*x^2)^(5/2),x,7,-1/3*e*(A+B*x)*sqrt(e*x)/(c*(a+c*x^2)^(3/2))+1/6*e*(A+3*B*x)*sqrt(e*x)/(a*c*sqrt(a+c*x^2))-1/2*B*e^2*x*sqrt(a+c*x^2)/(a*c^(3/2)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+1/2*B*e^2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))-1/12*e^2*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(3*B*sqrt(a)-A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(5/4)*c^(7/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(e*x)^(1/2)*(A+B*x)/(a+c*x^2)^(5/2),x,7,-1/3*(a*B-A*c*x)*sqrt(e*x)/(a*c*(a+c*x^2)^(3/2))+1/6*(a*B+3*A*c*x)*sqrt(e*x)/(a^2*c*sqrt(a+c*x^2))-1/2*A*e*x*sqrt(a+c*x^2)/(a^2*sqrt(c)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+1/2*A*e*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(7/4)*c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))+1/12*e*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(B*sqrt(a)-3*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(7/4)*c^(5/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((e*x)^(1/2)*(a+c*x^2)^(5/2)),x,7,1/3*(A+B*x)*sqrt(e*x)/(a*e*(a+c*x^2)^(3/2))+1/6*(5*A+3*B*x)*sqrt(e*x)/(a^2*e*sqrt(a+c*x^2))-1/2*B*x*sqrt(a+c*x^2)/(a^2*sqrt(c)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+1/2*B*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(7/4)*c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))-1/12*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(3*B*sqrt(a)-5*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(9/4)*c^(3/4)*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((e*x)^(3/2)*(a+c*x^2)^(5/2)),x,8,1/3*(A+B*x)/(a*e*(a+c*x^2)^(3/2)*sqrt(e*x))+1/6*(7*A+5*B*x)/(a^2*e*sqrt(e*x)*sqrt(a+c*x^2))-7/2*A*sqrt(a+c*x^2)/(a^3*e*sqrt(e*x))+7/2*A*x*sqrt(c)*sqrt(a+c*x^2)/(a^3*e*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-7/2*A*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(11/4)*e*sqrt(e*x)*sqrt(a+c*x^2))+1/12*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(5*B*sqrt(a)+21*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(11/4)*c^(1/4)*e*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((e*x)^(5/2)*(a+c*x^2)^(5/2)),x,9,1/3*(A+B*x)/(a*e*(e*x)^(3/2)*(a+c*x^2)^(3/2))+1/6*(9*A+7*B*x)/(a^2*e*(e*x)^(3/2)*sqrt(a+c*x^2))-5/2*A*sqrt(a+c*x^2)/(a^3*e*(e*x)^(3/2))-7/2*B*sqrt(a+c*x^2)/(a^3*e^2*sqrt(e*x))+7/2*B*x*sqrt(c)*sqrt(a+c*x^2)/(a^3*e^2*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-7/2*B*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(11/4)*e^2*sqrt(e*x)*sqrt(a+c*x^2))+1/4*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(7*B*sqrt(a)-5*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(13/4)*e^2*sqrt(e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((e*x)^(7/2)*(a+c*x^2)^(5/2)),x,10,1/3*(A+B*x)/(a*e*(e*x)^(5/2)*(a+c*x^2)^(3/2))+1/6*(11*A+9*B*x)/(a^2*e*(e*x)^(5/2)*sqrt(a+c*x^2))-77/30*A*sqrt(a+c*x^2)/(a^3*e*(e*x)^(5/2))-5/2*B*sqrt(a+c*x^2)/(a^3*e^2*(e*x)^(3/2))+77/10*A*c*sqrt(a+c*x^2)/(a^4*e^3*sqrt(e*x))-77/10*A*c^(3/2)*x*sqrt(a+c*x^2)/(a^4*e^3*(sqrt(a)+x*sqrt(c))*sqrt(e*x))+77/10*A*c^(5/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(15/4)*e^3*sqrt(e*x)*sqrt(a+c*x^2))-1/20*c^(3/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/2))*(25*B*sqrt(a)+77*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(15/4)*e^3*sqrt(e*x)*sqrt(a+c*x^2))],

# Integrands of the form (e x)^m (A+B x) (a+c x^2)^p when m symbolic
[(e*x)^m*(A+B*x)*(a+c*x^2)^4,x,2,a^4*A*(e*x)^(1+m)/(e*(1+m))+a^4*B*(e*x)^(2+m)/(e^2*(2+m))+4*a^3*A*c*(e*x)^(3+m)/(e^3*(3+m))+4*a^3*B*c*(e*x)^(4+m)/(e^4*(4+m))+6*a^2*A*c^2*(e*x)^(5+m)/(e^5*(5+m))+6*a^2*B*c^2*(e*x)^(6+m)/(e^6*(6+m))+4*a*A*c^3*(e*x)^(7+m)/(e^7*(7+m))+4*a*B*c^3*(e*x)^(8+m)/(e^8*(8+m))+A*c^4*(e*x)^(9+m)/(e^9*(9+m))+B*c^4*(e*x)^(10+m)/(e^10*(10+m))],
[(e*x)^m*(A+B*x)*(a+c*x^2)^3,x,2,a^3*A*(e*x)^(1+m)/(e*(1+m))+a^3*B*(e*x)^(2+m)/(e^2*(2+m))+3*a^2*A*c*(e*x)^(3+m)/(e^3*(3+m))+3*a^2*B*c*(e*x)^(4+m)/(e^4*(4+m))+3*a*A*c^2*(e*x)^(5+m)/(e^5*(5+m))+3*a*B*c^2*(e*x)^(6+m)/(e^6*(6+m))+A*c^3*(e*x)^(7+m)/(e^7*(7+m))+B*c^3*(e*x)^(8+m)/(e^8*(8+m))],
[(e*x)^m*(A+B*x)*(a+c*x^2)^2,x,2,a^2*A*(e*x)^(1+m)/(e*(1+m))+a^2*B*(e*x)^(2+m)/(e^2*(2+m))+2*a*A*c*(e*x)^(3+m)/(e^3*(3+m))+2*a*B*c*(e*x)^(4+m)/(e^4*(4+m))+A*c^2*(e*x)^(5+m)/(e^5*(5+m))+B*c^2*(e*x)^(6+m)/(e^6*(6+m))],
[(e*x)^m*(A+B*x)*(a+c*x^2),x,2,a*A*(e*x)^(1+m)/(e*(1+m))+a*B*(e*x)^(2+m)/(e^2*(2+m))+A*c*(e*x)^(3+m)/(e^3*(3+m))+B*c*(e*x)^(4+m)/(e^4*(4+m))],
[(e*x)^m*(A+B*x)/(a+c*x^2),x,3,A*(e*x)^(1+m)*hypergeom([1,1/2*(1+m)],[1/2*(3+m)],-c*x^2/a)/(a*e*(1+m))+B*(e*x)^(2+m)*hypergeom([1,1/2*(2+m)],[1/2*(4+m)],-c*x^2/a)/(a*e^2*(2+m))],
[(e*x)^m*(A+B*x)/(a+c*x^2)^2,x,3,A*(e*x)^(1+m)*hypergeom([2,1/2*(1+m)],[1/2*(3+m)],-c*x^2/a)/(a^2*e*(1+m))+B*(e*x)^(2+m)*hypergeom([2,1/2*(2+m)],[1/2*(4+m)],-c*x^2/a)/(a^2*e^2*(2+m))],
[(e*x)^m*(A+B*x)/(a+c*x^2)^3,x,3,A*(e*x)^(1+m)*hypergeom([3,1/2*(1+m)],[1/2*(3+m)],-c*x^2/a)/(a^3*e*(1+m))+B*(e*x)^(2+m)*hypergeom([3,1/2*(2+m)],[1/2*(4+m)],-c*x^2/a)/(a^3*e^2*(2+m))],
[(e*x)^m*(A+B*x)*(a+c*x^2)^(5/2),x,5,a^2*A*(e*x)^(1+m)*hypergeom([-5/2,1/2*(1+m)],[1/2*(3+m)],-c*x^2/a)*sqrt(a+c*x^2)/(e*(1+m)*sqrt(1+c*x^2/a))+a^2*B*(e*x)^(2+m)*hypergeom([-5/2,1/2*(2+m)],[1/2*(4+m)],-c*x^2/a)*sqrt(a+c*x^2)/(e^2*(2+m)*sqrt(1+c*x^2/a))],
[(e*x)^m*(A+B*x)*(a+c*x^2)^(3/2),x,5,a*A*(e*x)^(1+m)*hypergeom([-3/2,1/2*(1+m)],[1/2*(3+m)],-c*x^2/a)*sqrt(a+c*x^2)/(e*(1+m)*sqrt(1+c*x^2/a))+a*B*(e*x)^(2+m)*hypergeom([-3/2,1/2*(2+m)],[1/2*(4+m)],-c*x^2/a)*sqrt(a+c*x^2)/(e^2*(2+m)*sqrt(1+c*x^2/a))],
[(e*x)^m*(A+B*x)*(a+c*x^2)^(1/2),x,5,A*(e*x)^(1+m)*hypergeom([-1/2,1/2*(1+m)],[1/2*(3+m)],-c*x^2/a)*sqrt(a+c*x^2)/(e*(1+m)*sqrt(1+c*x^2/a))+B*(e*x)^(2+m)*hypergeom([-1/2,1/2*(2+m)],[1/2*(4+m)],-c*x^2/a)*sqrt(a+c*x^2)/(e^2*(2+m)*sqrt(1+c*x^2/a))],
[(e*x)^m*(A+B*x)/(a+c*x^2)^(1/2),x,5,A*(e*x)^(1+m)*hypergeom([1/2,1/2*(1+m)],[1/2*(3+m)],-c*x^2/a)*sqrt(1+c*x^2/a)/(e*(1+m)*sqrt(a+c*x^2))+B*(e*x)^(2+m)*hypergeom([1/2,1/2*(2+m)],[1/2*(4+m)],-c*x^2/a)*sqrt(1+c*x^2/a)/(e^2*(2+m)*sqrt(a+c*x^2))],
[(e*x)^m*(A+B*x)/(a+c*x^2)^(3/2),x,5,A*(e*x)^(1+m)*hypergeom([3/2,1/2*(1+m)],[1/2*(3+m)],-c*x^2/a)*sqrt(1+c*x^2/a)/(a*e*(1+m)*sqrt(a+c*x^2))+B*(e*x)^(2+m)*hypergeom([3/2,1/2*(2+m)],[1/2*(4+m)],-c*x^2/a)*sqrt(1+c*x^2/a)/(a*e^2*(2+m)*sqrt(a+c*x^2))],
[(e*x)^m*(A+B*x)/(a+c*x^2)^(5/2),x,5,A*(e*x)^(1+m)*hypergeom([5/2,1/2*(1+m)],[1/2*(3+m)],-c*x^2/a)*sqrt(1+c*x^2/a)/(a^2*e*(1+m)*sqrt(a+c*x^2))+B*(e*x)^(2+m)*hypergeom([5/2,1/2*(2+m)],[1/2*(4+m)],-c*x^2/a)*sqrt(1+c*x^2/a)/(a^2*e^2*(2+m)*sqrt(a+c*x^2))],

#  Following integrands are equal: 
[x^m*(1+a*x)/(1-a^2*x^2)^2,x,3,x^(1+m)*hypergeom([2,1/2*(1+m)],[1/2*(3+m)],a^2*x^2)/(1+m)+a*x^(2+m)*hypergeom([2,1/2*(2+m)],[1/2*(4+m)],a^2*x^2)/(2+m)],
[x^m/((1-a*x)^2*(1+a*x)),x,5,x^(1+m)*hypergeom([2,1/2*(1+m)],[1/2*(3+m)],a^2*x^2)/(1+m)+a*x^(2+m)*hypergeom([2,1/2*(2+m)],[1/2*(4+m)],a^2*x^2)/(2+m)],
[x^m/(1-a^2*x^2)^2+a*x^(1+m)/(1-a^2*x^2)^2,x,3,x^(1+m)*hypergeom([2,1/2*(1+m)],[1/2*(3+m)],a^2*x^2)/(1+m)+a*x^(2+m)*hypergeom([2,1/2*(2+m)],[1/2*(4+m)],a^2*x^2)/(2+m)],
[x^m/((1-a*x)*(1-a^2*x^2)),x,6,x^(1+m)*hypergeom([2,1/2*(1+m)],[1/2*(3+m)],a^2*x^2)/(1+m)+a*x^(2+m)*hypergeom([2,1/2*(2+m)],[1/2*(4+m)],a^2*x^2)/(2+m)],

# Integrands of the form (e x)^m (A+B x) (a+c x^2)^p when p symbolic
[(e*x)^m*(A+B*x)*(a+c*x^2)^p,x,5,A*(e*x)^(1+m)*(a+c*x^2)^p*hypergeom([1/2*(1+m),-p],[1/2*(3+m)],-c*x^2/a)/(e*(1+m)*(1+c*x^2/a)^p)+B*(e*x)^(2+m)*(a+c*x^2)^p*hypergeom([1/2*(2+m),-p],[1/2*(4+m)],-c*x^2/a)/(e^2*(2+m)*(1+c*x^2/a)^p)],
[x^3*(d+e*x)*(a+c*x^2)^p,x,6,-1/2*a*d*(a+c*x^2)^(1+p)/(c^2*(1+p))+1/2*d*(a+c*x^2)^(2+p)/(c^2*(2+p))+1/5*e*x^5*(a+c*x^2)^p*hypergeom([5/2,-p],[7/2],-c*x^2/a)/(1+c*x^2/a)^p],
[x^2*(d+e*x)*(a+c*x^2)^p,x,6,-1/2*a*e*(a+c*x^2)^(1+p)/(c^2*(1+p))+1/2*e*(a+c*x^2)^(2+p)/(c^2*(2+p))+1/3*d*x^3*(a+c*x^2)^p*hypergeom([3/2,-p],[5/2],-c*x^2/a)/(1+c*x^2/a)^p],
[x*(d+e*x)*(a+c*x^2)^p,x,4,1/2*d*(a+c*x^2)^(1+p)/(c*(1+p))+1/3*e*x^3*(a+c*x^2)^p*hypergeom([3/2,-p],[5/2],-c*x^2/a)/(1+c*x^2/a)^p],
[(d+e*x)*(a+c*x^2)^p,x,3,1/2*e*(a+c*x^2)^(1+p)/(c*(1+p))+d*x*(a+c*x^2)^p*hypergeom([1/2,-p],[3/2],-c*x^2/a)/(1+c*x^2/a)^p],
[(d+e*x)*(a+c*x^2)^p/x,x,5,e*x*(a+c*x^2)^p*hypergeom([1/2,-p],[3/2],-c*x^2/a)/(1+c*x^2/a)^p-1/2*d*(a+c*x^2)^(1+p)*hypergeom([1,1+p],[2+p],1+c*x^2/a)/(a*(1+p))],
[(d+e*x)*(a+c*x^2)^p/x^2,x,5,-d*(a+c*x^2)^p*hypergeom([-1/2,-p],[1/2],-c*x^2/a)/(x*(1+c*x^2/a)^p)-1/2*e*(a+c*x^2)^(1+p)*hypergeom([1,1+p],[2+p],1+c*x^2/a)/(a*(1+p))],
[(d+e*x)*(a+c*x^2)^p/x^3,x,5,-e*(a+c*x^2)^p*hypergeom([-1/2,-p],[1/2],-c*x^2/a)/(x*(1+c*x^2/a)^p)+1/2*c*d*(a+c*x^2)^(1+p)*hypergeom([2,1+p],[2+p],1+c*x^2/a)/(a^2*(1+p))],

# Integrands of the form (e x)^m (f+g x) (a+b x+c x^2)^p when b^2-4 a c=0

# Integrands of the form x^m (A+B x) (a^2+2 a b x+b^2 x^2)^p

# p>0
[x^4*(A+B*x)*(a^2+2*a*b*x+b^2*x^2),x,3,1/5*a^2*A*x^5+1/6*a*(2*A*b+a*B)*x^6+1/7*b*(A*b+2*a*B)*x^7+1/8*b^2*B*x^8],
[x^3*(A+B*x)*(a^2+2*a*b*x+b^2*x^2),x,3,1/4*a^2*A*x^4+1/5*a*(2*A*b+a*B)*x^5+1/6*b*(A*b+2*a*B)*x^6+1/7*b^2*B*x^7],
[x^2*(A+B*x)*(a^2+2*a*b*x+b^2*x^2),x,3,1/3*a^2*A*x^3+1/4*a*(2*A*b+a*B)*x^4+1/5*b*(A*b+2*a*B)*x^5+1/6*b^2*B*x^6],
[x*(A+B*x)*(a^2+2*a*b*x+b^2*x^2),x,3,1/2*a^2*A*x^2+1/3*a*(2*A*b+a*B)*x^3+1/4*b*(A*b+2*a*B)*x^4+1/5*b^2*B*x^5],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2),x,3,1/3*(A*b-a*B)*(a+b*x)^3/b^2+1/4*B*(a+b*x)^4/b^2],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/x,x,4,2*a*A*b*x+1/2*A*b^2*x^2+1/3*B*(a+b*x)^3/b+a^2*A*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/x^2,x,3,-a^2*A/x+b*(A*b+2*a*B)*x+1/2*b^2*B*x^2+a*(2*A*b+a*B)*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/x^3,x,3,-1/2*a^2*A/x^2-a*(2*A*b+a*B)/x+b^2*B*x+b*(A*b+2*a*B)*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/x^4,x,3,-1/3*a^2*A/x^3-1/2*a*(2*A*b+a*B)/x^2-b*(A*b+2*a*B)/x+b^2*B*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/x^5,x,3,-1/4*A*(a+b*x)^3/(a*x^4)+1/12*(A*b-4*a*B)*(a+b*x)^3/(a^2*x^3)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/x^6,x,3,-1/5*a^2*A/x^5-1/4*a*(2*A*b+a*B)/x^4-1/3*b*(A*b+2*a*B)/x^3-1/2*b^2*B/x^2],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/x^7,x,3,-1/6*a^2*A/x^6-1/5*a*(2*A*b+a*B)/x^5-1/4*b*(A*b+2*a*B)/x^4-1/3*b^2*B/x^3],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/x^8,x,3,-1/7*a^2*A/x^7-1/6*a*(2*A*b+a*B)/x^6-1/5*b*(A*b+2*a*B)/x^5-1/4*b^2*B/x^4],
[x^4*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/5*a^4*A*x^5+1/6*a^3*(4*A*b+a*B)*x^6+2/7*a^2*b*(3*A*b+2*a*B)*x^7+1/4*a*b^2*(2*A*b+3*a*B)*x^8+1/9*b^3*(A*b+4*a*B)*x^9+1/10*b^4*B*x^10],
[x^3*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/4*a^4*A*x^4+1/5*a^3*(4*A*b+a*B)*x^5+1/3*a^2*b*(3*A*b+2*a*B)*x^6+2/7*a*b^2*(2*A*b+3*a*B)*x^7+1/8*b^3*(A*b+4*a*B)*x^8+1/9*b^4*B*x^9],
[x^2*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/5*a^2*(A*b-a*B)*(a+b*x)^5/b^4-1/6*a*(2*A*b-3*a*B)*(a+b*x)^6/b^4+1/7*(A*b-3*a*B)*(a+b*x)^7/b^4+1/8*B*(a+b*x)^8/b^4],
[x*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,-1/5*a*(A*b-a*B)*(a+b*x)^5/b^3+1/6*(A*b-2*a*B)*(a+b*x)^6/b^3+1/7*B*(a+b*x)^7/b^3],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/5*(A*b-a*B)*(a+b*x)^5/b^2+1/6*B*(a+b*x)^6/b^2],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x,x,4,4*a^3*A*b*x+3*a^2*A*b^2*x^2+4/3*a*A*b^3*x^3+1/4*A*b^4*x^4+1/5*B*(a+b*x)^5/b+a^4*A*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^2,x,3,-a^4*A/x+2*a^2*b*(3*A*b+2*a*B)*x+a*b^2*(2*A*b+3*a*B)*x^2+1/3*b^3*(A*b+4*a*B)*x^3+1/4*b^4*B*x^4+a^3*(4*A*b+a*B)*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^3,x,3,-1/2*a^4*A/x^2-a^3*(4*A*b+a*B)/x+2*a*b^2*(2*A*b+3*a*B)*x+1/2*b^3*(A*b+4*a*B)*x^2+1/3*b^4*B*x^3+2*a^2*b*(3*A*b+2*a*B)*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^4,x,3,-1/3*a^4*A/x^3-1/2*a^3*(4*A*b+a*B)/x^2-2*a^2*b*(3*A*b+2*a*B)/x+b^3*(A*b+4*a*B)*x+1/2*b^4*B*x^2+2*a*b^2*(2*A*b+3*a*B)*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^5,x,3,-1/4*a^4*A/x^4-1/3*a^3*(4*A*b+a*B)/x^3-a^2*b*(3*A*b+2*a*B)/x^2-2*a*b^2*(2*A*b+3*a*B)/x+b^4*B*x+b^3*(A*b+4*a*B)*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^6,x,4,-1/4*a^4*B/x^4-4/3*a^3*b*B/x^3-3*a^2*b^2*B/x^2-4*a*b^3*B/x-1/5*A*(a+b*x)^5/(a*x^5)+b^4*B*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^7,x,3,-1/6*A*(a+b*x)^5/(a*x^6)+1/30*(A*b-6*a*B)*(a+b*x)^5/(a^2*x^5)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^8,x,3,-1/7*a^4*A/x^7-1/6*a^3*(4*A*b+a*B)/x^6-2/5*a^2*b*(3*A*b+2*a*B)/x^5-1/2*a*b^2*(2*A*b+3*a*B)/x^4-1/3*b^3*(A*b+4*a*B)/x^3-1/2*b^4*B/x^2],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^9,x,3,-1/8*a^4*A/x^8-1/7*a^3*(4*A*b+a*B)/x^7-1/3*a^2*b*(3*A*b+2*a*B)/x^6-2/5*a*b^2*(2*A*b+3*a*B)/x^5-1/4*b^3*(A*b+4*a*B)/x^4-1/3*b^4*B/x^3],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^10,x,3,-1/9*a^4*A/x^9-1/8*a^3*(4*A*b+a*B)/x^8-2/7*a^2*b*(3*A*b+2*a*B)/x^7-1/3*a*b^2*(2*A*b+3*a*B)/x^6-1/5*b^3*(A*b+4*a*B)/x^5-1/4*b^4*B/x^4],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^11,x,3,-1/10*a^4*A/x^10-1/9*a^3*(4*A*b+a*B)/x^9-1/4*a^2*b*(3*A*b+2*a*B)/x^8-2/7*a*b^2*(2*A*b+3*a*B)/x^7-1/6*b^3*(A*b+4*a*B)/x^6-1/5*b^4*B/x^5],
[x^5*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/6*a^6*A*x^6+1/7*a^5*(6*A*b+a*B)*x^7+3/8*a^4*b*(5*A*b+2*a*B)*x^8+5/9*a^3*b^2*(4*A*b+3*a*B)*x^9+1/2*a^2*b^3*(3*A*b+4*a*B)*x^10+3/11*a*b^4*(2*A*b+5*a*B)*x^11+1/12*b^5*(A*b+6*a*B)*x^12+1/13*b^6*B*x^13],
[x^4*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/7*a^4*(A*b-a*B)*(a+b*x)^7/b^6-1/8*a^3*(4*A*b-5*a*B)*(a+b*x)^8/b^6+2/9*a^2*(3*A*b-5*a*B)*(a+b*x)^9/b^6-1/5*a*(2*A*b-5*a*B)*(a+b*x)^10/b^6+1/11*(A*b-5*a*B)*(a+b*x)^11/b^6+1/12*B*(a+b*x)^12/b^6],
[x^3*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,-1/7*a^3*(A*b-a*B)*(a+b*x)^7/b^5+1/8*a^2*(3*A*b-4*a*B)*(a+b*x)^8/b^5-1/3*a*(A*b-2*a*B)*(a+b*x)^9/b^5+1/10*(A*b-4*a*B)*(a+b*x)^10/b^5+1/11*B*(a+b*x)^11/b^5],
[x^2*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/7*a^2*(A*b-a*B)*(a+b*x)^7/b^4-1/8*a*(2*A*b-3*a*B)*(a+b*x)^8/b^4+1/9*(A*b-3*a*B)*(a+b*x)^9/b^4+1/10*B*(a+b*x)^10/b^4],
[x*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,-1/7*a*(A*b-a*B)*(a+b*x)^7/b^3+1/8*(A*b-2*a*B)*(a+b*x)^8/b^3+1/9*B*(a+b*x)^9/b^3],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/7*(A*b-a*B)*(a+b*x)^7/b^2+1/8*B*(a+b*x)^8/b^2],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x,x,4,6*a^5*A*b*x+15/2*a^4*A*b^2*x^2+20/3*a^3*A*b^3*x^3+15/4*a^2*A*b^4*x^4+6/5*a*A*b^5*x^5+1/6*A*b^6*x^6+1/7*B*(a+b*x)^7/b+a^6*A*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^2,x,3,-a^6*A/x+3*a^4*b*(5*A*b+2*a*B)*x+5/2*a^3*b^2*(4*A*b+3*a*B)*x^2+5/3*a^2*b^3*(3*A*b+4*a*B)*x^3+3/4*a*b^4*(2*A*b+5*a*B)*x^4+1/5*b^5*(A*b+6*a*B)*x^5+1/6*b^6*B*x^6+a^5*(6*A*b+a*B)*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^3,x,3,-1/2*a^6*A/x^2-a^5*(6*A*b+a*B)/x+5*a^3*b^2*(4*A*b+3*a*B)*x+5/2*a^2*b^3*(3*A*b+4*a*B)*x^2+a*b^4*(2*A*b+5*a*B)*x^3+1/4*b^5*(A*b+6*a*B)*x^4+1/5*b^6*B*x^5+3*a^4*b*(5*A*b+2*a*B)*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^4,x,3,-1/3*a^6*A/x^3-1/2*a^5*(6*A*b+a*B)/x^2-3*a^4*b*(5*A*b+2*a*B)/x+5*a^2*b^3*(3*A*b+4*a*B)*x+3/2*a*b^4*(2*A*b+5*a*B)*x^2+1/3*b^5*(A*b+6*a*B)*x^3+1/4*b^6*B*x^4+5*a^3*b^2*(4*A*b+3*a*B)*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^5,x,3,-1/4*a^6*A/x^4-1/3*a^5*(6*A*b+a*B)/x^3-3/2*a^4*b*(5*A*b+2*a*B)/x^2-5*a^3*b^2*(4*A*b+3*a*B)/x+3*a*b^4*(2*A*b+5*a*B)*x+1/2*b^5*(A*b+6*a*B)*x^2+1/3*b^6*B*x^3+5*a^2*b^3*(3*A*b+4*a*B)*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^6,x,3,-1/5*a^6*A/x^5-1/4*a^5*(6*A*b+a*B)/x^4-a^4*b*(5*A*b+2*a*B)/x^3-5/2*a^3*b^2*(4*A*b+3*a*B)/x^2-5*a^2*b^3*(3*A*b+4*a*B)/x+b^5*(A*b+6*a*B)*x+1/2*b^6*B*x^2+3*a*b^4*(2*A*b+5*a*B)*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^7,x,3,-1/6*a^6*A/x^6-1/5*a^5*(6*A*b+a*B)/x^5-3/4*a^4*b*(5*A*b+2*a*B)/x^4-5/3*a^3*b^2*(4*A*b+3*a*B)/x^3-5/2*a^2*b^3*(3*A*b+4*a*B)/x^2-3*a*b^4*(2*A*b+5*a*B)/x+b^6*B*x+b^5*(A*b+6*a*B)*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^8,x,4,-1/6*a^6*B/x^6-6/5*a^5*b*B/x^5-15/4*a^4*b^2*B/x^4-20/3*a^3*b^3*B/x^3-15/2*a^2*b^4*B/x^2-6*a*b^5*B/x-1/7*A*(a+b*x)^7/(a*x^7)+b^6*B*log(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^9,x,3,-1/8*A*(a+b*x)^7/(a*x^8)+1/56*(A*b-8*a*B)*(a+b*x)^7/(a^2*x^7)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^10,x,4,-1/9*A*(a+b*x)^7/(a*x^9)+1/72*(2*A*b-9*a*B)*(a+b*x)^7/(a^2*x^8)-1/504*b*(2*A*b-9*a*B)*(a+b*x)^7/(a^3*x^7)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^11,x,3,-1/10*a^6*A/x^10-1/9*a^5*(6*A*b+a*B)/x^9-3/8*a^4*b*(5*A*b+2*a*B)/x^8-5/7*a^3*b^2*(4*A*b+3*a*B)/x^7-5/6*a^2*b^3*(3*A*b+4*a*B)/x^6-3/5*a*b^4*(2*A*b+5*a*B)/x^5-1/4*b^5*(A*b+6*a*B)/x^4-1/3*b^6*B/x^3],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^12,x,3,-1/11*a^6*A/x^11-1/10*a^5*(6*A*b+a*B)/x^10-1/3*a^4*b*(5*A*b+2*a*B)/x^9-5/8*a^3*b^2*(4*A*b+3*a*B)/x^8-5/7*a^2*b^3*(3*A*b+4*a*B)/x^7-1/2*a*b^4*(2*A*b+5*a*B)/x^6-1/5*b^5*(A*b+6*a*B)/x^5-1/4*b^6*B/x^4],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^13,x,3,-1/12*a^6*A/x^12-1/11*a^5*(6*A*b+a*B)/x^11-3/10*a^4*b*(5*A*b+2*a*B)/x^10-5/9*a^3*b^2*(4*A*b+3*a*B)/x^9-5/8*a^2*b^3*(3*A*b+4*a*B)/x^8-3/7*a*b^4*(2*A*b+5*a*B)/x^7-1/6*b^5*(A*b+6*a*B)/x^6-1/5*b^6*B/x^5],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^14,x,3,-1/13*a^6*A/x^13-1/12*a^5*(6*A*b+a*B)/x^12-3/11*a^4*b*(5*A*b+2*a*B)/x^11-1/2*a^3*b^2*(4*A*b+3*a*B)/x^10-5/9*a^2*b^3*(3*A*b+4*a*B)/x^9-3/8*a*b^4*(2*A*b+5*a*B)/x^8-1/7*b^5*(A*b+6*a*B)/x^7-1/6*b^6*B/x^6],
[x^7*(d+e*x)*(1+2*x+x^2)^5,x,3,-1/11*(d-e)*(1+x)^11+1/12*(7*d-8*e)*(1+x)^12-7/13*(3*d-4*e)*(1+x)^13+1/2*(5*d-8*e)*(1+x)^14-7/3*(d-2*e)*(1+x)^15+7/16*(3*d-8*e)*(1+x)^16-7/17*(d-4*e)*(1+x)^17+1/18*(d-8*e)*(1+x)^18+1/19*e*(1+x)^19],
[x^6*(d+e*x)*(1+2*x+x^2)^5,x,3,1/11*(d-e)*(1+x)^11-1/12*(6*d-7*e)*(1+x)^12+3/13*(5*d-7*e)*(1+x)^13-5/14*(4*d-7*e)*(1+x)^14+1/3*(3*d-7*e)*(1+x)^15-3/16*(2*d-7*e)*(1+x)^16+1/17*(d-7*e)*(1+x)^17+1/18*e*(1+x)^18],
[x^5*(d+e*x)*(1+2*x+x^2)^5,x,3,-1/11*(d-e)*(1+x)^11+1/12*(5*d-6*e)*(1+x)^12-5/13*(2*d-3*e)*(1+x)^13+5/7*(d-2*e)*(1+x)^14-1/3*(d-3*e)*(1+x)^15+1/16*(d-6*e)*(1+x)^16+1/17*e*(1+x)^17],
[x^4*(d+e*x)*(1+2*x+x^2)^5,x,3,1/11*(d-e)*(1+x)^11-1/12*(4*d-5*e)*(1+x)^12+2/13*(3*d-5*e)*(1+x)^13-1/7*(2*d-5*e)*(1+x)^14+1/15*(d-5*e)*(1+x)^15+1/16*e*(1+x)^16],
[x^3*(d+e*x)*(1+2*x+x^2)^5,x,3,-1/11*(d-e)*(1+x)^11+1/12*(3*d-4*e)*(1+x)^12-3/13*(d-2*e)*(1+x)^13+1/14*(d-4*e)*(1+x)^14+1/15*e*(1+x)^15],
[x^2*(d+e*x)*(1+2*x+x^2)^5,x,3,1/11*(d-e)*(1+x)^11-1/12*(2*d-3*e)*(1+x)^12+1/13*(d-3*e)*(1+x)^13+1/14*e*(1+x)^14],
[x*(d+e*x)*(1+2*x+x^2)^5,x,3,-1/11*(d-e)*(1+x)^11+1/12*(d-2*e)*(1+x)^12+1/13*e*(1+x)^13],
[(d+e*x)*(1+2*x+x^2)^5,x,3,1/11*(d-e)*(1+x)^11+1/12*e*(1+x)^12],
[(d+e*x)*(1+2*x+x^2)^5/x,x,4,10*d*x+45/2*d*x^2+40*d*x^3+105/2*d*x^4+252/5*d*x^5+35*d*x^6+120/7*d*x^7+45/8*d*x^8+10/9*d*x^9+1/10*d*x^10+1/11*e*(1+x)^11+d*log(x)],
[(d+e*x)*(1+2*x+x^2)^5/x^2,x,3,-d/x+5*(9*d+2*e)*x+15/2*(8*d+3*e)*x^2+10*(7*d+4*e)*x^3+21/2*(6*d+5*e)*x^4+42/5*(5*d+6*e)*x^5+5*(4*d+7*e)*x^6+15/7*(3*d+8*e)*x^7+5/8*(2*d+9*e)*x^8+1/9*(d+10*e)*x^9+1/10*e*x^10+(10*d+e)*log(x)],
[(d+e*x)*(1+2*x+x^2)^5/x^3,x,3,-1/2*d/x^2+(-10*d-e)/x+15*(8*d+3*e)*x+15*(7*d+4*e)*x^2+14*(6*d+5*e)*x^3+21/2*(5*d+6*e)*x^4+6*(4*d+7*e)*x^5+5/2*(3*d+8*e)*x^6+5/7*(2*d+9*e)*x^7+1/8*(d+10*e)*x^8+1/9*e*x^9+5*(9*d+2*e)*log(x)],
[(d+e*x)*(1+2*x+x^2)^5/x^4,x,3,-1/3*d/x^3+1/2*(-10*d-e)/x^2-5*(9*d+2*e)/x+30*(7*d+4*e)*x+21*(6*d+5*e)*x^2+14*(5*d+6*e)*x^3+15/2*(4*d+7*e)*x^4+3*(3*d+8*e)*x^5+5/6*(2*d+9*e)*x^6+1/7*(d+10*e)*x^7+1/8*e*x^8+15*(8*d+3*e)*log(x)],
[(d+e*x)*(1+2*x+x^2)^5/x^5,x,3,-1/4*d/x^4+1/3*(-10*d-e)/x^3-5/2*(9*d+2*e)/x^2-15*(8*d+3*e)/x+42*(6*d+5*e)*x+21*(5*d+6*e)*x^2+10*(4*d+7*e)*x^3+15/4*(3*d+8*e)*x^4+(2*d+9*e)*x^5+1/6*(d+10*e)*x^6+1/7*e*x^7+30*(7*d+4*e)*log(x)],
[(d+e*x)*(1+2*x+x^2)^5/x^6,x,3,-1/5*d/x^5+1/4*(-10*d-e)/x^4-5/3*(9*d+2*e)/x^3-15/2*(8*d+3*e)/x^2-30*(7*d+4*e)/x+42*(5*d+6*e)*x+15*(4*d+7*e)*x^2+5*(3*d+8*e)*x^3+5/4*(2*d+9*e)*x^4+1/5*(d+10*e)*x^5+1/6*e*x^6+42*(6*d+5*e)*log(x)],
[(d+e*x)*(1+2*x+x^2)^5/x^7,x,3,-1/6*d/x^6+1/5*(-10*d-e)/x^5-5/4*(9*d+2*e)/x^4-5*(8*d+3*e)/x^3-15*(7*d+4*e)/x^2-42*(6*d+5*e)/x+30*(4*d+7*e)*x+15/2*(3*d+8*e)*x^2+5/3*(2*d+9*e)*x^3+1/4*(d+10*e)*x^4+1/5*e*x^5+42*(5*d+6*e)*log(x)],
[(d+e*x)*(1+2*x+x^2)^5/x^8,x,3,-1/7*d/x^7+1/6*(-10*d-e)/x^6+(-9*d-2*e)/x^5-15/4*(8*d+3*e)/x^4-10*(7*d+4*e)/x^3-21*(6*d+5*e)/x^2-42*(5*d+6*e)/x+15*(3*d+8*e)*x+5/2*(2*d+9*e)*x^2+1/3*(d+10*e)*x^3+1/4*e*x^4+30*(4*d+7*e)*log(x)],
[(d+e*x)*(1+2*x+x^2)^5/x^9,x,3,-1/8*d/x^8+1/7*(-10*d-e)/x^7-5/6*(9*d+2*e)/x^6-3*(8*d+3*e)/x^5-15/2*(7*d+4*e)/x^4-14*(6*d+5*e)/x^3-21*(5*d+6*e)/x^2-30*(4*d+7*e)/x+5*(2*d+9*e)*x+1/2*(d+10*e)*x^2+1/3*e*x^3+15*(3*d+8*e)*log(x)],
[(d+e*x)*(1+2*x+x^2)^5/x^10,x,3,-1/9*d/x^9+1/8*(-10*d-e)/x^8-5/7*(9*d+2*e)/x^7-5/2*(8*d+3*e)/x^6-6*(7*d+4*e)/x^5-21/2*(6*d+5*e)/x^4-14*(5*d+6*e)/x^3-15*(4*d+7*e)/x^2-15*(3*d+8*e)/x+(d+10*e)*x+1/2*e*x^2+5*(2*d+9*e)*log(x)],
[(d+e*x)*(1+2*x+x^2)^5/x^11,x,3,-1/10*d/x^10+1/9*(-10*d-e)/x^9-5/8*(9*d+2*e)/x^8-15/7*(8*d+3*e)/x^7-5*(7*d+4*e)/x^6-42/5*(6*d+5*e)/x^5-21/2*(5*d+6*e)/x^4-10*(4*d+7*e)/x^3-15/2*(3*d+8*e)/x^2-5*(2*d+9*e)/x+e*x+(d+10*e)*log(x)],
[(d+e*x)*(1+2*x+x^2)^5/x^12,x,4,-1/10*e/x^10-10/9*e/x^9-45/8*e/x^8-120/7*e/x^7-35*e/x^6-252/5*e/x^5-105/2*e/x^4-40*e/x^3-45/2*e/x^2-10*e/x-1/11*d*(1+x)^11/x^11+e*log(x)],
[(d+e*x)*(1+2*x+x^2)^5/x^13,x,3,-1/12*d*(1+x)^11/x^12+1/132*(d-12*e)*(1+x)^11/x^11],
[(d+e*x)*(1+2*x+x^2)^5/x^14,x,4,-1/13*d*(1+x)^11/x^13+1/156*(2*d-13*e)*(1+x)^11/x^12-1/1716*(2*d-13*e)*(1+x)^11/x^11],
[(d+e*x)*(1+2*x+x^2)^5/x^15,x,5,-1/14*d*(1+x)^11/x^14+1/182*(3*d-14*e)*(1+x)^11/x^13-1/1092*(3*d-14*e)*(1+x)^11/x^12+1/12012*(3*d-14*e)*(1+x)^11/x^11],
[(d+e*x)*(1+2*x+x^2)^5/x^16,x,6,-1/15*d*(1+x)^11/x^15+1/210*(4*d-15*e)*(1+x)^11/x^14-1/910*(4*d-15*e)*(1+x)^11/x^13+1/5460*(4*d-15*e)*(1+x)^11/x^12-1/60060*(4*d-15*e)*(1+x)^11/x^11],
[(d+e*x)*(1+2*x+x^2)^5/x^17,x,7,-1/16*d*(1+x)^11/x^16+1/240*(5*d-16*e)*(1+x)^11/x^15-1/840*(5*d-16*e)*(1+x)^11/x^14+1/3640*(5*d-16*e)*(1+x)^11/x^13-1/21840*(5*d-16*e)*(1+x)^11/x^12+1/240240*(5*d-16*e)*(1+x)^11/x^11],
[(d+e*x)*(1+2*x+x^2)^5/x^18,x,8,-1/17*d*(1+x)^11/x^17+1/272*(6*d-17*e)*(1+x)^11/x^16-1/816*(6*d-17*e)*(1+x)^11/x^15+1/2856*(6*d-17*e)*(1+x)^11/x^14-1/12376*(6*d-17*e)*(1+x)^11/x^13+1/74256*(6*d-17*e)*(1+x)^11/x^12-1/816816*(6*d-17*e)*(1+x)^11/x^11],
[(d+e*x)*(1+2*x+x^2)^5/x^19,x,3,-1/18*d/x^18+1/17*(-10*d-e)/x^17-5/16*(9*d+2*e)/x^16+(-8*d-3*e)/x^15-15/7*(7*d+4*e)/x^14-42/13*(6*d+5*e)/x^13-7/2*(5*d+6*e)/x^12-30/11*(4*d+7*e)/x^11-3/2*(3*d+8*e)/x^10-5/9*(2*d+9*e)/x^9+1/8*(-d-10*e)/x^8-1/7*e/x^7],
[(d+e*x)*(1+2*x+x^2)^5/x^20,x,3,-1/19*d/x^19+1/18*(-10*d-e)/x^18-5/17*(9*d+2*e)/x^17-15/16*(8*d+3*e)/x^16-2*(7*d+4*e)/x^15-3*(6*d+5*e)/x^14-42/13*(5*d+6*e)/x^13-5/2*(4*d+7*e)/x^12-15/11*(3*d+8*e)/x^11+1/2*(-2*d-9*e)/x^10+1/9*(-d-10*e)/x^9-1/8*e/x^8],
[(d+e*x)*(1+2*x+x^2)^5/x^21,x,3,-1/20*d/x^20+1/19*(-10*d-e)/x^19-5/18*(9*d+2*e)/x^18-15/17*(8*d+3*e)/x^17-15/8*(7*d+4*e)/x^16-14/5*(6*d+5*e)/x^15-3*(5*d+6*e)/x^14-30/13*(4*d+7*e)/x^13-5/4*(3*d+8*e)/x^12-5/11*(2*d+9*e)/x^11+1/10*(-d-10*e)/x^10-1/9*e/x^9],
[x^11*(1+x)*(1+2*x+x^2)^5,x,3,1/12*x^12+11/13*x^13+55/14*x^14+11*x^15+165/8*x^16+462/17*x^17+77/3*x^18+330/19*x^19+33/4*x^20+55/21*x^21+1/2*x^22+1/23*x^23],
[x^10*(1+x)*(1+2*x+x^2)^5,x,3,1/11*x^11+11/12*x^12+55/13*x^13+165/14*x^14+22*x^15+231/8*x^16+462/17*x^17+55/3*x^18+165/19*x^19+11/4*x^20+11/21*x^21+1/22*x^22],
[x^9*(1+x)*(1+2*x+x^2)^5,x,3,-1/12*(1+x)^12+9/13*(1+x)^13-18/7*(1+x)^14+28/5*(1+x)^15-63/8*(1+x)^16+126/17*(1+x)^17-14/3*(1+x)^18+36/19*(1+x)^19-9/20*(1+x)^20+1/21*(1+x)^21],
[x^8*(1+x)*(1+2*x+x^2)^5,x,3,1/12*(1+x)^12-8/13*(1+x)^13+2*(1+x)^14-56/15*(1+x)^15+35/8*(1+x)^16-56/17*(1+x)^17+14/9*(1+x)^18-8/19*(1+x)^19+1/20*(1+x)^20],
[x^7*(1+x)*(1+2*x+x^2)^5,x,3,-1/12*(1+x)^12+7/13*(1+x)^13-3/2*(1+x)^14+7/3*(1+x)^15-35/16*(1+x)^16+21/17*(1+x)^17-7/18*(1+x)^18+1/19*(1+x)^19],
[x^6*(1+x)*(1+2*x+x^2)^5,x,3,1/12*(1+x)^12-6/13*(1+x)^13+15/14*(1+x)^14-4/3*(1+x)^15+15/16*(1+x)^16-6/17*(1+x)^17+1/18*(1+x)^18],
[x^5*(1+x)*(1+2*x+x^2)^5,x,3,-1/12*(1+x)^12+5/13*(1+x)^13-5/7*(1+x)^14+2/3*(1+x)^15-5/16*(1+x)^16+1/17*(1+x)^17],
[x^4*(1+x)*(1+2*x+x^2)^5,x,3,1/12*(1+x)^12-4/13*(1+x)^13+3/7*(1+x)^14-4/15*(1+x)^15+1/16*(1+x)^16],
[x^3*(1+x)*(1+2*x+x^2)^5,x,3,-1/12*(1+x)^12+3/13*(1+x)^13-3/14*(1+x)^14+1/15*(1+x)^15],
[x^2*(1+x)*(1+2*x+x^2)^5,x,3,1/12*(1+x)^12-2/13*(1+x)^13+1/14*(1+x)^14],
[x*(1+x)*(1+2*x+x^2)^5,x,3,-1/12*(1+x)^12+1/13*(1+x)^13],
[(1+x)*(1+2*x+x^2)^5,x,2,1/12*(1+x)^12],
[(1+x)*(1+2*x+x^2)^5/x,x,3,11*x+55/2*x^2+55*x^3+165/2*x^4+462/5*x^5+77*x^6+330/7*x^7+165/8*x^8+55/9*x^9+11/10*x^10+1/11*x^11+log(x)],
[(1+x)*(1+2*x+x^2)^5/x^2,x,3,(-1)/x+55*x+165/2*x^2+110*x^3+231/2*x^4+462/5*x^5+55*x^6+165/7*x^7+55/8*x^8+11/9*x^9+1/10*x^10+11*log(x)],
[(1+x)*(1+2*x+x^2)^5/x^3,x,3,(-1/2)/x^2+(-11)/x+165*x+165*x^2+154*x^3+231/2*x^4+66*x^5+55/2*x^6+55/7*x^7+11/8*x^8+1/9*x^9+55*log(x)],
[(1+x)*(1+2*x+x^2)^5/x^4,x,3,(-1/3)/x^3+(-11/2)/x^2+(-55)/x+330*x+231*x^2+154*x^3+165/2*x^4+33*x^5+55/6*x^6+11/7*x^7+1/8*x^8+165*log(x)],
[(1+x)*(1+2*x+x^2)^5/x^5,x,3,(-1/4)/x^4+(-11/3)/x^3+(-55/2)/x^2+(-165)/x+462*x+231*x^2+110*x^3+165/4*x^4+11*x^5+11/6*x^6+1/7*x^7+330*log(x)],
[(1+x)*(1+2*x+x^2)^5/x^6,x,3,(-1/5)/x^5+(-11/4)/x^4+(-55/3)/x^3+(-165/2)/x^2+(-330)/x+462*x+165*x^2+55*x^3+55/4*x^4+11/5*x^5+1/6*x^6+462*log(x)],
[(1+x)*(1+2*x+x^2)^5/x^7,x,3,(-1/6)/x^6+(-11/5)/x^5+(-55/4)/x^4+(-55)/x^3+(-165)/x^2+(-462)/x+330*x+165/2*x^2+55/3*x^3+11/4*x^4+1/5*x^5+462*log(x)],
[(1+x)*(1+2*x+x^2)^5/x^8,x,3,(-1/7)/x^7+(-11/6)/x^6+(-11)/x^5+(-165/4)/x^4+(-110)/x^3+(-231)/x^2+(-462)/x+165*x+55/2*x^2+11/3*x^3+1/4*x^4+330*log(x)],
[(1+x)*(1+2*x+x^2)^5/x^9,x,3,(-1/8)/x^8+(-11/7)/x^7+(-55/6)/x^6+(-33)/x^5+(-165/2)/x^4+(-154)/x^3+(-231)/x^2+(-330)/x+55*x+11/2*x^2+1/3*x^3+165*log(x)],
[(1+x)*(1+2*x+x^2)^5/x^10,x,3,(-1/9)/x^9+(-11/8)/x^8+(-55/7)/x^7+(-55/2)/x^6+(-66)/x^5+(-231/2)/x^4+(-154)/x^3+(-165)/x^2+(-165)/x+11*x+1/2*x^2+55*log(x)],
[(1+x)*(1+2*x+x^2)^5/x^11,x,3,(-1/10)/x^10+(-11/9)/x^9+(-55/8)/x^8+(-165/7)/x^7+(-55)/x^6+(-462/5)/x^5+(-231/2)/x^4+(-110)/x^3+(-165/2)/x^2+(-55)/x+x+11*log(x)],
[(1+x)*(1+2*x+x^2)^5/x^12,x,3,(-1/11)/x^11+(-11/10)/x^10+(-55/9)/x^9+(-165/8)/x^8+(-330/7)/x^7+(-77)/x^6+(-462/5)/x^5+(-165/2)/x^4+(-55)/x^3+(-55/2)/x^2+(-11)/x+log(x)],
[(1+x)*(1+2*x+x^2)^5/x^13,x,2,-1/12*(1+x)^12/x^12],
[(1+x)*(1+2*x+x^2)^5/x^14,x,3,-1/13*(1+x)^12/x^13+1/156*(1+x)^12/x^12],
[(1+x)*(1+2*x+x^2)^5/x^15,x,4,-1/14*(1+x)^12/x^14+1/91*(1+x)^12/x^13-1/1092*(1+x)^12/x^12],
[(1+x)*(1+2*x+x^2)^5/x^16,x,5,-1/15*(1+x)^12/x^15+1/70*(1+x)^12/x^14-1/455*(1+x)^12/x^13+1/5460*(1+x)^12/x^12],
[(1+x)*(1+2*x+x^2)^5/x^17,x,6,-1/16*(1+x)^12/x^16+1/60*(1+x)^12/x^15-1/280*(1+x)^12/x^14+1/1820*(1+x)^12/x^13-1/21840*(1+x)^12/x^12],
[(1+x)*(1+2*x+x^2)^5/x^18,x,7,-1/17*(1+x)^12/x^17+5/272*(1+x)^12/x^16-1/204*(1+x)^12/x^15+1/952*(1+x)^12/x^14-1/6188*(1+x)^12/x^13+1/74256*(1+x)^12/x^12],
[(1+x)*(1+2*x+x^2)^5/x^19,x,8,-1/18*(1+x)^12/x^18+1/51*(1+x)^12/x^17-5/816*(1+x)^12/x^16+1/612*(1+x)^12/x^15-1/2856*(1+x)^12/x^14+1/18564*(1+x)^12/x^13-1/222768*(1+x)^12/x^12],
[(1+x)*(1+2*x+x^2)^5/x^20,x,9,-1/19*(1+x)^12/x^19+7/342*(1+x)^12/x^18-7/969*(1+x)^12/x^17+35/15504*(1+x)^12/x^16-7/11628*(1+x)^12/x^15+1/7752*(1+x)^12/x^14-1/50388*(1+x)^12/x^13+1/604656*(1+x)^12/x^12],
[(1+x)*(1+2*x+x^2)^5/x^21,x,3,(-1/20)/x^20+(-11/19)/x^19+(-55/18)/x^18+(-165/17)/x^17+(-165/8)/x^16+(-154/5)/x^15+(-33)/x^14+(-330/13)/x^13+(-55/4)/x^12+(-5)/x^11+(-11/10)/x^10+(-1/9)/x^9],
[(1+x)*(1+2*x+x^2)^5/x^22,x,3,(-1/21)/x^21+(-11/20)/x^20+(-55/19)/x^19+(-55/6)/x^18+(-330/17)/x^17+(-231/8)/x^16+(-154/5)/x^15+(-165/7)/x^14+(-165/13)/x^13+(-55/12)/x^12+(-1)/x^11+(-1/10)/x^10],

# p<0
[x^5*(A+B*x)/(a^2+2*a*b*x+b^2*x^2),x,3,-a^3*(4*A*b-5*a*B)*x/b^6+1/2*a^2*(3*A*b-4*a*B)*x^2/b^5-1/3*a*(2*A*b-3*a*B)*x^3/b^4+1/4*(A*b-2*a*B)*x^4/b^3+1/5*B*x^5/b^2+a^5*(A*b-a*B)/(b^7*(a+b*x))+a^4*(5*A*b-6*a*B)*log(a+b*x)/b^7],
[x^4*(A+B*x)/(a^2+2*a*b*x+b^2*x^2),x,3,a^2*(3*A*b-4*a*B)*x/b^5-1/2*a*(2*A*b-3*a*B)*x^2/b^4+1/3*(A*b-2*a*B)*x^3/b^3+1/4*B*x^4/b^2-a^4*(A*b-a*B)/(b^6*(a+b*x))-a^3*(4*A*b-5*a*B)*log(a+b*x)/b^6],
[x^3*(A+B*x)/(a^2+2*a*b*x+b^2*x^2),x,3,-a*(2*A*b-3*a*B)*x/b^4+1/2*(A*b-2*a*B)*x^2/b^3+1/3*B*x^3/b^2+a^3*(A*b-a*B)/(b^5*(a+b*x))+a^2*(3*A*b-4*a*B)*log(a+b*x)/b^5],
[x^2*(A+B*x)/(a^2+2*a*b*x+b^2*x^2),x,3,(A*b-2*a*B)*x/b^3+1/2*B*x^2/b^2-a^2*(A*b-a*B)/(b^4*(a+b*x))-a*(2*A*b-3*a*B)*log(a+b*x)/b^4],
[x*(A+B*x)/(a^2+2*a*b*x+b^2*x^2),x,3,B*x/b^2+a*(A*b-a*B)/(b^3*(a+b*x))+(A*b-2*a*B)*log(a+b*x)/b^3],
[(A+B*x)/(a^2+2*a*b*x+b^2*x^2),x,3,(-A*b+a*B)/(b^2*(a+b*x))+B*log(a+b*x)/b^2],
[(A+B*x)/(x*(a^2+2*a*b*x+b^2*x^2)),x,3,(A*b-a*B)/(a*b*(a+b*x))+A*log(x)/a^2-A*log(a+b*x)/a^2],
[(A+B*x)/(x^2*(a^2+2*a*b*x+b^2*x^2)),x,3,-A/(a^2*x)+(-A*b+a*B)/(a^2*(a+b*x))-(2*A*b-a*B)*log(x)/a^3+(2*A*b-a*B)*log(a+b*x)/a^3],
[(A+B*x)/(x^3*(a^2+2*a*b*x+b^2*x^2)),x,3,-1/2*A/(a^2*x^2)+(2*A*b-a*B)/(a^3*x)+b*(A*b-a*B)/(a^3*(a+b*x))+b*(3*A*b-2*a*B)*log(x)/a^4-b*(3*A*b-2*a*B)*log(a+b*x)/a^4],
[(A+B*x)/(x^4*(a^2+2*a*b*x+b^2*x^2)),x,3,-1/3*A/(a^2*x^3)+1/2*(2*A*b-a*B)/(a^3*x^2)-b*(3*A*b-2*a*B)/(a^4*x)-b^2*(A*b-a*B)/(a^4*(a+b*x))-b^2*(4*A*b-3*a*B)*log(x)/a^5+b^2*(4*A*b-3*a*B)*log(a+b*x)/a^5],
[(A+B*x)/(x^5*(a^2+2*a*b*x+b^2*x^2)),x,3,-1/4*A/(a^2*x^4)+1/3*(2*A*b-a*B)/(a^3*x^3)-1/2*b*(3*A*b-2*a*B)/(a^4*x^2)+b^2*(4*A*b-3*a*B)/(a^5*x)+b^3*(A*b-a*B)/(a^5*(a+b*x))+b^3*(5*A*b-4*a*B)*log(x)/a^6-b^3*(5*A*b-4*a*B)*log(a+b*x)/a^6],
[x^5*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,3,-2*a*(2*A*b-5*a*B)*x/b^6+1/2*(A*b-4*a*B)*x^2/b^5+1/3*B*x^3/b^4+1/3*a^5*(A*b-a*B)/(b^7*(a+b*x)^3)-1/2*a^4*(5*A*b-6*a*B)/(b^7*(a+b*x)^2)+5*a^3*(2*A*b-3*a*B)/(b^7*(a+b*x))+10*a^2*(A*b-2*a*B)*log(a+b*x)/b^7],
[x^4*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,3,(A*b-4*a*B)*x/b^5+1/2*B*x^2/b^4-1/3*a^4*(A*b-a*B)/(b^6*(a+b*x)^3)+1/2*a^3*(4*A*b-5*a*B)/(b^6*(a+b*x)^2)-2*a^2*(3*A*b-5*a*B)/(b^6*(a+b*x))-2*a*(2*A*b-5*a*B)*log(a+b*x)/b^6],
[x^3*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,3,B*x/b^4+1/3*a^3*(A*b-a*B)/(b^5*(a+b*x)^3)-1/2*a^2*(3*A*b-4*a*B)/(b^5*(a+b*x)^2)+3*a*(A*b-2*a*B)/(b^5*(a+b*x))+(A*b-4*a*B)*log(a+b*x)/b^5],
[x^2*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,4,1/3*(A*b-a*B)*x^3/(a*b*(a+b*x)^3)-1/2*a^2*B/(b^4*(a+b*x)^2)+2*a*B/(b^4*(a+b*x))+B*log(a+b*x)/b^4],
[x*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/3*a*(A*b-a*B)/(b^3*(a+b*x)^3)+1/2*(-A*b+2*a*B)/(b^3*(a+b*x)^2)-B/(b^3*(a+b*x))],
[(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/3*(-A*b+a*B)/(b^2*(a+b*x)^3)-1/2*B/(b^2*(a+b*x)^2)],
[(A+B*x)/(x*(a^2+2*a*b*x+b^2*x^2)^2),x,3,1/3*(A*b-a*B)/(a*b*(a+b*x)^3)+1/2*A/(a^2*(a+b*x)^2)+A/(a^3*(a+b*x))+A*log(x)/a^4-A*log(a+b*x)/a^4],
[(A+B*x)/(x^2*(a^2+2*a*b*x+b^2*x^2)^2),x,3,-A/(a^4*x)+1/3*(-A*b+a*B)/(a^2*(a+b*x)^3)+1/2*(-2*A*b+a*B)/(a^3*(a+b*x)^2)+(-3*A*b+a*B)/(a^4*(a+b*x))-(4*A*b-a*B)*log(x)/a^5+(4*A*b-a*B)*log(a+b*x)/a^5],
[(A+B*x)/(x^3*(a^2+2*a*b*x+b^2*x^2)^2),x,3,-1/2*A/(a^4*x^2)+(4*A*b-a*B)/(a^5*x)+1/3*b*(A*b-a*B)/(a^3*(a+b*x)^3)+1/2*b*(3*A*b-2*a*B)/(a^4*(a+b*x)^2)+3*b*(2*A*b-a*B)/(a^5*(a+b*x))+2*b*(5*A*b-2*a*B)*log(x)/a^6-2*b*(5*A*b-2*a*B)*log(a+b*x)/a^6],
[(A+B*x)/(x^4*(a^2+2*a*b*x+b^2*x^2)^2),x,3,-1/3*A/(a^4*x^3)+1/2*(4*A*b-a*B)/(a^5*x^2)-2*b*(5*A*b-2*a*B)/(a^6*x)-1/3*b^2*(A*b-a*B)/(a^4*(a+b*x)^3)-1/2*b^2*(4*A*b-3*a*B)/(a^5*(a+b*x)^2)-2*b^2*(5*A*b-3*a*B)/(a^6*(a+b*x))-10*b^2*(2*A*b-a*B)*log(x)/a^7+10*b^2*(2*A*b-a*B)*log(a+b*x)/a^7],
[x^6*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,3,(A*b-6*a*B)*x/b^7+1/2*B*x^2/b^6-1/5*a^6*(A*b-a*B)/(b^8*(a+b*x)^5)+1/4*a^5*(6*A*b-7*a*B)/(b^8*(a+b*x)^4)-a^4*(5*A*b-7*a*B)/(b^8*(a+b*x)^3)+5/2*a^3*(4*A*b-7*a*B)/(b^8*(a+b*x)^2)-5*a^2*(3*A*b-7*a*B)/(b^8*(a+b*x))-3*a*(2*A*b-7*a*B)*log(a+b*x)/b^8],
[x^5*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,3,B*x/b^6+1/5*a^5*(A*b-a*B)/(b^7*(a+b*x)^5)-1/4*a^4*(5*A*b-6*a*B)/(b^7*(a+b*x)^4)+5/3*a^3*(2*A*b-3*a*B)/(b^7*(a+b*x)^3)-5*a^2*(A*b-2*a*B)/(b^7*(a+b*x)^2)+5*a*(A*b-3*a*B)/(b^7*(a+b*x))+(A*b-6*a*B)*log(a+b*x)/b^7],
[x^4*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,4,1/5*(A*b-a*B)*x^5/(a*b*(a+b*x)^5)-1/4*a^4*B/(b^6*(a+b*x)^4)+4/3*a^3*B/(b^6*(a+b*x)^3)-3*a^2*B/(b^6*(a+b*x)^2)+4*a*B/(b^6*(a+b*x))+B*log(a+b*x)/b^6],
[x^3*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/5*(A*b-a*B)*x^4/(a*b*(a+b*x)^5)+1/20*(A*b+4*a*B)*x^4/(a^2*b*(a+b*x)^4)],
[x^2*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,3,-1/5*a^2*(A*b-a*B)/(b^4*(a+b*x)^5)+1/4*a*(2*A*b-3*a*B)/(b^4*(a+b*x)^4)+1/3*(-A*b+3*a*B)/(b^4*(a+b*x)^3)-1/2*B/(b^4*(a+b*x)^2)],
[x*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/5*a*(A*b-a*B)/(b^3*(a+b*x)^5)+1/4*(-A*b+2*a*B)/(b^3*(a+b*x)^4)-1/3*B/(b^3*(a+b*x)^3)],
[(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/5*(-A*b+a*B)/(b^2*(a+b*x)^5)-1/4*B/(b^2*(a+b*x)^4)],
[(A+B*x)/(x*(a^2+2*a*b*x+b^2*x^2)^3),x,3,1/5*(A*b-a*B)/(a*b*(a+b*x)^5)+1/4*A/(a^2*(a+b*x)^4)+1/3*A/(a^3*(a+b*x)^3)+1/2*A/(a^4*(a+b*x)^2)+A/(a^5*(a+b*x))+A*log(x)/a^6-A*log(a+b*x)/a^6],
[(A+B*x)/(x^2*(a^2+2*a*b*x+b^2*x^2)^3),x,3,-A/(a^6*x)+1/5*(-A*b+a*B)/(a^2*(a+b*x)^5)+1/4*(-2*A*b+a*B)/(a^3*(a+b*x)^4)+1/3*(-3*A*b+a*B)/(a^4*(a+b*x)^3)+1/2*(-4*A*b+a*B)/(a^5*(a+b*x)^2)+(-5*A*b+a*B)/(a^6*(a+b*x))-(6*A*b-a*B)*log(x)/a^7+(6*A*b-a*B)*log(a+b*x)/a^7],
[(A+B*x)/(x^3*(a^2+2*a*b*x+b^2*x^2)^3),x,3,-1/2*A/(a^6*x^2)+(6*A*b-a*B)/(a^7*x)+1/5*b*(A*b-a*B)/(a^3*(a+b*x)^5)+1/4*b*(3*A*b-2*a*B)/(a^4*(a+b*x)^4)+b*(2*A*b-a*B)/(a^5*(a+b*x)^3)+b*(5*A*b-2*a*B)/(a^6*(a+b*x)^2)+5*b*(3*A*b-a*B)/(a^7*(a+b*x))+3*b*(7*A*b-2*a*B)*log(x)/a^8-3*b*(7*A*b-2*a*B)*log(a+b*x)/a^8],

# Integrands of the form x^m (A+B x) (a^2+2 a b x+b^2 x^2)^(p/2)

# p>0
[x^4*(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,1/5*a*A*x^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/6*(A*b+a*B)*x^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/7*b*B*x^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^3*(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,1/4*a*A*x^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/5*(A*b+a*B)*x^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/6*b*B*x^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^2*(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,1/3*a*A*x^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/4*(A*b+a*B)*x^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/5*b*B*x^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x*(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,1/2*a*A*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/3*(A*b+a*B)*x^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/4*b*B*x^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,2,1/3*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/2*(A*b-a*B)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/x,x,3,(A*b+a*B)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/2*b*B*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+a*A*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/x^2,x,3,-a*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x*(a+b*x))+b*B*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+(A*b+a*B)*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/x^3,x,3,-1/2*a*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^2*(a+b*x))-(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x*(a+b*x))+b*B*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/x^4,x,3,-1/3*A*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(a^2*x^3)+1/2*(A*b-a*B)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a^2*x^2)],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/x^5,x,3,-1/4*a*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^4*(a+b*x))-1/3*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^3*(a+b*x))-1/2*b*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^2*(a+b*x))],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/x^6,x,3,-1/5*a*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^5*(a+b*x))-1/4*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^4*(a+b*x))-1/3*b*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^3*(a+b*x))],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/x^7,x,3,-1/6*a*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^6*(a+b*x))-1/5*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^5*(a+b*x))-1/4*b*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^4*(a+b*x))],
[x^5*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,1/6*a^3*A*x^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/7*a^2*(3*A*b+a*B)*x^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+3/8*a*b*(A*b+a*B)*x^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/9*b^2*(A*b+3*a*B)*x^9*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/10*b^3*B*x^10*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^4*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,1/5*a^3*A*x^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/6*a^2*(3*A*b+a*B)*x^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+3/7*a*b*(A*b+a*B)*x^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/8*b^2*(A*b+3*a*B)*x^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/9*b^3*B*x^9*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^3*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,1/4*a^3*A*x^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/5*a^2*(3*A*b+a*B)*x^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/2*a*b*(A*b+a*B)*x^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/7*b^2*(A*b+3*a*B)*x^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/8*b^3*B*x^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^2*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,1/3*a^3*A*x^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/4*a^2*(3*A*b+a*B)*x^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+3/5*a*b*(A*b+a*B)*x^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/6*b^2*(A*b+3*a*B)*x^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/7*b^3*B*x^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,-1/4*a*(A*b-a*B)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/5*(A*b-2*a*B)*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/6*B*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,2,1/4*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/5*B*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x,x,4,3*a^2*A*b*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+3/2*a*A*b^2*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/3*A*b^3*x^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/4*B*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/b+a^3*A*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^2,x,3,-a^3*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x*(a+b*x))+3*a*b*(A*b+a*B)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/2*b^2*(A*b+3*a*B)*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/3*b^3*B*x^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+a^2*(3*A*b+a*B)*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^3,x,3,-1/2*a^3*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^2*(a+b*x))-a^2*(3*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x*(a+b*x))+b^2*(A*b+3*a*B)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/2*b^3*B*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+3*a*b*(A*b+a*B)*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^4,x,3,-1/3*a^3*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^3*(a+b*x))-1/2*a^2*(3*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^2*(a+b*x))-3*a*b*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x*(a+b*x))+b^3*B*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+b^2*(A*b+3*a*B)*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^5,x,4,-1/3*a^3*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^3*(a+b*x))-3/2*a^2*b*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^2*(a+b*x))-3*a*b^2*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x*(a+b*x))-1/4*A*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(a*x^4)+b^3*B*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^6,x,3,-1/5*A*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(a^2*x^5)+1/4*(A*b-a*B)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(a^2*x^4)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^7,x,3,-1/6*a^3*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^6*(a+b*x))-1/5*a^2*(3*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^5*(a+b*x))-3/4*a*b*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^4*(a+b*x))-1/3*b^2*(A*b+3*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^3*(a+b*x))-1/2*b^3*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^2*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^8,x,3,-1/7*a^3*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^7*(a+b*x))-1/6*a^2*(3*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^6*(a+b*x))-3/5*a*b*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^5*(a+b*x))-1/4*b^2*(A*b+3*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^4*(a+b*x))-1/3*b^3*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^3*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^9,x,3,-1/8*a^3*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^8*(a+b*x))-1/7*a^2*(3*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^7*(a+b*x))-1/2*a*b*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^6*(a+b*x))-1/5*b^2*(A*b+3*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^5*(a+b*x))-1/4*b^3*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^4*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^10,x,3,-1/9*a^3*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^9*(a+b*x))-1/8*a^2*(3*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^8*(a+b*x))-3/7*a*b*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^7*(a+b*x))-1/6*b^2*(A*b+3*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^6*(a+b*x))-1/5*b^3*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^5*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^11,x,3,-1/10*a^3*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^10*(a+b*x))-1/9*a^2*(3*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^9*(a+b*x))-3/8*a*b*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^8*(a+b*x))-1/7*b^2*(A*b+3*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^7*(a+b*x))-1/6*b^3*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^6*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^12,x,3,-1/11*a^3*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^11*(a+b*x))-1/10*a^2*(3*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^10*(a+b*x))-1/3*a*b*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^9*(a+b*x))-1/8*b^2*(A*b+3*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^8*(a+b*x))-1/7*b^3*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^7*(a+b*x))],
[x^6*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,1/7*a^5*A*x^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/8*a^4*(5*A*b+a*B)*x^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+5/9*a^3*b*(2*A*b+a*B)*x^9*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+a^2*b^2*(A*b+a*B)*x^10*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+5/11*a*b^3*(A*b+2*a*B)*x^11*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/12*b^4*(A*b+5*a*B)*x^12*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/13*b^5*B*x^13*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^5*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,1/6*a^5*A*x^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/7*a^4*(5*A*b+a*B)*x^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+5/8*a^3*b*(2*A*b+a*B)*x^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+10/9*a^2*b^2*(A*b+a*B)*x^9*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/2*a*b^3*(A*b+2*a*B)*x^10*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/11*b^4*(A*b+5*a*B)*x^11*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/12*b^5*B*x^12*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^4*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,1/5*a^5*A*x^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/6*a^4*(5*A*b+a*B)*x^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+5/7*a^3*b*(2*A*b+a*B)*x^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+5/4*a^2*b^2*(A*b+a*B)*x^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+5/9*a*b^3*(A*b+2*a*B)*x^9*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/10*b^4*(A*b+5*a*B)*x^10*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/11*b^5*B*x^11*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^3*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,-1/6*a^3*(A*b-a*B)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/7*a^2*(3*A*b-4*a*B)*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5-3/8*a*(A*b-2*a*B)*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/9*(A*b-4*a*B)*(a+b*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/10*B*(a+b*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5],
[x^2*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,1/6*a^2*(A*b-a*B)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4-1/7*a*(2*A*b-3*a*B)*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+1/8*(A*b-3*a*B)*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+1/9*B*(a+b*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4],
[x*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,-1/6*a*(A*b-a*B)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/7*(A*b-2*a*B)*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/8*B*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,2,1/6*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/7*B*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x,x,4,5*a^4*A*b*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+5*a^3*A*b^2*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+10/3*a^2*A*b^3*x^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+5/4*a*A*b^4*x^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/5*A*b^5*x^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/6*B*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b+a^5*A*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^2,x,3,-a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x*(a+b*x))+5*a^3*b*(2*A*b+a*B)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+5*a^2*b^2*(A*b+a*B)*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+5/3*a*b^3*(A*b+2*a*B)*x^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/4*b^4*(A*b+5*a*B)*x^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/5*b^5*B*x^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+a^4*(5*A*b+a*B)*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^3,x,3,-1/2*a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^2*(a+b*x))-a^4*(5*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x*(a+b*x))+10*a^2*b^2*(A*b+a*B)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+5/2*a*b^3*(A*b+2*a*B)*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/3*b^4*(A*b+5*a*B)*x^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/4*b^5*B*x^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+5*a^3*b*(2*A*b+a*B)*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^4,x,3,-1/3*a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^3*(a+b*x))-1/2*a^4*(5*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^2*(a+b*x))-5*a^3*b*(2*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x*(a+b*x))+5*a*b^3*(A*b+2*a*B)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/2*b^4*(A*b+5*a*B)*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/3*b^5*B*x^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+10*a^2*b^2*(A*b+a*B)*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^5,x,3,-1/4*a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^4*(a+b*x))-1/3*a^4*(5*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^3*(a+b*x))-5/2*a^3*b*(2*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^2*(a+b*x))-10*a^2*b^2*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x*(a+b*x))+b^4*(A*b+5*a*B)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/2*b^5*B*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+5*a*b^3*(A*b+2*a*B)*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^6,x,3,-1/5*a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^5*(a+b*x))-1/4*a^4*(5*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^4*(a+b*x))-5/3*a^3*b*(2*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^3*(a+b*x))-5*a^2*b^2*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^2*(a+b*x))-5*a*b^3*(A*b+2*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x*(a+b*x))+b^5*B*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+b^4*(A*b+5*a*B)*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^7,x,4,-1/5*a^5*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^5*(a+b*x))-5/4*a^4*b*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^4*(a+b*x))-10/3*a^3*b^2*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^3*(a+b*x))-5*a^2*b^3*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^2*(a+b*x))-5*a*b^4*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x*(a+b*x))-1/6*A*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a*x^6)+b^5*B*log(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^8,x,3,-1/7*A*(a^2+2*a*b*x+b^2*x^2)^(7/2)/(a^2*x^7)+1/6*(A*b-a*B)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a^2*x^6)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^9,x,4,-1/8*A*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a*x^8)+1/28*(A*b-4*a*B)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a^2*x^7)-1/168*b*(A*b-4*a*B)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(a^3*x^6)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^10,x,3,-1/9*a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^9*(a+b*x))-1/8*a^4*(5*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^8*(a+b*x))-5/7*a^3*b*(2*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^7*(a+b*x))-5/3*a^2*b^2*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^6*(a+b*x))-a*b^3*(A*b+2*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^5*(a+b*x))-1/4*b^4*(A*b+5*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^4*(a+b*x))-1/3*b^5*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^3*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^11,x,3,-1/10*a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^10*(a+b*x))-1/9*a^4*(5*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^9*(a+b*x))-5/8*a^3*b*(2*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^8*(a+b*x))-10/7*a^2*b^2*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^7*(a+b*x))-5/6*a*b^3*(A*b+2*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^6*(a+b*x))-1/5*b^4*(A*b+5*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^5*(a+b*x))-1/4*b^5*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^4*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^12,x,3,-1/11*a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^11*(a+b*x))-1/10*a^4*(5*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^10*(a+b*x))-5/9*a^3*b*(2*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^9*(a+b*x))-5/4*a^2*b^2*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^8*(a+b*x))-5/7*a*b^3*(A*b+2*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^7*(a+b*x))-1/6*b^4*(A*b+5*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^6*(a+b*x))-1/5*b^5*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^5*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^13,x,3,-1/12*a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^12*(a+b*x))-1/11*a^4*(5*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^11*(a+b*x))-1/2*a^3*b*(2*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^10*(a+b*x))-10/9*a^2*b^2*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^9*(a+b*x))-5/8*a*b^3*(A*b+2*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^8*(a+b*x))-1/7*b^4*(A*b+5*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^7*(a+b*x))-1/6*b^5*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^6*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^14,x,3,-1/13*a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^13*(a+b*x))-1/12*a^4*(5*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^12*(a+b*x))-5/11*a^3*b*(2*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^11*(a+b*x))-a^2*b^2*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^10*(a+b*x))-5/9*a*b^3*(A*b+2*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^9*(a+b*x))-1/8*b^4*(A*b+5*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^8*(a+b*x))-1/7*b^5*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^7*(a+b*x))],

# p<0
[x^4*(A+B*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,-a^3*(A*b-a*B)*x*(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*a^2*(A*b-a*B)*x^2*(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-1/3*a*(A*b-a*B)*x^3*(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(A*b-a*B)*x^4*(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/5*B*x^5*(a+b*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+a^4*(A*b-a*B)*(a+b*x)*log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^3*(A+B*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,a^2*(A*b-a*B)*x*(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*a*(A*b-a*B)*x^2*(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*(A*b-a*B)*x^3*(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*B*x^4*(a+b*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-a^3*(A*b-a*B)*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^2*(A+B*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,-a*(A*b-a*B)*x*(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-a*B)*x^2*(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*B*x^3*(a+b*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+a^2*(A*b-a*B)*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x*(A+B*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,(A*b-a*B)*x*(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*B*x^2*(a+b*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-a*(A*b-a*B)*(a+b*x)*log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,(A*b-a*B)*(a+b*x)*log(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+B*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2],
[(A+B*x)/(x*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,A*(a+b*x)*log(x)/(a*sqrt(a^2+2*a*b*x+b^2*x^2))-(A*b-a*B)*(a+b*x)*log(a+b*x)/(a*b*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^2*sqrt(a^2+2*a*b*x+b^2*x^2)),x,5,-(A*b-a*B)*(a+b*x)*log(x)/(a^2*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*(a+b*x)*log(a+b*x)/(a^2*sqrt(a^2+2*a*b*x+b^2*x^2))-A*sqrt(a^2+2*a*b*x+b^2*x^2)/(a^2*x)],
[(A+B*x)/(x^3*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,-1/2*A*(a+b*x)/(a*x^2*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*(a+b*x)/(a^2*x*sqrt(a^2+2*a*b*x+b^2*x^2))+b*(A*b-a*B)*(a+b*x)*log(x)/(a^3*sqrt(a^2+2*a*b*x+b^2*x^2))-b*(A*b-a*B)*(a+b*x)*log(a+b*x)/(a^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^4*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,-1/3*A*(a+b*x)/(a*x^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-a*B)*(a+b*x)/(a^2*x^2*sqrt(a^2+2*a*b*x+b^2*x^2))-b*(A*b-a*B)*(a+b*x)/(a^3*x*sqrt(a^2+2*a*b*x+b^2*x^2))-b^2*(A*b-a*B)*(a+b*x)*log(x)/(a^4*sqrt(a^2+2*a*b*x+b^2*x^2))+b^2*(A*b-a*B)*(a+b*x)*log(a+b*x)/(a^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^5*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,-1/4*A*(a+b*x)/(a*x^4*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*(A*b-a*B)*(a+b*x)/(a^2*x^3*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*b*(A*b-a*B)*(a+b*x)/(a^3*x^2*sqrt(a^2+2*a*b*x+b^2*x^2))+b^2*(A*b-a*B)*(a+b*x)/(a^4*x*sqrt(a^2+2*a*b*x+b^2*x^2))+b^3*(A*b-a*B)*(a+b*x)*log(x)/(a^5*sqrt(a^2+2*a*b*x+b^2*x^2))-b^3*(A*b-a*B)*(a+b*x)*log(a+b*x)/(a^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^4*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,a^3*(4*A*b-5*a*B)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*a^4*(A*b-a*B)/(b^6*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-3*a*(A*b-2*a*B)*x*(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-3*a*B)*x^2*(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*B*x^3*(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2*a^2*(3*A*b-5*a*B)*(a+b*x)*log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^3*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,-a^2*(3*A*b-4*a*B)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*a^3*(A*b-a*B)/(b^5*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-3*a*B)*x*(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*B*x^2*(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-3*a*(A*b-2*a*B)*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^2*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,a*(2*A*b-3*a*B)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*a^2*(A*b-a*B)/(b^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+B*x*(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-3*a*B)*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,(-A*b+2*a*B)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*a*(A*b-a*B)/(b^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+B*(a+b*x)*log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,2,-B/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(-A*b+a*B)/(b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,3,A/(a^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-a*B)/(a*b*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+A*(a+b*x)*log(x)/(a^3*sqrt(a^2+2*a*b*x+b^2*x^2))-A*(a+b*x)*log(a+b*x)/(a^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,3,(-2*A*b+a*B)/(a^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(-A*b+a*B)/(a^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-A*(a+b*x)/(a^3*x*sqrt(a^2+2*a*b*x+b^2*x^2))-(3*A*b-a*B)*(a+b*x)*log(x)/(a^4*sqrt(a^2+2*a*b*x+b^2*x^2))+(3*A*b-a*B)*(a+b*x)*log(a+b*x)/(a^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,3,b*(3*A*b-2*a*B)/(a^4*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*b*(A*b-a*B)/(a^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*A*(a+b*x)/(a^3*x^2*sqrt(a^2+2*a*b*x+b^2*x^2))+(3*A*b-a*B)*(a+b*x)/(a^4*x*sqrt(a^2+2*a*b*x+b^2*x^2))+3*b*(2*A*b-a*B)*(a+b*x)*log(x)/(a^5*sqrt(a^2+2*a*b*x+b^2*x^2))-3*b*(2*A*b-a*B)*(a+b*x)*log(a+b*x)/(a^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^4*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,2*a*(2*A*b-5*a*B)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*a^4*(A*b-a*B)/(b^6*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*a^3*(4*A*b-5*a*B)/(b^6*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-a^2*(3*A*b-5*a*B)/(b^6*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+B*x*(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-5*a*B)*(a+b*x)*log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^3*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,3*a*B/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(A*b-a*B)*x^4/(a*b*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*a^3*B/(b^5*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-3/2*a^2*B/(b^5*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+B*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^2*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,1/3*A*x^3/(a^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/4*(A*b-a*B)*x^4/(a^2*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,1/4*a*(A*b-a*B)/(b^3*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*(-A*b+2*a*B)/(b^3*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*B/(b^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,2,-1/3*B/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/4*(-A*b+a*B)/(b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2))],
[(A+B*x)/(x*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,3,A/(a^4*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(A*b-a*B)/(a*b*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*A/(a^2*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*A/(a^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+A*(a+b*x)*log(x)/(a^5*sqrt(a^2+2*a*b*x+b^2*x^2))-A*(a+b*x)*log(a+b*x)/(a^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,3,(-4*A*b+a*B)/(a^5*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(-A*b+a*B)/(a^2*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*(-2*A*b+a*B)/(a^3*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(-3*A*b+a*B)/(a^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-A*(a+b*x)/(a^5*x*sqrt(a^2+2*a*b*x+b^2*x^2))-(5*A*b-a*B)*(a+b*x)*log(x)/(a^6*sqrt(a^2+2*a*b*x+b^2*x^2))+(5*A*b-a*B)*(a+b*x)*log(a+b*x)/(a^6*sqrt(a^2+2*a*b*x+b^2*x^2))],

# Integrands of the form (e x)^(m/2) (A+B x) (a^2+2 a b x+b^2 x^2)^p

# p>0
[x^(7/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2),x,3,2/9*a^2*A*x^(9/2)+2/11*a*(2*A*b+a*B)*x^(11/2)+2/13*b*(A*b+2*a*B)*x^(13/2)+2/15*b^2*B*x^(15/2)],
[x^(5/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2),x,3,2/7*a^2*A*x^(7/2)+2/9*a*(2*A*b+a*B)*x^(9/2)+2/11*b*(A*b+2*a*B)*x^(11/2)+2/13*b^2*B*x^(13/2)],
[x^(3/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2),x,3,2/5*a^2*A*x^(5/2)+2/7*a*(2*A*b+a*B)*x^(7/2)+2/9*b*(A*b+2*a*B)*x^(9/2)+2/11*b^2*B*x^(11/2)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)*sqrt(x),x,3,2/3*a^2*A*x^(3/2)+2/5*a*(2*A*b+a*B)*x^(5/2)+2/7*b*(A*b+2*a*B)*x^(7/2)+2/9*b^2*B*x^(9/2)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/sqrt(x),x,3,2/3*a*(2*A*b+a*B)*x^(3/2)+2/5*b*(A*b+2*a*B)*x^(5/2)+2/7*b^2*B*x^(7/2)+2*a^2*A*sqrt(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/x^(3/2),x,3,2/3*b*(A*b+2*a*B)*x^(3/2)+2/5*b^2*B*x^(5/2)-2*a^2*A/sqrt(x)+2*a*(2*A*b+a*B)*sqrt(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/x^(5/2),x,3,-2/3*a^2*A/x^(3/2)+2/3*b^2*B*x^(3/2)-2*a*(2*A*b+a*B)/sqrt(x)+2*b*(A*b+2*a*B)*sqrt(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/x^(7/2),x,3,-2/5*a^2*A/x^(5/2)-2/3*a*(2*A*b+a*B)/x^(3/2)-2*b*(A*b+2*a*B)/sqrt(x)+2*b^2*B*sqrt(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/x^(9/2),x,3,-2/7*a^2*A/x^(7/2)-2/5*a*(2*A*b+a*B)/x^(5/2)-2/3*b*(A*b+2*a*B)/x^(3/2)-2*b^2*B/sqrt(x)],
[x^(7/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,2/9*a^4*A*x^(9/2)+2/11*a^3*(4*A*b+a*B)*x^(11/2)+4/13*a^2*b*(3*A*b+2*a*B)*x^(13/2)+4/15*a*b^2*(2*A*b+3*a*B)*x^(15/2)+2/17*b^3*(A*b+4*a*B)*x^(17/2)+2/19*b^4*B*x^(19/2)],
[x^(5/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,2/7*a^4*A*x^(7/2)+2/9*a^3*(4*A*b+a*B)*x^(9/2)+4/11*a^2*b*(3*A*b+2*a*B)*x^(11/2)+4/13*a*b^2*(2*A*b+3*a*B)*x^(13/2)+2/15*b^3*(A*b+4*a*B)*x^(15/2)+2/17*b^4*B*x^(17/2)],
[x^(3/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,2/5*a^4*A*x^(5/2)+2/7*a^3*(4*A*b+a*B)*x^(7/2)+4/9*a^2*b*(3*A*b+2*a*B)*x^(9/2)+4/11*a*b^2*(2*A*b+3*a*B)*x^(11/2)+2/13*b^3*(A*b+4*a*B)*x^(13/2)+2/15*b^4*B*x^(15/2)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2*sqrt(x),x,3,2/3*a^4*A*x^(3/2)+2/5*a^3*(4*A*b+a*B)*x^(5/2)+4/7*a^2*b*(3*A*b+2*a*B)*x^(7/2)+4/9*a*b^2*(2*A*b+3*a*B)*x^(9/2)+2/11*b^3*(A*b+4*a*B)*x^(11/2)+2/13*b^4*B*x^(13/2)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/sqrt(x),x,3,2/3*a^3*(4*A*b+a*B)*x^(3/2)+4/5*a^2*b*(3*A*b+2*a*B)*x^(5/2)+4/7*a*b^2*(2*A*b+3*a*B)*x^(7/2)+2/9*b^3*(A*b+4*a*B)*x^(9/2)+2/11*b^4*B*x^(11/2)+2*a^4*A*sqrt(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^(3/2),x,3,4/3*a^2*b*(3*A*b+2*a*B)*x^(3/2)+4/5*a*b^2*(2*A*b+3*a*B)*x^(5/2)+2/7*b^3*(A*b+4*a*B)*x^(7/2)+2/9*b^4*B*x^(9/2)-2*a^4*A/sqrt(x)+2*a^3*(4*A*b+a*B)*sqrt(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^(5/2),x,3,-2/3*a^4*A/x^(3/2)+4/3*a*b^2*(2*A*b+3*a*B)*x^(3/2)+2/5*b^3*(A*b+4*a*B)*x^(5/2)+2/7*b^4*B*x^(7/2)-2*a^3*(4*A*b+a*B)/sqrt(x)+4*a^2*b*(3*A*b+2*a*B)*sqrt(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^(7/2),x,3,-2/5*a^4*A/x^(5/2)-2/3*a^3*(4*A*b+a*B)/x^(3/2)+2/3*b^3*(A*b+4*a*B)*x^(3/2)+2/5*b^4*B*x^(5/2)-4*a^2*b*(3*A*b+2*a*B)/sqrt(x)+4*a*b^2*(2*A*b+3*a*B)*sqrt(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/x^(9/2),x,3,-2/7*a^4*A/x^(7/2)-2/5*a^3*(4*A*b+a*B)/x^(5/2)-4/3*a^2*b*(3*A*b+2*a*B)/x^(3/2)+2/3*b^4*B*x^(3/2)-4*a*b^2*(2*A*b+3*a*B)/sqrt(x)+2*b^3*(A*b+4*a*B)*sqrt(x)],
[x^(7/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,2/9*a^6*A*x^(9/2)+2/11*a^5*(6*A*b+a*B)*x^(11/2)+6/13*a^4*b*(5*A*b+2*a*B)*x^(13/2)+2/3*a^3*b^2*(4*A*b+3*a*B)*x^(15/2)+10/17*a^2*b^3*(3*A*b+4*a*B)*x^(17/2)+6/19*a*b^4*(2*A*b+5*a*B)*x^(19/2)+2/21*b^5*(A*b+6*a*B)*x^(21/2)+2/23*b^6*B*x^(23/2)],
[x^(5/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,2/7*a^6*A*x^(7/2)+2/9*a^5*(6*A*b+a*B)*x^(9/2)+6/11*a^4*b*(5*A*b+2*a*B)*x^(11/2)+10/13*a^3*b^2*(4*A*b+3*a*B)*x^(13/2)+2/3*a^2*b^3*(3*A*b+4*a*B)*x^(15/2)+6/17*a*b^4*(2*A*b+5*a*B)*x^(17/2)+2/19*b^5*(A*b+6*a*B)*x^(19/2)+2/21*b^6*B*x^(21/2)],
[x^(3/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,2/5*a^6*A*x^(5/2)+2/7*a^5*(6*A*b+a*B)*x^(7/2)+2/3*a^4*b*(5*A*b+2*a*B)*x^(9/2)+10/11*a^3*b^2*(4*A*b+3*a*B)*x^(11/2)+10/13*a^2*b^3*(3*A*b+4*a*B)*x^(13/2)+2/5*a*b^4*(2*A*b+5*a*B)*x^(15/2)+2/17*b^5*(A*b+6*a*B)*x^(17/2)+2/19*b^6*B*x^(19/2)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3*sqrt(x),x,3,2/3*a^6*A*x^(3/2)+2/5*a^5*(6*A*b+a*B)*x^(5/2)+6/7*a^4*b*(5*A*b+2*a*B)*x^(7/2)+10/9*a^3*b^2*(4*A*b+3*a*B)*x^(9/2)+10/11*a^2*b^3*(3*A*b+4*a*B)*x^(11/2)+6/13*a*b^4*(2*A*b+5*a*B)*x^(13/2)+2/15*b^5*(A*b+6*a*B)*x^(15/2)+2/17*b^6*B*x^(17/2)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/sqrt(x),x,3,2/3*a^5*(6*A*b+a*B)*x^(3/2)+6/5*a^4*b*(5*A*b+2*a*B)*x^(5/2)+10/7*a^3*b^2*(4*A*b+3*a*B)*x^(7/2)+10/9*a^2*b^3*(3*A*b+4*a*B)*x^(9/2)+6/11*a*b^4*(2*A*b+5*a*B)*x^(11/2)+2/13*b^5*(A*b+6*a*B)*x^(13/2)+2/15*b^6*B*x^(15/2)+2*a^6*A*sqrt(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^(3/2),x,3,2*a^4*b*(5*A*b+2*a*B)*x^(3/2)+2*a^3*b^2*(4*A*b+3*a*B)*x^(5/2)+10/7*a^2*b^3*(3*A*b+4*a*B)*x^(7/2)+2/3*a*b^4*(2*A*b+5*a*B)*x^(9/2)+2/11*b^5*(A*b+6*a*B)*x^(11/2)+2/13*b^6*B*x^(13/2)-2*a^6*A/sqrt(x)+2*a^5*(6*A*b+a*B)*sqrt(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^(5/2),x,3,-2/3*a^6*A/x^(3/2)+10/3*a^3*b^2*(4*A*b+3*a*B)*x^(3/2)+2*a^2*b^3*(3*A*b+4*a*B)*x^(5/2)+6/7*a*b^4*(2*A*b+5*a*B)*x^(7/2)+2/9*b^5*(A*b+6*a*B)*x^(9/2)+2/11*b^6*B*x^(11/2)-2*a^5*(6*A*b+a*B)/sqrt(x)+6*a^4*b*(5*A*b+2*a*B)*sqrt(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^(7/2),x,3,-2/5*a^6*A/x^(5/2)-2/3*a^5*(6*A*b+a*B)/x^(3/2)+10/3*a^2*b^3*(3*A*b+4*a*B)*x^(3/2)+6/5*a*b^4*(2*A*b+5*a*B)*x^(5/2)+2/7*b^5*(A*b+6*a*B)*x^(7/2)+2/9*b^6*B*x^(9/2)-6*a^4*b*(5*A*b+2*a*B)/sqrt(x)+10*a^3*b^2*(4*A*b+3*a*B)*sqrt(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^(9/2),x,3,-2/7*a^6*A/x^(7/2)-2/5*a^5*(6*A*b+a*B)/x^(5/2)-2*a^4*b*(5*A*b+2*a*B)/x^(3/2)+2*a*b^4*(2*A*b+5*a*B)*x^(3/2)+2/5*b^5*(A*b+6*a*B)*x^(5/2)+2/7*b^6*B*x^(7/2)-10*a^3*b^2*(4*A*b+3*a*B)/sqrt(x)+10*a^2*b^3*(3*A*b+4*a*B)*sqrt(x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/x^(11/2),x,3,-2/9*a^6*A/x^(9/2)-2/7*a^5*(6*A*b+a*B)/x^(7/2)-6/5*a^4*b*(5*A*b+2*a*B)/x^(5/2)-10/3*a^3*b^2*(4*A*b+3*a*B)/x^(3/2)+2/3*b^5*(A*b+6*a*B)*x^(3/2)+2/5*b^6*B*x^(5/2)-10*a^2*b^3*(3*A*b+4*a*B)/sqrt(x)+6*a*b^4*(2*A*b+5*a*B)*sqrt(x)],

# p<0
[x^(7/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2),x,8,-1/3*a*(7*A*b-9*a*B)*x^(3/2)/b^4+1/5*(7*A*b-9*a*B)*x^(5/2)/b^3-1/7*(7*A*b-9*a*B)*x^(7/2)/(a*b^2)+(A*b-a*B)*x^(9/2)/(a*b*(a+b*x))-a^(5/2)*(7*A*b-9*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/b^(11/2)+a^2*(7*A*b-9*a*B)*sqrt(x)/b^5],
[x^(5/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2),x,7,1/3*(5*A*b-7*a*B)*x^(3/2)/b^3-1/5*(5*A*b-7*a*B)*x^(5/2)/(a*b^2)+(A*b-a*B)*x^(7/2)/(a*b*(a+b*x))+a^(3/2)*(5*A*b-7*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/b^(9/2)-a*(5*A*b-7*a*B)*sqrt(x)/b^4],
[x^(3/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2),x,6,-1/3*(3*A*b-5*a*B)*x^(3/2)/(a*b^2)+(A*b-a*B)*x^(5/2)/(a*b*(a+b*x))-(3*A*b-5*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(7/2)+(3*A*b-5*a*B)*sqrt(x)/b^3],
[(A+B*x)*sqrt(x)/(a^2+2*a*b*x+b^2*x^2),x,5,(A*b-a*B)*x^(3/2)/(a*b*(a+b*x))+(A*b-3*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(5/2)*sqrt(a))-(A*b-3*a*B)*sqrt(x)/(a*b^2)],
[(A+B*x)/((a^2+2*a*b*x+b^2*x^2)*sqrt(x)),x,4,(A*b+a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*b^(3/2))+(A*b-a*B)*sqrt(x)/(a*b*(a+b*x))],
[(A+B*x)/(x^(3/2)*(a^2+2*a*b*x+b^2*x^2)),x,5,-(3*A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(5/2)*sqrt(b))+(-3*A*b+a*B)/(a^2*b*sqrt(x))+(A*b-a*B)/(a*b*(a+b*x)*sqrt(x))],
[(A+B*x)/(x^(5/2)*(a^2+2*a*b*x+b^2*x^2)),x,6,1/3*(-5*A*b+3*a*B)/(a^2*b*x^(3/2))+(A*b-a*B)/(a*b*x^(3/2)*(a+b*x))+(5*A*b-3*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(7/2)+(5*A*b-3*a*B)/(a^3*sqrt(x))],
[(A+B*x)/(x^(7/2)*(a^2+2*a*b*x+b^2*x^2)),x,7,1/5*(-7*A*b+5*a*B)/(a^2*b*x^(5/2))+1/3*(7*A*b-5*a*B)/(a^3*x^(3/2))+(A*b-a*B)/(a*b*x^(5/2)*(a+b*x))-b^(3/2)*(7*A*b-5*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/a^(9/2)-b*(7*A*b-5*a*B)/(a^4*sqrt(x))],
[(A+B*x)/(x^(9/2)*(a^2+2*a*b*x+b^2*x^2)),x,8,1/7*(-9*A*b+7*a*B)/(a^2*b*x^(7/2))+1/5*(9*A*b-7*a*B)/(a^3*x^(5/2))-1/3*b*(9*A*b-7*a*B)/(a^4*x^(3/2))+(A*b-a*B)/(a*b*x^(7/2)*(a+b*x))+b^(5/2)*(9*A*b-7*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/a^(11/2)+b^2*(9*A*b-7*a*B)/(a^5*sqrt(x))],
[x^(7/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,8,-35/24*(A*b-3*a*B)*x^(3/2)/(a*b^4)+1/3*(A*b-a*B)*x^(9/2)/(a*b*(a+b*x)^3)+1/4*(A*b-3*a*B)*x^(7/2)/(a*b^2*(a+b*x)^2)+7/8*(A*b-3*a*B)*x^(5/2)/(a*b^3*(a+b*x))-35/8*(A*b-3*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(11/2)+35/8*(A*b-3*a*B)*sqrt(x)/b^5],
[x^(5/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,7,1/3*(A*b-a*B)*x^(7/2)/(a*b*(a+b*x)^3)+1/12*(A*b-7*a*B)*x^(5/2)/(a*b^2*(a+b*x)^2)+5/24*(A*b-7*a*B)*x^(3/2)/(a*b^3*(a+b*x))+5/8*(A*b-7*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(9/2)*sqrt(a))-5/8*(A*b-7*a*B)*sqrt(x)/(a*b^4)],
[x^(3/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,6,1/3*(A*b-a*B)*x^(5/2)/(a*b*(a+b*x)^3)-1/12*(A*b+5*a*B)*x^(3/2)/(a*b^2*(a+b*x)^2)+1/8*(A*b+5*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*b^(7/2))-1/8*(A*b+5*a*B)*sqrt(x)/(a*b^3*(a+b*x))],
[(A+B*x)*sqrt(x)/(a^2+2*a*b*x+b^2*x^2)^2,x,6,1/3*(A*b-a*B)*x^(3/2)/(a*b*(a+b*x)^3)+1/8*(A*b+a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(5/2)*b^(5/2))-1/4*(A*b+a*B)*sqrt(x)/(a*b^2*(a+b*x)^2)+1/8*(A*b+a*B)*sqrt(x)/(a^2*b^2*(a+b*x))],
[(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^2*sqrt(x)),x,6,1/8*(5*A*b+a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(7/2)*b^(3/2))+1/3*(A*b-a*B)*sqrt(x)/(a*b*(a+b*x)^3)+1/12*(5*A*b+a*B)*sqrt(x)/(a^2*b*(a+b*x)^2)+1/8*(5*A*b+a*B)*sqrt(x)/(a^3*b*(a+b*x))],
[(A+B*x)/(x^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2),x,7,-5/8*(7*A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(9/2)*sqrt(b))-5/8*(7*A*b-a*B)/(a^4*b*sqrt(x))+1/3*(A*b-a*B)/(a*b*(a+b*x)^3*sqrt(x))+1/12*(7*A*b-a*B)/(a^2*b*(a+b*x)^2*sqrt(x))+5/24*(7*A*b-a*B)/(a^3*b*(a+b*x)*sqrt(x))],
[(A+B*x)/(x^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2),x,8,-35/24*(3*A*b-a*B)/(a^4*b*x^(3/2))+1/3*(A*b-a*B)/(a*b*x^(3/2)*(a+b*x)^3)+1/4*(3*A*b-a*B)/(a^2*b*x^(3/2)*(a+b*x)^2)+7/8*(3*A*b-a*B)/(a^3*b*x^(3/2)*(a+b*x))+35/8*(3*A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(11/2)+35/8*(3*A*b-a*B)/(a^5*sqrt(x))],
[x^(11/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,10,-77/128*(3*A*b-13*a*B)*x^(3/2)/(a*b^6)+1/5*(A*b-a*B)*x^(13/2)/(a*b*(a+b*x)^5)+1/40*(3*A*b-13*a*B)*x^(11/2)/(a*b^2*(a+b*x)^4)+11/240*(3*A*b-13*a*B)*x^(9/2)/(a*b^3*(a+b*x)^3)+33/320*(3*A*b-13*a*B)*x^(7/2)/(a*b^4*(a+b*x)^2)+231/640*(3*A*b-13*a*B)*x^(5/2)/(a*b^5*(a+b*x))-231/128*(3*A*b-13*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/b^(15/2)+231/128*(3*A*b-13*a*B)*sqrt(x)/b^7],
[x^(9/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,9,1/5*(A*b-a*B)*x^(11/2)/(a*b*(a+b*x)^5)+1/40*(A*b-11*a*B)*x^(9/2)/(a*b^2*(a+b*x)^4)+3/80*(A*b-11*a*B)*x^(7/2)/(a*b^3*(a+b*x)^3)+21/320*(A*b-11*a*B)*x^(5/2)/(a*b^4*(a+b*x)^2)+21/128*(A*b-11*a*B)*x^(3/2)/(a*b^5*(a+b*x))+63/128*(A*b-11*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(13/2)*sqrt(a))-63/128*(A*b-11*a*B)*sqrt(x)/(a*b^6)],
[x^(7/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,8,1/5*(A*b-a*B)*x^(9/2)/(a*b*(a+b*x)^5)-1/40*(A*b+9*a*B)*x^(7/2)/(a*b^2*(a+b*x)^4)-7/240*(A*b+9*a*B)*x^(5/2)/(a*b^3*(a+b*x)^3)-7/192*(A*b+9*a*B)*x^(3/2)/(a*b^4*(a+b*x)^2)+7/128*(A*b+9*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*b^(11/2))-7/128*(A*b+9*a*B)*sqrt(x)/(a*b^5*(a+b*x))],
[x^(5/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,8,1/5*(A*b-a*B)*x^(7/2)/(a*b*(a+b*x)^5)-1/40*(3*A*b+7*a*B)*x^(5/2)/(a*b^2*(a+b*x)^4)-1/48*(3*A*b+7*a*B)*x^(3/2)/(a*b^3*(a+b*x)^3)+1/128*(3*A*b+7*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(5/2)*b^(9/2))-1/64*(3*A*b+7*a*B)*sqrt(x)/(a*b^4*(a+b*x)^2)+1/128*(3*A*b+7*a*B)*sqrt(x)/(a^2*b^4*(a+b*x))],
[x^(3/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,8,1/5*(A*b-a*B)*x^(5/2)/(a*b*(a+b*x)^5)-1/8*(A*b+a*B)*x^(3/2)/(a*b^2*(a+b*x)^4)+3/128*(A*b+a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(7/2)*b^(7/2))-1/16*(A*b+a*B)*sqrt(x)/(a*b^3*(a+b*x)^3)+1/64*(A*b+a*B)*sqrt(x)/(a^2*b^3*(a+b*x)^2)+3/128*(A*b+a*B)*sqrt(x)/(a^3*b^3*(a+b*x))],
[(A+B*x)*sqrt(x)/(a^2+2*a*b*x+b^2*x^2)^3,x,8,1/5*(A*b-a*B)*x^(3/2)/(a*b*(a+b*x)^5)+1/128*(7*A*b+3*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(9/2)*b^(5/2))-1/40*(7*A*b+3*a*B)*sqrt(x)/(a*b^2*(a+b*x)^4)+1/240*(7*A*b+3*a*B)*sqrt(x)/(a^2*b^2*(a+b*x)^3)+1/192*(7*A*b+3*a*B)*sqrt(x)/(a^3*b^2*(a+b*x)^2)+1/128*(7*A*b+3*a*B)*sqrt(x)/(a^4*b^2*(a+b*x))],
[(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^3*sqrt(x)),x,8,7/128*(9*A*b+a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(11/2)*b^(3/2))+1/5*(A*b-a*B)*sqrt(x)/(a*b*(a+b*x)^5)+1/40*(9*A*b+a*B)*sqrt(x)/(a^2*b*(a+b*x)^4)+7/240*(9*A*b+a*B)*sqrt(x)/(a^3*b*(a+b*x)^3)+7/192*(9*A*b+a*B)*sqrt(x)/(a^4*b*(a+b*x)^2)+7/128*(9*A*b+a*B)*sqrt(x)/(a^5*b*(a+b*x))],
[(A+B*x)/(x^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3),x,9,-63/128*(11*A*b-a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(13/2)*sqrt(b))-63/128*(11*A*b-a*B)/(a^6*b*sqrt(x))+1/5*(A*b-a*B)/(a*b*(a+b*x)^5*sqrt(x))+1/40*(11*A*b-a*B)/(a^2*b*(a+b*x)^4*sqrt(x))+3/80*(11*A*b-a*B)/(a^3*b*(a+b*x)^3*sqrt(x))+21/320*(11*A*b-a*B)/(a^4*b*(a+b*x)^2*sqrt(x))+21/128*(11*A*b-a*B)/(a^5*b*(a+b*x)*sqrt(x))],
[(A+B*x)/(x^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3),x,10,-77/128*(13*A*b-3*a*B)/(a^6*b*x^(3/2))+1/5*(A*b-a*B)/(a*b*x^(3/2)*(a+b*x)^5)+1/40*(13*A*b-3*a*B)/(a^2*b*x^(3/2)*(a+b*x)^4)+11/240*(13*A*b-3*a*B)/(a^3*b*x^(3/2)*(a+b*x)^3)+33/320*(13*A*b-3*a*B)/(a^4*b*x^(3/2)*(a+b*x)^2)+231/640*(13*A*b-3*a*B)/(a^5*b*x^(3/2)*(a+b*x))+231/128*(13*A*b-3*a*B)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/a^(15/2)+231/128*(13*A*b-3*a*B)/(a^7*sqrt(x))],

# Integrands of the form (e x)^(m/2) (A+B x) (a^2+2 a b x+b^2 x^2)^(p/2)

# p>0
[x^(7/2)*(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,2/9*a*A*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/11*(A*b+a*B)*x^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/13*b*B*x^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^(5/2)*(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,2/7*a*A*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/9*(A*b+a*B)*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/11*b*B*x^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^(3/2)*(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,2/5*a*A*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/7*(A*b+a*B)*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/9*b*B*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,2/3*a*A*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/5*(A*b+a*B)*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/7*b*B*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/sqrt(x),x,3,2/3*(A*b+a*B)*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/5*b*B*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2*a*A*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/x^(3/2),x,3,2/3*b*B*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)-2*a*A*sqrt(a^2+2*a*b*x+b^2*x^2)/((a+b*x)*sqrt(x))+2*(A*b+a*B)*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/x^(5/2),x,3,-2/3*a*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(3/2)*(a+b*x))-2*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/((a+b*x)*sqrt(x))+2*b*B*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/x^(7/2),x,3,-2/5*a*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(5/2)*(a+b*x))-2/3*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(3/2)*(a+b*x))-2*b*B*sqrt(a^2+2*a*b*x+b^2*x^2)/((a+b*x)*sqrt(x))],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/x^(9/2),x,3,-2/7*a*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(7/2)*(a+b*x))-2/5*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(5/2)*(a+b*x))-2/3*b*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(3/2)*(a+b*x))],
[x^(7/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,2/9*a^3*A*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/11*a^2*(3*A*b+a*B)*x^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+6/13*a*b*(A*b+a*B)*x^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/15*b^2*(A*b+3*a*B)*x^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/17*b^3*B*x^(17/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^(5/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,2/7*a^3*A*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/9*a^2*(3*A*b+a*B)*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+6/11*a*b*(A*b+a*B)*x^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/13*b^2*(A*b+3*a*B)*x^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/15*b^3*B*x^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^(3/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,2/5*a^3*A*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/7*a^2*(3*A*b+a*B)*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/3*a*b*(A*b+a*B)*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/11*b^2*(A*b+3*a*B)*x^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/13*b^3*B*x^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(x),x,3,2/3*a^3*A*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/5*a^2*(3*A*b+a*B)*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+6/7*a*b*(A*b+a*B)*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/9*b^2*(A*b+3*a*B)*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/11*b^3*B*x^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/sqrt(x),x,3,2/3*a^2*(3*A*b+a*B)*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+6/5*a*b*(A*b+a*B)*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/7*b^2*(A*b+3*a*B)*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/9*b^3*B*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2*a^3*A*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^(3/2),x,3,2*a*b*(A*b+a*B)*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/5*b^2*(A*b+3*a*B)*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/7*b^3*B*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)-2*a^3*A*sqrt(a^2+2*a*b*x+b^2*x^2)/((a+b*x)*sqrt(x))+2*a^2*(3*A*b+a*B)*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^(5/2),x,3,-2/3*a^3*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(3/2)*(a+b*x))+2/3*b^2*(A*b+3*a*B)*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/5*b^3*B*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)-2*a^2*(3*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/((a+b*x)*sqrt(x))+6*a*b*(A*b+a*B)*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^(7/2),x,3,-2/5*a^3*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(5/2)*(a+b*x))-2/3*a^2*(3*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(3/2)*(a+b*x))+2/3*b^3*B*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)-6*a*b*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/((a+b*x)*sqrt(x))+2*b^2*(A*b+3*a*B)*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/x^(9/2),x,3,-2/7*a^3*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(7/2)*(a+b*x))-2/5*a^2*(3*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(5/2)*(a+b*x))-2*a*b*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(3/2)*(a+b*x))-2*b^2*(A*b+3*a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/((a+b*x)*sqrt(x))+2*b^3*B*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^(7/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,2/9*a^5*A*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/11*a^4*(5*A*b+a*B)*x^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+10/13*a^3*b*(2*A*b+a*B)*x^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+4/3*a^2*b^2*(A*b+a*B)*x^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+10/17*a*b^3*(A*b+2*a*B)*x^(17/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/19*b^4*(A*b+5*a*B)*x^(19/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/21*b^5*B*x^(21/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^(5/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,2/7*a^5*A*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/9*a^4*(5*A*b+a*B)*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+10/11*a^3*b*(2*A*b+a*B)*x^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+20/13*a^2*b^2*(A*b+a*B)*x^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/3*a*b^3*(A*b+2*a*B)*x^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/17*b^4*(A*b+5*a*B)*x^(17/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/19*b^5*B*x^(19/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[x^(3/2)*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,2/5*a^5*A*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/7*a^4*(5*A*b+a*B)*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+10/9*a^3*b*(2*A*b+a*B)*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+20/11*a^2*b^2*(A*b+a*B)*x^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+10/13*a*b^3*(A*b+2*a*B)*x^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/15*b^4*(A*b+5*a*B)*x^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/17*b^5*B*x^(17/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(x),x,3,2/3*a^5*A*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/5*a^4*(5*A*b+a*B)*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+10/7*a^3*b*(2*A*b+a*B)*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+20/9*a^2*b^2*(A*b+a*B)*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+10/11*a*b^3*(A*b+2*a*B)*x^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/13*b^4*(A*b+5*a*B)*x^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/15*b^5*B*x^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/sqrt(x),x,3,2/3*a^4*(5*A*b+a*B)*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2*a^3*b*(2*A*b+a*B)*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+20/7*a^2*b^2*(A*b+a*B)*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+10/9*a*b^3*(A*b+2*a*B)*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/11*b^4*(A*b+5*a*B)*x^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/13*b^5*B*x^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2*a^5*A*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^(3/2),x,3,10/3*a^3*b*(2*A*b+a*B)*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+4*a^2*b^2*(A*b+a*B)*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+10/7*a*b^3*(A*b+2*a*B)*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/9*b^4*(A*b+5*a*B)*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/11*b^5*B*x^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)-2*a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/((a+b*x)*sqrt(x))+2*a^4*(5*A*b+a*B)*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^(5/2),x,3,-2/3*a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(3/2)*(a+b*x))+20/3*a^2*b^2*(A*b+a*B)*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2*a*b^3*(A*b+2*a*B)*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/7*b^4*(A*b+5*a*B)*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/9*b^5*B*x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)-2*a^4*(5*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/((a+b*x)*sqrt(x))+10*a^3*b*(2*A*b+a*B)*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^(7/2),x,3,-2/5*a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(5/2)*(a+b*x))-2/3*a^4*(5*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(3/2)*(a+b*x))+10/3*a*b^3*(A*b+2*a*B)*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/5*b^4*(A*b+5*a*B)*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/7*b^5*B*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)-10*a^3*b*(2*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/((a+b*x)*sqrt(x))+20*a^2*b^2*(A*b+a*B)*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/x^(9/2),x,3,-2/7*a^5*A*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(7/2)*(a+b*x))-2/5*a^4*(5*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(5/2)*(a+b*x))-10/3*a^3*b*(2*A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/(x^(3/2)*(a+b*x))+2/3*b^4*(A*b+5*a*B)*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+2/5*b^5*B*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)-20*a^2*b^2*(A*b+a*B)*sqrt(a^2+2*a*b*x+b^2*x^2)/((a+b*x)*sqrt(x))+10*a*b^3*(A*b+2*a*B)*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],

# p<0
[x^(7/2)*(A+B*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,8,2/3*a^2*(A*b-a*B)*x^(3/2)*(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-2/5*a*(A*b-a*B)*x^(5/2)*(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2/7*(A*b-a*B)*x^(7/2)*(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+2/9*B*x^(9/2)*(a+b*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+2*a^(7/2)*(A*b-a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-2*a^3*(A*b-a*B)*(a+b*x)*sqrt(x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^(5/2)*(A+B*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,7,-2/3*a*(A*b-a*B)*x^(3/2)*(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2/5*(A*b-a*B)*x^(5/2)*(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+2/7*B*x^(7/2)*(a+b*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-2*a^(5/2)*(A*b-a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*a^2*(A*b-a*B)*(a+b*x)*sqrt(x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^(3/2)*(A+B*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,6,2/3*(A*b-a*B)*x^(3/2)*(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+2/5*B*x^(5/2)*(a+b*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+2*a^(3/2)*(A*b-a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-2*a*(A*b-a*B)*(a+b*x)*sqrt(x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*sqrt(x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,5,2/3*B*x^(3/2)*(a+b*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-2*(A*b-a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/(b^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*(a+b*x)*sqrt(x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,4,2*(A*b-a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(3/2)*sqrt(a)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*B*(a+b*x)*sqrt(x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,4,-2*(A*b-a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-2*A*(a+b*x)/(a*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,5,-2/3*A*(a+b*x)/(a*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/(a^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*(a+b*x)/(a^2*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,6,-2/5*A*(a+b*x)/(a*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2/3*(A*b-a*B)*(a+b*x)/(a^2*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-2*b^(3/2)*(A*b-a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-2*b*(A*b-a*B)*(a+b*x)/(a^3*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,7,-2/7*A*(a+b*x)/(a*x^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2/5*(A*b-a*B)*(a+b*x)/(a^2*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-2/3*b*(A*b-a*B)*(a+b*x)/(a^3*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*b^(5/2)*(A*b-a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*b^2*(A*b-a*B)*(a+b*x)/(a^4*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^(7/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,8,1/4*(5*A*b-9*a*B)*x^(7/2)/(a*b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-a*B)*x^(9/2)/(a*b*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/12*(5*A*b-9*a*B)*x^(3/2)*(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-7/20*(5*A*b-9*a*B)*x^(5/2)*(a+b*x)/(a*b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+7/4*a^(3/2)*(5*A*b-9*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/4*a*(5*A*b-9*a*B)*(a+b*x)*sqrt(x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^(5/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,7,1/4*(3*A*b-7*a*B)*x^(5/2)/(a*b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-a*B)*x^(7/2)/(a*b*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/12*(3*A*b-7*a*B)*x^(3/2)*(a+b*x)/(a*b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-5/4*(3*A*b-7*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/(b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5/4*(3*A*b-7*a*B)*(a+b*x)*sqrt(x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^(3/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,6,1/4*(A*b-5*a*B)*x^(3/2)/(a*b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-a*B)*x^(5/2)/(a*b*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+3/4*(A*b-5*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(7/2)*sqrt(a)*sqrt(a^2+2*a*b*x+b^2*x^2))-3/4*(A*b-5*a*B)*(a+b*x)*sqrt(x)/(a*b^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*sqrt(x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,5,1/2*(A*b-a*B)*x^(3/2)/(a*b*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(A*b+3*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*b^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(A*b+3*a*B)*sqrt(x)/(a*b^2*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(x)),x,5,1/4*(3*A*b+a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(5/2)*b^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(3*A*b+a*B)*sqrt(x)/(a^2*b*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-a*B)*sqrt(x)/(a*b*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,6,-3/4*(5*A*b-a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(7/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(5*A*b-a*B)/(a^2*b*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-a*B)/(a*b*(a+b*x)*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))-3/4*(5*A*b-a*B)*(a+b*x)/(a^3*b*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,7,1/4*(7*A*b-3*a*B)/(a^2*b*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-a*B)/(a*b*x^(3/2)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/12*(7*A*b-3*a*B)*(a+b*x)/(a^3*b*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5/4*(7*A*b-3*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/(a^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5/4*(7*A*b-3*a*B)*(a+b*x)/(a^4*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,8,1/4*(9*A*b-5*a*B)/(a^2*b*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-a*B)/(a*b*x^(5/2)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/20*(9*A*b-5*a*B)*(a+b*x)/(a^3*b*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/12*(9*A*b-5*a*B)*(a+b*x)/(a^4*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/4*b^(3/2)*(9*A*b-5*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/4*b*(9*A*b-5*a*B)*(a+b*x)/(a^5*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^(11/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,10,33/64*(5*A*b-13*a*B)*x^(7/2)/(a*b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(A*b-a*B)*x^(13/2)/(a*b*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/24*(5*A*b-13*a*B)*x^(11/2)/(a*b^2*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+11/96*(5*A*b-13*a*B)*x^(9/2)/(a*b^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+77/64*(5*A*b-13*a*B)*x^(3/2)*(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))-231/320*(5*A*b-13*a*B)*x^(5/2)*(a+b*x)/(a*b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+231/64*a^(3/2)*(5*A*b-13*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-231/64*a*(5*A*b-13*a*B)*(a+b*x)*sqrt(x)/(b^7*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^(9/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,9,21/64*(3*A*b-11*a*B)*x^(5/2)/(a*b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(A*b-a*B)*x^(11/2)/(a*b*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/24*(3*A*b-11*a*B)*x^(9/2)/(a*b^2*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+3/32*(3*A*b-11*a*B)*x^(7/2)/(a*b^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*(3*A*b-11*a*B)*x^(3/2)*(a+b*x)/(a*b^5*sqrt(a^2+2*a*b*x+b^2*x^2))-105/64*(3*A*b-11*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(a)/(b^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+105/64*(3*A*b-11*a*B)*(a+b*x)*sqrt(x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^(7/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,8,35/192*(A*b-9*a*B)*x^(3/2)/(a*b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(A*b-a*B)*x^(9/2)/(a*b*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/24*(A*b-9*a*B)*x^(7/2)/(a*b^2*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+7/96*(A*b-9*a*B)*x^(5/2)/(a*b^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+35/64*(A*b-9*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(b^(11/2)*sqrt(a)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*(A*b-9*a*B)*(a+b*x)*sqrt(x)/(a*b^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^(5/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,7,1/4*(A*b-a*B)*x^(7/2)/(a*b*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-1/24*(A*b+7*a*B)*x^(5/2)/(a*b^2*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-5/96*(A*b+7*a*B)*x^(3/2)/(a*b^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+5/64*(A*b+7*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(3/2)*b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/64*(A*b+7*a*B)*sqrt(x)/(a*b^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[x^(3/2)*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,7,1/4*(A*b-a*B)*x^(5/2)/(a*b*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-1/24*(3*A*b+5*a*B)*x^(3/2)/(a*b^2*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/64*(3*A*b+5*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(5/2)*b^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/64*(3*A*b+5*a*B)*sqrt(x)/(a^2*b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-1/32*(3*A*b+5*a*B)*sqrt(x)/(a*b^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*sqrt(x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,7,1/4*(A*b-a*B)*x^(3/2)/(a*b*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/64*(5*A*b+3*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(7/2)*b^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/64*(5*A*b+3*a*B)*sqrt(x)/(a^3*b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-1/24*(5*A*b+3*a*B)*sqrt(x)/(a*b^2*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/96*(5*A*b+3*a*B)*sqrt(x)/(a^2*b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(x)),x,7,5/64*(7*A*b+a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(9/2)*b^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5/64*(7*A*b+a*B)*sqrt(x)/(a^4*b*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(A*b-a*B)*sqrt(x)/(a*b*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/24*(7*A*b+a*B)*sqrt(x)/(a^2*b*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+5/96*(7*A*b+a*B)*sqrt(x)/(a^3*b*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,8,-35/64*(9*A*b-a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(11/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))+35/192*(9*A*b-a*B)/(a^4*b*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(A*b-a*B)/(a*b*(a+b*x)^3*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/24*(9*A*b-a*B)/(a^2*b*(a+b*x)^2*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/96*(9*A*b-a*B)/(a^3*b*(a+b*x)*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*(9*A*b-a*B)*(a+b*x)/(a^5*b*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,9,21/64*(11*A*b-3*a*B)/(a^4*b*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(A*b-a*B)/(a*b*x^(3/2)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/24*(11*A*b-3*a*B)/(a^2*b*x^(3/2)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+3/32*(11*A*b-3*a*B)/(a^3*b*x^(3/2)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*(11*A*b-3*a*B)*(a+b*x)/(a^5*b*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+105/64*(11*A*b-3*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))*sqrt(b)/(a^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+105/64*(11*A*b-3*a*B)*(a+b*x)/(a^6*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(x^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,10,33/64*(13*A*b-5*a*B)/(a^4*b*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(A*b-a*B)/(a*b*x^(5/2)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/24*(13*A*b-5*a*B)/(a^2*b*x^(5/2)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+11/96*(13*A*b-5*a*B)/(a^3*b*x^(5/2)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-231/320*(13*A*b-5*a*B)*(a+b*x)/(a^5*b*x^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+77/64*(13*A*b-5*a*B)*(a+b*x)/(a^6*x^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-231/64*b^(3/2)*(13*A*b-5*a*B)*(a+b*x)*arctan(sqrt(b)*sqrt(x)/sqrt(a))/(a^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-231/64*b*(13*A*b-5*a*B)*(a+b*x)/(a^7*sqrt(x)*sqrt(a^2+2*a*b*x+b^2*x^2))],

# Integrands of the form x^m (A+B x) (a^2+2 a b x+b^2 x^2)^p when m symbolic
[x^m*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,a^6*A*x^(1+m)/(1+m)+a^5*(6*A*b+a*B)*x^(2+m)/(2+m)+3*a^4*b*(5*A*b+2*a*B)*x^(3+m)/(3+m)+5*a^3*b^2*(4*A*b+3*a*B)*x^(4+m)/(4+m)+5*a^2*b^3*(3*A*b+4*a*B)*x^(5+m)/(5+m)+3*a*b^4*(2*A*b+5*a*B)*x^(6+m)/(6+m)+b^5*(A*b+6*a*B)*x^(7+m)/(7+m)+b^6*B*x^(8+m)/(8+m)],
[x^m*(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,a^4*A*x^(1+m)/(1+m)+a^3*(4*A*b+a*B)*x^(2+m)/(2+m)+2*a^2*b*(3*A*b+2*a*B)*x^(3+m)/(3+m)+2*a*b^2*(2*A*b+3*a*B)*x^(4+m)/(4+m)+b^3*(A*b+4*a*B)*x^(5+m)/(5+m)+b^4*B*x^(6+m)/(6+m)],
[x^m*(A+B*x)*(a^2+2*a*b*x+b^2*x^2),x,3,a^2*A*x^(1+m)/(1+m)+a*(2*A*b+a*B)*x^(2+m)/(2+m)+b*(A*b+2*a*B)*x^(3+m)/(3+m)+b^2*B*x^(4+m)/(4+m)],
[x^m*(A+B*x)/(a^2+2*a*b*x+b^2*x^2),x,3,(A*b-a*B)*x^(1+m)/(a*b*(a+b*x))-(A*b*m-a*B*(1+m))*x^(1+m)*hypergeom([1,1+m],[2+m],-b*x/a)/(a^2*b*(1+m))],
[x^m*(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/3*(A*b-a*B)*x^(1+m)/(a*b*(a+b*x)^3)+1/3*(A*b*(2-m)+a*B*(1+m))*x^(1+m)*hypergeom([3,1+m],[2+m],-b*x/a)/(a^4*b*(1+m))],
[x^m*(1+x)*(1+2*x+x^2)^5,x,3,x^(1+m)/(1+m)+11*x^(2+m)/(2+m)+55*x^(3+m)/(3+m)+165*x^(4+m)/(4+m)+330*x^(5+m)/(5+m)+462*x^(6+m)/(6+m)+462*x^(7+m)/(7+m)+330*x^(8+m)/(8+m)+165*x^(9+m)/(9+m)+55*x^(10+m)/(10+m)+11*x^(11+m)/(11+m)+x^(12+m)/(12+m)],
[x^m*(d+e*x)*(1+2*x+x^2)^5,x,3,d*x^(1+m)/(1+m)+(10*d+e)*x^(2+m)/(2+m)+5*(9*d+2*e)*x^(3+m)/(3+m)+15*(8*d+3*e)*x^(4+m)/(4+m)+30*(7*d+4*e)*x^(5+m)/(5+m)+42*(6*d+5*e)*x^(6+m)/(6+m)+42*(5*d+6*e)*x^(7+m)/(7+m)+30*(4*d+7*e)*x^(8+m)/(8+m)+15*(3*d+8*e)*x^(9+m)/(9+m)+5*(2*d+9*e)*x^(10+m)/(10+m)+(d+10*e)*x^(11+m)/(11+m)+e*x^(12+m)/(12+m)],

# Integrands of the form (e x)^m (f+g x) (a+b x+c x^2)^p

# Integrands of the form x^m (A+B x) (a+b x+c x^2)^p

# p>0
[x^3*(A+B*x)*(a+b*x+c*x^2),x,2,1/4*a*A*x^4+1/5*(A*b+a*B)*x^5+1/6*(b*B+A*c)*x^6+1/7*B*c*x^7],
[x^2*(A+B*x)*(a+b*x+c*x^2),x,2,1/3*a*A*x^3+1/4*(A*b+a*B)*x^4+1/5*(b*B+A*c)*x^5+1/6*B*c*x^6],
[x*(A+B*x)*(a+b*x+c*x^2),x,2,1/2*a*A*x^2+1/3*(A*b+a*B)*x^3+1/4*(b*B+A*c)*x^4+1/5*B*c*x^5],
[(A+B*x)*(a+b*x+c*x^2),x,2,a*A*x+1/2*(A*b+a*B)*x^2+1/3*(b*B+A*c)*x^3+1/4*B*c*x^4],
[(A+B*x)*(a+b*x+c*x^2)/x,x,2,(A*b+a*B)*x+1/2*(b*B+A*c)*x^2+1/3*B*c*x^3+a*A*log(x)],
[(A+B*x)*(a+b*x+c*x^2)/x^2,x,2,-a*A/x+(b*B+A*c)*x+1/2*B*c*x^2+(A*b+a*B)*log(x)],
[(A+B*x)*(a+b*x+c*x^2)/x^3,x,2,-1/2*a*A/x^2+(-A*b-a*B)/x+B*c*x+(b*B+A*c)*log(x)],
[(A+B*x)*(a+b*x+c*x^2)/x^4,x,2,-1/3*a*A/x^3+1/2*(-A*b-a*B)/x^2+(-b*B-A*c)/x+B*c*log(x)],
[(A+B*x)*(a+b*x+c*x^2)/x^5,x,2,-1/4*a*A/x^4+1/3*(-A*b-a*B)/x^3+1/2*(-b*B-A*c)/x^2-B*c/x],
[(A+B*x)*(a+b*x+c*x^2)/x^6,x,2,-1/5*a*A/x^5+1/4*(-A*b-a*B)/x^4+1/3*(-b*B-A*c)/x^3-1/2*B*c/x^2],
[(A+B*x)*(a+b*x+c*x^2)/x^7,x,2,-1/6*a*A/x^6+1/5*(-A*b-a*B)/x^5+1/4*(-b*B-A*c)/x^4-1/3*B*c/x^3],
[(A+B*x)*(a+b*x+c*x^2)/x^8,x,2,-1/7*a*A/x^7+1/6*(-A*b-a*B)/x^6+1/5*(-b*B-A*c)/x^5-1/4*B*c/x^4],
[x^2*(A+B*x)*(a+b*x+c*x^2)^2,x,2,1/3*a^2*A*x^3+1/4*a*(2*A*b+a*B)*x^4+1/5*(2*a*b*B+A*(b^2+2*a*c))*x^5+1/6*(b^2*B+2*A*b*c+2*a*B*c)*x^6+1/7*c*(2*b*B+A*c)*x^7+1/8*B*c^2*x^8],
[x*(A+B*x)*(a+b*x+c*x^2)^2,x,2,1/2*a^2*A*x^2+1/3*a*(2*A*b+a*B)*x^3+1/4*(2*a*b*B+A*(b^2+2*a*c))*x^4+1/5*(b^2*B+2*A*b*c+2*a*B*c)*x^5+1/6*c*(2*b*B+A*c)*x^6+1/7*B*c^2*x^7],
[(A+B*x)*(a+b*x+c*x^2)^2,x,2,a^2*A*x+1/2*a*(2*A*b+a*B)*x^2+1/3*(2*a*b*B+A*(b^2+2*a*c))*x^3+1/4*(b^2*B+2*A*b*c+2*a*B*c)*x^4+1/5*c*(2*b*B+A*c)*x^5+1/6*B*c^2*x^6],
[(A+B*x)*(a+b*x+c*x^2)^2/x,x,2,a*(2*A*b+a*B)*x+1/2*(2*a*b*B+A*(b^2+2*a*c))*x^2+1/3*(b^2*B+2*A*b*c+2*a*B*c)*x^3+1/4*c*(2*b*B+A*c)*x^4+1/5*B*c^2*x^5+a^2*A*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^2/x^2,x,2,-a^2*A/x+(2*a*b*B+A*(b^2+2*a*c))*x+1/2*(b^2*B+2*A*b*c+2*a*B*c)*x^2+1/3*c*(2*b*B+A*c)*x^3+1/4*B*c^2*x^4+a*(2*A*b+a*B)*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^2/x^3,x,2,-1/2*a^2*A/x^2-a*(2*A*b+a*B)/x+(b^2*B+2*A*b*c+2*a*B*c)*x+1/2*c*(2*b*B+A*c)*x^2+1/3*B*c^2*x^3+(2*a*b*B+A*(b^2+2*a*c))*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^2/x^4,x,2,-1/3*a^2*A/x^3-1/2*a*(2*A*b+a*B)/x^2+(-2*a*b*B-A*(b^2+2*a*c))/x+c*(2*b*B+A*c)*x+1/2*B*c^2*x^2+(b^2*B+2*A*b*c+2*a*B*c)*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^2/x^5,x,2,-1/4*a^2*A/x^4-1/3*a*(2*A*b+a*B)/x^3+1/2*(-2*a*b*B-A*(b^2+2*a*c))/x^2+(-b^2*B-2*A*b*c-2*a*B*c)/x+B*c^2*x+c*(2*b*B+A*c)*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^2/x^6,x,2,-1/5*a^2*A/x^5-1/4*a*(2*A*b+a*B)/x^4+1/3*(-2*a*b*B-A*(b^2+2*a*c))/x^3+1/2*(-b^2*B-2*A*b*c-2*a*B*c)/x^2-c*(2*b*B+A*c)/x+B*c^2*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^2/x^7,x,2,-1/6*a^2*A/x^6-1/5*a*(2*A*b+a*B)/x^5+1/4*(-2*a*b*B-A*(b^2+2*a*c))/x^4+1/3*(-b^2*B-2*A*b*c-2*a*B*c)/x^3-1/2*c*(2*b*B+A*c)/x^2-B*c^2/x],
[(A+B*x)*(a+b*x+c*x^2)^2/x^8,x,2,-1/7*a^2*A/x^7-1/6*a*(2*A*b+a*B)/x^6+1/5*(-2*a*b*B-A*(b^2+2*a*c))/x^5+1/4*(-b^2*B-2*A*b*c-2*a*B*c)/x^4-1/3*c*(2*b*B+A*c)/x^3-1/2*B*c^2/x^2],
[(A+B*x)*(a+b*x+c*x^2)^2/x^9,x,2,-1/8*a^2*A/x^8-1/7*a*(2*A*b+a*B)/x^7+1/6*(-2*a*b*B-A*(b^2+2*a*c))/x^6+1/5*(-b^2*B-2*A*b*c-2*a*B*c)/x^5-1/4*c*(2*b*B+A*c)/x^4-1/3*B*c^2/x^3],
[x^2*(A+B*x)*(a+b*x+c*x^2)^3,x,2,1/3*a^3*A*x^3+1/4*a^2*(3*A*b+a*B)*x^4+3/5*a*(a*b*B+A*(b^2+a*c))*x^5+1/6*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^6+1/7*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^7+3/8*c*(b^2*B+A*b*c+a*B*c)*x^8+1/9*c^2*(3*b*B+A*c)*x^9+1/10*B*c^3*x^10],
[x*(A+B*x)*(a+b*x+c*x^2)^3,x,2,1/2*a^3*A*x^2+1/3*a^2*(3*A*b+a*B)*x^3+3/4*a*(a*b*B+A*(b^2+a*c))*x^4+1/5*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^5+1/6*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^6+3/7*c*(b^2*B+A*b*c+a*B*c)*x^7+1/8*c^2*(3*b*B+A*c)*x^8+1/9*B*c^3*x^9],
[(A+B*x)*(a+b*x+c*x^2)^3,x,2,a^3*A*x+1/2*a^2*(3*A*b+a*B)*x^2+a*(a*b*B+A*(b^2+a*c))*x^3+1/4*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^4+1/5*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^5+1/2*c*(b^2*B+A*b*c+a*B*c)*x^6+1/7*c^2*(3*b*B+A*c)*x^7+1/8*B*c^3*x^8],
[(A+B*x)*(a+b*x+c*x^2)^3/x,x,2,a^2*(3*A*b+a*B)*x+3/2*a*(a*b*B+A*(b^2+a*c))*x^2+1/3*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^3+1/4*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^4+3/5*c*(b^2*B+A*b*c+a*B*c)*x^5+1/6*c^2*(3*b*B+A*c)*x^6+1/7*B*c^3*x^7+a^3*A*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^3/x^2,x,2,-a^3*A/x+3*a*(a*b*B+A*(b^2+a*c))*x+1/2*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^2+1/3*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^3+3/4*c*(b^2*B+A*b*c+a*B*c)*x^4+1/5*c^2*(3*b*B+A*c)*x^5+1/6*B*c^3*x^6+a^2*(3*A*b+a*B)*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^3/x^3,x,2,-1/2*a^3*A/x^2-a^2*(3*A*b+a*B)/x+(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x+1/2*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^2+c*(b^2*B+A*b*c+a*B*c)*x^3+1/4*c^2*(3*b*B+A*c)*x^4+1/5*B*c^3*x^5+3*a*(a*b*B+A*(b^2+a*c))*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^3/x^4,x,2,-1/3*a^3*A/x^3-1/2*a^2*(3*A*b+a*B)/x^2-3*a*(a*b*B+A*(b^2+a*c))/x+(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x+3/2*c*(b^2*B+A*b*c+a*B*c)*x^2+1/3*c^2*(3*b*B+A*c)*x^3+1/4*B*c^3*x^4+(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^3/x^5,x,2,-1/4*a^3*A/x^4-1/3*a^2*(3*A*b+a*B)/x^3-3/2*a*(a*b*B+A*(b^2+a*c))/x^2+(-3*a*B*(b^2+a*c)-A*(b^3+6*a*b*c))/x+3*c*(b^2*B+A*b*c+a*B*c)*x+1/2*c^2*(3*b*B+A*c)*x^2+1/3*B*c^3*x^3+(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^3/x^6,x,2,-1/5*a^3*A/x^5-1/4*a^2*(3*A*b+a*B)/x^4-a*(a*b*B+A*(b^2+a*c))/x^3+1/2*(-3*a*B*(b^2+a*c)-A*(b^3+6*a*b*c))/x^2+(-b^3*B-3*A*b^2*c-6*a*b*B*c-3*a*A*c^2)/x+c^2*(3*b*B+A*c)*x+1/2*B*c^3*x^2+3*c*(b^2*B+A*b*c+a*B*c)*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^3/x^7,x,2,-1/6*a^3*A/x^6-1/5*a^2*(3*A*b+a*B)/x^5-3/4*a*(a*b*B+A*(b^2+a*c))/x^4+1/3*(-3*a*B*(b^2+a*c)-A*(b^3+6*a*b*c))/x^3+1/2*(-b^3*B-3*A*b^2*c-6*a*b*B*c-3*a*A*c^2)/x^2-3*c*(b^2*B+A*b*c+a*B*c)/x+B*c^3*x+c^2*(3*b*B+A*c)*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^3/x^8,x,2,-1/7*a^3*A/x^7-1/6*a^2*(3*A*b+a*B)/x^6-3/5*a*(a*b*B+A*(b^2+a*c))/x^5+1/4*(-3*a*B*(b^2+a*c)-A*(b^3+6*a*b*c))/x^4+1/3*(-b^3*B-3*A*b^2*c-6*a*b*B*c-3*a*A*c^2)/x^3-3/2*c*(b^2*B+A*b*c+a*B*c)/x^2-c^2*(3*b*B+A*c)/x+B*c^3*log(x)],
[(A+B*x)*(a+b*x+c*x^2)^3/x^9,x,2,-1/8*a^3*A/x^8-1/7*a^2*(3*A*b+a*B)/x^7-1/2*a*(a*b*B+A*(b^2+a*c))/x^6+1/5*(-3*a*B*(b^2+a*c)-A*(b^3+6*a*b*c))/x^5+1/4*(-b^3*B-3*A*b^2*c-6*a*b*B*c-3*a*A*c^2)/x^4-c*(b^2*B+A*b*c+a*B*c)/x^3-1/2*c^2*(3*b*B+A*c)/x^2-B*c^3/x],
[(A+B*x)*(a+b*x+c*x^2)^3/x^10,x,2,-1/9*a^3*A/x^9-1/8*a^2*(3*A*b+a*B)/x^8-3/7*a*(a*b*B+A*(b^2+a*c))/x^7+1/6*(-3*a*B*(b^2+a*c)-A*(b^3+6*a*b*c))/x^6+1/5*(-b^3*B-3*A*b^2*c-6*a*b*B*c-3*a*A*c^2)/x^5-3/4*c*(b^2*B+A*b*c+a*B*c)/x^4-1/3*c^2*(3*b*B+A*c)/x^3-1/2*B*c^3/x^2],
[(A+B*x)*(a+b*x+c*x^2)^3/x^11,x,2,-1/10*a^3*A/x^10-1/9*a^2*(3*A*b+a*B)/x^9-3/8*a*(a*b*B+A*(b^2+a*c))/x^8+1/7*(-3*a*B*(b^2+a*c)-A*(b^3+6*a*b*c))/x^7+1/6*(-b^3*B-3*A*b^2*c-6*a*b*B*c-3*a*A*c^2)/x^6-3/5*c*(b^2*B+A*b*c+a*B*c)/x^5-1/4*c^2*(3*b*B+A*c)/x^4-1/3*B*c^3/x^3],

# p<0
[x^4*(d+e*x)/(a+b*x+c*x^2),x,6,(b^2*c*d-a*c^2*d-b^3*e+2*a*b*c*e)*x/c^4-1/2*(b*c*d-b^2*e+a*c*e)*x^2/c^3+1/3*(c*d-b*e)*x^3/c^2+1/4*e*x^4/c-1/2*(b^3*c*d-2*a*b*c^2*d-b^4*e+3*a*b^2*c*e-a^2*c^2*e)*log(a+b*x+c*x^2)/c^5-(b^4*c*d-4*a*b^2*c^2*d+2*a^2*c^3*d-b^5*e+5*a*b^3*c*e-5*a^2*b*c^2*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^5*sqrt(b^2-4*a*c))],
[x^3*(d+e*x)/(a+b*x+c*x^2),x,6,-(b*c*d-b^2*e+a*c*e)*x/c^3+1/2*(c*d-b*e)*x^2/c^2+1/3*e*x^3/c+1/2*(b^2*c*d-a*c^2*d-b^3*e+2*a*b*c*e)*log(a+b*x+c*x^2)/c^4+(b^3*c*d-3*a*b*c^2*d-b^4*e+4*a*b^2*c*e-2*a^2*c^2*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^4*sqrt(b^2-4*a*c))],
[x^2*(d+e*x)/(a+b*x+c*x^2),x,6,(c*d-b*e)*x/c^2+1/2*e*x^2/c-1/2*(b*c*d-b^2*e+a*c*e)*log(a+b*x+c*x^2)/c^3-(b^2*c*d-2*a*c^2*d-b^3*e+3*a*b*c*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*sqrt(b^2-4*a*c))],
[x*(d+e*x)/(a+b*x+c*x^2),x,5,e*x/c+1/2*(c*d-b*e)*log(a+b*x+c*x^2)/c^2+(b*c*d-b^2*e+2*a*c*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^2*sqrt(b^2-4*a*c))],
[(d+e*x)/(a+b*x+c*x^2),x,4,1/2*e*log(a+b*x+c*x^2)/c-(2*c*d-b*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c*sqrt(b^2-4*a*c))],
[(d+e*x)/(x*(a+b*x+c*x^2)),x,6,d*log(x)/a-1/2*d*log(a+b*x+c*x^2)/a+(b*d-2*a*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(a*sqrt(b^2-4*a*c))],
[(d+e*x)/(x^2*(a+b*x+c*x^2)),x,6,-d/(a*x)-(b*d-a*e)*log(x)/a^2+1/2*(b*d-a*e)*log(a+b*x+c*x^2)/a^2-(b^2*d-2*a*c*d-a*b*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(a^2*sqrt(b^2-4*a*c))],
[(d+e*x)/(x^3*(a+b*x+c*x^2)),x,6,-1/2*d/(a*x^2)+(b*d-a*e)/(a^2*x)+(b^2*d-a*c*d-a*b*e)*log(x)/a^3-1/2*(b^2*d-a*c*d-a*b*e)*log(a+b*x+c*x^2)/a^3+(b^3*d-3*a*b*c*d-a*b^2*e+2*a^2*c*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(a^3*sqrt(b^2-4*a*c))],
[(d+e*x)/(x^4*(a+b*x+c*x^2)),x,6,-1/3*d/(a*x^3)+1/2*(b*d-a*e)/(a^2*x^2)+(-b^2*d+a*c*d+a*b*e)/(a^3*x)-(b^3*d-2*a*b*c*d-a*b^2*e+a^2*c*e)*log(x)/a^4+1/2*(b^3*d-2*a*b*c*d-a*b^2*e+a^2*c*e)*log(a+b*x+c*x^2)/a^4-(b^4*d-4*a*b^2*c*d+2*a^2*c^2*d-a*b^3*e+3*a^2*b*c*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(a^4*sqrt(b^2-4*a*c))],
[x^4*(d+e*x)/(a+b*x+c*x^2)^2,x,7,(2*b^2*c*d-6*a*c^2*d-3*b^3*e+11*a*b*c*e)*x/(c^3*(b^2-4*a*c))-1/2*(2*b*c*d-3*b^2*e+8*a*c*e)*x^2/(c^2*(b^2-4*a*c))+x^3*(a*(2*c*d-b*e)+(b*c*d-b^2*e+2*a*c*e)*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2))-(2*b^4*c*d-12*a*b^2*c^2*d+12*a^2*c^3*d-3*b^5*e+20*a*b^3*c*e-30*a^2*b*c^2*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^4*(b^2-4*a*c)^(3/2))-1/2*(2*b*c*d-3*b^2*e+2*a*c*e)*log(a+b*x+c*x^2)/c^4],
[x^3*(d+e*x)/(a+b*x+c*x^2)^2,x,6,-(b*c*d-2*b^2*e+6*a*c*e)*x/(c^2*(b^2-4*a*c))+x^2*(a*(2*c*d-b*e)+(b*c*d-b^2*e+2*a*c*e)*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2))+(b^3*c*d-6*a*b*c^2*d-2*b^4*e+12*a*b^2*c*e-12*a^2*c^2*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*(b^2-4*a*c)^(3/2))+1/2*(c*d-2*b*e)*log(a+b*x+c*x^2)/c^3],
[x^2*(d+e*x)/(a+b*x+c*x^2)^2,x,5,x*(a*(2*c*d-b*e)+(b*c*d-b^2*e+2*a*c*e)*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2))+(b^3*e+2*a*c*(2*c*d-3*b*e))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^2*(b^2-4*a*c)^(3/2))+1/2*e*log(a+b*x+c*x^2)/c^2],
[x*(d+e*x)/(a+b*x+c*x^2)^2,x,3,(a*(2*c*d-b*e)+(b*c*d-b^2*e+2*a*c*e)*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2))-2*(b*d-2*a*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(b^2-4*a*c)^(3/2)],
[(d+e*x)/(a+b*x+c*x^2)^2,x,3,(-b*d+2*a*e-(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+2*(2*c*d-b*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(b^2-4*a*c)^(3/2)],
[(d+e*x)/(x*(a+b*x+c*x^2)^2),x,7,(b^2*d-2*a*c*d-a*b*e+c*(b*d-2*a*e)*x)/(a*(b^2-4*a*c)*(a+b*x+c*x^2))+(b^3*d-6*a*b*c*d+4*a^2*c*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(a^2*(b^2-4*a*c)^(3/2))+d*log(x)/a^2-1/2*d*log(a+b*x+c*x^2)/a^2],
[(d+e*x)/(x^2*(a+b*x+c*x^2)^2),x,7,(-2*b^2*d+6*a*c*d+a*b*e)/(a^2*(b^2-4*a*c)*x)+(b^2*d-2*a*c*d-a*b*e+c*(b*d-2*a*e)*x)/(a*(b^2-4*a*c)*x*(a+b*x+c*x^2))-(2*b^4*d-12*a*b^2*c*d+12*a^2*c^2*d-a*b^3*e+6*a^2*b*c*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(a^3*(b^2-4*a*c)^(3/2))-(2*b*d-a*e)*log(x)/a^3+1/2*(2*b*d-a*e)*log(a+b*x+c*x^2)/a^3],
[(d+e*x)/(x^3*(a+b*x+c*x^2)^2),x,7,1/2*(-3*b^2*d+8*a*c*d+2*a*b*e)/(a^2*(b^2-4*a*c)*x^2)+(3*b^3*d-11*a*b*c*d-2*a*b^2*e+6*a^2*c*e)/(a^3*(b^2-4*a*c)*x)+(b^2*d-2*a*c*d-a*b*e+c*(b*d-2*a*e)*x)/(a*(b^2-4*a*c)*x^2*(a+b*x+c*x^2))+(3*b^5*d-20*a*b^3*c*d+30*a^2*b*c^2*d-2*a*b^4*e+12*a^2*b^2*c*e-12*a^3*c^2*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(a^4*(b^2-4*a*c)^(3/2))+(3*b^2*d-2*a*c*d-2*a*b*e)*log(x)/a^4-1/2*(3*b^2*d-2*a*c*d-2*a*b*e)*log(a+b*x+c*x^2)/a^4],
[(5+2*x)/(4+5*x+x^2),x,1,log(4+5*x+x^2)],
[(7+3*x)/(8+6*x+x^2),x,3,1/2*log(2+x)+5/2*log(4+x)],
[(5+2*x)/(5+4*x+x^2),x,4,arctan(2+x)+log(5+4*x+x^2)],
[(-2+7*x)/(42-16*x+2*x^2),x,4,7/4*log(21-8*x+x^2)-13*arctan((4-x)/sqrt(5))/sqrt(5)],
[(3+x)/(1+3*x+x^2),x,3,1/10*log(3+2*x+sqrt(5))*(5-3*sqrt(5))+1/10*log(3+2*x-sqrt(5))*(5+3*sqrt(5))],
[(-1+2*x)/(1+8*x+4*x^2),x,3,1/4*log(2+2*x-sqrt(3))*(1-sqrt(3))+1/4*log(2+2*x+sqrt(3))*(1+sqrt(3))],
[(3+2*x)/(13+12*x+4*x^2)^2,x,1,(-1/4)/(13+12*x+4*x^2)],
[(4+x)/(5+4*x+x^2)^2,x,3,1/2*(3+2*x)/(5+4*x+x^2)+arctan(2+x)],
[(-1+3*x)/(1+x+x^2)^2,x,3,1/3*(-7-5*x)/(1+x+x^2)-10/3*arctan((1+2*x)/sqrt(3))/sqrt(3)],
[(1+x)/(1-x+x^2)^3,x,4,1/2*(-1+x)/(1-x+x^2)^2+1/2*(-1+2*x)/(1-x+x^2)-2*arctan((1-2*x)/sqrt(3))/sqrt(3)],

#  The following integrands are equal. 
[1/(A+B*x),x,1,log(A+B*x)/B],
[(A+B*x)/(A^2+2*A*B*x+B^2*x^2),x,2,log(A+B*x)/B],

# Integrands of the form x^m (A+B x) (a+b x+c x^2)^(p/2)

# p>0
[x^4*(A+B*x)*sqrt(a+b*x+c*x^2),x,7,1/280*(33*b^2*B-42*A*b*c-32*a*B*c)*x^2*(a+b*x+c*x^2)^(3/2)/c^3-1/84*(11*b*B-14*A*c)*x^3*(a+b*x+c*x^2)^(3/2)/c^2+1/7*B*x^4*(a+b*x+c*x^2)^(3/2)/c+1/13440*(1155*b^4*B-1470*A*b^3*c-3276*a*b^2*B*c+2744*a*A*b*c^2+1024*a^2*B*c^2-6*c*(231*b^3*B-294*A*b^2*c-444*a*b*B*c+280*a*A*c^2)*x)*(a+b*x+c*x^2)^(3/2)/c^5+1/2048*(b^2-4*a*c)*(33*b^5*B-42*A*b^4*c-120*a*b^3*B*c+112*a*A*b^2*c^2+80*a^2*b*B*c^2-32*a^2*A*c^3)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(13/2)-1/1024*(33*b^5*B-42*A*b^4*c-120*a*b^3*B*c+112*a*A*b^2*c^2+80*a^2*b*B*c^2-32*a^2*A*c^3)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^6],
[x^3*(A+B*x)*sqrt(a+b*x+c*x^2),x,6,-1/20*(3*b*B-4*A*c)*x^2*(a+b*x+c*x^2)^(3/2)/c^2+1/6*B*x^3*(a+b*x+c*x^2)^(3/2)/c-1/960*(105*b^3*B-140*A*b^2*c-196*a*b*B*c+128*a*A*c^2-6*c*(21*b^2*B-28*A*b*c-20*a*B*c)*x)*(a+b*x+c*x^2)^(3/2)/c^4-1/1024*(b^2-4*a*c)*(21*b^4*B-28*A*b^3*c-56*a*b^2*B*c+48*a*A*b*c^2+16*a^2*B*c^2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(11/2)+1/512*(21*b^4*B-28*A*b^3*c-56*a*b^2*B*c+48*a*A*b*c^2+16*a^2*B*c^2)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5],
[x^2*(A+B*x)*sqrt(a+b*x+c*x^2),x,5,1/5*B*x^2*(a+b*x+c*x^2)^(3/2)/c+1/240*(35*b^2*B-50*A*b*c-32*a*B*c-6*c*(7*b*B-10*A*c)*x)*(a+b*x+c*x^2)^(3/2)/c^3+1/256*(b^2-4*a*c)*(7*b^3*B-10*A*b^2*c-12*a*b*B*c+8*a*A*c^2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)-1/128*(7*b^3*B-10*A*b^2*c-12*a*b*B*c+8*a*A*c^2)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4],
[x*(A+B*x)*sqrt(a+b*x+c*x^2),x,4,-1/24*(5*b*B-8*A*c-6*B*c*x)*(a+b*x+c*x^2)^(3/2)/c^2-1/128*(b^2-4*a*c)*(5*b^2*B-8*A*b*c-4*a*B*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+1/64*(5*b^2*B-8*A*b*c-4*a*B*c)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^3],
[(A+B*x)*sqrt(a+b*x+c*x^2),x,4,1/3*B*(a+b*x+c*x^2)^(3/2)/c+1/16*(b^2-4*a*c)*(b*B-2*A*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-1/8*(b*B-2*A*c)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^2],
[(A+B*x)*sqrt(a+b*x+c*x^2)/x,x,6,-1/8*(b^2*B-4*A*b*c-4*a*B*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-A*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))*sqrt(a)+1/4*(b*B+4*A*c+2*B*c*x)*sqrt(a+b*x+c*x^2)/c],
[(A+B*x)*sqrt(a+b*x+c*x^2)/x^2,x,6,-1/2*(A*b+2*a*B)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/sqrt(a)+1/2*(b*B+2*A*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/sqrt(c)-(A-B*x)*sqrt(a+b*x+c*x^2)/x],
[(A+B*x)*sqrt(a+b*x+c*x^2)/x^3,x,6,1/8*(A*b^2-4*a*b*B-4*a*A*c)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(3/2)+B*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)-1/4*(2*a*A+(A*b+4*a*B)*x)*sqrt(a+b*x+c*x^2)/(a*x^2)],
[(A+B*x)*sqrt(a+b*x+c*x^2)/x^4,x,4,-1/3*A*(a+b*x+c*x^2)^(3/2)/(a*x^3)-1/16*(A*b-2*a*B)*(b^2-4*a*c)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(5/2)+1/8*(A*b-2*a*B)*(2*a+b*x)*sqrt(a+b*x+c*x^2)/(a^2*x^2)],
[(A+B*x)*sqrt(a+b*x+c*x^2)/x^5,x,5,-1/4*A*(a+b*x+c*x^2)^(3/2)/(a*x^4)+1/24*(5*A*b-8*a*B)*(a+b*x+c*x^2)^(3/2)/(a^2*x^3)+1/128*(b^2-4*a*c)*(5*A*b^2-8*a*b*B-4*a*A*c)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(7/2)-1/64*(5*A*b^2-8*a*b*B-4*a*A*c)*(2*a+b*x)*sqrt(a+b*x+c*x^2)/(a^3*x^2)],
[(A+B*x)*sqrt(a+b*x+c*x^2)/x^6,x,6,-1/5*A*(a+b*x+c*x^2)^(3/2)/(a*x^5)+1/40*(7*A*b-10*a*B)*(a+b*x+c*x^2)^(3/2)/(a^2*x^4)-1/240*(35*A*b^2-50*a*b*B-32*a*A*c)*(a+b*x+c*x^2)^(3/2)/(a^3*x^3)+1/256*(b^2-4*a*c)*(2*a*B*(5*b^2-4*a*c)-A*(7*b^3-12*a*b*c))*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(9/2)+1/128*(7*A*b^3-10*a*b^2*B-12*a*A*b*c+8*a^2*B*c)*(2*a+b*x)*sqrt(a+b*x+c*x^2)/(a^4*x^2)],
[(A+B*x)*sqrt(a+b*x+c*x^2)/x^7,x,7,-1/6*A*(a+b*x+c*x^2)^(3/2)/(a*x^6)+1/20*(3*A*b-4*a*B)*(a+b*x+c*x^2)^(3/2)/(a^2*x^5)-1/160*(21*A*b^2-28*a*b*B-20*a*A*c)*(a+b*x+c*x^2)^(3/2)/(a^3*x^4)+1/960*(105*A*b^3-140*a*b^2*B-196*a*A*b*c+128*a^2*B*c)*(a+b*x+c*x^2)^(3/2)/(a^4*x^3)-1/1024*(b^2-4*a*c)*(4*a*b*B*(7*b^2-12*a*c)-A*(21*b^4-56*a*b^2*c+16*a^2*c^2))*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(11/2)+1/512*(4*a*b*B*(7*b^2-12*a*c)-A*(21*b^4-56*a*b^2*c+16*a^2*c^2))*(2*a+b*x)*sqrt(a+b*x+c*x^2)/(a^5*x^2)],
[x^4*(A+B*x)*(a+b*x+c*x^2)^(3/2),x,8,-1/12288*(143*b^5*B-198*A*b^4*c-440*a*b^3*B*c+432*a*A*b^2*c^2+240*a^2*b*B*c^2-96*a^2*A*c^3)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^6+1/2016*(143*b^2*B-198*A*b*c-128*a*B*c)*x^2*(a+b*x+c*x^2)^(5/2)/c^3-1/144*(13*b*B-18*A*c)*x^3*(a+b*x+c*x^2)^(5/2)/c^2+1/9*B*x^4*(a+b*x+c*x^2)^(5/2)/c+1/80640*(3003*b^4*B-4158*A*b^3*c-7524*a*b^2*B*c+6696*a*A*b*c^2+2048*a^2*B*c^2-10*c*(429*b^3*B-594*A*b^2*c-748*a*b*B*c+504*a*A*c^2)*x)*(a+b*x+c*x^2)^(5/2)/c^5-1/65536*(b^2-4*a*c)^2*(143*b^5*B-198*A*b^4*c-440*a*b^3*B*c+432*a*A*b^2*c^2+240*a^2*b*B*c^2-96*a^2*A*c^3)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(15/2)+1/32768*(b^2-4*a*c)*(143*b^5*B-198*A*b^4*c-440*a*b^3*B*c+432*a*A*b^2*c^2+240*a^2*b*B*c^2-96*a^2*A*c^3)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^7],
[x^3*(A+B*x)*(a+b*x+c*x^2)^(3/2),x,7,1/2048*(33*b^4*B-48*A*b^3*c-72*a*b^2*B*c+64*a*A*b*c^2+16*a^2*B*c^2)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^5-1/112*(11*b*B-16*A*c)*x^2*(a+b*x+c*x^2)^(5/2)/c^2+1/8*B*x^3*(a+b*x+c*x^2)^(5/2)/c-1/4480*(231*b^3*B-336*A*b^2*c-372*a*b*B*c+256*a*A*c^2-10*c*(33*b^2*B-48*A*b*c-28*a*B*c)*x)*(a+b*x+c*x^2)^(5/2)/c^4+3/32768*(b^2-4*a*c)^2*(33*b^4*B-48*A*b^3*c-72*a*b^2*B*c+64*a*A*b*c^2+16*a^2*B*c^2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(13/2)-3/16384*(b^2-4*a*c)*(33*b^4*B-48*A*b^3*c-72*a*b^2*B*c+64*a*A*b*c^2+16*a^2*B*c^2)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^6],
[x^2*(A+B*x)*(a+b*x+c*x^2)^(3/2),x,6,-1/384*(9*b^3*B-14*A*b^2*c-12*a*b*B*c+8*a*A*c^2)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^4+1/7*B*x^2*(a+b*x+c*x^2)^(5/2)/c+1/840*(63*b^2*B-98*A*b*c-48*a*B*c-10*c*(9*b*B-14*A*c)*x)*(a+b*x+c*x^2)^(5/2)/c^3-1/2048*(b^2-4*a*c)^2*(9*b^3*B-14*A*b^2*c-12*a*b*B*c+8*a*A*c^2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(11/2)+1/1024*(b^2-4*a*c)*(9*b^3*B-14*A*b^2*c-12*a*b*B*c+8*a*A*c^2)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5],
[x*(A+B*x)*(a+b*x+c*x^2)^(3/2),x,5,1/192*(7*b^2*B-12*A*b*c-4*a*B*c)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^3-1/60*(7*b*B-12*A*c-10*B*c*x)*(a+b*x+c*x^2)^(5/2)/c^2+1/1024*(b^2-4*a*c)^2*(7*b^2*B-12*A*b*c-4*a*B*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)-1/512*(b^2-4*a*c)*(7*b^2*B-12*A*b*c-4*a*B*c)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4],
[(A+B*x)*(a+b*x+c*x^2)^(3/2),x,5,-1/16*(b*B-2*A*c)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^2+1/5*B*(a+b*x+c*x^2)^(5/2)/c-3/256*(b^2-4*a*c)^2*(b*B-2*A*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+3/128*(b^2-4*a*c)*(b*B-2*A*c)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^3],
[(A+B*x)*(a+b*x+c*x^2)^(3/2)/x,x,7,1/24*(3*b*B+8*A*c+6*B*c*x)*(a+b*x+c*x^2)^(3/2)/c-a^(3/2)*A*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))+1/128*(64*a*A*b*c^2+(b^2-4*a*c)*(3*b^2*B-8*A*b*c-12*a*B*c))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-1/64*(3*b^3*B-8*A*b^2*c-12*a*b*B*c-64*a*A*c^2+2*c*(3*b^2*B-8*A*b*c-12*a*B*c)*x)*sqrt(a+b*x+c*x^2)/c^2],
[(A+B*x)*(a+b*x+c*x^2)^(3/2)/x^2,x,7,-1/3*(3*A-B*x)*(a+b*x+c*x^2)^(3/2)/x-1/16*(b^3*B-6*A*b^2*c-12*a*b*B*c-24*a*A*c^2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-1/2*(3*A*b+2*a*B)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))*sqrt(a)+1/8*(b^2*B+18*A*b*c+8*a*B*c+2*c*(b*B+6*A*c)*x)*sqrt(a+b*x+c*x^2)/c],
[(A+B*x)*(a+b*x+c*x^2)^(3/2)/x^3,x,7,-1/2*(A-B*x)*(a+b*x+c*x^2)^(3/2)/x^2-3/8*(4*a*b*B+A*(b^2+4*a*c))*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/sqrt(a)+3/8*(b^2*B+4*A*b*c+4*a*B*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/sqrt(c)-3/4*(A*b+2*a*B-(b*B+2*A*c)*x)*sqrt(a+b*x+c*x^2)/x],
[(A+B*x)*(a+b*x+c*x^2)^(3/2)/x^4,x,7,-1/12*(4*a*A+3*(A*b+2*a*B)*x)*(a+b*x+c*x^2)^(3/2)/(a*x^3)-1/16*(6*a*B*(b^2+4*a*c)-A*(b^3-12*a*b*c))*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(3/2)+1/2*(3*b*B+2*A*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)+1/8*(A*b^2-6*a*b*B-8*a*A*c+2*(A*b+6*a*B)*c*x)*sqrt(a+b*x+c*x^2)/(a*x)],
[(A+B*x)*(a+b*x+c*x^2)^(3/2)/x^5,x,7,-1/24*(6*a*A+(3*A*b+8*a*B)*x)*(a+b*x+c*x^2)^(3/2)/(a*x^4)+1/128*(8*a*b*B*(b^2-12*a*c)-3*A*(b^2-4*a*c)^2)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(5/2)+B*c^(3/2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))-1/64*(2*a*(8*a*b*B-3*A*(b^2-4*a*c))+(8*a*B*(b^2+8*a*c)-3*A*(b^3-4*a*b*c))*x)*sqrt(a+b*x+c*x^2)/(a^2*x^2)],
[(A+B*x)*(a+b*x+c*x^2)^(3/2)/x^6,x,5,1/16*(A*b-2*a*B)*(2*a+b*x)*(a+b*x+c*x^2)^(3/2)/(a^2*x^4)-1/5*A*(a+b*x+c*x^2)^(5/2)/(a*x^5)+3/256*(A*b-2*a*B)*(b^2-4*a*c)^2*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(7/2)-3/128*(A*b-2*a*B)*(b^2-4*a*c)*(2*a+b*x)*sqrt(a+b*x+c*x^2)/(a^3*x^2)],
[(A+B*x)*(a+b*x+c*x^2)^(3/2)/x^7,x,6,-1/192*(7*A*b^2-12*a*b*B-4*a*A*c)*(2*a+b*x)*(a+b*x+c*x^2)^(3/2)/(a^3*x^4)-1/6*A*(a+b*x+c*x^2)^(5/2)/(a*x^6)+1/60*(7*A*b-12*a*B)*(a+b*x+c*x^2)^(5/2)/(a^2*x^5)-1/1024*(b^2-4*a*c)^2*(7*A*b^2-12*a*b*B-4*a*A*c)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(9/2)+1/512*(b^2-4*a*c)*(7*A*b^2-12*a*b*B-4*a*A*c)*(2*a+b*x)*sqrt(a+b*x+c*x^2)/(a^4*x^2)],
[(A+B*x)*(a+b*x+c*x^2)^(3/2)/x^8,x,7,1/384*(9*A*b^3-14*a*b^2*B-12*a*A*b*c+8*a^2*B*c)*(2*a+b*x)*(a+b*x+c*x^2)^(3/2)/(a^4*x^4)-1/7*A*(a+b*x+c*x^2)^(5/2)/(a*x^7)+1/84*(9*A*b-14*a*B)*(a+b*x+c*x^2)^(5/2)/(a^2*x^6)-1/840*(63*A*b^2-98*a*b*B-48*a*A*c)*(a+b*x+c*x^2)^(5/2)/(a^3*x^5)-1/2048*(b^2-4*a*c)^2*(2*a*B*(7*b^2-4*a*c)-A*(9*b^3-12*a*b*c))*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(11/2)-1/1024*(b^2-4*a*c)*(9*A*b^3-14*a*b^2*B-12*a*A*b*c+8*a^2*B*c)*(2*a+b*x)*sqrt(a+b*x+c*x^2)/(a^5*x^2)],
[x^4*(A+B*x)*(a+b*x+c*x^2)^(5/2),x,9,1/98304*(b^2-4*a*c)*(195*b^5*B-286*A*b^4*c-520*a*b^3*B*c+528*a*A*b^2*c^2+240*a^2*b*B*c^2-96*a^2*A*c^3)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^7-1/30720*(195*b^5*B-286*A*b^4*c-520*a*b^3*B*c+528*a*A*b^2*c^2+240*a^2*b*B*c^2-96*a^2*A*c^3)*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^6+1/3960*(195*b^2*B-286*A*b*c-160*a*B*c)*x^2*(a+b*x+c*x^2)^(7/2)/c^3-1/220*(15*b*B-22*A*c)*x^3*(a+b*x+c*x^2)^(7/2)/c^2+1/11*B*x^4*(a+b*x+c*x^2)^(7/2)/c+1/887040*(19305*b^4*B-28314*A*b^3*c-42900*a*b^2*B*c+39688*a*A*b*c^2+10240*a^2*B*c^2-14*c*(2145*b^3*B-3146*A*b^2*c-3380*a*b*B*c+2376*a*A*c^2)*x)*(a+b*x+c*x^2)^(7/2)/c^5+1/524288*(b^2-4*a*c)^3*(195*b^5*B-286*A*b^4*c-520*a*b^3*B*c+528*a*A*b^2*c^2+240*a^2*b*B*c^2-96*a^2*A*c^3)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(17/2)-1/262144*(b^2-4*a*c)^2*(195*b^5*B-286*A*b^4*c-520*a*b^3*B*c+528*a*A*b^2*c^2+240*a^2*b*B*c^2-96*a^2*A*c^3)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^8],
[x^3*(A+B*x)*(a+b*x+c*x^2)^(5/2),x,8,-1/49152*(b^2-4*a*c)*(143*b^4*B-220*A*b^3*c-264*a*b^2*B*c+240*a*A*b*c^2+48*a^2*B*c^2)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^6+1/15360*(143*b^4*B-220*A*b^3*c-264*a*b^2*B*c+240*a*A*b*c^2+48*a^2*B*c^2)*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^5-1/180*(13*b*B-20*A*c)*x^2*(a+b*x+c*x^2)^(7/2)/c^2+1/10*B*x^3*(a+b*x+c*x^2)^(7/2)/c-1/40320*(1287*b^3*B-1980*A*b^2*c-1804*a*b*B*c+1280*a*A*c^2-14*c*(143*b^2*B-220*A*b*c-108*a*B*c)*x)*(a+b*x+c*x^2)^(7/2)/c^4-1/262144*(b^2-4*a*c)^3*(143*b^4*B-220*A*b^3*c-264*a*b^2*B*c+240*a*A*b*c^2+48*a^2*B*c^2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(15/2)+1/131072*(b^2-4*a*c)^2*(143*b^4*B-220*A*b^3*c-264*a*b^2*B*c+240*a*A*b*c^2+48*a^2*B*c^2)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^7],
[x^2*(A+B*x)*(a+b*x+c*x^2)^(5/2),x,7,5/12288*(b^2-4*a*c)*(11*b^3*B-18*A*b^2*c-12*a*b*B*c+8*a*A*c^2)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^5-1/768*(11*b^3*B-18*A*b^2*c-12*a*b*B*c+8*a*A*c^2)*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^4+1/9*B*x^2*(a+b*x+c*x^2)^(7/2)/c+1/2016*(99*b^2*B-162*A*b*c-64*a*B*c-14*c*(11*b*B-18*A*c)*x)*(a+b*x+c*x^2)^(7/2)/c^3+5/65536*(b^2-4*a*c)^3*(11*b^3*B-18*A*b^2*c-12*a*b*B*c+8*a*A*c^2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(13/2)-5/32768*(b^2-4*a*c)^2*(11*b^3*B-18*A*b^2*c-12*a*b*B*c+8*a*A*c^2)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^6],
[x*(A+B*x)*(a+b*x+c*x^2)^(5/2),x,6,-5/6144*(b^2-4*a*c)*(9*b^2*B-16*A*b*c-4*a*B*c)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^4+1/384*(9*b^2*B-16*A*b*c-4*a*B*c)*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^3-1/112*(9*b*B-16*A*c-14*B*c*x)*(a+b*x+c*x^2)^(7/2)/c^2-5/32768*(b^2-4*a*c)^3*(9*b^2*B-16*A*b*c-4*a*B*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(11/2)+5/16384*(b^2-4*a*c)^2*(9*b^2*B-16*A*b*c-4*a*B*c)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5],
[(A+B*x)*(a+b*x+c*x^2)^(5/2),x,6,5/384*(b^2-4*a*c)*(b*B-2*A*c)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^3-1/24*(b*B-2*A*c)*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^2+1/7*B*(a+b*x+c*x^2)^(7/2)/c+5/2048*(b^2-4*a*c)^3*(b*B-2*A*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)-5/1024*(b^2-4*a*c)^2*(b*B-2*A*c)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4],
[(A+B*x)*(a+b*x+c*x^2)^(5/2)/x,x,8,-1/192*(5*b^3*B-12*A*b^2*c-20*a*b*B*c-64*a*A*c^2+2*c*(5*b^2*B-12*A*b*c-20*a*B*c)*x)*(a+b*x+c*x^2)^(3/2)/c^2+1/60*(5*b*B+12*A*c+10*B*c*x)*(a+b*x+c*x^2)^(5/2)/c-a^(5/2)*A*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))+1/1024*(512*a^2*A*b*c^3-(b^2-4*a*c)*(5*b^4*B-12*A*b^3*c-40*a*b^2*B*c+112*a*A*b*c^2+80*a^2*B*c^2))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+1/512*(512*a^2*A*c^3+b*(64*a*A*b*c^2+(b^2-4*a*c)*(5*b^2*B-12*A*b*c-20*a*B*c))+2*c*(64*a*A*b*c^2+(b^2-4*a*c)*(5*b^2*B-12*A*b*c-20*a*B*c))*x)*sqrt(a+b*x+c*x^2)/c^3],
[(A+B*x)*(a+b*x+c*x^2)^(5/2)/x^2,x,8,1/48*(3*b^2*B+70*A*b*c+16*a*B*c+6*c*(b*B+10*A*c)*x)*(a+b*x+c*x^2)^(3/2)/c-1/5*(5*A-B*x)*(a+b*x+c*x^2)^(5/2)/x-1/2*a^(3/2)*(5*A*b+2*a*B)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))+1/256*(3*b^5*B-10*A*b^4*c-40*a*b^3*B*c+240*a*A*b^2*c^2+240*a^2*b*B*c^2+480*a^2*A*c^3)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-1/128*(3*b^4*B-10*A*b^3*c-28*a*b^2*B*c-440*a*A*b*c^2-128*a^2*B*c^2+2*c*(3*b^3*B-10*A*b^2*c-28*a*b*B*c-120*a*A*c^2)*x)*sqrt(a+b*x+c*x^2)/c^2],
[(A+B*x)*(a+b*x+c*x^2)^(5/2)/x^3,x,8,-5/24*(6*(A*b+a*B)-(b*B+4*A*c)*x)*(a+b*x+c*x^2)^(3/2)/x-1/4*(2*A-B*x)*(a+b*x+c*x^2)^(5/2)/x^2-5/128*(b^4*B-8*A*b^3*c-24*a*b^2*B*c-96*a*A*b*c^2-48*a^2*B*c^2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-5/8*(3*A*b^2+4*a*b*B+4*a*A*c)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))*sqrt(a)+5/64*(b^3*B+40*A*b^2*c+44*a*b*B*c+32*a*A*c^2+2*c*(b^2*B+16*A*b*c+12*a*B*c)*x)*sqrt(a+b*x+c*x^2)/c],
[(A+B*x)*(a+b*x+c*x^2)^(5/2)/x^4,x,8,-5/12*(A*b+2*a*B-(b*B+2*A*c)*x)*(a+b*x+c*x^2)^(3/2)/x^2-1/3*(A-B*x)*(a+b*x+c*x^2)^(5/2)/x^3-5/16*(2*a*B*(3*b^2+4*a*c)+A*(b^3+12*a*b*c))*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/sqrt(a)+5/16*(b^3*B+6*A*b^2*c+12*a*b*B*c+8*a*A*c^2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/sqrt(c)-5/8*(4*a*b*B+A*(b^2+4*a*c)-(b^2*B+4*A*b*c+4*a*B*c)*x)*sqrt(a+b*x+c*x^2)/x],
[(A+B*x)*(a+b*x+c*x^2)^(5/2)/x^5,x,8,-5/96*(4*a*(A*b+4*a*B)+3*(8*a*b*B+A*(b^2+4*a*c))*x)*(a+b*x+c*x^2)^(3/2)/(a*x^3)-1/4*(A-2*B*x)*(a+b*x+c*x^2)^(5/2)/x^4-5/128*(8*a*b*B*(b^2+12*a*c)-A*(b^4-24*a*b^2*c-48*a^2*c^2))*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(3/2)+5/8*(3*b^2*B+4*A*b*c+4*a*B*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)-5/64*(8*a*B*(b^2+4*a*c)-A*(b^3-20*a*b*c)-2*c*(16*a*b*B+A*(b^2+12*a*c))*x)*sqrt(a+b*x+c*x^2)/(a*x)],
[(A+B*x)*(a+b*x+c*x^2)^(5/2)/x^6,x,8,1/192*(4*a*(3*A*b^2-10*a*b*B-16*a*A*c)-3*(10*a*B*(b^2+4*a*c)-A*(3*b^3-20*a*b*c))*x)*(a+b*x+c*x^2)^(3/2)/(a^2*x^3)-1/40*(8*a*A+5*(A*b+2*a*B)*x)*(a+b*x+c*x^2)^(5/2)/(a*x^5)+1/256*(10*a*B*(b^4-24*a*b^2*c-48*a^2*c^2)-A*(3*b^5-40*a*b^3*c+240*a^2*b*c^2))*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(5/2)+1/2*c^(3/2)*(5*b*B+2*A*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))+1/128*(10*a*b*B*(b^2-20*a*c)-A*(3*b^4-28*a*b^2*c+128*a^2*c^2)+2*c*(10*a*B*(b^2+12*a*c)-A*(3*b^3-28*a*b*c))*x)*sqrt(a+b*x+c*x^2)/(a^2*x)],
[(A+B*x)*(a+b*x+c*x^2)^(5/2)/x^7,x,8,-1/192*(2*a*(12*a*b*B-5*A*(b^2-4*a*c))+(4*a*B*(3*b^2+16*a*c)-5*A*(b^3-4*a*b*c))*x)*(a+b*x+c*x^2)^(3/2)/(a^2*x^4)-1/60*(10*a*A+(5*A*b+12*a*B)*x)*(a+b*x+c*x^2)^(5/2)/(a*x^6)+1/1024*(5*A*(b^2-4*a*c)^3-4*a*b*B*(3*b^4-40*a*b^2*c+240*a^2*c^2))*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(7/2)+B*c^(5/2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))+1/512*(2*a*(4*a*b*B*(3*b^2-28*a*c)-5*A*(b^2-4*a*c)^2)-(5*A*b*(b^2-4*a*c)^2-4*a*B*(3*b^4-28*a*b^2*c-128*a^2*c^2))*x)*sqrt(a+b*x+c*x^2)/(a^3*x^2)],
[(A+B*x)*(a+b*x+c*x^2)^(5/2)/x^8,x,6,-5/384*(A*b-2*a*B)*(b^2-4*a*c)*(2*a+b*x)*(a+b*x+c*x^2)^(3/2)/(a^3*x^4)+1/24*(A*b-2*a*B)*(2*a+b*x)*(a+b*x+c*x^2)^(5/2)/(a^2*x^6)-1/7*A*(a+b*x+c*x^2)^(7/2)/(a*x^7)-5/2048*(A*b-2*a*B)*(b^2-4*a*c)^3*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(9/2)+5/1024*(A*b-2*a*B)*(b^2-4*a*c)^2*(2*a+b*x)*sqrt(a+b*x+c*x^2)/(a^4*x^2)],
[(A+B*x)*(a+b*x+c*x^2)^(5/2)/x^9,x,7,5/6144*(b^2-4*a*c)*(9*A*b^2-16*a*b*B-4*a*A*c)*(2*a+b*x)*(a+b*x+c*x^2)^(3/2)/(a^4*x^4)-1/384*(9*A*b^2-16*a*b*B-4*a*A*c)*(2*a+b*x)*(a+b*x+c*x^2)^(5/2)/(a^3*x^6)-1/8*A*(a+b*x+c*x^2)^(7/2)/(a*x^8)+1/112*(9*A*b-16*a*B)*(a+b*x+c*x^2)^(7/2)/(a^2*x^7)+5/32768*(b^2-4*a*c)^3*(9*A*b^2-16*a*b*B-4*a*A*c)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(11/2)-5/16384*(b^2-4*a*c)^2*(9*A*b^2-16*a*b*B-4*a*A*c)*(2*a+b*x)*sqrt(a+b*x+c*x^2)/(a^5*x^2)],
[(A+B*x)*(a+b*x+c*x^2)^(5/2)/x^10,x,8,5/12288*(b^2-4*a*c)*(2*a*B*(9*b^2-4*a*c)-A*(11*b^3-12*a*b*c))*(2*a+b*x)*(a+b*x+c*x^2)^(3/2)/(a^5*x^4)+1/768*(11*A*b^3-18*a*b^2*B-12*a*A*b*c+8*a^2*B*c)*(2*a+b*x)*(a+b*x+c*x^2)^(5/2)/(a^4*x^6)-1/9*A*(a+b*x+c*x^2)^(7/2)/(a*x^9)+1/144*(11*A*b-18*a*B)*(a+b*x+c*x^2)^(7/2)/(a^2*x^8)-1/2016*(99*A*b^2-162*a*b*B-64*a*A*c)*(a+b*x+c*x^2)^(7/2)/(a^3*x^7)+5/65536*(b^2-4*a*c)^3*(2*a*B*(9*b^2-4*a*c)-A*(11*b^3-12*a*b*c))*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(13/2)-5/32768*(b^2-4*a*c)^2*(2*a*B*(9*b^2-4*a*c)-A*(11*b^3-12*a*b*c))*(2*a+b*x)*sqrt(a+b*x+c*x^2)/(a^6*x^2)],

# p<0
[x^4*(A+B*x)/sqrt(a+b*x+c*x^2),x,6,-1/256*(63*b^5*B-70*A*b^4*c-280*a*b^3*B*c+240*a*A*b^2*c^2+240*a^2*b*B*c^2-96*a^2*A*c^3)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(11/2)+1/240*(63*b^2*B-70*A*b*c-64*a*B*c)*x^2*sqrt(a+b*x+c*x^2)/c^3-1/40*(9*b*B-10*A*c)*x^3*sqrt(a+b*x+c*x^2)/c^2+1/5*B*x^4*sqrt(a+b*x+c*x^2)/c+1/1920*(945*b^4*B-1050*A*b^3*c-2940*a*b^2*B*c+2200*a*A*b*c^2+1024*a^2*B*c^2-2*c*(315*b^3*B-350*A*b^2*c-644*a*b*B*c+360*a*A*c^2)*x)*sqrt(a+b*x+c*x^2)/c^5],
[x^3*(A+B*x)/sqrt(a+b*x+c*x^2),x,5,1/128*(35*b^4*B-40*A*b^3*c-120*a*b^2*B*c+96*a*A*b*c^2+48*a^2*B*c^2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)-1/24*(7*b*B-8*A*c)*x^2*sqrt(a+b*x+c*x^2)/c^2+1/4*B*x^3*sqrt(a+b*x+c*x^2)/c-1/192*(105*b^3*B-120*A*b^2*c-220*a*b*B*c+128*a*A*c^2-2*c*(35*b^2*B-40*A*b*c-36*a*B*c)*x)*sqrt(a+b*x+c*x^2)/c^4],
[x^2*(A+B*x)/sqrt(a+b*x+c*x^2),x,4,-1/16*(5*b^3*B-6*A*b^2*c-12*a*b*B*c+8*a*A*c^2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+1/3*B*x^2*sqrt(a+b*x+c*x^2)/c+1/24*(15*b^2*B-18*A*b*c-16*a*B*c-2*c*(5*b*B-6*A*c)*x)*sqrt(a+b*x+c*x^2)/c^3],
[x*(A+B*x)/sqrt(a+b*x+c*x^2),x,3,1/8*(3*b^2*B-4*A*b*c-4*a*B*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-1/4*(3*b*B-4*A*c-2*B*c*x)*sqrt(a+b*x+c*x^2)/c^2],
[(A+B*x)/sqrt(a+b*x+c*x^2),x,3,-1/2*(b*B-2*A*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)+B*sqrt(a+b*x+c*x^2)/c],
[(A+B*x)/(x*sqrt(a+b*x+c*x^2)),x,5,-A*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/sqrt(a)+B*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/sqrt(c)],
[(A+B*x)/(x^2*sqrt(a+b*x+c*x^2)),x,3,1/2*(A*b-2*a*B)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(3/2)-A*sqrt(a+b*x+c*x^2)/(a*x)],
[(A+B*x)/(x^3*sqrt(a+b*x+c*x^2)),x,4,-1/8*(3*A*b^2-4*a*b*B-4*a*A*c)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(5/2)-1/2*A*sqrt(a+b*x+c*x^2)/(a*x^2)+1/4*(3*A*b-4*a*B)*sqrt(a+b*x+c*x^2)/(a^2*x)],
[(A+B*x)/(x^4*sqrt(a+b*x+c*x^2)),x,5,1/16*(5*A*b^3-6*a*b^2*B-12*a*A*b*c+8*a^2*B*c)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(7/2)-1/3*A*sqrt(a+b*x+c*x^2)/(a*x^3)+1/12*(5*A*b-6*a*B)*sqrt(a+b*x+c*x^2)/(a^2*x^2)-1/24*(15*A*b^2-18*a*b*B-16*a*A*c)*sqrt(a+b*x+c*x^2)/(a^3*x)],
[(A+B*x)/(x^5*sqrt(a+b*x+c*x^2)),x,6,1/128*(8*a*b*B*(5*b^2-12*a*c)-A*(35*b^4-120*a*b^2*c+48*a^2*c^2))*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(9/2)-1/4*A*sqrt(a+b*x+c*x^2)/(a*x^4)+1/24*(7*A*b-8*a*B)*sqrt(a+b*x+c*x^2)/(a^2*x^3)-1/96*(35*A*b^2-40*a*b*B-36*a*A*c)*sqrt(a+b*x+c*x^2)/(a^3*x^2)+1/192*(105*A*b^3-120*a*b^2*B-220*a*A*b*c+128*a^2*B*c)*sqrt(a+b*x+c*x^2)/(a^4*x)],
[(A+B*x)/(x^6*sqrt(a+b*x+c*x^2)),x,7,-1/256*(2*a*B*(35*b^4-120*a*b^2*c+48*a^2*c^2)-A*(63*b^5-280*a*b^3*c+240*a^2*b*c^2))*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(11/2)-1/5*A*sqrt(a+b*x+c*x^2)/(a*x^5)+1/40*(9*A*b-10*a*B)*sqrt(a+b*x+c*x^2)/(a^2*x^4)-1/240*(63*A*b^2-70*a*b*B-64*a*A*c)*sqrt(a+b*x+c*x^2)/(a^3*x^3)+1/960*(315*A*b^3-350*a*b^2*B-644*a*A*b*c+360*a^2*B*c)*sqrt(a+b*x+c*x^2)/(a^4*x^2)+1/1920*(50*a*b*B*(21*b^2-44*a*c)-A*(945*b^4-2940*a*b^2*c+1024*a^2*c^2))*sqrt(a+b*x+c*x^2)/(a^5*x)],
[x^4*(A+B*x)/(a+b*x+c*x^2)^(3/2),x,5,-1/16*(35*b^3*B-30*A*b^2*c-60*a*b*B*c+24*a*A*c^2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)-2*x^3*(a*(b*B-2*A*c)+(b^2*B-A*b*c-2*a*B*c)*x)/(c*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))+1/3*(7*b^2*B-6*A*b*c-16*a*B*c)*x^2*sqrt(a+b*x+c*x^2)/(c^2*(b^2-4*a*c))+1/24*(105*b^4*B-90*A*b^3*c-460*a*b^2*B*c+312*a*A*b*c^2+256*a^2*B*c^2-2*c*(35*b^3*B-30*A*b^2*c-116*a*b*B*c+72*a*A*c^2)*x)*sqrt(a+b*x+c*x^2)/(c^4*(b^2-4*a*c))],
[x^3*(A+B*x)/(a+b*x+c*x^2)^(3/2),x,4,3/8*(5*b^2*B-4*A*b*c-4*a*B*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)-2*x^2*(a*(b*B-2*A*c)+(b^2*B-A*b*c-2*a*B*c)*x)/(c*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))-1/4*(15*b^3*B-12*A*b^2*c-52*a*b*B*c+32*a*A*c^2-2*c*(5*b^2*B-4*A*b*c-12*a*B*c)*x)*sqrt(a+b*x+c*x^2)/(c^3*(b^2-4*a*c))],
[x^2*(A+B*x)/(a+b*x+c*x^2)^(3/2),x,4,-1/2*(3*b*B-2*A*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-2*x*(a*(b*B-2*A*c)+(b^2*B-A*b*c-2*a*B*c)*x)/(c*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))+(3*b^2*B-2*A*b*c-8*a*B*c)*sqrt(a+b*x+c*x^2)/(c^2*(b^2-4*a*c))],
[x*(A+B*x)/(a+b*x+c*x^2)^(3/2),x,3,B*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-2*(a*(b*B-2*A*c)+(b^2*B-A*b*c-2*a*B*c)*x)/(c*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))],
[(A+B*x)/(a+b*x+c*x^2)^(3/2),x,1,-2*(A*b-2*a*B-(b*B-2*A*c)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))],
[(A+B*x)/(x*(a+b*x+c*x^2)^(3/2)),x,4,-A*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(3/2)+2*(A*b^2-a*b*B-2*a*A*c+(A*b-2*a*B)*c*x)/(a*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))],
[(A+B*x)/(x^2*(a+b*x+c*x^2)^(3/2)),x,4,1/2*(3*A*b-2*a*B)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(5/2)+2*(A*b^2-a*b*B-2*a*A*c+(A*b-2*a*B)*c*x)/(a*(b^2-4*a*c)*x*sqrt(a+b*x+c*x^2))-(3*A*b^2-2*a*b*B-8*a*A*c)*sqrt(a+b*x+c*x^2)/(a^2*(b^2-4*a*c)*x)],
[(A+B*x)/(x^3*(a+b*x+c*x^2)^(3/2)),x,5,-3/8*(5*A*b^2-4*a*b*B-4*a*A*c)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(7/2)+2*(A*b^2-a*b*B-2*a*A*c+(A*b-2*a*B)*c*x)/(a*(b^2-4*a*c)*x^2*sqrt(a+b*x+c*x^2))-1/2*(5*A*b^2-4*a*b*B-12*a*A*c)*sqrt(a+b*x+c*x^2)/(a^2*(b^2-4*a*c)*x^2)-1/4*(4*a*B*(3*b^2-8*a*c)-A*(15*b^3-52*a*b*c))*sqrt(a+b*x+c*x^2)/(a^3*(b^2-4*a*c)*x)],
[(A+B*x)/(x^4*(a+b*x+c*x^2)^(3/2)),x,6,-1/16*(6*a*B*(5*b^2-4*a*c)-A*(35*b^3-60*a*b*c))*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(9/2)+2*(A*b^2-a*b*B-2*a*A*c+(A*b-2*a*B)*c*x)/(a*(b^2-4*a*c)*x^3*sqrt(a+b*x+c*x^2))-1/3*(7*A*b^2-6*a*b*B-16*a*A*c)*sqrt(a+b*x+c*x^2)/(a^2*(b^2-4*a*c)*x^3)-1/12*(6*a*B*(5*b^2-12*a*c)-A*(35*b^3-116*a*b*c))*sqrt(a+b*x+c*x^2)/(a^3*(b^2-4*a*c)*x^2)+1/24*(6*a*b*B*(15*b^2-52*a*c)-A*(105*b^4-460*a*b^2*c+256*a^2*c^2))*sqrt(a+b*x+c*x^2)/(a^4*(b^2-4*a*c)*x)],
[x^4*(A+B*x)/(a+b*x+c*x^2)^(5/2),x,5,-2/3*x^3*(a*(b*B-2*A*c)+(b^2*B-A*b*c-2*a*B*c)*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^(3/2))-1/2*(5*b*B-2*A*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)-2/3*x*(a*(5*b^3*B-2*A*b^2*c-28*a*b*B*c+24*a*A*c^2)+(5*b^4*B-2*A*b^3*c-32*a*b^2*B*c+16*a*A*b*c^2+32*a^2*B*c^2)*x)/(c^2*(b^2-4*a*c)^2*sqrt(a+b*x+c*x^2))+1/3*(15*b^4*B-6*A*b^3*c-100*a*b^2*B*c+40*a*A*b*c^2+128*a^2*B*c^2)*sqrt(a+b*x+c*x^2)/(c^3*(b^2-4*a*c)^2)],
[x^3*(A+B*x)/(a+b*x+c*x^2)^(5/2),x,4,-2/3*x^2*(a*(b*B-2*A*c)+(b^2*B-A*b*c-2*a*B*c)*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^(3/2))+B*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-2/3*(a*(3*b^3*B-20*a*b*B*c+16*a*A*c^2)+(3*b^4*B-22*a*b^2*B*c+8*a*A*b*c^2+24*a^2*B*c^2)*x)/(c^2*(b^2-4*a*c)^2*sqrt(a+b*x+c*x^2))],
[x^2*(A+B*x)/(a+b*x+c*x^2)^(5/2),x,2,-2/3*x^2*(A*b-2*a*B-(b*B-2*A*c)*x)/((b^2-4*a*c)*(a+b*x+c*x^2)^(3/2))+8/3*(A*b-2*a*B)*(2*a+b*x)/((b^2-4*a*c)^2*sqrt(a+b*x+c*x^2))],
[x*(A+B*x)/(a+b*x+c*x^2)^(5/2),x,2,-2/3*(a*(b*B-2*A*c)+(b^2*B-A*b*c-2*a*B*c)*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^(3/2))+2/3*(b^2*B-4*A*b*c+4*a*B*c)*(b+2*c*x)/(c*(b^2-4*a*c)^2*sqrt(a+b*x+c*x^2))],
[(A+B*x)/(a+b*x+c*x^2)^(5/2),x,2,-2/3*(A*b-2*a*B-(b*B-2*A*c)*x)/((b^2-4*a*c)*(a+b*x+c*x^2)^(3/2))-8/3*(b*B-2*A*c)*(b+2*c*x)/((b^2-4*a*c)^2*sqrt(a+b*x+c*x^2))],
[(A+B*x)/(x*(a+b*x+c*x^2)^(5/2)),x,5,2/3*(A*b^2-a*b*B-2*a*A*c+(A*b-2*a*B)*c*x)/(a*(b^2-4*a*c)*(a+b*x+c*x^2)^(3/2))-A*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(5/2)+2/3*(8*a^2*b*B*c+A*(3*b^4-22*a*b^2*c+24*a^2*c^2)+c*(3*A*b^3-20*a*A*b*c+16*a^2*B*c)*x)/(a^2*(b^2-4*a*c)^2*sqrt(a+b*x+c*x^2))],
[(A+B*x)/(x^2*(a+b*x+c*x^2)^(5/2)),x,5,2/3*(A*b^2-a*b*B-2*a*A*c+(A*b-2*a*B)*c*x)/(a*(b^2-4*a*c)*x*(a+b*x+c*x^2)^(3/2))+1/2*(5*A*b-2*a*B)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(7/2)-2/3*(2*a*b*B*(b^2-8*a*c)-A*(5*b^4-32*a*b^2*c+32*a^2*c^2)-c*(5*A*b^3-2*a*b^2*B-28*a*A*b*c+24*a^2*B*c)*x)/(a^2*(b^2-4*a*c)^2*x*sqrt(a+b*x+c*x^2))+1/3*(2*a*b*B*(3*b^2-20*a*c)-A*(15*b^4-100*a*b^2*c+128*a^2*c^2))*sqrt(a+b*x+c*x^2)/(a^3*(b^2-4*a*c)^2*x)],
[(A+B*x)/(x^3*(a+b*x+c*x^2)^(5/2)),x,6,2/3*(A*b^2-a*b*B-2*a*A*c+(A*b-2*a*B)*c*x)/(a*(b^2-4*a*c)*x^2*(a+b*x+c*x^2)^(3/2))-5/8*(7*A*b^2-4*a*b*B-4*a*A*c)*arctanh(1/2*(2*a+b*x)/(sqrt(a)*sqrt(a+b*x+c*x^2)))/a^(9/2)-2/3*(4*a*b*B*(b^2-6*a*c)-A*(7*b^4-42*a*b^2*c+40*a^2*c^2)-c*(7*A*b^3-4*a*b^2*B-36*a*A*b*c+32*a^2*B*c)*x)/(a^2*(b^2-4*a*c)^2*x^2*sqrt(a+b*x+c*x^2))+1/6*(4*a*b*B*(5*b^2-28*a*c)-A*(35*b^4-216*a*b^2*c+240*a^2*c^2))*sqrt(a+b*x+c*x^2)/(a^3*(b^2-4*a*c)^2*x^2)-1/12*(4*a*B*(15*b^4-100*a*b^2*c+128*a^2*c^2)-A*(105*b^5-760*a*b^3*c+1296*a^2*b*c^2))*sqrt(a+b*x+c*x^2)/(a^4*(b^2-4*a*c)^2*x)],
[(d+e*x)/(a+b*x+c*x^2)^(7/2),x,3,-2/5*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2)^(5/2))+16/15*(2*c*d-b*e)*(b+2*c*x)/((b^2-4*a*c)^2*(a+b*x+c*x^2)^(3/2))-128/15*c*(2*c*d-b*e)*(b+2*c*x)/((b^2-4*a*c)^3*sqrt(a+b*x+c*x^2))],
[(d+e*x)/(a+b*x+c*x^2)^(9/2),x,4,-2/7*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2)^(7/2))+24/35*(2*c*d-b*e)*(b+2*c*x)/((b^2-4*a*c)^2*(a+b*x+c*x^2)^(5/2))-128/35*c*(2*c*d-b*e)*(b+2*c*x)/((b^2-4*a*c)^3*(a+b*x+c*x^2)^(3/2))+1024/35*c^2*(2*c*d-b*e)*(b+2*c*x)/((b^2-4*a*c)^4*sqrt(a+b*x+c*x^2))],
[(1-x)/(x*sqrt(1+3*x+x^2)),x,2,-2*arctanh((1+x)/sqrt(1+3*x+x^2))],

# Integrands of the form (e x)^(m/2) (A+B x) (a+b x+c x^2)^p

# p>0
[x^(7/2)*(A+B*x)*(a+b*x+c*x^2),x,2,2/9*a*A*x^(9/2)+2/11*(A*b+a*B)*x^(11/2)+2/13*(b*B+A*c)*x^(13/2)+2/15*B*c*x^(15/2)],
[x^(5/2)*(A+B*x)*(a+b*x+c*x^2),x,2,2/7*a*A*x^(7/2)+2/9*(A*b+a*B)*x^(9/2)+2/11*(b*B+A*c)*x^(11/2)+2/13*B*c*x^(13/2)],
[x^(3/2)*(A+B*x)*(a+b*x+c*x^2),x,2,2/5*a*A*x^(5/2)+2/7*(A*b+a*B)*x^(7/2)+2/9*(b*B+A*c)*x^(9/2)+2/11*B*c*x^(11/2)],
[(A+B*x)*(a+b*x+c*x^2)*sqrt(x),x,2,2/3*a*A*x^(3/2)+2/5*(A*b+a*B)*x^(5/2)+2/7*(b*B+A*c)*x^(7/2)+2/9*B*c*x^(9/2)],
[(A+B*x)*(a+b*x+c*x^2)/sqrt(x),x,2,2/3*(A*b+a*B)*x^(3/2)+2/5*(b*B+A*c)*x^(5/2)+2/7*B*c*x^(7/2)+2*a*A*sqrt(x)],
[(A+B*x)*(a+b*x+c*x^2)/x^(3/2),x,2,2/3*(b*B+A*c)*x^(3/2)+2/5*B*c*x^(5/2)-2*a*A/sqrt(x)+2*(A*b+a*B)*sqrt(x)],
[(A+B*x)*(a+b*x+c*x^2)/x^(5/2),x,2,-2/3*a*A/x^(3/2)+2/3*B*c*x^(3/2)-2*(A*b+a*B)/sqrt(x)+2*(b*B+A*c)*sqrt(x)],
[(A+B*x)*(a+b*x+c*x^2)/x^(7/2),x,2,-2/5*a*A/x^(5/2)-2/3*(A*b+a*B)/x^(3/2)-2*(b*B+A*c)/sqrt(x)+2*B*c*sqrt(x)],
[(A+B*x)*(a+b*x+c*x^2)/x^(9/2),x,2,-2/7*a*A/x^(7/2)-2/5*(A*b+a*B)/x^(5/2)-2/3*(b*B+A*c)/x^(3/2)-2*B*c/sqrt(x)],
[x^(7/2)*(A+B*x)*(a+b*x+c*x^2)^2,x,2,2/9*a^2*A*x^(9/2)+2/11*a*(2*A*b+a*B)*x^(11/2)+2/13*(2*a*b*B+A*(b^2+2*a*c))*x^(13/2)+2/15*(b^2*B+2*A*b*c+2*a*B*c)*x^(15/2)+2/17*c*(2*b*B+A*c)*x^(17/2)+2/19*B*c^2*x^(19/2)],
[x^(5/2)*(A+B*x)*(a+b*x+c*x^2)^2,x,2,2/7*a^2*A*x^(7/2)+2/9*a*(2*A*b+a*B)*x^(9/2)+2/11*(2*a*b*B+A*(b^2+2*a*c))*x^(11/2)+2/13*(b^2*B+2*A*b*c+2*a*B*c)*x^(13/2)+2/15*c*(2*b*B+A*c)*x^(15/2)+2/17*B*c^2*x^(17/2)],
[x^(3/2)*(A+B*x)*(a+b*x+c*x^2)^2,x,2,2/5*a^2*A*x^(5/2)+2/7*a*(2*A*b+a*B)*x^(7/2)+2/9*(2*a*b*B+A*(b^2+2*a*c))*x^(9/2)+2/11*(b^2*B+2*A*b*c+2*a*B*c)*x^(11/2)+2/13*c*(2*b*B+A*c)*x^(13/2)+2/15*B*c^2*x^(15/2)],
[(A+B*x)*(a+b*x+c*x^2)^2*sqrt(x),x,2,2/3*a^2*A*x^(3/2)+2/5*a*(2*A*b+a*B)*x^(5/2)+2/7*(2*a*b*B+A*(b^2+2*a*c))*x^(7/2)+2/9*(b^2*B+2*A*b*c+2*a*B*c)*x^(9/2)+2/11*c*(2*b*B+A*c)*x^(11/2)+2/13*B*c^2*x^(13/2)],
[(A+B*x)*(a+b*x+c*x^2)^2/sqrt(x),x,2,2/3*a*(2*A*b+a*B)*x^(3/2)+2/5*(2*a*b*B+A*(b^2+2*a*c))*x^(5/2)+2/7*(b^2*B+2*A*b*c+2*a*B*c)*x^(7/2)+2/9*c*(2*b*B+A*c)*x^(9/2)+2/11*B*c^2*x^(11/2)+2*a^2*A*sqrt(x)],
[(A+B*x)*(a+b*x+c*x^2)^2/x^(3/2),x,2,2/3*(2*a*b*B+A*(b^2+2*a*c))*x^(3/2)+2/5*(b^2*B+2*A*b*c+2*a*B*c)*x^(5/2)+2/7*c*(2*b*B+A*c)*x^(7/2)+2/9*B*c^2*x^(9/2)-2*a^2*A/sqrt(x)+2*a*(2*A*b+a*B)*sqrt(x)],
[(A+B*x)*(a+b*x+c*x^2)^2/x^(5/2),x,2,-2/3*a^2*A/x^(3/2)+2/3*(b^2*B+2*A*b*c+2*a*B*c)*x^(3/2)+2/5*c*(2*b*B+A*c)*x^(5/2)+2/7*B*c^2*x^(7/2)-2*a*(2*A*b+a*B)/sqrt(x)+2*(2*a*b*B+A*(b^2+2*a*c))*sqrt(x)],
[(A+B*x)*(a+b*x+c*x^2)^2/x^(7/2),x,2,-2/5*a^2*A/x^(5/2)-2/3*a*(2*A*b+a*B)/x^(3/2)+2/3*c*(2*b*B+A*c)*x^(3/2)+2/5*B*c^2*x^(5/2)-2*(2*a*b*B+A*(b^2+2*a*c))/sqrt(x)+2*(b^2*B+2*A*b*c+2*a*B*c)*sqrt(x)],
[(A+B*x)*(a+b*x+c*x^2)^2/x^(9/2),x,2,-2/7*a^2*A/x^(7/2)-2/5*a*(2*A*b+a*B)/x^(5/2)-2/3*(2*a*b*B+A*(b^2+2*a*c))/x^(3/2)+2/3*B*c^2*x^(3/2)-2*(b^2*B+2*A*b*c+2*a*B*c)/sqrt(x)+2*c*(2*b*B+A*c)*sqrt(x)],
[x^(7/2)*(A+B*x)*(a+b*x+c*x^2)^3,x,2,2/9*a^3*A*x^(9/2)+2/11*a^2*(3*A*b+a*B)*x^(11/2)+6/13*a*(a*b*B+A*(b^2+a*c))*x^(13/2)+2/15*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^(15/2)+2/17*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^(17/2)+6/19*c*(b^2*B+A*b*c+a*B*c)*x^(19/2)+2/21*c^2*(3*b*B+A*c)*x^(21/2)+2/23*B*c^3*x^(23/2)],
[x^(5/2)*(A+B*x)*(a+b*x+c*x^2)^3,x,2,2/7*a^3*A*x^(7/2)+2/9*a^2*(3*A*b+a*B)*x^(9/2)+6/11*a*(a*b*B+A*(b^2+a*c))*x^(11/2)+2/13*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^(13/2)+2/15*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^(15/2)+6/17*c*(b^2*B+A*b*c+a*B*c)*x^(17/2)+2/19*c^2*(3*b*B+A*c)*x^(19/2)+2/21*B*c^3*x^(21/2)],
[x^(3/2)*(A+B*x)*(a+b*x+c*x^2)^3,x,2,2/5*a^3*A*x^(5/2)+2/7*a^2*(3*A*b+a*B)*x^(7/2)+2/3*a*(a*b*B+A*(b^2+a*c))*x^(9/2)+2/11*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^(11/2)+2/13*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^(13/2)+2/5*c*(b^2*B+A*b*c+a*B*c)*x^(15/2)+2/17*c^2*(3*b*B+A*c)*x^(17/2)+2/19*B*c^3*x^(19/2)],
[(A+B*x)*(a+b*x+c*x^2)^3*sqrt(x),x,2,2/3*a^3*A*x^(3/2)+2/5*a^2*(3*A*b+a*B)*x^(5/2)+6/7*a*(a*b*B+A*(b^2+a*c))*x^(7/2)+2/9*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^(9/2)+2/11*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^(11/2)+6/13*c*(b^2*B+A*b*c+a*B*c)*x^(13/2)+2/15*c^2*(3*b*B+A*c)*x^(15/2)+2/17*B*c^3*x^(17/2)],
[(A+B*x)*(a+b*x+c*x^2)^3/sqrt(x),x,2,2/3*a^2*(3*A*b+a*B)*x^(3/2)+6/5*a*(a*b*B+A*(b^2+a*c))*x^(5/2)+2/7*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^(7/2)+2/9*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^(9/2)+6/11*c*(b^2*B+A*b*c+a*B*c)*x^(11/2)+2/13*c^2*(3*b*B+A*c)*x^(13/2)+2/15*B*c^3*x^(15/2)+2*a^3*A*sqrt(x)],
[(A+B*x)*(a+b*x+c*x^2)^3/x^(3/2),x,2,2*a*(a*b*B+A*(b^2+a*c))*x^(3/2)+2/5*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^(5/2)+2/7*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^(7/2)+2/3*c*(b^2*B+A*b*c+a*B*c)*x^(9/2)+2/11*c^2*(3*b*B+A*c)*x^(11/2)+2/13*B*c^3*x^(13/2)-2*a^3*A/sqrt(x)+2*a^2*(3*A*b+a*B)*sqrt(x)],
[(A+B*x)*(a+b*x+c*x^2)^3/x^(5/2),x,2,-2/3*a^3*A/x^(3/2)+2/3*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^(3/2)+2/5*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^(5/2)+6/7*c*(b^2*B+A*b*c+a*B*c)*x^(7/2)+2/9*c^2*(3*b*B+A*c)*x^(9/2)+2/11*B*c^3*x^(11/2)-2*a^2*(3*A*b+a*B)/sqrt(x)+6*a*(a*b*B+A*(b^2+a*c))*sqrt(x)],
[(A+B*x)*(a+b*x+c*x^2)^3/x^(7/2),x,2,-2/5*a^3*A/x^(5/2)-2/3*a^2*(3*A*b+a*B)/x^(3/2)+2/3*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^(3/2)+6/5*c*(b^2*B+A*b*c+a*B*c)*x^(5/2)+2/7*c^2*(3*b*B+A*c)*x^(7/2)+2/9*B*c^3*x^(9/2)-6*a*(a*b*B+A*(b^2+a*c))/sqrt(x)+2*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*sqrt(x)],
[(A+B*x)*(a+b*x+c*x^2)^3/x^(9/2),x,2,-2/7*a^3*A/x^(7/2)-2/5*a^2*(3*A*b+a*B)/x^(5/2)-2*a*(a*b*B+A*(b^2+a*c))/x^(3/2)+2*c*(b^2*B+A*b*c+a*B*c)*x^(3/2)+2/5*c^2*(3*b*B+A*c)*x^(5/2)+2/7*B*c^3*x^(7/2)-2*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))/sqrt(x)+2*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*sqrt(x)],
[(A+B*x)*(a+b*x+c*x^2)^3/x^(11/2),x,2,-2/9*a^3*A/x^(9/2)-2/7*a^2*(3*A*b+a*B)/x^(7/2)-6/5*a*(a*b*B+A*(b^2+a*c))/x^(5/2)-2/3*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))/x^(3/2)+2/3*c^2*(3*b*B+A*c)*x^(3/2)+2/5*B*c^3*x^(5/2)-2*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)/sqrt(x)+6*c*(b^2*B+A*b*c+a*B*c)*sqrt(x)],

# p<0
[x^(5/2)*(A+B*x)/(a+b*x+c*x^2),x,7,-2/3*(b*B-A*c)*x^(3/2)/c^2+2/5*B*x^(5/2)/c+2*(b^2*B-A*b*c-a*B*c)*sqrt(x)/c^3-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(2)*(b^3*B-A*b^2*c-2*a*b*B*c+a*A*c^2+(-b^4*B+A*b^3*c+4*a*b^2*B*c-3*a*A*b*c^2-2*a^2*B*c^2)/sqrt(b^2-4*a*c))/(c^(7/2)*sqrt(b-sqrt(b^2-4*a*c)))-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(2)*(b^3*B-A*b^2*c-2*a*b*B*c+a*A*c^2+(b^4*B-A*b^3*c-4*a*b^2*B*c+3*a*A*b*c^2+2*a^2*B*c^2)/sqrt(b^2-4*a*c))/(c^(7/2)*sqrt(b+sqrt(b^2-4*a*c)))],
[x^(3/2)*(A+B*x)/(a+b*x+c*x^2),x,6,2/3*B*x^(3/2)/c-2*(b*B-A*c)*sqrt(x)/c^2+arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(2)*(b^2*B-A*b*c-a*B*c+(-b^3*B+A*b^2*c+3*a*b*B*c-2*a*A*c^2)/sqrt(b^2-4*a*c))/(c^(5/2)*sqrt(b-sqrt(b^2-4*a*c)))+arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(2)*(b^2*B-A*b*c-a*B*c+(b^3*B-A*b^2*c-3*a*b*B*c+2*a*A*c^2)/sqrt(b^2-4*a*c))/(c^(5/2)*sqrt(b+sqrt(b^2-4*a*c)))],
[(A+B*x)*sqrt(x)/(a+b*x+c*x^2),x,5,2*B*sqrt(x)/c-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(2)*(b*B-A*c+(-b^2*B+A*b*c+2*a*B*c)/sqrt(b^2-4*a*c))/(c^(3/2)*sqrt(b-sqrt(b^2-4*a*c)))-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(2)*(b*B-A*c+(b^2*B-A*b*c-2*a*B*c)/sqrt(b^2-4*a*c))/(c^(3/2)*sqrt(b+sqrt(b^2-4*a*c)))],
[(A+B*x)/((a+b*x+c*x^2)*sqrt(x)),x,4,arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(2)*(B+(-b*B+2*A*c)/sqrt(b^2-4*a*c))/(sqrt(c)*sqrt(b-sqrt(b^2-4*a*c)))+arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(2)*(B+(b*B-2*A*c)/sqrt(b^2-4*a*c))/(sqrt(c)*sqrt(b+sqrt(b^2-4*a*c)))],
[(A+B*x)/(x^(3/2)*(a+b*x+c*x^2)),x,5,-2*A/(a*sqrt(x))-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(2)*sqrt(c)*(A+(A*b-2*a*B)/sqrt(b^2-4*a*c))/(a*sqrt(b-sqrt(b^2-4*a*c)))-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(2)*sqrt(c)*(A+(-A*b+2*a*B)/sqrt(b^2-4*a*c))/(a*sqrt(b+sqrt(b^2-4*a*c)))],
[(A+B*x)/(x^(5/2)*(a+b*x+c*x^2)),x,6,-2/3*A/(a*x^(3/2))+2*(A*b-a*B)/(a^2*sqrt(x))-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(2)*sqrt(c)*(a*B*(b+sqrt(b^2-4*a*c))-A*(b^2-2*a*c+b*sqrt(b^2-4*a*c)))/(a^2*sqrt(b^2-4*a*c)*sqrt(b-sqrt(b^2-4*a*c)))+arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(2)*sqrt(c)*(a*B*(b-sqrt(b^2-4*a*c))-A*(b^2-2*a*c-b*sqrt(b^2-4*a*c)))/(a^2*sqrt(b^2-4*a*c)*sqrt(b+sqrt(b^2-4*a*c)))],
[(A+B*x)/(x^(7/2)*(a+b*x+c*x^2)),x,7,-2/5*A/(a*x^(5/2))+2/3*(A*b-a*B)/(a^2*x^(3/2))-2*(A*b^2-a*b*B-a*A*c)/(a^3*sqrt(x))-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(2)*sqrt(c)*(A*b^2-a*b*B-a*A*c+(-a*B*(b^2-2*a*c)+A*(b^3-3*a*b*c))/sqrt(b^2-4*a*c))/(a^3*sqrt(b-sqrt(b^2-4*a*c)))-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(2)*sqrt(c)*(A*b^2-a*b*B-a*A*c+(a*B*(b^2-2*a*c)-A*(b^3-3*a*b*c))/sqrt(b^2-4*a*c))/(a^3*sqrt(b+sqrt(b^2-4*a*c)))],
[(A+B*x)/(x^(9/2)*(a+b*x+c*x^2)),x,8,-2/7*A/(a*x^(7/2))+2/5*(A*b-a*B)/(a^2*x^(5/2))-2/3*(A*b^2-a*b*B-a*A*c)/(a^3*x^(3/2))-2*(a*B*(b^2-a*c)-A*(b^3-2*a*b*c))/(a^4*sqrt(x))-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(2)*sqrt(c)*(a*B*(b^2-a*c)-A*(b^3-2*a*b*c)+(a*b*B*(b^2-3*a*c)-A*(b^4-4*a*b^2*c+2*a^2*c^2))/sqrt(b^2-4*a*c))/(a^4*sqrt(b-sqrt(b^2-4*a*c)))-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(2)*sqrt(c)*(a*B*(b^2-a*c)-A*(b^3-2*a*b*c)+(-a*b*B*(b^2-3*a*c)+A*(b^4-4*a*b^2*c+2*a^2*c^2))/sqrt(b^2-4*a*c))/(a^4*sqrt(b+sqrt(b^2-4*a*c)))],
[x^(5/2)*(A+B*x)/(a+b*x+c*x^2)^2,x,6,-x^(3/2)*(a*(b*B-2*A*c)+(b^2*B-A*b*c-2*a*B*c)*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2))+(3*b^2*B-A*b*c-10*a*B*c)*sqrt(x)/(c^2*(b^2-4*a*c))-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*(3*b^3*B-A*b^2*c-13*a*b*B*c+6*a*A*c^2+(-3*b^4*B+A*b^3*c+19*a*b^2*B*c-8*a*A*b*c^2-20*a^2*B*c^2)/sqrt(b^2-4*a*c))/(c^(5/2)*(b^2-4*a*c)*sqrt(2)*sqrt(b-sqrt(b^2-4*a*c)))-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*(3*b^3*B-A*b^2*c-13*a*b*B*c+6*a*A*c^2+(3*b^4*B-A*b^3*c-19*a*b^2*B*c+8*a*A*b*c^2+20*a^2*B*c^2)/sqrt(b^2-4*a*c))/(c^(5/2)*(b^2-4*a*c)*sqrt(2)*sqrt(b+sqrt(b^2-4*a*c)))],
[x^(3/2)*(A+B*x)/(a+b*x+c*x^2)^2,x,5,-(a*(b*B-2*A*c)+(b^2*B-A*b*c-2*a*B*c)*x)*sqrt(x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2))+arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*(b^2*B+A*b*c-6*a*B*c+(-b^3*B-A*b^2*c+8*a*b*B*c-4*a*A*c^2)/sqrt(b^2-4*a*c))/(c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(b-sqrt(b^2-4*a*c)))+arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*(b^2*B+A*b*c-6*a*B*c+(b^3*B+A*b^2*c-8*a*b*B*c+4*a*A*c^2)/sqrt(b^2-4*a*c))/(c^(3/2)*(b^2-4*a*c)*sqrt(2)*sqrt(b+sqrt(b^2-4*a*c)))],
[(A+B*x)*sqrt(x)/(a+b*x+c*x^2)^2,x,5,-(A*b-2*a*B-(b*B-2*A*c)*x)*sqrt(x)/((b^2-4*a*c)*(a+b*x+c*x^2))+arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*(b*B-2*A*c+(-b^2*B+4*A*b*c-4*a*B*c)/sqrt(b^2-4*a*c))/((b^2-4*a*c)*sqrt(2)*sqrt(c)*sqrt(b-sqrt(b^2-4*a*c)))+arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*(b*B-2*A*c+(b^2*B-4*A*b*c+4*a*B*c)/sqrt(b^2-4*a*c))/((b^2-4*a*c)*sqrt(2)*sqrt(c)*sqrt(b+sqrt(b^2-4*a*c)))],
[(A+B*x)/((a+b*x+c*x^2)^2*sqrt(x)),x,5,(A*b^2-a*b*B-2*a*A*c+(A*b-2*a*B)*c*x)*sqrt(x)/(a*(b^2-4*a*c)*(a+b*x+c*x^2))+arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(c)*(2*a*B*(2*b-sqrt(b^2-4*a*c))+A*(b^2-12*a*c+b*sqrt(b^2-4*a*c)))/(a*(b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(b-sqrt(b^2-4*a*c)))+arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(c)*(A*b-2*a*B+(-A*b^2-4*a*b*B+12*a*A*c)/sqrt(b^2-4*a*c))/(a*(b^2-4*a*c)*sqrt(2)*sqrt(b+sqrt(b^2-4*a*c)))],
[(A+B*x)/(x^(3/2)*(a+b*x+c*x^2)^2),x,6,(-3*A*b^2+a*b*B+10*a*A*c)/(a^2*(b^2-4*a*c)*sqrt(x))+(A*b^2-a*b*B-2*a*A*c+(A*b-2*a*B)*c*x)/(a*(b^2-4*a*c)*(a+b*x+c*x^2)*sqrt(x))+arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(c)*(a*B*(b^2-12*a*c+b*sqrt(b^2-4*a*c))-A*(3*b^3-16*a*b*c+3*b^2*sqrt(b^2-4*a*c)-10*a*c*sqrt(b^2-4*a*c)))/(a^2*(b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(b-sqrt(b^2-4*a*c)))-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(c)*(a*B*(b^2-12*a*c-b*sqrt(b^2-4*a*c))-A*(3*b^3-16*a*b*c-3*b^2*sqrt(b^2-4*a*c)+10*a*c*sqrt(b^2-4*a*c)))/(a^2*(b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(b+sqrt(b^2-4*a*c)))],
[(A+B*x)/(x^(5/2)*(a+b*x+c*x^2)^2),x,7,1/3*(-5*A*b^2+3*a*b*B+14*a*A*c)/(a^2*(b^2-4*a*c)*x^(3/2))+(A*b^2-a*b*B-2*a*A*c+(A*b-2*a*B)*c*x)/(a*(b^2-4*a*c)*x^(3/2)*(a+b*x+c*x^2))+(-a*B*(3*b^2-10*a*c)+A*(5*b^3-19*a*b*c))/(a^3*(b^2-4*a*c)*sqrt(x))-arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(c)*(a*B*(3*b^3-16*a*b*c+3*b^2*sqrt(b^2-4*a*c)-10*a*c*sqrt(b^2-4*a*c))-A*(5*b^4-29*a*b^2*c+28*a^2*c^2+5*b^3*sqrt(b^2-4*a*c)-19*a*b*c*sqrt(b^2-4*a*c)))/(a^3*(b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(b-sqrt(b^2-4*a*c)))+arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(c)*(a*B*(3*b^3-16*a*b*c-3*b^2*sqrt(b^2-4*a*c)+10*a*c*sqrt(b^2-4*a*c))-A*(5*b^4-29*a*b^2*c+28*a^2*c^2-5*b^3*sqrt(b^2-4*a*c)+19*a*b*c*sqrt(b^2-4*a*c)))/(a^3*(b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(b+sqrt(b^2-4*a*c)))],
[x^(7/2)*(A+B*x)/(a+b*x+c*x^2)^3,x,6,-1/2*x^(5/2)*(a*(b*B-2*A*c)+(b^2*B-A*b*c-2*a*B*c)*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^2)-1/4*(a*(3*b^3*B+A*b^2*c-24*a*b*B*c+20*a*A*c^2)+(3*b^4*B+A*b^3*c-25*a*b^2*B*c+8*a*A*b*c^2+28*a^2*B*c^2)*x)*sqrt(x)/(c^2*(b^2-4*a*c)^2*(a+b*x+c*x^2))+1/4*arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*(3*b^4*B+A*b^3*c-27*a*b^2*B*c-16*a*A*b*c^2+84*a^2*B*c^2+(-3*b^5*B-A*b^4*c+33*a*b^3*B*c+18*a*A*b^2*c^2-132*a^2*b*B*c^2+40*a^2*A*c^3)/sqrt(b^2-4*a*c))/(c^(5/2)*(b^2-4*a*c)^2*sqrt(2)*sqrt(b-sqrt(b^2-4*a*c)))+1/4*arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*(3*b^4*B+A*b^3*c-27*a*b^2*B*c-16*a*A*b*c^2+84*a^2*B*c^2+(3*b^5*B+A*b^4*c-33*a*b^3*B*c-18*a*A*b^2*c^2+132*a^2*b*B*c^2-40*a^2*A*c^3)/sqrt(b^2-4*a*c))/(c^(5/2)*(b^2-4*a*c)^2*sqrt(2)*sqrt(b+sqrt(b^2-4*a*c)))],
[x^(5/2)*(A+B*x)/(a+b*x+c*x^2)^3,x,6,-1/2*x^(3/2)*(a*(b*B-2*A*c)+(b^2*B-A*b*c-2*a*B*c)*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^2)-1/4*(a*(b^2*B-12*A*b*c+20*a*B*c)-(b^3*B+3*A*b^2*c-16*a*b*B*c+12*a*A*c^2)*x)*sqrt(x)/(c*(b^2-4*a*c)^2*(a+b*x+c*x^2))+1/4*arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*(b^3*B+3*A*b^2*c-16*a*b*B*c+12*a*A*c^2+(-b^4*B-3*A*b^3*c+18*a*b^2*B*c-36*a*A*b*c^2+40*a^2*B*c^2)/sqrt(b^2-4*a*c))/(c^(3/2)*(b^2-4*a*c)^2*sqrt(2)*sqrt(b-sqrt(b^2-4*a*c)))+1/4*arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*(b^3*B+3*A*b^2*c-16*a*b*B*c+12*a*A*c^2+(b^4*B+3*A*b^3*c-18*a*b^2*B*c+36*a*A*b*c^2-40*a^2*B*c^2)/sqrt(b^2-4*a*c))/(c^(3/2)*(b^2-4*a*c)^2*sqrt(2)*sqrt(b+sqrt(b^2-4*a*c)))],
[x^(3/2)*(A+B*x)/(a+b*x+c*x^2)^3,x,6,-1/2*(a*(b*B-2*A*c)+(b^2*B-A*b*c-2*a*B*c)*x)*sqrt(x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^2)+1/4*(2*b^3*B-7*A*b^2*c+4*a*b*B*c+4*a*A*c^2+3*c*(b^2*B-4*A*b*c+4*a*B*c)*x)*sqrt(x)/(c*(b^2-4*a*c)^2*(a+b*x+c*x^2))+3/4*arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*(b^2*B-4*A*b*c+4*a*B*c+(-b^3*B+6*A*b^2*c-12*a*b*B*c+8*a*A*c^2)/sqrt(b^2-4*a*c))/((b^2-4*a*c)^2*sqrt(2)*sqrt(c)*sqrt(b-sqrt(b^2-4*a*c)))+3/4*arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*(b^2*B-4*A*b*c+4*a*B*c+(b^3*B-6*A*b^2*c+12*a*b*B*c-8*a*A*c^2)/sqrt(b^2-4*a*c))/((b^2-4*a*c)^2*sqrt(2)*sqrt(c)*sqrt(b+sqrt(b^2-4*a*c)))],
[(A+B*x)*sqrt(x)/(a+b*x+c*x^2)^3,x,6,-1/2*(A*b-2*a*B-(b*B-2*A*c)*x)*sqrt(x)/((b^2-4*a*c)*(a+b*x+c*x^2)^2)-1/4*(a*B*(7*b^2-4*a*c)-A*(b^3+8*a*b*c)+c*(12*a*b*B-A*(b^2+20*a*c))*x)*sqrt(x)/(a*(b^2-4*a*c)^2*(a+b*x+c*x^2))+1/4*arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(c)*(6*a*B*(3*b^2+4*a*c-2*b*sqrt(b^2-4*a*c))+A*(b^3-52*a*b*c+b^2*sqrt(b^2-4*a*c)+20*a*c*sqrt(b^2-4*a*c)))/(a*(b^2-4*a*c)^(5/2)*sqrt(2)*sqrt(b-sqrt(b^2-4*a*c)))-1/4*arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(c)*(12*a*b*B-A*(b^2+20*a*c)+(6*a*B*(3*b^2+4*a*c)+A*(b^3-52*a*b*c))/sqrt(b^2-4*a*c))/(a*(b^2-4*a*c)^2*sqrt(2)*sqrt(b+sqrt(b^2-4*a*c)))],
[(A+B*x)/((a+b*x+c*x^2)^3*sqrt(x)),x,6,1/2*(A*b^2-a*b*B-2*a*A*c+(A*b-2*a*B)*c*x)*sqrt(x)/(a*(b^2-4*a*c)*(a+b*x+c*x^2)^2)+1/4*(a*b*B*(b^2+8*a*c)+A*(3*b^4-25*a*b^2*c+28*a^2*c^2)+c*(a*B*(b^2+20*a*c)+3*A*(b^3-8*a*b*c))*x)*sqrt(x)/(a^2*(b^2-4*a*c)^2*(a+b*x+c*x^2))+1/4*arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(c)*(a*B*(b^2+20*a*c)+3*A*(b^3-8*a*b*c)+(a*b*B*(b^2-52*a*c)+3*A*(b^4-10*a*b^2*c+56*a^2*c^2))/sqrt(b^2-4*a*c))/(a^2*(b^2-4*a*c)^2*sqrt(2)*sqrt(b-sqrt(b^2-4*a*c)))+1/4*arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(c)*(a*B*(b^2+20*a*c)+3*A*(b^3-8*a*b*c)+(-a*b*B*(b^2-52*a*c)-3*A*(b^4-10*a*b^2*c+56*a^2*c^2))/sqrt(b^2-4*a*c))/(a^2*(b^2-4*a*c)^2*sqrt(2)*sqrt(b+sqrt(b^2-4*a*c)))],
[(A+B*x)/(x^(3/2)*(a+b*x+c*x^2)^3),x,7,3/4*(a*b*B*(b^2-8*a*c)-A*(5*b^4-37*a*b^2*c+60*a^2*c^2))/(a^3*(b^2-4*a*c)^2*sqrt(x))+1/2*(A*b^2-a*b*B-2*a*A*c+(A*b-2*a*B)*c*x)/(a*(b^2-4*a*c)*(a+b*x+c*x^2)^2*sqrt(x))+1/4*(-a*b*B*(b^2-16*a*c)+A*(5*b^4-35*a*b^2*c+36*a^2*c^2)-c*(a*B*(b^2-28*a*c)-A*(5*b^3-32*a*b*c))*x)/(a^2*(b^2-4*a*c)^2*(a+b*x+c*x^2)*sqrt(x))+3/4*arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b-sqrt(b^2-4*a*c)))*sqrt(c)*(a*B*(b^4-10*a*b^2*c+56*a^2*c^2+b^3*sqrt(b^2-4*a*c)-8*a*b*c*sqrt(b^2-4*a*c))-A*(5*b^5-47*a*b^3*c+124*a^2*b*c^2+5*b^4*sqrt(b^2-4*a*c)-37*a*b^2*c*sqrt(b^2-4*a*c)+60*a^2*c^2*sqrt(b^2-4*a*c)))/(a^3*(b^2-4*a*c)^(5/2)*sqrt(2)*sqrt(b-sqrt(b^2-4*a*c)))-3/4*arctan(sqrt(2)*sqrt(c)*sqrt(x)/sqrt(b+sqrt(b^2-4*a*c)))*sqrt(c)*(a*B*(b^4-10*a*b^2*c+56*a^2*c^2-b^3*sqrt(b^2-4*a*c)+8*a*b*c*sqrt(b^2-4*a*c))-A*(5*b^5-47*a*b^3*c+124*a^2*b*c^2-5*b^4*sqrt(b^2-4*a*c)+37*a*b^2*c*sqrt(b^2-4*a*c)-60*a^2*c^2*sqrt(b^2-4*a*c)))/(a^3*(b^2-4*a*c)^(5/2)*sqrt(2)*sqrt(b+sqrt(b^2-4*a*c)))],

# Integrands of the form (e x)^(m/2) (A+B x) (a+b x+c x^2)^(p/2)

# p>0
[(A+B*x)*sqrt(x)*sqrt(a+b*x+c*x^2),x,6,2/7*B*(a+b*x+c*x^2)^(3/2)*sqrt(x)/c-2/105*(4*b^2*B-7*A*b*c+5*a*B*c+3*c*(4*b*B-7*A*c)*x)*sqrt(x)*sqrt(a+b*x+c*x^2)/c^2-2/105*(5*a*b*B*c-2*(b^2-3*a*c)*(4*b*B-7*A*c))*sqrt(x)*sqrt(a+b*x+c*x^2)/(c^(5/2)*(sqrt(a)+x*sqrt(c)))+2/105*a^(1/4)*(5*a*b*B*c-2*(b^2-3*a*c)*(4*b*B-7*A*c))*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/4*(2-b/(sqrt(a)*sqrt(c)))))*(sqrt(a)+x*sqrt(c))*sqrt((a+b*x+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(11/4)*sqrt(a+b*x+c*x^2))-1/105*a^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/4*(2-b/(sqrt(a)*sqrt(c)))))*(sqrt(a)+x*sqrt(c))*(5*a*b*B*c-2*(b^2-3*a*c)*(4*b*B-7*A*c)-(4*b^2*B-7*A*b*c-10*a*B*c)*sqrt(a)*sqrt(c))*sqrt((a+b*x+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(11/4)*sqrt(a+b*x+c*x^2))],
[(A+B*x)*sqrt(a+b*x+c*x^2)/sqrt(x),x,5,2/15*(b*B+5*A*c+3*B*c*x)*sqrt(x)*sqrt(a+b*x+c*x^2)/c-2/15*(2*b^2*B-5*A*b*c-6*a*B*c)*sqrt(x)*sqrt(a+b*x+c*x^2)/(c^(3/2)*(sqrt(a)+x*sqrt(c)))+2/15*a^(1/4)*(2*b^2*B-5*A*b*c-6*a*B*c)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/4*(2-b/(sqrt(a)*sqrt(c)))))*(sqrt(a)+x*sqrt(c))*sqrt((a+b*x+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(a+b*x+c*x^2))-1/15*a^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/4*(2-b/(sqrt(a)*sqrt(c)))))*(sqrt(a)+x*sqrt(c))*(b+2*sqrt(a)*sqrt(c))*(2*b*B-5*A*c-3*B*sqrt(a)*sqrt(c))*sqrt((a+b*x+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(7/4)*sqrt(a+b*x+c*x^2))],
[(A+B*x)*sqrt(a+b*x+c*x^2)/x^(3/2),x,5,-2/3*(3*A-B*x)*sqrt(a+b*x+c*x^2)/sqrt(x)+2/3*(b*B+6*A*c)*sqrt(x)*sqrt(a+b*x+c*x^2)/(sqrt(c)*(sqrt(a)+x*sqrt(c)))-2/3*a^(1/4)*(b*B+6*A*c)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/4*(2-b/(sqrt(a)*sqrt(c)))))*(sqrt(a)+x*sqrt(c))*sqrt((a+b*x+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(a+b*x+c*x^2))+1/3*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/4*(2-b/(sqrt(a)*sqrt(c)))))*(B*sqrt(a)+3*A*sqrt(c))*(sqrt(a)+x*sqrt(c))*(b+2*sqrt(a)*sqrt(c))*sqrt((a+b*x+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(1/4)*c^(3/4)*sqrt(a+b*x+c*x^2))],
[(A+B*x)*sqrt(a+b*x+c*x^2)/x^(5/2),x,5,-2/3*(a*A+(A*b+3*a*B)*x)*sqrt(a+b*x+c*x^2)/(a*x^(3/2))+2/3*(A*b+6*a*B)*sqrt(c)*sqrt(x)*sqrt(a+b*x+c*x^2)/(a*(sqrt(a)+x*sqrt(c)))-2/3*(A*b+6*a*B)*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/4*(2-b/(sqrt(a)*sqrt(c)))))*(sqrt(a)+x*sqrt(c))*sqrt((a+b*x+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*sqrt(a+b*x+c*x^2))+1/3*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/4*(2-b/(sqrt(a)*sqrt(c)))))*((3*b*B+2*A*c)*sqrt(a)+(A*b+6*a*B)*sqrt(c))*(sqrt(a)+x*sqrt(c))*sqrt((a+b*x+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(3/4)*c^(1/4)*sqrt(a+b*x+c*x^2))],
[(A+B*x)*sqrt(a+b*x+c*x^2)/x^(7/2),x,6,-2/15*(3*a*A+(A*b+5*a*B)*x)*sqrt(a+b*x+c*x^2)/(a*x^(5/2))+2/15*(2*A*b^2-5*a*b*B-6*a*A*c)*sqrt(a+b*x+c*x^2)/(a^2*sqrt(x))+2/15*(5*a*b*B-2*A*(b^2-3*a*c))*sqrt(c)*sqrt(x)*sqrt(a+b*x+c*x^2)/(a^2*(sqrt(a)+x*sqrt(c)))-2/15*c^(1/4)*(5*a*b*B-2*A*(b^2-3*a*c))*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/4*(2-b/(sqrt(a)*sqrt(c)))))*(sqrt(a)+x*sqrt(c))*sqrt((a+b*x+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(7/4)*sqrt(a+b*x+c*x^2))-1/15*c^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/4*(2-b/(sqrt(a)*sqrt(c)))))*(sqrt(a)+x*sqrt(c))*(b+2*sqrt(a)*sqrt(c))*(2*A*b-5*a*B-3*A*sqrt(a)*sqrt(c))*sqrt((a+b*x+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(a^(7/4)*sqrt(a+b*x+c*x^2))],
[(2-5*x)*x^(7/2)*sqrt(2+5*x+3*x^2),x,9,-21620/34749*x^(3/2)*(2+5*x+3*x^2)^(3/2)+656/1287*x^(5/2)*(2+5*x+3*x^2)^(3/2)-10/39*x^(7/2)*(2+5*x+3*x^2)^(3/2)+157160/243243*(2+5*x+3*x^2)^(3/2)*sqrt(x)+1543648/6567561*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-1543648/6567561*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+349240/2189187*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-8/2189187*(397265+502911*x)*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*x^(5/2)*sqrt(2+5*x+3*x^2),x,8,532/891*x^(3/2)*(2+5*x+3*x^2)^(3/2)-10/33*x^(5/2)*(2+5*x+3*x^2)^(3/2)-4420/6237*(2+5*x+3*x^2)^(3/2)*sqrt(x)-261784/841995*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+261784/841995*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-13016/56133*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+8/280665*(57860+74313*x)*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*x^(3/2)*sqrt(2+5*x+3*x^2),x,7,-10/27*x^(3/2)*(2+5*x+3*x^2)^(3/2)+136/189*(2+5*x+3*x^2)^(3/2)*sqrt(x)+2360/5103*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-2360/5103*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+668/1701*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-4/1701*(779+1035*x)*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*sqrt(x)*sqrt(2+5*x+3*x^2),x,6,-10/21*(2+5*x+3*x^2)^(3/2)*sqrt(x)-2476/2835*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+2476/2835*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-164/189*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+4/945*(430+639*x)*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*sqrt(2+5*x+3*x^2)/sqrt(x),x,5,88/27*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-88/27*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+34/9*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+2/9*(1-9*x)*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*sqrt(2+5*x+3*x^2)/x^(3/2),x,5,22/9*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-22/9*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+10/3*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-2/3*(6+5*x)*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)*sqrt(2+5*x+3*x^2)/x^(5/2),x,5,-50/3*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+50/3*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-21*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-4/3*(1-5*x)*sqrt(2+5*x+3*x^2)/x^(3/2)],
[(2-5*x)*sqrt(2+5*x+3*x^2)/x^(7/2),x,6,-139/15*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+139/15*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-11*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-4/15*(3-10*x)*sqrt(2+5*x+3*x^2)/x^(5/2)+139/15*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)*sqrt(2+5*x+3*x^2)/x^(9/2),x,7,62/21*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+43/7*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))-62/21*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-4/7*(1-3*x)*sqrt(2+5*x+3*x^2)/x^(7/2)+43/21*sqrt(2+5*x+3*x^2)/x^(3/2)-62/21*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)*sqrt(2+5*x+3*x^2)/x^(11/2),x,8,-1331/630*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+1331/315*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))-79/21*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))-4/63*(7-20*x)*sqrt(2+5*x+3*x^2)/x^(9/2)+97/105*sqrt(2+5*x+3*x^2)/x^(5/2)-79/63*sqrt(2+5*x+3*x^2)/x^(3/2)+1331/630*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)*x^(5/2)*(2+5*x+3*x^2)^(3/2),x,9,136/351*x^(3/2)*(2+5*x+3*x^2)^(5/2)-2/9*x^(5/2)*(2+5*x+3*x^2)^(5/2)+8/243243*(27010+32921*x)*(2+5*x+3*x^2)^(3/2)*sqrt(x)-4660/11583*(2+5*x+3*x^2)^(5/2)*sqrt(x)-497824/32837805*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+497824/32837805*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-61736/2189187*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-8/10945935*(190465+205407*x)*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*x^(3/2)*(2+5*x+3*x^2)^(3/2),x,8,-10/39*x^(3/2)*(2+5*x+3*x^2)^(5/2)-4/27027*(6959+8575*x)*(2+5*x+3*x^2)^(3/2)*sqrt(x)+556/1287*(2+5*x+3*x^2)^(5/2)*sqrt(x)+55112/729729*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-55112/729729*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+25448/243243*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+8/243243*(6908+6381*x)*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*(2+5*x+3*x^2)^(3/2)*sqrt(x),x,7,4/231*(65+84*x)*(2+5*x+3*x^2)^(3/2)*sqrt(x)-10/33*(2+5*x+3*x^2)^(5/2)*sqrt(x)-424/1155*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+424/1155*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-36/77*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-4/385*(55+39*x)*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*(2+5*x+3*x^2)^(3/2)/sqrt(x),x,6,-2/9*(1+5*x)*(2+5*x+3*x^2)^(3/2)*sqrt(x)+860/243*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-860/243*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+356/81*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+4/81*(82+45*x)*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*(2+5*x+3*x^2)^(3/2)/x^(3/2),x,6,-2/7*(14+5*x)*(2+5*x+3*x^2)^(3/2)/sqrt(x)+5848/315*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-5848/315*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+482/21*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+2/105*(1045+531*x)*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*(2+5*x+3*x^2)^(3/2)/x^(5/2),x,6,-2/3*(2+3*x)*(2+5*x+3*x^2)^(3/2)/x^(3/2)-34/3*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+34/3*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-14*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+2*(2-x)*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)*(2+5*x+3*x^2)^(3/2)/x^(7/2),x,6,-4/15*(3-5*x)*(2+5*x+3*x^2)^(3/2)/x^(5/2)-1418/15*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+1418/15*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-117*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+2/5*(89-35*x)*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)*(2+5*x+3*x^2)^(3/2)/x^(9/2),x,6,-4/7*(1-2*x)*(2+5*x+3*x^2)^(3/2)/x^(7/2)-633/7*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+633/7*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-783/7*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+3/7*(22+133*x)*sqrt(2+5*x+3*x^2)/x^(3/2)],
[(2-5*x)*(2+5*x+3*x^2)^(3/2)/x^(11/2),x,7,-4/63*(7-15*x)*(2+5*x+3*x^2)^(3/2)/x^(9/2)-5438/315*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-899/21*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))+5438/315*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+1/315*(1446+4055*x)*sqrt(2+5*x+3*x^2)/x^(5/2)+5438/315*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)*(2+5*x+3*x^2)^(3/2)/x^(13/2),x,8,-4/99*(9-20*x)*(2+5*x+3*x^2)^(3/2)/x^(11/2)+3229/1386*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-3229/693*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))+1357/231*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))+1357/693*sqrt(2+5*x+3*x^2)/x^(3/2)+1/231*(634+1367*x)*sqrt(2+5*x+3*x^2)/x^(7/2)-3229/1386*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)*(2+5*x+3*x^2)^(3/2)/x^(15/2),x,9,-4/143*(11-25*x)*(2+5*x+3*x^2)^(3/2)/x^(13/2)-6907/10010*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+6907/5005*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))-3693/2002*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))+204/385*sqrt(2+5*x+3*x^2)/x^(5/2)-1231/2002*sqrt(2+5*x+3*x^2)/x^(3/2)+1/1001*(1834+3445*x)*sqrt(2+5*x+3*x^2)/x^(9/2)+6907/10010*sqrt(2+5*x+3*x^2)/sqrt(x)],

# p<0
[(A+B*x)/(sqrt(e*x)*sqrt(a+b*x+c*x^2)),x,5,2*B*x*sqrt(a+b*x+c*x^2)/(sqrt(c)*(sqrt(a)+x*sqrt(c))*sqrt(e*x))-2*a^(1/4)*B*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticE(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/4*(2-b/(sqrt(a)*sqrt(c)))))*(sqrt(a)+x*sqrt(c))*sqrt(x)*sqrt((a+b*x+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+b*x+c*x^2))+a^(1/4)*sqrt(cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))^2)/cos(2*arctan(c^(1/4)*sqrt(x)/a^(1/4)))*EllipticF(sin(2*arctan(c^(1/4)*sqrt(x)/a^(1/4))),sqrt(1/4*(2-b/(sqrt(a)*sqrt(c)))))*(sqrt(a)+x*sqrt(c))*(B+A*sqrt(c)/sqrt(a))*sqrt(x)*sqrt((a+b*x+c*x^2)/(sqrt(a)+x*sqrt(c))^2)/(c^(3/4)*sqrt(e*x)*sqrt(a+b*x+c*x^2))],
[(2-5*x)*x^(7/2)/sqrt(2+5*x+3*x^2),x,8,-68920/15309*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+68920/15309*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-11320/5103*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-820/567*x^(3/2)*sqrt(2+5*x+3*x^2)+508/567*x^(5/2)*sqrt(2+5*x+3*x^2)-10/27*x^(7/2)*sqrt(2+5*x+3*x^2)+11320/5103*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*x^(5/2)/sqrt(2+5*x+3*x^2),x,7,13688/2835*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-13688/2835*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+412/189*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+128/105*x^(3/2)*sqrt(2+5*x+3*x^2)-10/21*x^(5/2)*sqrt(2+5*x+3*x^2)-412/189*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*x^(3/2)/sqrt(2+5*x+3*x^2),x,6,-412/81*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+412/81*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-52/27*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-2/3*x^(3/2)*sqrt(2+5*x+3*x^2)+52/27*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*sqrt(x)/sqrt(2+5*x+3*x^2),x,5,136/27*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-136/27*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+10/9*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-10/9*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)/(sqrt(x)*sqrt(2+5*x+3*x^2)),x,4,-10/3*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+10/3*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+2*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)],
[(2-5*x)/(x^(3/2)*sqrt(2+5*x+3*x^2)),x,5,2*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-2*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-5*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-2*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)/(x^(5/2)*sqrt(2+5*x+3*x^2)),x,6,-25/3*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+25/3*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-2/3*sqrt(2+5*x+3*x^2)/x^(3/2)+25/3*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)/(x^(7/2)*sqrt(2+5*x+3*x^2)),x,7,66/5*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+9*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))-66/5*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-2/5*sqrt(2+5*x+3*x^2)/x^(5/2)+3*sqrt(2+5*x+3*x^2)/x^(3/2)-66/5*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)*x^(7/2)/(2+5*x+3*x^2)^(3/2),x,7,2/3*x^(5/2)*(74+95*x)/sqrt(2+5*x+3*x^2)-24*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+24*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-20*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-64/3*x^(3/2)*sqrt(2+5*x+3*x^2)+20*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*x^(5/2)/(2+5*x+3*x^2)^(3/2),x,6,2/3*x^(3/2)*(74+95*x)/sqrt(2+5*x+3*x^2)+1804/81*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-1804/81*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+580/27*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-580/27*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*x^(3/2)/(2+5*x+3*x^2)^(3/2),x,5,-200/9*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+2/3*(74+95*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+200/9*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-74/3*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)],
[(2-5*x)*sqrt(x)/(2+5*x+3*x^2)^(3/2),x,5,74/3*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-2*(30+37*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-74/3*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+30*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)],
[(2-5*x)/((2+5*x+3*x^2)^(3/2)*sqrt(x)),x,5,-30*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+2*(38+45*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+30*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-37*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)],
[(2-5*x)/(x^(3/2)*(2+5*x+3*x^2)^(3/2)),x,6,2*(38+45*x)/(sqrt(x)*sqrt(2+5*x+3*x^2))+39*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-39*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+45*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-39*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)/(x^(5/2)*(2+5*x+3*x^2)^(3/2)),x,7,2*(38+45*x)/(x^(3/2)*sqrt(2+5*x+3*x^2))-170/3*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-115*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))+170/3*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-115/3*sqrt(2+5*x+3*x^2)/x^(3/2)+170/3*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)/(x^(7/2)*(2+5*x+3*x^2)^(3/2)),x,8,2*(38+45*x)/(x^(5/2)*sqrt(2+5*x+3*x^2))+2693/30*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-2693/15*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))+157*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))-191/5*sqrt(2+5*x+3*x^2)/x^(5/2)+157/3*sqrt(2+5*x+3*x^2)/x^(3/2)-2693/30*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)*x^(13/2)/(2+5*x+3*x^2)^(5/2),x,9,2/9*x^(11/2)*(74+95*x)/(2+5*x+3*x^2)^(3/2)-4/27*x^(7/2)*(1484+1685*x)/sqrt(2+5*x+3*x^2)-1521056/76545*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+1521056/76545*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-211144/5103*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-167336/2835*x^(3/2)*sqrt(2+5*x+3*x^2)+45820/567*x^(5/2)*sqrt(2+5*x+3*x^2)+211144/5103*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*x^(11/2)/(2+5*x+3*x^2)^(5/2),x,8,2/9*x^(9/2)*(74+95*x)/(2+5*x+3*x^2)^(3/2)-8/27*x^(5/2)*(773+905*x)/sqrt(2+5*x+3*x^2)+33608/729*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-33608/729*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+16040/243*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+2348/27*x^(3/2)*sqrt(2+5*x+3*x^2)-16040/243*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*x^(9/2)/(2+5*x+3*x^2)^(5/2),x,7,2/9*x^(7/2)*(74+95*x)/(2+5*x+3*x^2)^(3/2)-4/9*x^(3/2)*(536+645*x)/sqrt(2+5*x+3*x^2)-17512/243*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+17512/243*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-7540/81*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+7540/81*sqrt(x)*sqrt(2+5*x+3*x^2)],
[(2-5*x)*x^(7/2)/(2+5*x+3*x^2)^(5/2),x,6,2/9*x^(5/2)*(74+95*x)/(2+5*x+3*x^2)^(3/2)+8020/81*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-40/27*(167+206*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-8020/81*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+3340/27*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)],
[(2-5*x)*x^(5/2)/(2+5*x+3*x^2)^(5/2),x,6,2/9*x^(3/2)*(74+95*x)/(2+5*x+3*x^2)^(3/2)-3464/27*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+4/9*(715+866*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+3464/27*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-1430/9*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)],
[(2-5*x)*x^(3/2)/(2+5*x+3*x^2)^(5/2),x,6,2/9*(74+95*x)*sqrt(x)/(2+5*x+3*x^2)^(3/2)+1450/9*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-2/9*(1831+2175*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-1450/9*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+598/3*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)],
[(2-5*x)*sqrt(x)/(2+5*x+3*x^2)^(5/2),x,6,-2/3*(30+37*x)*sqrt(x)/(2+5*x+3*x^2)^(3/2)-198*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+2*(250+297*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+198*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)-245*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)],
[(2-5*x)/((2+5*x+3*x^2)^(5/2)*sqrt(x)),x,6,2/3*(38+45*x)*sqrt(x)/(2+5*x+3*x^2)^(3/2)+715/3*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-5/3*(361+429*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-715/3*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+295*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)],
[(2-5*x)/(x^(3/2)*(2+5*x+3*x^2)^(5/2)),x,7,2/3*(38+45*x)/((2+5*x+3*x^2)^(3/2)*sqrt(x))+1/3*(-1717-2085*x)/(sqrt(x)*sqrt(2+5*x+3*x^2))-838/3*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-695*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))+838/3*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt(2)*sqrt((2+3*x)/(1+x))/sqrt(2+5*x+3*x^2)+838/3*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)/(x^(5/2)*(2+5*x+3*x^2)^(5/2)),x,8,2/3*(38+45*x)/(x^(3/2)*(2+5*x+3*x^2)^(3/2))-3*(181+225*x)/(x^(3/2)*sqrt(2+5*x+3*x^2))+625/2*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)-625*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))+795*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))+265*sqrt(2+5*x+3*x^2)/x^(3/2)-625/2*sqrt(2+5*x+3*x^2)/sqrt(x)],
[(2-5*x)/(x^(7/2)*(2+5*x+3*x^2)^(5/2)),x,9,2/3*(38+45*x)/(x^(5/2)*(2+5*x+3*x^2)^(3/2))+1/3*(-1541-1965*x)/(x^(5/2)*sqrt(2+5*x+3*x^2))-9521/30*(2+3*x)*sqrt(x)/sqrt(2+5*x+3*x^2)+9521/15*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticE(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))-1733/2*(1+x)*sqrt(cos(arctan(sqrt(x)))^2)/cos(arctan(sqrt(x)))*EllipticF(sin(arctan(sqrt(x))),sqrt(-1/2))*sqrt((2+3*x)/(1+x))/(sqrt(2)*sqrt(2+5*x+3*x^2))+1252/5*sqrt(2+5*x+3*x^2)/x^(5/2)-1733/6*sqrt(2+5*x+3*x^2)/x^(3/2)+9521/30*sqrt(2+5*x+3*x^2)/sqrt(x)],

# Integrands of the form (e x)^m (A+B x) (a+b x+c x^2)^p when m symbolic
[(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^3,x,2,a^3*A*(e*x)^(1+m)/(e*(1+m))+a^2*(3*A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+3*a*(a*b*B+A*(b^2+a*c))*(e*x)^(3+m)/(e^3*(3+m))+(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*(e*x)^(4+m)/(e^4*(4+m))+(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*(e*x)^(5+m)/(e^5*(5+m))+3*c*(b^2*B+A*b*c+a*B*c)*(e*x)^(6+m)/(e^6*(6+m))+c^2*(3*b*B+A*c)*(e*x)^(7+m)/(e^7*(7+m))+B*c^3*(e*x)^(8+m)/(e^8*(8+m))],
[(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^2,x,2,a^2*A*(e*x)^(1+m)/(e*(1+m))+a*(2*A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+(2*a*b*B+A*(b^2+2*a*c))*(e*x)^(3+m)/(e^3*(3+m))+(b^2*B+2*A*b*c+2*a*B*c)*(e*x)^(4+m)/(e^4*(4+m))+c*(2*b*B+A*c)*(e*x)^(5+m)/(e^5*(5+m))+B*c^2*(e*x)^(6+m)/(e^6*(6+m))],
[(e*x)^m*(A+B*x)*(a+b*x+c*x^2),x,2,a*A*(e*x)^(1+m)/(e*(1+m))+(A*b+a*B)*(e*x)^(2+m)/(e^2*(2+m))+(b*B+A*c)*(e*x)^(3+m)/(e^3*(3+m))+B*c*(e*x)^(4+m)/(e^4*(4+m))],
[(e*x)^m*(A+B*x)/(a+b*x+c*x^2),x,4,(e*x)^(1+m)*hypergeom([1,1+m],[2+m],-2*c*x/(b-sqrt(b^2-4*a*c)))*(B+(-b*B+2*A*c)/sqrt(b^2-4*a*c))/(e*(1+m)*(b-sqrt(b^2-4*a*c)))+(e*x)^(1+m)*hypergeom([1,1+m],[2+m],-2*c*x/(b+sqrt(b^2-4*a*c)))*(B+(b*B-2*A*c)/sqrt(b^2-4*a*c))/(e*(1+m)*(b+sqrt(b^2-4*a*c)))],
[(e*x)^m*(A+B*x)/(a+b*x+c*x^2)^2,x,5,(e*x)^(1+m)*(A*b^2-a*b*B-2*a*A*c+(A*b-2*a*B)*c*x)/(a*(b^2-4*a*c)*e*(a+b*x+c*x^2))-c*(e*x)^(1+m)*hypergeom([1,1+m],[2+m],-2*c*x/(b+sqrt(b^2-4*a*c)))*((A*b-2*a*B)*m+(2*a*(b*B-2*A*c*(1-m))-A*b^2*m)/sqrt(b^2-4*a*c))/(a*(b^2-4*a*c)*e*(1+m)*(b+sqrt(b^2-4*a*c)))-c*(e*x)^(1+m)*hypergeom([1,1+m],[2+m],-2*c*x/(b-sqrt(b^2-4*a*c)))*(A*b*m*(b+sqrt(b^2-4*a*c))-2*a*(b*B-2*A*c*(1-m)+B*m*sqrt(b^2-4*a*c)))/(a*(b^2-4*a*c)^(3/2)*e*(1+m)*(b-sqrt(b^2-4*a*c)))],
[(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^(5/2),x,5,A*(e*x)^(1+m)*(a+b*x+c*x^2)^(5/2)*AppellF1(1+m,-5/2,-5/2,2+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))/(e*(1+m)*(1+2*c*x/(b-sqrt(b^2-4*a*c)))^(5/2)*(1+2*c*x/(b+sqrt(b^2-4*a*c)))^(5/2))+B*(e*x)^(2+m)*(a+b*x+c*x^2)^(5/2)*AppellF1(2+m,-5/2,-5/2,3+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))/(e^2*(2+m)*(1+2*c*x/(b-sqrt(b^2-4*a*c)))^(5/2)*(1+2*c*x/(b+sqrt(b^2-4*a*c)))^(5/2))],
[(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^(3/2),x,5,A*(e*x)^(1+m)*(a+b*x+c*x^2)^(3/2)*AppellF1(1+m,-3/2,-3/2,2+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))/(e*(1+m)*(1+2*c*x/(b-sqrt(b^2-4*a*c)))^(3/2)*(1+2*c*x/(b+sqrt(b^2-4*a*c)))^(3/2))+B*(e*x)^(2+m)*(a+b*x+c*x^2)^(3/2)*AppellF1(2+m,-3/2,-3/2,3+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))/(e^2*(2+m)*(1+2*c*x/(b-sqrt(b^2-4*a*c)))^(3/2)*(1+2*c*x/(b+sqrt(b^2-4*a*c)))^(3/2))],
[(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^(1/2),x,5,A*(e*x)^(1+m)*AppellF1(1+m,-1/2,-1/2,2+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))*sqrt(a+b*x+c*x^2)/(e*(1+m)*sqrt(1+2*c*x/(b-sqrt(b^2-4*a*c)))*sqrt(1+2*c*x/(b+sqrt(b^2-4*a*c))))+B*(e*x)^(2+m)*AppellF1(2+m,-1/2,-1/2,3+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))*sqrt(a+b*x+c*x^2)/(e^2*(2+m)*sqrt(1+2*c*x/(b-sqrt(b^2-4*a*c)))*sqrt(1+2*c*x/(b+sqrt(b^2-4*a*c))))],
[(e*x)^m*(A+B*x)/(a+b*x+c*x^2)^(1/2),x,5,A*(e*x)^(1+m)*AppellF1(1+m,1/2,1/2,2+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))*sqrt(1+2*c*x/(b-sqrt(b^2-4*a*c)))*sqrt(1+2*c*x/(b+sqrt(b^2-4*a*c)))/(e*(1+m)*sqrt(a+b*x+c*x^2))+B*(e*x)^(2+m)*AppellF1(2+m,1/2,1/2,3+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))*sqrt(1+2*c*x/(b-sqrt(b^2-4*a*c)))*sqrt(1+2*c*x/(b+sqrt(b^2-4*a*c)))/(e^2*(2+m)*sqrt(a+b*x+c*x^2))],
[(e*x)^m*(A+B*x)/(a+b*x+c*x^2)^(3/2),x,5,A*(e*x)^(1+m)*AppellF1(1+m,3/2,3/2,2+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))*(1+2*c*x/(b-sqrt(b^2-4*a*c)))^(3/2)*(1+2*c*x/(b+sqrt(b^2-4*a*c)))^(3/2)/(e*(1+m)*(a+b*x+c*x^2)^(3/2))+B*(e*x)^(2+m)*AppellF1(2+m,3/2,3/2,3+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))*(1+2*c*x/(b-sqrt(b^2-4*a*c)))^(3/2)*(1+2*c*x/(b+sqrt(b^2-4*a*c)))^(3/2)/(e^2*(2+m)*(a+b*x+c*x^2)^(3/2))],
[(e*x)^m*(A+B*x)/(a+b*x+c*x^2)^(5/2),x,5,A*(e*x)^(1+m)*AppellF1(1+m,5/2,5/2,2+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))*(1+2*c*x/(b-sqrt(b^2-4*a*c)))^(5/2)*(1+2*c*x/(b+sqrt(b^2-4*a*c)))^(5/2)/(e*(1+m)*(a+b*x+c*x^2)^(5/2))+B*(e*x)^(2+m)*AppellF1(2+m,5/2,5/2,3+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))*(1+2*c*x/(b-sqrt(b^2-4*a*c)))^(5/2)*(1+2*c*x/(b+sqrt(b^2-4*a*c)))^(5/2)/(e^2*(2+m)*(a+b*x+c*x^2)^(5/2))],

# Integrands of the form (e x)^m (A+B x) (a+b x+c x^2)^p when p symbolic
[(e*x)^m*(A+B*x)*(a+b*x+c*x^2)^p,x,5,A*(e*x)^(1+m)*(a+b*x+c*x^2)^p*AppellF1(1+m,-p,-p,2+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))/(e*(1+m)*(1+2*c*x/(b-sqrt(b^2-4*a*c)))^p*(1+2*c*x/(b+sqrt(b^2-4*a*c)))^p)+B*(e*x)^(2+m)*(a+b*x+c*x^2)^p*AppellF1(2+m,-p,-p,3+m,-2*c*x/(b-sqrt(b^2-4*a*c)),-2*c*x/(b+sqrt(b^2-4*a*c)))/(e^2*(2+m)*(1+2*c*x/(b-sqrt(b^2-4*a*c)))^p*(1+2*c*x/(b+sqrt(b^2-4*a*c)))^p)],
[x^3*(A+B*x)*(a+b*x+c*x^2)^p,x,4,-1/2*(b*B*(4+p)-A*c*(5+2*p))*x^2*(a+b*x+c*x^2)^(1+p)/(c^2*(2+p)*(5+2*p))+B*x^3*(a+b*x+c*x^2)^(1+p)/(c*(5+2*p))+1/4*(2*a*c*(3+2*p)*(b*B*(4+p)-A*c*(5+2*p))+b*(2+p)*(6*a*B*c*(2+p)-b^2*B*(12+7*p+p^2)+A*b*c*(15+11*p+2*p^2))-2*c*(1+p)*(6*a*B*c*(2+p)-b^2*B*(12+7*p+p^2)+A*b*c*(15+11*p+2*p^2))*x)*(a+b*x+c*x^2)^(1+p)/(c^4*(30+77*p+71*p^2+28*p^3+4*p^4))-2^(-1+p)*(12*a^2*B*c^2-12*a*b^2*B*c*(3+p)+6*a*A*b*c^2*(5+2*p)+b^4*B*(12+7*p+p^2)-A*b^3*c*(15+11*p+2*p^2))*(a+b*x+c*x^2)^(1+p)*hypergeom([-p,1+p],[2+p],1/2*(b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))*((-b-2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))^(-1-p)/(c^4*(1+p)*(3+2*p)*(5+2*p)*sqrt(b^2-4*a*c))],
[x^2*(A+B*x)*(a+b*x+c*x^2)^p,x,3,1/2*B*x^2*(a+b*x+c*x^2)^(1+p)/(c*(2+p))-1/4*(2*a*B*c*(3+2*p)+b*(2+p)*(2*A*c*(2+p)-b*B*(3+p))-2*c*(1+p)*(2*A*c*(2+p)-b*B*(3+p))*x)*(a+b*x+c*x^2)^(1+p)/(c^3*(2+p)*(3+5*p+2*p^2))-2^(-1+p)*(6*a*b*B*c-4*a*A*c^2+2*A*b^2*c*(2+p)-b^3*B*(3+p))*(a+b*x+c*x^2)^(1+p)*hypergeom([-p,1+p],[2+p],1/2*(b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))*((-b-2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))^(-1-p)/(c^3*(1+p)*(3+2*p)*sqrt(b^2-4*a*c))],
[x*(A+B*x)*(a+b*x+c*x^2)^p,x,2,-1/2*(b*B*(2+p)-A*c*(3+2*p)-2*B*c*(1+p)*x)*(a+b*x+c*x^2)^(1+p)/(c^2*(3+5*p+2*p^2))+2^p*(2*a*B*c-b^2*B*(2+p)+A*b*c*(3+2*p))*(a+b*x+c*x^2)^(1+p)*hypergeom([-p,1+p],[2+p],1/2*(b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))*((-b-2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))^(-1-p)/(c^2*(1+p)*(3+2*p)*sqrt(b^2-4*a*c))],
[(A+B*x)*(a+b*x+c*x^2)^p,x,2,1/2*B*(a+b*x+c*x^2)^(1+p)/(c*(1+p))+2^p*(b*B-2*A*c)*(a+b*x+c*x^2)^(1+p)*hypergeom([-p,1+p],[2+p],1/2*(b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))*((-b-2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))^(-1-p)/(c*(1+p)*sqrt(b^2-4*a*c))],
[(A+B*x)*(a+b*x+c*x^2)^p/x,x,4,-2^(1+p)*B*(a+b*x+c*x^2)^(1+p)*hypergeom([-p,1+p],[2+p],1/2*(b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))*((-b-2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))^(-1-p)/((1+p)*sqrt(b^2-4*a*c))+2^(-1+2*p)*A*(a+b*x+c*x^2)^p*AppellF1(-2*p,-p,-p,1-2*p,1/2*(-b+sqrt(b^2-4*a*c))/(c*x),1/2*(-b-sqrt(b^2-4*a*c))/(c*x))/(p*((b+2*c*x-sqrt(b^2-4*a*c))/(c*x))^p*((b+2*c*x+sqrt(b^2-4*a*c))/(c*x))^p)],
[(A+B*x)*(a+b*x+c*x^2)^p/x^2,x,5,-A*(a+b*x+c*x^2)^(1+p)/(a*x)-2^(1+p)*A*c*(1+2*p)*(a+b*x+c*x^2)^(1+p)*hypergeom([-p,1+p],[2+p],1/2*(b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))*((-b-2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))^(-1-p)/(a*(1+p)*sqrt(b^2-4*a*c))+2^(-1+2*p)*(a*B+A*b*p)*(a+b*x+c*x^2)^p*AppellF1(-2*p,-p,-p,1-2*p,1/2*(-b+sqrt(b^2-4*a*c))/(c*x),1/2*(-b-sqrt(b^2-4*a*c))/(c*x))/(a*p*((b+2*c*x-sqrt(b^2-4*a*c))/(c*x))^p*((b+2*c*x+sqrt(b^2-4*a*c))/(c*x))^p)],
[(A+B*x)*(a+b*x+c*x^2)^p/x^3,x,6,-1/2*A*(a+b*x+c*x^2)^(1+p)/(a*x^2)-1/2*(2*a*B-A*b*(1-p))*(a+b*x+c*x^2)^(1+p)/(a^2*x)-2^p*c*(2*a*B-A*b*(1-p))*(1+2*p)*(a+b*x+c*x^2)^(1+p)*hypergeom([-p,1+p],[2+p],1/2*(b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))*((-b-2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))^(-1-p)/(a^2*(1+p)*sqrt(b^2-4*a*c))+4^(-1+p)*(2*a*b*B+A*(2*a*c-b^2*(1-p)))*(a+b*x+c*x^2)^p*AppellF1(-2*p,-p,-p,1-2*p,1/2*(-b+sqrt(b^2-4*a*c))/(c*x),1/2*(-b-sqrt(b^2-4*a*c))/(c*x))/(a^2*((b+2*c*x-sqrt(b^2-4*a*c))/(c*x))^p*((b+2*c*x+sqrt(b^2-4*a*c))/(c*x))^p)],

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

# Integrands of the form (d+e x)^m (f+g x) (a+b x+c x^2)^p when a=0

# Integrands of the form (d+e x)^m (A+B x) (b x+c x^2)^p

# p>0
[(A+B*x)*(d+e*x)^m*(b*x+c*x^2),x,2,-d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(1+m)/(e^4*(1+m))+(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^4*(2+m))-(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(3+m)/(e^4*(3+m))+B*c*(d+e*x)^(4+m)/(e^4*(4+m))],
[(A+B*x)*(d+e*x)^4*(b*x+c*x^2),x,2,-1/5*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^5/e^4+1/6*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*(d+e*x)^6/e^4-1/7*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^7/e^4+1/8*B*c*(d+e*x)^8/e^4],
[(A+B*x)*(d+e*x)^3*(b*x+c*x^2),x,2,-1/4*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^4/e^4+1/5*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*(d+e*x)^5/e^4-1/6*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^6/e^4+1/7*B*c*(d+e*x)^7/e^4],
[(A+B*x)*(d+e*x)^2*(b*x+c*x^2),x,2,1/2*A*b*d^2*x^2+1/3*d*(b*B*d+A*c*d+2*A*b*e)*x^3+1/4*(A*e*(2*c*d+b*e)+B*d*(c*d+2*b*e))*x^4+1/5*e*(2*B*c*d+b*B*e+A*c*e)*x^5+1/6*B*c*e^2*x^6],
[(A+B*x)*(d+e*x)*(b*x+c*x^2),x,2,1/2*A*b*d*x^2+1/3*(b*B*d+A*c*d+A*b*e)*x^3+1/4*(B*c*d+b*B*e+A*c*e)*x^4+1/5*B*c*e*x^5],
[(A+B*x)*(b*x+c*x^2),x,2,1/2*A*b*x^2+1/3*(b*B+A*c)*x^3+1/4*B*c*x^4],
[(A+B*x)*(b*x+c*x^2)/(d+e*x),x,2,(B*d-A*e)*(c*d-b*e)*x/e^3-1/2*(B*c*d-b*B*e-A*c*e)*x^2/e^2+1/3*B*c*x^3/e-d*(B*d-A*e)*(c*d-b*e)*log(d+e*x)/e^4],
[(A+B*x)*(b*x+c*x^2)/(d+e*x)^2,x,2,-(2*B*c*d-b*B*e-A*c*e)*x/e^3+1/2*B*c*x^2/e^2+d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x))+(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*log(d+e*x)/e^4],
[(A+B*x)*(b*x+c*x^2)/(d+e*x)^3,x,2,B*c*x/e^3+1/2*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^2)+(-B*d*(3*c*d-2*b*e)+A*e*(2*c*d-b*e))/(e^4*(d+e*x))-(3*B*c*d-b*B*e-A*c*e)*log(d+e*x)/e^4],
[(A+B*x)*(b*x+c*x^2)/(d+e*x)^4,x,2,1/3*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^3)+1/2*(-B*d*(3*c*d-2*b*e)+A*e*(2*c*d-b*e))/(e^4*(d+e*x)^2)+(3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x))+B*c*log(d+e*x)/e^4],
[(A+B*x)*(b*x+c*x^2)/(d+e*x)^5,x,2,1/4*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^4)+1/3*(-B*d*(3*c*d-2*b*e)+A*e*(2*c*d-b*e))/(e^4*(d+e*x)^3)+1/2*(3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x)^2)-B*c/(e^4*(d+e*x))],
[(A+B*x)*(b*x+c*x^2)/(d+e*x)^6,x,2,1/5*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^5)+1/4*(-B*d*(3*c*d-2*b*e)+A*e*(2*c*d-b*e))/(e^4*(d+e*x)^4)+1/3*(3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x)^3)-1/2*B*c/(e^4*(d+e*x)^2)],
[(A+B*x)*(d+e*x)^m*(b*x+c*x^2)^2,x,2,-d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(1+m)/(e^6*(1+m))+d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^6*(2+m))+(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*(d+e*x)^(3+m)/(e^6*(3+m))-(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(4+m)/(e^6*(4+m))-c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*(d+e*x)^(6+m)/(e^6*(6+m))],
[(A+B*x)*(d+e*x)^3*(b*x+c*x^2)^2,x,2,1/3*A*b^2*d^3*x^3+1/4*b*d^2*(b*B*d+2*A*c*d+3*A*b*e)*x^4+1/5*d*(A*c^2*d^2+3*b^2*e*(B*d+A*e)+2*b*c*d*(B*d+3*A*e))*x^5+1/6*(A*e*(3*c^2*d^2+6*b*c*d*e+b^2*e^2)+B*d*(c^2*d^2+6*b*c*d*e+3*b^2*e^2))*x^6+1/7*e*(A*c*e*(3*c*d+2*b*e)+B*(3*c^2*d^2+6*b*c*d*e+b^2*e^2))*x^7+1/8*c*e^2*(3*B*c*d+2*b*B*e+A*c*e)*x^8+1/9*B*c^2*e^3*x^9],
[(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^2,x,2,1/3*A*b^2*d^2*x^3+1/4*b*d*(b*B*d+2*A*c*d+2*A*b*e)*x^4+1/5*(A*c^2*d^2+b^2*e*(2*B*d+A*e)+2*b*c*d*(B*d+2*A*e))*x^5+1/6*(2*A*c*e*(c*d+b*e)+B*(c^2*d^2+4*b*c*d*e+b^2*e^2))*x^6+1/7*c*e*(A*c*e+2*B*(c*d+b*e))*x^7+1/8*B*c^2*e^2*x^8],
[(A+B*x)*(d+e*x)*(b*x+c*x^2)^2,x,2,1/3*A*b^2*d*x^3+1/4*b*(b*B*d+2*A*c*d+A*b*e)*x^4+1/5*(A*c^2*d+b^2*B*e+2*b*c*(B*d+A*e))*x^5+1/6*c*(B*c*d+2*b*B*e+A*c*e)*x^6+1/7*B*c^2*e*x^7],
[(A+B*x)*(b*x+c*x^2)^2,x,2,1/3*A*b^2*x^3+1/4*b*(b*B+2*A*c)*x^4+1/5*c*(2*b*B+A*c)*x^5+1/6*B*c^2*x^6],
[(A+B*x)*(b*x+c*x^2)^2/(d+e*x),x,2,d*(B*d-A*e)*(c*d-b*e)^2*x/e^5-1/2*(B*d-A*e)*(c*d-b*e)^2*x^2/e^4-1/3*(A*c*e*(c*d-2*b*e)-B*(c*d-b*e)^2)*x^3/e^3-1/4*c*(B*c*d-2*b*B*e-A*c*e)*x^4/e^2+1/5*B*c^2*x^5/e-d^2*(B*d-A*e)*(c*d-b*e)^2*log(d+e*x)/e^6],
[(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^2,x,2,-(c*d-b*e)*(2*B*d*(2*c*d-b*e)-A*e*(3*c*d-b*e))*x/e^5+1/2*(c*d-b*e)*(3*B*c*d-b*B*e-2*A*c*e)*x^2/e^4-1/3*c*(2*B*c*d-2*b*B*e-A*c*e)*x^3/e^3+1/4*B*c^2*x^4/e^2+d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x))+d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*log(d+e*x)/e^6],
[(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^3,x,2,-(A*c*e*(3*c*d-2*b*e)-B*(6*c^2*d^2-6*b*c*d*e+b^2*e^2))*x/e^5-1/2*c*(3*B*c*d-2*b*B*e-A*c*e)*x^2/e^4+1/3*B*c^2*x^3/e^3+1/2*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^2)-d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*(d+e*x))+(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*log(d+e*x)/e^6],
[(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^4,x,2,-c*(4*B*c*d-2*b*B*e-A*c*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^3)-1/2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^2)+(-A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)+B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))/(e^6*(d+e*x))-(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*log(d+e*x)/e^6],
[(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^5,x,2,B*c^2*x/e^5+1/4*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^4)-1/3*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^3)+1/2*(-A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)+B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))/(e^6*(d+e*x)^2)+(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))/(e^6*(d+e*x))-c*(5*B*c*d-2*b*B*e-A*c*e)*log(d+e*x)/e^6],
[(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^6,x,2,1/5*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^5)-1/4*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^4)+1/3*(-A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)+B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))/(e^6*(d+e*x)^3)+1/2*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))/(e^6*(d+e*x)^2)+c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x))+B*c^2*log(d+e*x)/e^6],
[(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^7,x,2,1/6*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^6)-1/5*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^5)+1/4*(-A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)+B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))/(e^6*(d+e*x)^4)+1/3*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))/(e^6*(d+e*x)^3)+1/2*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^2)-B*c^2/(e^6*(d+e*x))],
[(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^8,x,2,1/7*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^7)-1/6*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^6)+1/5*(-A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)+B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))/(e^6*(d+e*x)^5)+1/4*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))/(e^6*(d+e*x)^4)+1/3*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^3)-1/2*B*c^2/(e^6*(d+e*x)^2)],
[(A+B*x)*(d+e*x)^m*(b*x+c*x^2)^3,x,2,-d^3*(B*d-A*e)*(c*d-b*e)^3*(d+e*x)^(1+m)/(e^8*(1+m))+d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))*(d+e*x)^(2+m)/(e^8*(2+m))+3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-8*b*c*d*e+2*b^2*e^2))*(d+e*x)^(3+m)/(e^8*(3+m))+(B*d*(35*c^3*d^3-60*b*c^2*d^2*e+30*b^2*c*d*e^2-4*b^3*e^3)-A*e*(20*c^3*d^3-30*b*c^2*d^2*e+12*b^2*c*d*e^2-b^3*e^3))*(d+e*x)^(4+m)/(e^8*(4+m))+(3*A*c*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*(35*c^3*d^3-45*b*c^2*d^2*e+15*b^2*c*d*e^2-b^3*e^3))*(d+e*x)^(5+m)/(e^8*(5+m))-3*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2-6*b*c*d*e+b^2*e^2))*(d+e*x)^(6+m)/(e^8*(6+m))-c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*(d+e*x)^(8+m)/(e^8*(8+m))],
[(A+B*x)*(d+e*x)^4*(b*x+c*x^2)^3,x,2,1/4*A*b^3*d^4*x^4+1/5*b^2*d^3*(b*B*d+3*A*c*d+4*A*b*e)*x^5+1/6*b*d^2*(3*A*c^2*d^2+2*b^2*e*(2*B*d+3*A*e)+3*b*c*d*(B*d+4*A*e))*x^6+1/7*d*(A*c^3*d^3+2*b^3*e^2*(3*B*d+2*A*e)+6*b^2*c*d*e*(2*B*d+3*A*e)+3*b*c^2*d^2*(B*d+4*A*e))*x^7+1/8*(A*e*(4*c^3*d^3+18*b*c^2*d^2*e+12*b^2*c*d*e^2+b^3*e^3)+B*d*(c^3*d^3+12*b*c^2*d^2*e+18*b^2*c*d*e^2+4*b^3*e^3))*x^8+1/9*e*(3*A*c*e*(2*c^2*d^2+4*b*c*d*e+b^2*e^2)+B*(4*c^3*d^3+18*b*c^2*d^2*e+12*b^2*c*d*e^2+b^3*e^3))*x^9+1/10*c*e^2*(A*c*e*(4*c*d+3*b*e)+3*B*(2*c^2*d^2+4*b*c*d*e+b^2*e^2))*x^10+1/11*c^2*e^3*(4*B*c*d+3*b*B*e+A*c*e)*x^11+1/12*B*c^3*e^4*x^12],
[(A+B*x)*(d+e*x)^3*(b*x+c*x^2)^3,x,2,1/4*A*b^3*d^3*x^4+1/5*b^2*d^2*(b*B*d+3*A*c*d+3*A*b*e)*x^5+1/2*b*d*(A*c^2*d^2+b^2*e*(B*d+A*e)+b*c*d*(B*d+3*A*e))*x^6+1/7*(A*c^3*d^3+9*b^2*c*d*e*(B*d+A*e)+b^3*e^2*(3*B*d+A*e)+3*b*c^2*d^2*(B*d+3*A*e))*x^7+1/8*(3*A*c*e*(c^2*d^2+3*b*c*d*e+b^2*e^2)+B*(c^3*d^3+9*b*c^2*d^2*e+9*b^2*c*d*e^2+b^3*e^3))*x^8+1/3*c*e*(A*c*e*(c*d+b*e)+B*(c^2*d^2+3*b*c*d*e+b^2*e^2))*x^9+1/10*c^2*e^2*(A*c*e+3*B*(c*d+b*e))*x^10+1/11*B*c^3*e^3*x^11],
[(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^3,x,2,1/4*A*b^3*d^2*x^4+1/5*b^2*d*(b*B*d+3*A*c*d+2*A*b*e)*x^5+1/6*b*(3*A*c^2*d^2+b^2*e*(2*B*d+A*e)+3*b*c*d*(B*d+2*A*e))*x^6+1/7*(A*c^3*d^2+b^3*B*e^2+3*b^2*c*e*(2*B*d+A*e)+3*b*c^2*d*(B*d+2*A*e))*x^7+1/8*c*(A*c*e*(2*c*d+3*b*e)+B*(c^2*d^2+6*b*c*d*e+3*b^2*e^2))*x^8+1/9*c^2*e*(2*B*c*d+3*b*B*e+A*c*e)*x^9+1/10*B*c^3*e^2*x^10],
[(A+B*x)*(d+e*x)*(b*x+c*x^2)^3,x,2,1/4*A*b^3*d*x^4+1/5*b^2*(b*B*d+3*A*c*d+A*b*e)*x^5+1/6*b*(3*A*c^2*d+b^2*B*e+3*b*c*(B*d+A*e))*x^6+1/7*c*(A*c^2*d+3*b^2*B*e+3*b*c*(B*d+A*e))*x^7+1/8*c^2*(B*c*d+3*b*B*e+A*c*e)*x^8+1/9*B*c^3*e*x^9],
[(A+B*x)*(b*x+c*x^2)^3,x,2,1/4*A*b^3*x^4+1/5*b^2*(b*B+3*A*c)*x^5+1/2*b*c*(b*B+A*c)*x^6+1/7*c^2*(3*b*B+A*c)*x^7+1/8*B*c^3*x^8],
[(A+B*x)*(b*x+c*x^2)^3/(d+e*x),x,2,d^2*(B*d-A*e)*(c*d-b*e)^3*x/e^7-1/2*d*(B*d-A*e)*(c*d-b*e)^3*x^2/e^6+1/3*(B*d-A*e)*(c*d-b*e)^3*x^3/e^5-1/4*(B*(c*d-b*e)^3-A*c*e*(c^2*d^2-3*b*c*d*e+3*b^2*e^2))*x^4/e^4-1/5*c*(A*c*e*(c*d-3*b*e)-B*(c^2*d^2-3*b*c*d*e+3*b^2*e^2))*x^5/e^3-1/6*c^2*(B*c*d-3*b*B*e-A*c*e)*x^6/e^2+1/7*B*c^3*x^7/e-d^3*(B*d-A*e)*(c*d-b*e)^3*log(d+e*x)/e^8],
[(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^2,x,2,d*(c*d-b*e)^2*(A*e*(5*c*d-2*b*e)-3*B*d*(2*c*d-b*e))*x/e^7+1/2*(c*d-b*e)^2*(B*d*(5*c*d-2*b*e)-A*e*(4*c*d-b*e))*x^2/e^6-1/3*(c*d-b*e)^2*(4*B*c*d-b*B*e-3*A*c*e)*x^3/e^5-1/4*c*(A*c*e*(2*c*d-3*b*e)-3*B*(c*d-b*e)^2)*x^4/e^4-1/5*c^2*(2*B*c*d-3*b*B*e-A*c*e)*x^5/e^3+1/6*B*c^3*x^6/e^2+d^3*(B*d-A*e)*(c*d-b*e)^3/(e^8*(d+e*x))+d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))*log(d+e*x)/e^8],
[(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^3,x,2,-(c*d-b*e)*(A*e*(10*c^2*d^2-8*b*c*d*e+b^2*e^2)-3*B*d*(5*c^2*d^2-5*b*c*d*e+b^2*e^2))*x/e^7+1/2*(c*d-b*e)*(3*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*x^2/e^6+c*(c*d-b*e)*(2*B*c*d-b*B*e-A*c*e)*x^3/e^5-1/4*c^2*(3*B*c*d-3*b*B*e-A*c*e)*x^4/e^4+1/5*B*c^3*x^5/e^3+1/2*d^3*(B*d-A*e)*(c*d-b*e)^3/(e^8*(d+e*x)^2)-d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))/(e^8*(d+e*x))+3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-8*b*c*d*e+2*b^2*e^2))*log(d+e*x)/e^8],
[(A+B*x)*(b*x+c*x^2)^3/(d+e*x)^4,x,2,(A*c*e*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2)-B*(20*c^3*d^3-30*b*c^2*d^2*e+12*b^2*c*d*e^2-b^3*e^3))*x/e^7-1/2*c*(A*c*e*(4*c*d-3*b*e)-B*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*x^2/e^6-1/3*c^2*(4*B*c*d-3*b*B*e-A*c*e)*x^3/e^5+1/4*B*c^3*x^4/e^4+1/3*d^3*(B*d-A*e)*(c*d-b*e)^3/(e^8*(d+e*x)^3)-1/2*d^2*(c*d-b*e)^2*(B*d*(7*c*d-4*b*e)-3*A*e*(2*c*d-b*e))/(e^8*(d+e*x)^2)-3*d*(c*d-b*e)*(A*e*(5*c^2*d^2-5*b*c*d*e+b^2*e^2)-B*d*(7*c^2*d^2-8*b*c*d*e+2*b^2*e^2))/(e^8*(d+e*x))+(B*d*(35*c^3*d^3-60*b*c^2*d^2*e+30*b^2*c*d*e^2-4*b^3*e^3)-A*e*(20*c^3*d^3-30*b*c^2*d^2*e+12*b^2*c*d*e^2-b^3*e^3))*log(d+e*x)/e^8],

# p<0
[(A+B*x)*(d+e*x)^4/(b*x+c*x^2),x,2,e*(A*c*e*(6*c^2*d^2-4*b*c*d*e+b^2*e^2)+B*(4*c^3*d^3-6*b*c^2*d^2*e+4*b^2*c*d*e^2-b^3*e^3))*x/c^4+1/2*e^2*(A*c*e*(4*c*d-b*e)+B*(6*c^2*d^2-4*b*c*d*e+b^2*e^2))*x^2/c^3+1/3*e^3*(4*B*c*d-b*B*e+A*c*e)*x^3/c^2+1/4*B*e^4*x^4/c+A*d^4*log(x)/b+(b*B-A*c)*(c*d-b*e)^4*log(b+c*x)/(b*c^5)],
[(A+B*x)*(d+e*x)^3/(b*x+c*x^2),x,2,e*(A*c*e*(3*c*d-b*e)+B*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))*x/c^3+1/2*e^2*(3*B*c*d-b*B*e+A*c*e)*x^2/c^2+1/3*B*e^3*x^3/c+A*d^3*log(x)/b+(b*B-A*c)*(c*d-b*e)^3*log(b+c*x)/(b*c^4)],
[(A+B*x)*(d+e*x)^2/(b*x+c*x^2),x,2,e*(2*B*c*d-b*B*e+A*c*e)*x/c^2+1/2*B*e^2*x^2/c+A*d^2*log(x)/b+(b*B-A*c)*(c*d-b*e)^2*log(b+c*x)/(b*c^3)],
[(A+B*x)*(d+e*x)/(b*x+c*x^2),x,2,B*e*x/c+A*d*log(x)/b+(b*B-A*c)*(c*d-b*e)*log(b+c*x)/(b*c^2)],
[(A+B*x)/(b*x+c*x^2),x,2,A*log(x)/b+(b*B-A*c)*log(b+c*x)/(b*c)],
[(A+B*x)/((d+e*x)*(b*x+c*x^2)),x,2,A*log(x)/(b*d)+(b*B-A*c)*log(b+c*x)/(b*(c*d-b*e))-(B*d-A*e)*log(d+e*x)/(d*(c*d-b*e))],
[(A+B*x)/((d+e*x)^2*(b*x+c*x^2)),x,2,(B*d-A*e)/(d*(c*d-b*e)*(d+e*x))+A*log(x)/(b*d^2)+c*(b*B-A*c)*log(b+c*x)/(b*(c*d-b*e)^2)-(B*c*d^2-A*e*(2*c*d-b*e))*log(d+e*x)/(d^2*(c*d-b*e)^2)],
[(A+B*x)/((d+e*x)^3*(b*x+c*x^2)),x,2,1/2*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^2)+(B*c*d^2-A*e*(2*c*d-b*e))/(d^2*(c*d-b*e)^2*(d+e*x))+A*log(x)/(b*d^3)+c^2*(b*B-A*c)*log(b+c*x)/(b*(c*d-b*e)^3)-(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))*log(d+e*x)/(d^3*(c*d-b*e)^3)],
[(A+B*x)/((d+e*x)^4*(b*x+c*x^2)),x,2,1/3*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^3)+1/2*(B*c*d^2-A*e*(2*c*d-b*e))/(d^2*(c*d-b*e)^2*(d+e*x)^2)+(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))/(d^3*(c*d-b*e)^3*(d+e*x))+A*log(x)/(b*d^4)+c^3*(b*B-A*c)*log(b+c*x)/(b*(c*d-b*e)^4)-(B*c^3*d^4-A*e*(4*c^3*d^3-6*b*c^2*d^2*e+4*b^2*c*d*e^2-b^3*e^3))*log(d+e*x)/(d^4*(c*d-b*e)^4)],
[(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^2,x,2,-A*d^4/(b^2*x)+e^3*(4*B*c*d-2*b*B*e+A*c*e)*x/c^3+1/2*B*e^4*x^2/c^2+(b*B-A*c)*(c*d-b*e)^4/(b^2*c^4*(b+c*x))+d^3*(b*B*d-2*A*c*d+4*A*b*e)*log(x)/b^3+(c*d-b*e)^3*(2*A*c^2*d-3*b^2*B*e-b*c*(B*d-2*A*e))*log(b+c*x)/(b^3*c^4)],
[(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^2,x,2,-A*d^3/(b^2*x)+B*e^3*x/c^2+(b*B-A*c)*(c*d-b*e)^3/(b^2*c^3*(b+c*x))+d^2*(b*B*d-2*A*c*d+3*A*b*e)*log(x)/b^3+(c*d-b*e)^2*(2*A*c^2*d-2*b^2*B*e-b*c*(B*d-A*e))*log(b+c*x)/(b^3*c^3)],
[(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^2,x,2,-A*d^2/(b^2*x)+(b*B-A*c)*(c*d-b*e)^2/(b^2*c^2*(b+c*x))+d*(b*B*d-2*A*c*d+2*A*b*e)*log(x)/b^3-(c*d-b*e)*(b*B*c*d-2*A*c^2*d+b^2*B*e)*log(b+c*x)/(b^3*c^2)],
[(A+B*x)*(d+e*x)/(b*x+c*x^2)^2,x,2,-A*d/(b^2*x)+(b*B-A*c)*(c*d-b*e)/(b^2*c*(b+c*x))+(b*B*d-2*A*c*d+A*b*e)*log(x)/b^3-(b*B*d-2*A*c*d+A*b*e)*log(b+c*x)/b^3],
[(A+B*x)/(b*x+c*x^2)^2,x,2,-A/(b^2*x)+(b*B-A*c)/(b^2*(b+c*x))+(b*B-2*A*c)*log(x)/b^3-(b*B-2*A*c)*log(b+c*x)/b^3],
[(A+B*x)/((d+e*x)*(b*x+c*x^2)^2),x,2,-A/(b^2*d*x)+c*(b*B-A*c)/(b^2*(c*d-b*e)*(b+c*x))+(b*B*d-2*A*c*d-A*b*e)*log(x)/(b^3*d^2)+c*(2*A*c^2*d+2*b^2*B*e-b*c*(B*d+3*A*e))*log(b+c*x)/(b^3*(c*d-b*e)^2)-e^2*(B*d-A*e)*log(d+e*x)/(d^2*(c*d-b*e)^2)],
[(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^2),x,2,-A/(b^2*d^2*x)+c^2*(b*B-A*c)/(b^2*(c*d-b*e)^2*(b+c*x))+e^2*(B*d-A*e)/(d^2*(c*d-b*e)^2*(d+e*x))+(b*B*d-2*A*c*d-2*A*b*e)*log(x)/(b^3*d^3)+c^2*(2*A*c^2*d+3*b^2*B*e-b*c*(B*d+4*A*e))*log(b+c*x)/(b^3*(c*d-b*e)^3)+e^2*(2*A*e*(2*c*d-b*e)-B*d*(3*c*d-b*e))*log(d+e*x)/(d^3*(c*d-b*e)^3)],
[(A+B*x)/((d+e*x)^3*(b*x+c*x^2)^2),x,2,-A/(b^2*d^3*x)+c^3*(b*B-A*c)/(b^2*(c*d-b*e)^3*(b+c*x))+1/2*e^2*(B*d-A*e)/(d^2*(c*d-b*e)^2*(d+e*x)^2)-e^2*(2*A*e*(2*c*d-b*e)-B*d*(3*c*d-b*e))/(d^3*(c*d-b*e)^3*(d+e*x))+(b*B*d-2*A*c*d-3*A*b*e)*log(x)/(b^3*d^4)+c^3*(2*A*c^2*d+4*b^2*B*e-b*c*(B*d+5*A*e))*log(b+c*x)/(b^3*(c*d-b*e)^4)-e^2*(B*d*(6*c^2*d^2-4*b*c*d*e+b^2*e^2)-A*e*(10*c^2*d^2-10*b*c*d*e+3*b^2*e^2))*log(d+e*x)/(d^4*(c*d-b*e)^4)],
[(A+B*x)*(d+e*x)^5/(b*x+c*x^2)^3,x,2,-1/2*A*d^5/(b^3*x^2)-d^4*(b*B*d-3*A*c*d+5*A*b*e)/(b^4*x)+B*e^5*x/c^3-1/2*(b*B-A*c)*(c*d-b*e)^5/(b^3*c^4*(b+c*x)^2)-(c*d-b*e)^4*(2*b*B*c*d-3*A*c^2*d+3*b^2*B*e-2*A*b*c*e)/(b^4*c^4*(b+c*x))+d^3*(6*A*c^2*d^2+5*b^2*e*(B*d+2*A*e)-3*b*c*d*(B*d+5*A*e))*log(x)/b^5-(c*d-b*e)^3*(6*A*c^3*d^2-3*b^3*B*e^2-3*b*c^2*d*(B*d-A*e)-b^2*c*e*(4*B*d-A*e))*log(b+c*x)/(b^5*c^4)],
[(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^3,x,2,-1/2*A*d^4/(b^3*x^2)-d^3*(b*B*d-3*A*c*d+4*A*b*e)/(b^4*x)-1/2*(b*B-A*c)*(c*d-b*e)^4/(b^3*c^3*(b+c*x)^2)-(c*d-b*e)^3*(2*b*B*c*d-3*A*c^2*d+2*b^2*B*e-A*b*c*e)/(b^4*c^3*(b+c*x))+d^2*(6*A*c^2*d^2+2*b^2*e*(2*B*d+3*A*e)-3*b*c*d*(B*d+4*A*e))*log(x)/b^5+(c*d-b*e)^2*(3*b*B*c^2*d^2-6*A*c^3*d^2+2*b^2*B*c*d*e+b^3*B*e^2)*log(b+c*x)/(b^5*c^3)],
[(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^3,x,2,-1/2*A*d^3/(b^3*x^2)-d^2*(b*B*d-3*A*c*d+3*A*b*e)/(b^4*x)-1/2*(b*B-A*c)*(c*d-b*e)^3/(b^3*c^2*(b+c*x)^2)-(c*d-b*e)^2*(2*b*B*c*d-3*A*c^2*d+b^2*B*e)/(b^4*c^2*(b+c*x))-3*d*(c*d-b*e)*(b*B*d-2*A*c*d+A*b*e)*log(x)/b^5+3*d*(c*d-b*e)*(b*B*d-2*A*c*d+A*b*e)*log(b+c*x)/b^5],
[(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^3,x,2,-1/2*A*d^2/(b^3*x^2)-d*(b*B*d-3*A*c*d+2*A*b*e)/(b^4*x)-1/2*(b*B-A*c)*(c*d-b*e)^2/(b^3*c*(b+c*x)^2)-(c*d-b*e)*(2*b*B*d-3*A*c*d+A*b*e)/(b^4*(b+c*x))+(6*A*c^2*d^2+b^2*e*(2*B*d+A*e)-3*b*c*d*(B*d+2*A*e))*log(x)/b^5-(6*A*c^2*d^2+b^2*e*(2*B*d+A*e)-3*b*c*d*(B*d+2*A*e))*log(b+c*x)/b^5],
[(A+B*x)*(d+e*x)/(b*x+c*x^2)^3,x,2,-1/2*A*d/(b^3*x^2)+(-b*B*d+3*A*c*d-A*b*e)/(b^4*x)-1/2*(b*B-A*c)*(c*d-b*e)/(b^3*(b+c*x)^2)+(3*A*c^2*d+b^2*B*e-2*b*c*(B*d+A*e))/(b^4*(b+c*x))+(6*A*c^2*d+b^2*B*e-3*b*c*(B*d+A*e))*log(x)/b^5-(6*A*c^2*d+b^2*B*e-3*b*c*(B*d+A*e))*log(b+c*x)/b^5],
[(A+B*x)/(b*x+c*x^2)^3,x,2,-1/2*A/(b^3*x^2)+(-b*B+3*A*c)/(b^4*x)-1/2*c*(b*B-A*c)/(b^3*(b+c*x)^2)-c*(2*b*B-3*A*c)/(b^4*(b+c*x))-3*c*(b*B-2*A*c)*log(x)/b^5+3*c*(b*B-2*A*c)*log(b+c*x)/b^5],
[(A+B*x)/((d+e*x)*(b*x+c*x^2)^3),x,2,-1/2*A/(b^3*d*x^2)+(-b*B*d+3*A*c*d+A*b*e)/(b^4*d^2*x)-1/2*c^2*(b*B-A*c)/(b^3*(c*d-b*e)*(b+c*x)^2)+c^2*(3*A*c^2*d+3*b^2*B*e-2*b*c*(B*d+2*A*e))/(b^4*(c*d-b*e)^2*(b+c*x))+(6*A*c^2*d^2-3*b*c*d*(B*d-A*e)-b^2*e*(B*d-A*e))*log(x)/(b^5*d^3)-c^2*(6*A*c^3*d^2-6*b^3*B*e^2-3*b*c^2*d*(B*d+5*A*e)+2*b^2*c*e*(4*B*d+5*A*e))*log(b+c*x)/(b^5*(c*d-b*e)^3)-e^4*(B*d-A*e)*log(d+e*x)/(d^3*(c*d-b*e)^3)],
[(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^3),x,2,-1/2*A/(b^3*d^2*x^2)+(-b*B*d+3*A*c*d+2*A*b*e)/(b^4*d^3*x)-1/2*c^3*(b*B-A*c)/(b^3*(c*d-b*e)^2*(b+c*x)^2)-c^3*(2*b*B*c*d-3*A*c^2*d-4*b^2*B*e+5*A*b*c*e)/(b^4*(c*d-b*e)^3*(b+c*x))+e^4*(B*d-A*e)/(d^3*(c*d-b*e)^3*(d+e*x))+(6*A*c^2*d^2-b^2*e*(2*B*d-3*A*e)-3*b*c*d*(B*d-2*A*e))*log(x)/(b^5*d^4)-c^3*(6*A*c^3*d^2-10*b^3*B*e^2+5*b^2*c*e*(2*B*d+3*A*e)-3*b*c^2*d*(B*d+6*A*e))*log(b+c*x)/(b^5*(c*d-b*e)^4)-e^4*(B*d*(5*c*d-2*b*e)-3*A*e*(2*c*d-b*e))*log(d+e*x)/(d^4*(c*d-b*e)^4)],

# Integrands of the form (d+e x)^m (A+B x) (b x+c x^2)^(p/2)

# p>0
[(A+B*x)*(d+e*x)^3*sqrt(b*x+c*x^2),x,6,1/20*(2*B*c*d-3*b*B*e+4*A*c*e)*(d+e*x)^2*(b*x+c*x^2)^(3/2)/c^2+1/6*B*(d+e*x)^3*(b*x+c*x^2)^(3/2)/c+1/960*(4*A*c*e*(192*c^2*d^2-150*b*c*d*e+35*b^2*e^2)+B*(64*c^3*d^3-456*b*c^2*d^2*e+420*b^2*c*d*e^2-105*b^3*e^3)+6*c*e*(28*A*c*e*(2*c*d-b*e)+B*(8*c^2*d^2-36*b*c*d*e+21*b^2*e^2))*x)*(b*x+c*x^2)^(3/2)/c^4-1/512*b^2*(128*A*c^4*d^3+21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-28*b^3*c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+1/512*(128*A*c^4*d^3+21*b^4*B*e^3+120*b^2*c^2*d*e*(B*d+A*e)-28*b^3*c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*(b+2*c*x)*sqrt(b*x+c*x^2)/c^5],
[(A+B*x)*(d+e*x)^2*sqrt(b*x+c*x^2),x,5,1/5*B*(d+e*x)^2*(b*x+c*x^2)^(3/2)/c+1/240*(10*A*c*e*(16*c*d-5*b*e)+B*(32*c^2*d^2-100*b*c*d*e+35*b^2*e^2)+6*c*e*(4*B*c*d-7*b*B*e+10*A*c*e)*x)*(b*x+c*x^2)^(3/2)/c^3-1/128*b^2*(32*A*c^3*d^2-7*b^3*B*e^2+10*b^2*c*e*(2*B*d+A*e)-16*b*c^2*d*(B*d+2*A*e))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)+1/128*(32*A*c^3*d^2-7*b^3*B*e^2+10*b^2*c*e*(2*B*d+A*e)-16*b*c^2*d*(B*d+2*A*e))*(b+2*c*x)*sqrt(b*x+c*x^2)/c^4],
[(A+B*x)*(d+e*x)*sqrt(b*x+c*x^2),x,4,-1/24*(5*b*B*e-8*c*(B*d+A*e)-6*B*c*e*x)*(b*x+c*x^2)^(3/2)/c^2-1/64*b^2*(16*A*c^2*d+5*b^2*B*e-8*b*c*(B*d+A*e))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/64*(16*A*c^2*d+5*b^2*B*e-8*b*c*(B*d+A*e))*(b+2*c*x)*sqrt(b*x+c*x^2)/c^3],
[(A+B*x)*sqrt(b*x+c*x^2),x,4,1/3*B*(b*x+c*x^2)^(3/2)/c+1/8*b^2*(b*B-2*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-1/8*(b*B-2*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^2],
[(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x),x,6,-1/4*(4*A*c*e*(2*c*d-b*e)-B*(8*c^2*d^2-4*b*c*d*e-b^2*e^2))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^3)-(B*d-A*e)*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-b*e)/e^3-1/4*(4*B*c*d-b*B*e-4*A*c*e-2*B*c*e*x)*sqrt(b*x+c*x^2)/(c*e^2)],
[(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^2,x,6,-(4*B*c*d-b*B*e-2*A*c*e)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^3*sqrt(c))+1/2*(B*d*(4*c*d-3*b*e)-A*e*(2*c*d-b*e))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^3*sqrt(d)*sqrt(c*d-b*e))+(2*B*d-A*e+B*e*x)*sqrt(b*x+c*x^2)/(e^2*(d+e*x))],
[(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^3,x,6,-1/8*(A*b^2*e^3+B*d*(8*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*e^3*(c*d-b*e)^(3/2))+2*B*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^3+1/4*(d*(A*b*e^2-B*d*(4*c*d-3*b*e))-e*(B*d*(6*c*d-5*b*e)-A*e*(2*c*d-b*e))*x)*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+e*x)^2)],
[(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^4,x,4,1/3*(B*d-A*e)*(b*x+c*x^2)^(3/2)/(d*(c*d-b*e)*(d+e*x)^3)+1/16*b^2*(b*B*d-2*A*c*d+A*b*e)*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))-1/8*(b*B*d-2*A*c*d+A*b*e)*(b*d+(2*c*d-b*e)*x)*sqrt(b*x+c*x^2)/(d^2*(c*d-b*e)^2*(d+e*x)^2)],
[(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^5,x,5,1/4*(B*d-A*e)*(b*x+c*x^2)^(3/2)/(d*(c*d-b*e)*(d+e*x)^4)-1/24*(5*A*e*(2*c*d-b*e)-B*d*(2*c*d+3*b*e))*(b*x+c*x^2)^(3/2)/(d^2*(c*d-b*e)^2*(d+e*x)^3)-1/128*b^2*(16*A*c^2*d^2-8*b*c*d*(B*d+2*A*e)+b^2*e*(3*B*d+5*A*e))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+1/64*(16*A*c^2*d^2-8*b*c*d*(B*d+2*A*e)+b^2*e*(3*B*d+5*A*e))*(b*d+(2*c*d-b*e)*x)*sqrt(b*x+c*x^2)/(d^3*(c*d-b*e)^3*(d+e*x)^2)],
[(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^6,x,6,1/5*(B*d-A*e)*(b*x+c*x^2)^(3/2)/(d*(c*d-b*e)*(d+e*x)^5)-1/40*(7*A*e*(2*c*d-b*e)-B*d*(4*c*d+3*b*e))*(b*x+c*x^2)^(3/2)/(d^2*(c*d-b*e)^2*(d+e*x)^4)+1/240*(B*d*(8*c^2*d^2+42*b*c*d*e-15*b^2*e^2)-A*e*(108*c^2*d^2-108*b*c*d*e+35*b^2*e^2))*(b*x+c*x^2)^(3/2)/(d^3*(c*d-b*e)^3*(d+e*x)^3)-1/256*b^2*(32*A*c^3*d^3-16*b*c^2*d^2*(B*d+3*A*e)+6*b^2*c*d*e*(2*B*d+5*A*e)-b^3*e^2*(3*B*d+7*A*e))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(9/2)*(c*d-b*e)^(9/2))+1/128*(32*A*c^3*d^3-16*b*c^2*d^2*(B*d+3*A*e)+6*b^2*c*d*e*(2*B*d+5*A*e)-b^3*e^2*(3*B*d+7*A*e))*(b*d+(2*c*d-b*e)*x)*sqrt(b*x+c*x^2)/(d^4*(c*d-b*e)^4*(d+e*x)^2)],
[(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^(3/2),x,6,1/384*(48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+2*A*e))*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^4+1/7*B*(d+e*x)^2*(b*x+c*x^2)^(5/2)/c+1/840*(14*A*c*e*(24*c*d-7*b*e)+B*(48*c^2*d^2-196*b*c*d*e+63*b^2*e^2)+10*c*e*(4*B*c*d-9*b*B*e+14*A*c*e)*x)*(b*x+c*x^2)^(5/2)/c^3+1/1024*b^4*(48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+2*A*e))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)-1/1024*b^2*(48*A*c^3*d^2-9*b^3*B*e^2+14*b^2*c*e*(2*B*d+A*e)-24*b*c^2*d*(B*d+2*A*e))*(b+2*c*x)*sqrt(b*x+c*x^2)/c^5],
[(A+B*x)*(d+e*x)*(b*x+c*x^2)^(3/2),x,5,1/192*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^3-1/60*(7*b*B*e-12*c*(B*d+A*e)-10*B*c*e*x)*(b*x+c*x^2)^(5/2)/c^2+1/512*b^4*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-1/512*b^2*(24*A*c^2*d+7*b^2*B*e-12*b*c*(B*d+A*e))*(b+2*c*x)*sqrt(b*x+c*x^2)/c^4],
[(A+B*x)*(b*x+c*x^2)^(3/2),x,5,-1/16*(b*B-2*A*c)*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^2+1/5*B*(b*x+c*x^2)^(5/2)/c-3/128*b^4*(b*B-2*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+3/128*b^2*(b*B-2*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^3],
[(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x),x,7,-1/24*(8*B*c*d-3*b*B*e-8*A*c*e-6*B*c*e*x)*(b*x+c*x^2)^(3/2)/(c*e^2)-1/64*(8*A*c*e*(16*c^3*d^3-24*b*c^2*d^2*e+6*b^2*c*d*e^2+b^3*e^3)-B*(128*c^4*d^4-192*b*c^3*d^3*e+48*b^2*c^2*d^2*e^2+8*b^3*c*d*e^3+3*b^4*e^4))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(5/2)*e^5)-d^(3/2)*(B*d-A*e)*(c*d-b*e)^(3/2)*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^5+1/64*(8*A*c*e*(8*c^2*d^2-10*b*c*d*e+b^2*e^2)-B*(64*c^3*d^3-80*b*c^2*d^2*e+8*b^2*c*d*e^2+3*b^3*e^3)-2*c*e*(8*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-8*b*c*d*e-3*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c^2*e^4)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^2,x,7,1/3*(4*B*d-3*A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x))+1/8*(4*b*c*e*(4*B*d-3*A*e)*(2*c*d-b*e)-(8*B*c*d-b*B*e-6*A*c*e)*(8*c^2*d^2-4*b*c*d*e-b^2*e^2))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^5)+1/2*(B*d*(8*c*d-5*b*e)-3*A*e*(2*c*d-b*e))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-b*e)/e^5-1/8*(6*A*c*e*(4*c*d-3*b*e)-B*(32*c^2*d^2-28*b*c*d*e+b^2*e^2)+2*c*e*(8*B*c*d-b*B*e-6*A*c*e)*x)*sqrt(b*x+c*x^2)/(c*e^4)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^3,x,7,1/2*(2*B*d-A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^2)-3/4*(4*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-12*b*c*d*e+b^2*e^2))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^5*sqrt(c))+3/8*(A*e*(8*c^2*d^2-8*b*c*d*e+b^2*e^2)-B*d*(16*c^2*d^2-20*b*c*d*e+5*b^2*e^2))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^5*sqrt(d)*sqrt(c*d-b*e))-3/4*(4*B*d*(2*c*d-b*e)-A*e*(4*c*d-b*e)+e*(4*B*c*d-b*B*e-2*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*(d+e*x))],
[(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^4,x,7,-1/12*(d*(B*d*(8*c*d-5*b*e)-A*e*(2*c*d+b*e))+3*e*(B*d*(4*c*d-3*b*e)-A*e*(2*c*d-b*e))*x)*(b*x+c*x^2)^(3/2)/(d*e^2*(c*d-b*e)*(d+e*x)^3)+1/16*(B*d*(64*c^3*d^3-120*b*c^2*d^2*e+60*b^2*c*d*e^2-5*b^3*e^3)-A*e*(16*c^3*d^3-24*b*c^2*d^2*e+6*b^2*c*d*e^2+b^3*e^3))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*e^5*(c*d-b*e)^(3/2))-(8*B*c*d-3*b*B*e-2*A*c*e)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^5-1/8*(A*e*(8*c^2*d^2-6*b*c*d*e-b^2*e^2)-B*d*(32*c^2*d^2-36*b*c*d*e+5*b^2*e^2)-2*c*e*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*x)*sqrt(b*x+c*x^2)/(d*e^4*(c*d-b*e)*(d+e*x))],
[(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^5,x,7,1/24*(d*(3*A*b*e^2-B*d*(8*c*d-5*b*e))-e*(B*d*(14*c*d-11*b*e)-3*A*e*(2*c*d-b*e))*x)*(b*x+c*x^2)^(3/2)/(d*e^2*(c*d-b*e)*(d+e*x)^4)+2*B*c^(3/2)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/e^5+1/128*(3*A*b^4*e^5-B*d*(128*c^4*d^4-320*b*c^3*d^3*e+240*b^2*c^2*d^2*e^2-40*b^3*c*d*e^3-5*b^4*e^4))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*e^5*(c*d-b*e)^(5/2))-1/64*(d*(3*A*b^3*e^4+B*d*(64*c^3*d^3-112*b*c^2*d^2*e+40*b^2*c*d*e^2+5*b^3*e^3))+e*(3*A*b^2*e^3*(2*c*d-b*e)+B*d*(96*c^3*d^3-192*b*c^2*d^2*e+98*b^2*c*d*e^2-5*b^3*e^3))*x)*sqrt(b*x+c*x^2)/(d^2*e^4*(c*d-b*e)^2*(d+e*x)^2)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^6,x,5,-1/16*(b*B*d-2*A*c*d+A*b*e)*(b*d+(2*c*d-b*e)*x)*(b*x+c*x^2)^(3/2)/(d^2*(c*d-b*e)^2*(d+e*x)^4)+1/5*(B*d-A*e)*(b*x+c*x^2)^(5/2)/(d*(c*d-b*e)*(d+e*x)^5)-3/256*b^4*(b*B*d-2*A*c*d+A*b*e)*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+3/128*b^2*(b*B*d-2*A*c*d+A*b*e)*(b*d+(2*c*d-b*e)*x)*sqrt(b*x+c*x^2)/(d^3*(c*d-b*e)^3*(d+e*x)^2)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^7,x,6,1/192*(24*A*c^2*d^2-12*b*c*d*(B*d+2*A*e)+b^2*e*(5*B*d+7*A*e))*(b*d+(2*c*d-b*e)*x)*(b*x+c*x^2)^(3/2)/(d^3*(c*d-b*e)^3*(d+e*x)^4)+1/6*(B*d-A*e)*(b*x+c*x^2)^(5/2)/(d*(c*d-b*e)*(d+e*x)^6)-1/60*(7*A*e*(2*c*d-b*e)-B*d*(2*c*d+5*b*e))*(b*x+c*x^2)^(5/2)/(d^2*(c*d-b*e)^2*(d+e*x)^5)+1/1024*b^4*(24*A*c^2*d^2-12*b*c*d*(B*d+2*A*e)+b^2*e*(5*B*d+7*A*e))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(9/2)*(c*d-b*e)^(9/2))-1/512*b^2*(24*A*c^2*d^2-12*b*c*d*(B*d+2*A*e)+b^2*e*(5*B*d+7*A*e))*(b*d+(2*c*d-b*e)*x)*sqrt(b*x+c*x^2)/(d^4*(c*d-b*e)^4*(d+e*x)^2)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^8,x,7,1/384*(48*A*c^3*d^3-24*b*c^2*d^2*(B*d+3*A*e)-b^3*e^2*(5*B*d+9*A*e)+2*b^2*c*d*e*(10*B*d+21*A*e))*(b*d+(2*c*d-b*e)*x)*(b*x+c*x^2)^(3/2)/(d^4*(c*d-b*e)^4*(d+e*x)^4)+1/7*(B*d-A*e)*(b*x+c*x^2)^(5/2)/(d*(c*d-b*e)*(d+e*x)^7)-1/84*(9*A*e*(2*c*d-b*e)-B*d*(4*c*d+5*b*e))*(b*x+c*x^2)^(5/2)/(d^2*(c*d-b*e)^2*(d+e*x)^6)+1/840*(B*d*(8*c^2*d^2+90*b*c*d*e-35*b^2*e^2)-3*A*e*(68*c^2*d^2-68*b*c*d*e+21*b^2*e^2))*(b*x+c*x^2)^(5/2)/(d^3*(c*d-b*e)^3*(d+e*x)^5)+1/2048*b^4*(48*A*c^3*d^3-24*b*c^2*d^2*(B*d+3*A*e)-b^3*e^2*(5*B*d+9*A*e)+2*b^2*c*d*e*(10*B*d+21*A*e))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(11/2)*(c*d-b*e)^(11/2))-1/1024*b^2*(48*A*c^3*d^3-24*b*c^2*d^2*(B*d+3*A*e)-b^3*e^2*(5*B*d+9*A*e)+2*b^2*c*d*e*(10*B*d+21*A*e))*(b*d+(2*c*d-b*e)*x)*sqrt(b*x+c*x^2)/(d^5*(c*d-b*e)^5*(d+e*x)^2)],
[(A+B*x)*(d+e*x)^2*(b*x+c*x^2)^(5/2),x,7,-5/12288*b^2*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^5+1/768*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*(b+2*c*x)*(b*x+c*x^2)^(5/2)/c^4+1/9*B*(d+e*x)^2*(b*x+c*x^2)^(7/2)/c+1/2016*(18*A*c*e*(32*c*d-9*b*e)+B*(64*c^2*d^2-324*b*c*d*e+99*b^2*e^2)+14*c*e*(4*B*c*d-11*b*B*e+18*A*c*e)*x)*(b*x+c*x^2)^(7/2)/c^3-5/32768*b^6*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(13/2)+5/32768*b^4*(64*A*c^3*d^2-11*b^3*B*e^2+18*b^2*c*e*(2*B*d+A*e)-32*b*c^2*d*(B*d+2*A*e))*(b+2*c*x)*sqrt(b*x+c*x^2)/c^6],
[(A+B*x)*(d+e*x)*(b*x+c*x^2)^(5/2),x,6,-5/6144*b^2*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^4+1/384*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*(b+2*c*x)*(b*x+c*x^2)^(5/2)/c^3-1/112*(9*b*B*e-16*c*(B*d+A*e)-14*B*c*e*x)*(b*x+c*x^2)^(7/2)/c^2-5/16384*b^6*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(11/2)+5/16384*b^4*(32*A*c^2*d+9*b^2*B*e-16*b*c*(B*d+A*e))*(b+2*c*x)*sqrt(b*x+c*x^2)/c^5],
[(A+B*x)*(b*x+c*x^2)^(5/2),x,6,5/384*b^2*(b*B-2*A*c)*(b+2*c*x)*(b*x+c*x^2)^(3/2)/c^3-1/24*(b*B-2*A*c)*(b+2*c*x)*(b*x+c*x^2)^(5/2)/c^2+1/7*B*(b*x+c*x^2)^(7/2)/c+5/1024*b^6*(b*B-2*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)-5/1024*b^4*(b*B-2*A*c)*(b+2*c*x)*sqrt(b*x+c*x^2)/c^4],
[(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x),x,8,1/192*(4*A*c*e*(16*c^2*d^2-22*b*c*d*e+3*b^2*e^2)-B*(64*c^3*d^3-88*b*c^2*d^2*e+12*b^2*c*d*e^2+5*b^3*e^3)-2*c*e*(12*A*c*e*(2*c*d-b*e)-B*(24*c^2*d^2-12*b*c*d*e-5*b^2*e^2))*x)*(b*x+c*x^2)^(3/2)/(c^2*e^4)-1/60*(12*B*c*d-5*b*B*e-12*A*c*e-10*B*c*e*x)*(b*x+c*x^2)^(5/2)/(c*e^2)-1/512*(4*A*c*e*(256*c^5*d^5-640*b*c^4*d^4*e+480*b^2*c^3*d^3*e^2-80*b^3*c^2*d^2*e^3-10*b^4*c*d*e^4-3*b^5*e^5)-B*(1024*c^6*d^6-2560*b*c^5*d^5*e+1920*b^2*c^4*d^4*e^2-320*b^3*c^3*d^3*e^3-40*b^4*c^2*d^2*e^4-12*b^5*c*d*e^5-5*b^6*e^6))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(7/2)*e^7)-d^(5/2)*(B*d-A*e)*(c*d-b*e)^(5/2)*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^7+1/1536*(3*(4*A*c*e*(128*c^4*d^4-288*b*c^3*d^3*e+176*b^2*c^2*d^2*e^2-10*b^3*c*d*e^3-3*b^4*e^4)-B*(512*c^5*d^5-1152*b*c^4*d^4*e+704*b^2*c^3*d^3*e^2-40*b^3*c^2*d^2*e^3-12*b^4*c*d*e^4-5*b^5*e^5))-2*c*e*(8*b*c*d*e*(2*c*d-b*e)*(12*B*c*d-5*b*B*e-12*A*c*e)+(16*c^2*d^2-8*b*c*d*e-3*b^2*e^2)*(12*A*c*e*(2*c*d-b*e)-B*(24*c^2*d^2-12*b*c*d*e-5*b^2*e^2)))*x)*sqrt(b*x+c*x^2)/(c^3*e^6)],
[(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^2,x,8,-1/48*(10*A*c*e*(8*c*d-7*b*e)-B*(96*c^2*d^2-92*b*c*d*e+3*b^2*e^2)+6*c*e*(12*B*c*d-b*B*e-10*A*c*e)*x)*(b*x+c*x^2)^(3/2)/(c*e^4)+1/5*(6*B*d-5*A*e+B*e*x)*(b*x+c*x^2)^(5/2)/(e^2*(d+e*x))+1/128*(10*A*c*e*(128*c^4*d^4-256*b*c^3*d^3*e+144*b^2*c^2*d^2*e^2-16*b^3*c*d*e^3-b^4*e^4)-B*(1536*c^5*d^5-3200*b*c^4*d^4*e+1920*b^2*c^3*d^3*e^2-240*b^3*c^2*d^2*e^3-20*b^4*c*d*e^4-3*b^5*e^5))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(5/2)*e^7)+1/2*d^(3/2)*(c*d-b*e)^(3/2)*(B*d*(12*c*d-7*b*e)-5*A*e*(2*c*d-b*e))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/e^7-1/128*(10*A*c*e*(64*c^3*d^3-112*b*c^2*d^2*e+48*b^2*c*d*e^2-b^3*e^3)-B*(768*c^4*d^4-1408*b*c^3*d^3*e+656*b^2*c^2*d^2*e^2-20*b^3*c*d*e^3-3*b^4*e^4)-2*c*e*(8*b*c*e*(6*B*d-5*A*e)*(2*c*d-b*e)-(12*B*c*d-b*B*e-10*A*c*e)*(16*c^2*d^2-8*b*c*d*e-3*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c^2*e^6)],
[(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^3,x,8,-5/24*(B*d*(24*c*d-13*b*e)-2*A*e*(8*c*d-3*b*e)+e*(6*B*c*d-b*B*e-4*A*c*e)*x)*(b*x+c*x^2)^(3/2)/(e^4*(d+e*x))+1/4*(3*B*d-2*A*e+B*e*x)*(b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^2)-5/64*(8*A*c*e*(32*c^3*d^3-48*b*c^2*d^2*e+18*b^2*c*d*e^2-b^3*e^3)-B*(384*c^4*d^4-640*b*c^3*d^3*e+288*b^2*c^2*d^2*e^2-24*b^3*c*d*e^3-b^4*e^4))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(c^(3/2)*e^7)+5/8*(A*e*(16*c^2*d^2-16*b*c*d*e+3*b^2*e^2)-B*d*(24*c^2*d^2-28*b*c*d*e+7*b^2*e^2))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))*sqrt(d)*sqrt(c*d-b*e)/e^7+5/64*(8*A*c*e*(16*c^2*d^2-20*b*c*d*e+5*b^2*e^2)-B*(192*c^3*d^3-272*b*c^2*d^2*e+88*b^2*c*d*e^2-b^3*e^3)-2*c*e*(16*A*c*e*(2*c*d-b*e)-B*(48*c^2*d^2-32*b*c*d*e+b^2*e^2))*x)*sqrt(b*x+c*x^2)/(c*e^6)],
[(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^4,x,8,-5/12*(4*B*d*(2*c*d-b*e)-A*e*(4*c*d-b*e)+e*(4*B*c*d-b*B*e-2*A*c*e)*x)*(b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^2)+1/3*(2*B*d-A*e+B*e*x)*(b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^3)+5/8*(2*A*c*e*(16*c^2*d^2-16*b*c*d*e+3*b^2*e^2)-B*(64*c^3*d^3-80*b*c^2*d^2*e+24*b^2*c*d*e^2-b^3*e^3))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e^7*sqrt(c))+5/16*(B*d*(64*c^3*d^3-112*b*c^2*d^2*e+56*b^2*c*d*e^2-7*b^3*e^3)-A*e*(32*c^3*d^3-48*b*c^2*d^2*e+18*b^2*c*d*e^2-b^3*e^3))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e^7*sqrt(d)*sqrt(c*d-b*e))-5/8*(A*e*(16*c^2*d^2-12*b*c*d*e+b^2*e^2)-2*B*d*(16*c^2*d^2-16*b*c*d*e+3*b^2*e^2)+e*(4*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-12*b*c*d*e+b^2*e^2))*x)*sqrt(b*x+c*x^2)/(e^6*(d+e*x))],
[(A+B*x)*(b*x+c*x^2)^(5/2)/(d+e*x)^5,x,8,-5/96*(d*(A*e*(16*c^2*d^2-12*b*c*d*e-b^2*e^2)-B*d*(48*c^2*d^2-52*b*c*d*e+7*b^2*e^2))+3*e*(A*e*(8*c^2*d^2-8*b*c*d*e+b^2*e^2)-B*d*(24*c^2*d^2-32*b*c*d*e+9*b^2*e^2))*x)*(b*x+c*x^2)^(3/2)/(d*e^4*(c*d-b*e)*(d+e*x)^3)+1/4*(3*B*d-A*e+2*B*e*x)*(b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^4)+5/128*(A*e*(128*c^4*d^4-256*b*c^3*d^3*e+144*b^2*c^2*d^2*e^2-16*b^3*c*d*e^3-b^4*e^4)-B*d*(384*c^4*d^4-896*b*c^3*d^3*e+672*b^2*c^2*d^2*e^2-168*b^3*c*d*e^3+7*b^4*e^4))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*e^7*(c*d-b*e)^(3/2))-5/4*(4*A*c*e*(2*c*d-b*e)-B*(24*c^2*d^2-20*b*c*d*e+3*b^2*e^2))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))*sqrt(c)/e^7-5/64*(B*d*(192*c^3*d^3-304*b*c^2*d^2*e+120*b^2*c*d*e^2-7*b^3*e^3)-A*e*(64*c^3*d^3-80*b*c^2*d^2*e+16*b^2*c*d*e^2+b^3*e^3)-2*c*e*(A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(48*c^2*d^2-64*b*c*d*e+17*b^2*e^2))*x)*sqrt(b*x+c*x^2)/(d*e^6*(c*d-b*e)*(d+e*x))],

# p<0
[(A+B*x)*(d+e*x)^3/sqrt(b*x+c*x^2),x,5,1/64*(128*A*c^4*d^3+35*b^4*B*e^3+144*b^2*c^2*d*e*(B*d+A*e)-40*b^3*c*e^2*(3*B*d+A*e)-64*b*c^3*d^2*(B*d+3*A*e))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(9/2)+1/24*(6*B*c*d-7*b*B*e+8*A*c*e)*(d+e*x)^2*sqrt(b*x+c*x^2)/c^2+1/4*B*(d+e*x)^3*sqrt(b*x+c*x^2)/c+1/192*(8*A*c*e*(64*c^2*d^2-54*b*c*d*e+15*b^2*e^2)+B*(96*c^3*d^3-376*b*c^2*d^2*e+360*b^2*c*d*e^2-105*b^3*e^3)+2*c*e*(40*A*c*e*(2*c*d-b*e)+B*(24*c^2*d^2-64*b*c*d*e+35*b^2*e^2))*x)*sqrt(b*x+c*x^2)/c^4],
[(A+B*x)*(d+e*x)^2/sqrt(b*x+c*x^2),x,4,1/8*(16*A*c^3*d^2-5*b^3*B*e^2+6*b^2*c*e*(2*B*d+A*e)-8*b*c^2*d*(B*d+2*A*e))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)+1/3*B*(d+e*x)^2*sqrt(b*x+c*x^2)/c+1/24*(6*A*c*e*(8*c*d-3*b*e)+B*(16*c^2*d^2-36*b*c*d*e+15*b^2*e^2)+2*c*e*(4*B*c*d-5*b*B*e+6*A*c*e)*x)*sqrt(b*x+c*x^2)/c^3],
[(A+B*x)*(d+e*x)/sqrt(b*x+c*x^2),x,3,1/4*(8*A*c^2*d+3*b^2*B*e-4*b*c*(B*d+A*e))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-1/4*(3*b*B*e-4*c*(B*d+A*e)-2*B*c*e*x)*sqrt(b*x+c*x^2)/c^2],
[(A+B*x)/sqrt(b*x+c*x^2),x,3,-(b*B-2*A*c)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)+B*sqrt(b*x+c*x^2)/c],
[(A+B*x)/((d+e*x)*sqrt(b*x+c*x^2)),x,5,2*B*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/(e*sqrt(c))-(B*d-A*e)*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(e*sqrt(d)*sqrt(c*d-b*e))],
[(A+B*x)/((d+e*x)^2*sqrt(b*x+c*x^2)),x,3,-1/2*(b*B*d-2*A*c*d+A*b*e)*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))+(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x))],
[(A+B*x)/((d+e*x)^3*sqrt(b*x+c*x^2)),x,4,1/8*(8*A*c^2*d^2-4*b*c*d*(B*d+2*A*e)+b^2*e*(B*d+3*A*e))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+1/2*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)^2)-1/4*(3*A*e*(2*c*d-b*e)-B*d*(2*c*d+b*e))*sqrt(b*x+c*x^2)/(d^2*(c*d-b*e)^2*(d+e*x))],
[(A+B*x)/((d+e*x)^4*sqrt(b*x+c*x^2)),x,5,1/16*(16*A*c^3*d^3-8*b*c^2*d^2*(B*d+3*A*e)-b^3*e^2*(B*d+5*A*e)+2*b^2*c*d*e*(2*B*d+9*A*e))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+1/3*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)^3)-1/12*(5*A*e*(2*c*d-b*e)-B*d*(4*c*d+b*e))*sqrt(b*x+c*x^2)/(d^2*(c*d-b*e)^2*(d+e*x)^2)+1/24*(B*d*(8*c^2*d^2+10*b*c*d*e-3*b^2*e^2)-A*e*(44*c^2*d^2-44*b*c*d*e+15*b^2*e^2))*sqrt(b*x+c*x^2)/(d^3*(c*d-b*e)^3*(d+e*x))],
[(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^(3/2),x,4,3/4*e*(4*A*c*e*(2*c*d-b*e)+B*(8*c^2*d^2-12*b*c*d*e+5*b^2*e^2))*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-2*(d+e*x)^2*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*sqrt(b*x+c*x^2))+1/4*e*(32*A*c^3*d^2-15*b^3*B*e^2+12*b^2*c*e*(3*B*d+A*e)-8*b*c^2*d*(2*B*d+3*A*e)+2*c*e*(8*A*c^2*d+5*b^2*B*e-4*b*c*(B*d+A*e))*x)*sqrt(b*x+c*x^2)/(b^2*c^3)],
[(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^(3/2),x,4,e*(4*B*c*d-3*b*B*e+2*A*c*e)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)-2*(d+e*x)*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*sqrt(b*x+c*x^2))+e*(4*A*c^2*d+3*b^2*B*e-2*b*c*(B*d+A*e))*sqrt(b*x+c*x^2)/(b^2*c^2)],
[(A+B*x)*(d+e*x)/(b*x+c*x^2)^(3/2),x,3,2*B*e*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(3/2)-2*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*sqrt(b*x+c*x^2))],
[(A+B*x)/(b*x+c*x^2)^(3/2),x,1,-2*(A*b-(b*B-2*A*c)*x)/(b^2*sqrt(b*x+c*x^2))],
[(A+B*x)/((d+e*x)*(b*x+c*x^2)^(3/2)),x,4,-e*(B*d-A*e)*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(3/2)*(c*d-b*e)^(3/2))-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*sqrt(b*x+c*x^2))],
[(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^(3/2)),x,4,1/2*e*(3*A*e*(2*c*d-b*e)-B*d*(4*c*d-b*e))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(d+e*x)*sqrt(b*x+c*x^2))-e*(4*A*c^2*d^2-b^2*e*(B*d-3*A*e)-2*b*c*d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x))],
[(A+B*x)/((d+e*x)^3*(b*x+c*x^2)^(3/2)),x,5,-3/8*e*(B*d*(8*c^2*d^2-4*b*c*d*e+b^2*e^2)-A*e*(16*c^2*d^2-16*b*c*d*e+5*b^2*e^2))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(d+e*x)^2*sqrt(b*x+c*x^2))-1/2*e*(8*A*c^2*d^2-b^2*e*(B*d-5*A*e)-4*b*c*d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)^2)-1/4*e*(16*A*c^3*d^3-2*b^2*c*d*e*(5*B*d-19*A*e)+3*b^3*e^2*(B*d-5*A*e)-8*b*c^2*d^2*(B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^2*d^3*(c*d-b*e)^3*(d+e*x))],
[(A+B*x)*(d+e*x)^4/(b*x+c*x^2)^(5/2),x,5,-2/3*(d+e*x)^3*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*(b*x+c*x^2)^(3/2))+e^3*(8*B*c*d-5*b*B*e+2*A*c*e)*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(7/2)-2/3*(d+e*x)*(b*c*d^2*(4*b*B*c*d-8*A*c^2*d-b^2*B*e+10*A*b*c*e)-(16*A*c^4*d^3-5*b^4*B*e^3+4*b^2*c^2*d*e*(B*d+A*e)+2*b^3*c*e^2*(3*B*d+A*e)-8*b*c^3*d^2*(B*d+3*A*e))*x)/(b^4*c^2*sqrt(b*x+c*x^2))-1/3*e*(32*A*c^4*d^3-15*b^4*B*e^3+4*b^2*c^2*d*e*(2*B*d+A*e)-16*b*c^3*d^2*(B*d+3*A*e)+2*b^3*c*e^2*(7*B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^4*c^3)],
[(A+B*x)*(d+e*x)^3/(b*x+c*x^2)^(5/2),x,4,-2/3*(d+e*x)^2*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*(b*x+c*x^2)^(3/2))+2*B*e^3*arctanh(x*sqrt(c)/sqrt(b*x+c*x^2))/c^(5/2)+2/3*(b*c*d^2*(8*A*c^2*d+b^2*B*e-4*b*c*(B*d+2*A*e))+(16*A*c^4*d^3+2*b^3*B*c*d*e^2-3*b^4*B*e^3-8*b*c^3*d^2*(B*d+3*A*e)+2*b^2*c^2*d*e*(3*B*d+4*A*e))*x)/(b^4*c^2*sqrt(b*x+c*x^2))],
[(A+B*x)*(d+e*x)^2/(b*x+c*x^2)^(5/2),x,2,-2/3*(A*b-(b*B-2*A*c)*x)*(d+e*x)^2/(b^2*(b*x+c*x^2)^(3/2))-8/3*(b*B*d-2*A*c*d+A*b*e)*(b*d+(2*c*d-b*e)*x)/(b^4*sqrt(b*x+c*x^2))],
[(A+B*x)*(d+e*x)/(b*x+c*x^2)^(5/2),x,2,-2/3*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*(b*x+c*x^2)^(3/2))+2/3*(8*A*c^2*d+b^2*B*e-4*b*c*(B*d+A*e))*(b+2*c*x)/(b^4*c*sqrt(b*x+c*x^2))],
[(A+B*x)/(b*x+c*x^2)^(5/2),x,2,-2/3*(A*b-(b*B-2*A*c)*x)/(b^2*(b*x+c*x^2)^(3/2))-8/3*(b*B-2*A*c)*(b+2*c*x)/(b^4*sqrt(b*x+c*x^2))],
[(A+B*x)/((d+e*x)*(b*x+c*x^2)^(5/2)),x,5,-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(b*x+c*x^2)^(3/2))-e^3*(B*d-A*e)*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(5/2)*(c*d-b*e)^(5/2))+2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+3*b^2*e*(B*d-A*e)-4*b*c*d*(B*d+A*e))+c*(16*A*c^3*d^3-3*b^3*e^2*(B*d-A*e)+2*b^2*c*d*e*(7*B*d+A*e)-8*b*c^2*d^2*(B*d+3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*sqrt(b*x+c*x^2))],
[(A+B*x)/((d+e*x)^2*(b*x+c*x^2)^(5/2)),x,5,-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(d+e*x)*(b*x+c*x^2)^(3/2))-1/2*e^3*(B*d*(8*c*d-3*b*e)-5*A*e*(2*c*d-b*e))*arctanh(1/2*(b*d+(2*c*d-b*e)*x)/(sqrt(d)*sqrt(c*d-b*e)*sqrt(b*x+c*x^2)))/(d^(7/2)*(c*d-b*e)^(7/2))+2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+b^2*e*(3*B*d-5*A*e)-2*b*c*d*(2*B*d+A*e))+c*(16*A*c^3*d^3-b^3*e^2*(3*B*d-5*A*e)+2*b^2*c*d*e*(8*B*d-A*e)-8*b*c^2*d^2*(B*d+3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*(d+e*x)*sqrt(b*x+c*x^2))+1/3*e*(32*A*c^4*d^4-2*b^3*c*d*e^2*(9*B*d-10*A*e)+3*b^4*e^3*(3*B*d-5*A*e)+4*b^2*c^2*d^2*e*(10*B*d+3*A*e)-16*b*c^3*d^3*(B*d+4*A*e))*sqrt(b*x+c*x^2)/(b^4*d^3*(c*d-b*e)^3*(d+e*x))],

# Integrands of the form (d+e x)^(m/2) (A+B x) (b x+c x^2)^p

# p>0
[(A+B*x)*(d+e*x)^(7/2)*(b*x+c*x^2),x,2,-2/9*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(9/2)/e^4+2/11*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*(d+e*x)^(11/2)/e^4-2/13*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(13/2)/e^4+2/15*B*c*(d+e*x)^(15/2)/e^4],
[(A+B*x)*(d+e*x)^(5/2)*(b*x+c*x^2),x,2,-2/7*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(7/2)/e^4+2/9*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*(d+e*x)^(9/2)/e^4-2/11*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(11/2)/e^4+2/13*B*c*(d+e*x)^(13/2)/e^4],
[(A+B*x)*(d+e*x)^(3/2)*(b*x+c*x^2),x,2,-2/5*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(5/2)/e^4+2/7*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*(d+e*x)^(7/2)/e^4-2/9*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(9/2)/e^4+2/11*B*c*(d+e*x)^(11/2)/e^4],
[(A+B*x)*(d+e*x)^(1/2)*(b*x+c*x^2),x,2,-2/3*d*(B*d-A*e)*(c*d-b*e)*(d+e*x)^(3/2)/e^4+2/5*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*(d+e*x)^(5/2)/e^4-2/7*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(7/2)/e^4+2/9*B*c*(d+e*x)^(9/2)/e^4],
[(A+B*x)*(b*x+c*x^2)/(d+e*x)^(1/2),x,2,2/3*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*(d+e*x)^(3/2)/e^4-2/5*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(5/2)/e^4+2/7*B*c*(d+e*x)^(7/2)/e^4-2*d*(B*d-A*e)*(c*d-b*e)*sqrt(d+e*x)/e^4],
[(A+B*x)*(b*x+c*x^2)/(d+e*x)^(3/2),x,2,-2/3*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(3/2)/e^4+2/5*B*c*(d+e*x)^(5/2)/e^4+2*d*(B*d-A*e)*(c*d-b*e)/(e^4*sqrt(d+e*x))+2*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))*sqrt(d+e*x)/e^4],
[(A+B*x)*(b*x+c*x^2)/(d+e*x)^(5/2),x,2,2/3*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^(3/2))+2/3*B*c*(d+e*x)^(3/2)/e^4-2*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))/(e^4*sqrt(d+e*x))-2*(3*B*c*d-b*B*e-A*c*e)*sqrt(d+e*x)/e^4],
[(A+B*x)*(b*x+c*x^2)/(d+e*x)^(7/2),x,2,2/5*d*(B*d-A*e)*(c*d-b*e)/(e^4*(d+e*x)^(5/2))-2/3*(B*d*(3*c*d-2*b*e)-A*e*(2*c*d-b*e))/(e^4*(d+e*x)^(3/2))+2*(3*B*c*d-b*B*e-A*c*e)/(e^4*sqrt(d+e*x))+2*B*c*sqrt(d+e*x)/e^4],
[(A+B*x)*(d+e*x)^(7/2)*(b*x+c*x^2)^2,x,2,-2/9*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(9/2)/e^6+2/11*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(11/2)/e^6+2/13*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*(d+e*x)^(13/2)/e^6-2/15*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(15/2)/e^6-2/17*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(17/2)/e^6+2/19*B*c^2*(d+e*x)^(19/2)/e^6],
[(A+B*x)*(d+e*x)^(5/2)*(b*x+c*x^2)^2,x,2,-2/7*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(7/2)/e^6+2/9*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(9/2)/e^6+2/11*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*(d+e*x)^(11/2)/e^6-2/13*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(13/2)/e^6-2/15*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(15/2)/e^6+2/17*B*c^2*(d+e*x)^(17/2)/e^6],
[(A+B*x)*(d+e*x)^(3/2)*(b*x+c*x^2)^2,x,2,-2/5*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(5/2)/e^6+2/7*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(7/2)/e^6+2/9*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*(d+e*x)^(9/2)/e^6-2/11*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(11/2)/e^6-2/13*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(13/2)/e^6+2/15*B*c^2*(d+e*x)^(15/2)/e^6],
[(A+B*x)*(d+e*x)^(1/2)*(b*x+c*x^2)^2,x,2,-2/3*d^2*(B*d-A*e)*(c*d-b*e)^2*(d+e*x)^(3/2)/e^6+2/5*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(5/2)/e^6+2/7*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*(d+e*x)^(7/2)/e^6-2/9*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(9/2)/e^6-2/11*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(11/2)/e^6+2/13*B*c^2*(d+e*x)^(13/2)/e^6],
[(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(1/2),x,2,2/3*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*(d+e*x)^(3/2)/e^6+2/5*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*(d+e*x)^(5/2)/e^6-2/7*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(7/2)/e^6-2/9*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(9/2)/e^6+2/11*B*c^2*(d+e*x)^(11/2)/e^6-2*d^2*(B*d-A*e)*(c*d-b*e)^2*sqrt(d+e*x)/e^6],
[(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(3/2),x,2,2/3*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*(d+e*x)^(3/2)/e^6-2/5*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(5/2)/e^6-2/7*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(7/2)/e^6+2/9*B*c^2*(d+e*x)^(9/2)/e^6+2*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*sqrt(d+e*x))+2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))*sqrt(d+e*x)/e^6],
[(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(5/2),x,2,2/3*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^(3/2))-2/3*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*(d+e*x)^(3/2)/e^6-2/5*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(5/2)/e^6+2/7*B*c^2*(d+e*x)^(7/2)/e^6-2*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*sqrt(d+e*x))+2*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))*sqrt(d+e*x)/e^6],
[(A+B*x)*(b*x+c*x^2)^2/(d+e*x)^(7/2),x,2,2/5*d^2*(B*d-A*e)*(c*d-b*e)^2/(e^6*(d+e*x)^(5/2))-2/3*d*(c*d-b*e)*(B*d*(5*c*d-3*b*e)-2*A*e*(2*c*d-b*e))/(e^6*(d+e*x)^(3/2))-2/3*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(3/2)/e^6+2/5*B*c^2*(d+e*x)^(5/2)/e^6-2*(A*e*(6*c^2*d^2-6*b*c*d*e+b^2*e^2)-B*d*(10*c^2*d^2-12*b*c*d*e+3*b^2*e^2))/(e^6*sqrt(d+e*x))-2*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2-8*b*c*d*e+b^2*e^2))*sqrt(d+e*x)/e^6],

# p<0
[(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2),x,8,2/3*(B*(c*d-b*e)^2+A*c*e*(2*c*d-b*e))*(d+e*x)^(3/2)/c^3+2/5*(B*c*d-b*B*e+A*c*e)*(d+e*x)^(5/2)/c^2+2/7*B*(d+e*x)^(7/2)/c-2*A*d^(7/2)*arctanh(sqrt(d+e*x)/sqrt(d))/b-2*(b*B-A*c)*(c*d-b*e)^(7/2)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(9/2))+2*(B*(c*d-b*e)^3+A*c*e*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))*sqrt(d+e*x)/c^4],
[(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2),x,7,2/3*(B*c*d-b*B*e+A*c*e)*(d+e*x)^(3/2)/c^2+2/5*B*(d+e*x)^(5/2)/c-2*A*d^(5/2)*arctanh(sqrt(d+e*x)/sqrt(d))/b-2*(b*B-A*c)*(c*d-b*e)^(5/2)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(7/2))+2*(B*(c*d-b*e)^2+A*c*e*(2*c*d-b*e))*sqrt(d+e*x)/c^3],
[(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2),x,6,2/3*B*(d+e*x)^(3/2)/c-2*A*d^(3/2)*arctanh(sqrt(d+e*x)/sqrt(d))/b-2*(b*B-A*c)*(c*d-b*e)^(3/2)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*c^(5/2))+2*(B*c*d-b*B*e+A*c*e)*sqrt(d+e*x)/c^2],
[(A+B*x)*(d+e*x)^(1/2)/(b*x+c*x^2),x,5,-2*A*arctanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b-2*(b*B-A*c)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c*d-b*e)/(b*c^(3/2))+2*B*sqrt(d+e*x)/c],
[(A+B*x)/((d+e*x)^(1/2)*(b*x+c*x^2)),x,4,-2*A*arctanh(sqrt(d+e*x)/sqrt(d))/(b*sqrt(d))-2*(b*B-A*c)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*sqrt(c)*sqrt(c*d-b*e))],
[(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)),x,5,-2*A*arctanh(sqrt(d+e*x)/sqrt(d))/(b*d^(3/2))-2*(b*B-A*c)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c)/(b*(c*d-b*e)^(3/2))+2*(B*d-A*e)/(d*(c*d-b*e)*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)),x,6,2/3*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(3/2))-2*A*arctanh(sqrt(d+e*x)/sqrt(d))/(b*d^(5/2))-2*c^(3/2)*(b*B-A*c)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*(c*d-b*e)^(5/2))+2*(B*c*d^2-A*e*(2*c*d-b*e))/(d^2*(c*d-b*e)^2*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(7/2)*(b*x+c*x^2)),x,7,2/5*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(5/2))+2/3*(B*c*d^2-A*e*(2*c*d-b*e))/(d^2*(c*d-b*e)^2*(d+e*x)^(3/2))-2*A*arctanh(sqrt(d+e*x)/sqrt(d))/(b*d^(7/2))-2*c^(5/2)*(b*B-A*c)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*(c*d-b*e)^(7/2))+2*(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))/(d^3*(c*d-b*e)^3*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(9/2)*(b*x+c*x^2)),x,8,2/7*(B*d-A*e)/(d*(c*d-b*e)*(d+e*x)^(7/2))+2/5*(B*c*d^2-A*e*(2*c*d-b*e))/(d^2*(c*d-b*e)^2*(d+e*x)^(5/2))+2/3*(B*c^2*d^3-A*e*(3*c^2*d^2-3*b*c*d*e+b^2*e^2))/(d^3*(c*d-b*e)^3*(d+e*x)^(3/2))-2*A*arctanh(sqrt(d+e*x)/sqrt(d))/(b*d^(9/2))-2*c^(7/2)*(b*B-A*c)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b*(c*d-b*e)^(9/2))+2*(B*c^3*d^4-A*e*(4*c^3*d^3-6*b*c^2*d^2*e+4*b^2*c*d*e^2-b^3*e^3))/(d^4*(c*d-b*e)^4*sqrt(d+e*x))],
[(A+B*x)*(d+e*x)^(9/2)/(b*x+c*x^2)^2,x,8,1/3*e*(6*A*c^3*d^2-7*b^3*B*e^2-3*b*c^2*d*(B*d+2*A*e)+b^2*c*e*(12*B*d+5*A*e))*(d+e*x)^(3/2)/(b^2*c^3)+1/5*e*(10*A*c^2*d+7*b^2*B*e-5*b*c*(B*d+A*e))*(d+e*x)^(5/2)/(b^2*c^2)-(d+e*x)^(7/2)*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*(b*x+c*x^2))-d^(7/2)*(2*b*B*d-4*A*c*d+9*A*b*e)*arctanh(sqrt(d+e*x)/sqrt(d))/b^3-(c*d-b*e)^(7/2)*(4*A*c^2*d-7*b^2*B*e-b*c*(2*B*d-5*A*e))*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(9/2))+e*(2*A*c^4*d^3+7*b^4*B*e^3-b*c^3*d^2*(B*d+3*A*e)-b^3*c*e^2*(19*B*d+5*A*e)+b^2*c^2*d*e*(15*B*d+11*A*e))*sqrt(d+e*x)/(b^2*c^4)],
[(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^2,x,7,1/3*e*(6*A*c^2*d+5*b^2*B*e-3*b*c*(B*d+A*e))*(d+e*x)^(3/2)/(b^2*c^2)-(d+e*x)^(5/2)*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*(b*x+c*x^2))-d^(5/2)*(2*b*B*d-4*A*c*d+7*A*b*e)*arctanh(sqrt(d+e*x)/sqrt(d))/b^3+(c*d-b*e)^(5/2)*(2*b*B*c*d-4*A*c^2*d+5*b^2*B*e-3*A*b*c*e)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(7/2))+e*(2*A*c^3*d^2-5*b^3*B*e^2-b*c^2*d*(B*d+2*A*e)+b^2*c*e*(8*B*d+3*A*e))*sqrt(d+e*x)/(b^2*c^3)],
[(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^2,x,6,-(d+e*x)^(3/2)*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*(b*x+c*x^2))-d^(3/2)*(2*b*B*d-4*A*c*d+5*A*b*e)*arctanh(sqrt(d+e*x)/sqrt(d))/b^3-(c*d-b*e)^(3/2)*(4*A*c^2*d-3*b^2*B*e-b*c*(2*B*d-A*e))*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*c^(5/2))+e*(2*A*c^2*d+3*b^2*B*e-b*c*(B*d+A*e))*sqrt(d+e*x)/(b^2*c^2)],
[(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^2,x,5,-(2*b*B*d-4*A*c*d+3*A*b*e)*arctanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b^3-(4*A*c^2*d-b^2*B*e-b*c*(2*B*d+A*e))*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c*d-b*e)/(b^3*c^(3/2))-(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)*sqrt(d+e*x)/(b^2*c*(b*x+c*x^2))],
[(A+B*x)*(d+e*x)^(1/2)/(b*x+c*x^2)^2,x,5,-(2*b*B*d-4*A*c*d+A*b*e)*arctanh(sqrt(d+e*x)/sqrt(d))/(b^3*sqrt(d))+(2*b*B*c*d-4*A*c^2*d-b^2*B*e+3*A*b*c*e)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*sqrt(c)*sqrt(c*d-b*e))-(A*b-(b*B-2*A*c)*x)*sqrt(d+e*x)/(b^2*(b*x+c*x^2))],
[(A+B*x)/((d+e*x)^(1/2)*(b*x+c*x^2)^2),x,5,-(2*b*B*d-4*A*c*d-A*b*e)*arctanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(3/2))+(2*b*B*c*d-4*A*c^2*d-3*b^2*B*e+5*A*b*c*e)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c)/(b^3*(c*d-b*e)^(3/2))-(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)*sqrt(d+e*x)/(b^2*d*(c*d-b*e)*(b*x+c*x^2))],
[(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^2),x,6,-(2*b*B*d-4*A*c*d-3*A*b*e)*arctanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(5/2))+c^(3/2)*(2*b*B*c*d-4*A*c^2*d-5*b^2*B*e+7*A*b*c*e)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*(c*d-b*e)^(5/2))-e*(2*A*c^2*d^2-b^2*e*(2*B*d-3*A*e)-b*c*d*(B*d+2*A*e))/(b^2*d^2*(c*d-b*e)^2*sqrt(d+e*x))+(-A*b*(c*d-b*e)-c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(b*x+c*x^2)*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^2),x,7,-1/3*e*(6*A*c^2*d^2-b^2*e*(2*B*d-5*A*e)-3*b*c*d*(B*d+2*A*e))/(b^2*d^2*(c*d-b*e)^2*(d+e*x)^(3/2))+(-A*b*(c*d-b*e)-c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(d+e*x)^(3/2)*(b*x+c*x^2))-(2*b*B*d-4*A*c*d-5*A*b*e)*arctanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(7/2))+c^(5/2)*(2*b*B*c*d-4*A*c^2*d-7*b^2*B*e+9*A*b*c*e)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*(c*d-b*e)^(7/2))-e*(2*A*c^3*d^3-b^2*c*d*e*(6*B*d-11*A*e)+b^3*e^2*(2*B*d-5*A*e)-b*c^2*d^2*(B*d+3*A*e))/(b^2*d^3*(c*d-b*e)^3*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(7/2)*(b*x+c*x^2)^2),x,8,-1/5*e*(10*A*c^2*d^2-b^2*e*(2*B*d-7*A*e)-5*b*c*d*(B*d+2*A*e))/(b^2*d^2*(c*d-b*e)^2*(d+e*x)^(5/2))-1/3*e*(6*A*c^3*d^3-b^2*c*d*e*(6*B*d-17*A*e)+b^3*e^2*(2*B*d-7*A*e)-3*b*c^2*d^2*(B*d+3*A*e))/(b^2*d^3*(c*d-b*e)^3*(d+e*x)^(3/2))+(-A*b*(c*d-b*e)-c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(d+e*x)^(5/2)*(b*x+c*x^2))-(2*b*B*d-4*A*c*d-7*A*b*e)*arctanh(sqrt(d+e*x)/sqrt(d))/(b^3*d^(9/2))+c^(7/2)*(2*b*B*c*d-4*A*c^2*d-9*b^2*B*e+11*A*b*c*e)*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^3*(c*d-b*e)^(9/2))-e*(2*A*c^4*d^4-2*b^2*c^2*d^2*e*(6*B*d-13*A*e)-b^4*e^3*(2*B*d-7*A*e)+8*b^3*c*d*e^2*(B*d-3*A*e)-b*c^3*d^3*(B*d+4*A*e))/(b^2*d^4*(c*d-b*e)^4*sqrt(d+e*x))],
[(A+B*x)*(d+e*x)^(9/2)/(b*x+c*x^2)^3,x,7,-1/2*(d+e*x)^(7/2)*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*(b*x+c*x^2)^2)+1/4*(d+e*x)^(3/2)*(b*c*d^2*(12*A*c^2*d+2*b^2*B*e-b*c*(6*B*d+13*A*e))+(24*A*c^4*d^3-5*b^4*B*e^3+b^3*c*e^2*(4*B*d+A*e)-12*b*c^3*d^2*(B*d+3*A*e)+b^2*c^2*d*e*(9*B*d+10*A*e))*x)/(b^4*c^2*(b*x+c*x^2))-3/4*d^(5/2)*(16*A*c^2*d^2+3*b^2*e*(4*B*d+7*A*e)-4*b*c*d*(2*B*d+9*A*e))*arctanh(sqrt(d+e*x)/sqrt(d))/b^5+3/4*(c*d-b*e)^(5/2)*(16*A*c^3*d^2-5*b^3*B*e^2-4*b*c^2*d*(2*B*d-A*e)-b^2*c*e*(8*B*d-A*e))*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*c^(7/2))-3/4*e*(8*A*c^4*d^3-5*b^4*B*e^3+b^3*c*e^2*(2*B*d+A*e)+b^2*c^2*d*e*(3*B*d+2*A*e)-4*b*c^3*d^2*(B*d+3*A*e))*sqrt(d+e*x)/(b^4*c^3)],
[(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^3,x,6,-1/2*(d+e*x)^(5/2)*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*(b*x+c*x^2)^2)-1/4*d^(3/2)*(48*A*c^2*d^2+7*b^2*e*(4*B*d+5*A*e)-12*b*c*d*(2*B*d+7*A*e))*arctanh(sqrt(d+e*x)/sqrt(d))/b^5+1/4*(c*d-b*e)^(3/2)*(48*A*c^3*d^2-3*b^3*B*e^2-12*b*c^2*d*(2*B*d+A*e)-b^2*c*e*(8*B*d+A*e))*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*c^(5/2))+1/4*(b*c*d^2*(12*A*c^2*d+2*b^2*B*e-b*c*(6*B*d+11*A*e))+(24*A*c^4*d^3-3*b^4*B*e^3-A*b^3*c*e^3-12*b*c^3*d^2*(B*d+3*A*e)+b^2*c^2*d*e*(11*B*d+14*A*e))*x)*sqrt(d+e*x)/(b^4*c^2*(b*x+c*x^2))],
[(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^3,x,6,-1/2*(d+e*x)^(3/2)*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*(b*x+c*x^2)^2)-1/4*(48*A*c^2*d^2+5*b^2*e*(4*B*d+3*A*e)-12*b*c*d*(2*B*d+5*A*e))*arctanh(sqrt(d+e*x)/sqrt(d))*sqrt(d)/b^5+1/4*(48*A*c^3*d^2+b^3*B*e^2-12*b*c^2*d*(2*B*d+3*A*e)+b^2*c*e*(8*B*d+3*A*e))*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c*d-b*e)/(b^5*c^(3/2))-1/4*(b*d*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+9*A*b*c*e)-(24*A*c^3*d^2+b^3*B*e^2-12*b*c^2*d*(B*d+2*A*e)+b^2*c*e*(7*B*d+3*A*e))*x)*sqrt(d+e*x)/(b^4*c*(b*x+c*x^2))],
[(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^3,x,6,-3/4*(16*A*c^2*d^2+b^2*e*(4*B*d+A*e)-4*b*c*d*(2*B*d+3*A*e))*arctanh(sqrt(d+e*x)/sqrt(d))/(b^5*sqrt(d))+3/4*(16*A*c^3*d^2-b^3*B*e^2-4*b*c^2*d*(2*B*d+5*A*e)+b^2*c*e*(8*B*d+5*A*e))*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*sqrt(c)*sqrt(c*d-b*e))-1/2*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)*sqrt(d+e*x)/(b^2*c*(b*x+c*x^2)^2)-1/4*(b*(c*d-b*e)*(6*b*B*c*d-12*A*c^2*d-2*b^2*B*e+7*A*b*c*e)-3*c*(c*d-b*e)*(8*A*c^2*d+b^2*B*e-4*b*c*(B*d+A*e))*x)*sqrt(d+e*x)/(b^4*c*(c*d-b*e)*(b*x+c*x^2))],
[(A+B*x)*(d+e*x)^(1/2)/(b*x+c*x^2)^3,x,6,-1/4*(48*A*c^2*d^2+b^2*e*(4*B*d-A*e)-12*b*c*d*(2*B*d+A*e))*arctanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(3/2))+1/4*(48*A*c^3*d^2-15*b^3*B*e^2-12*b*c^2*d*(2*B*d+7*A*e)+5*b^2*c*e*(8*B*d+7*A*e))*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))*sqrt(c)/(b^5*(c*d-b*e)^(3/2))-1/2*(A*b-(b*B-2*A*c)*x)*sqrt(d+e*x)/(b^2*(b*x+c*x^2)^2)-1/4*(b*(c*d-b*e)*(6*b*B*d-12*A*c*d+A*b*e)-c*(24*A*c^2*d^2+b^2*e*(11*B*d+A*e)-12*b*c*d*(B*d+2*A*e))*x)*sqrt(d+e*x)/(b^4*d*(c*d-b*e)*(b*x+c*x^2))],
[(A+B*x)/((d+e*x)^(1/2)*(b*x+c*x^2)^3),x,6,-1/4*(48*A*c^2*d^2-b^2*e*(4*B*d-3*A*e)-12*b*c*d*(2*B*d-A*e))*arctanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(5/2))+1/4*c^(3/2)*(48*A*c^3*d^2-35*b^3*B*e^2-12*b*c^2*d*(2*B*d+9*A*e)+7*b^2*c*e*(8*B*d+9*A*e))*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(5/2))-1/2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)*sqrt(d+e*x)/(b^2*d*(c*d-b*e)*(b*x+c*x^2)^2)+1/4*(b*(c*d-b*e)*(12*A*c^2*d^2+b^2*e*(4*B*d-3*A*e)-b*c*d*(6*B*d+7*A*e))+c*(24*A*c^3*d^3-b^3*e^2*(4*B*d-3*A*e)-12*b*c^2*d^2*(B*d+3*A*e)+b^2*c*d*e*(19*B*d+6*A*e))*x)*sqrt(d+e*x)/(b^4*d^2*(c*d-b*e)^2*(b*x+c*x^2))],
[(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^3),x,7,-3/4*(16*A*c^2*d^2-b^2*e*(4*B*d-5*A*e)-4*b*c*d*(2*B*d-3*A*e))*arctanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(7/2))+3/4*c^(5/2)*(16*A*c^3*d^2-21*b^3*B*e^2-4*b*c^2*d*(2*B*d+11*A*e)+3*b^2*c*e*(8*B*d+11*A*e))*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(7/2))+3/4*e*(8*A*c^4*d^4+b^4*e^3*(4*B*d-5*A*e)-b^3*c*d*e^2*(4*B*d-3*A*e)-4*b*c^3*d^3*(B*d+4*A*e)+b^2*c^2*d^2*e*(9*B*d+5*A*e))/(b^4*d^3*(c*d-b*e)^3*sqrt(d+e*x))+1/2*(-A*b*(c*d-b*e)-c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(b*x+c*x^2)^2*sqrt(d+e*x))+1/4*(b*(c*d-b*e)*(12*A*c^2*d^2+b^2*e*(4*B*d-5*A*e)-b*c*d*(6*B*d+5*A*e))+c*(24*A*c^3*d^3-b^3*e^2*(4*B*d-5*A*e)+b^2*c*d*e*(21*B*d+2*A*e)-12*b*c^2*d^2*(B*d+3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*(b*x+c*x^2)*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^3),x,8,1/12*e*(72*A*c^4*d^4+5*b^4*e^3*(4*B*d-7*A*e)-9*b^3*c*d*e^2*(4*B*d-5*A*e)-36*b*c^3*d^3*(B*d+4*A*e)+3*b^2*c^2*d^2*e*(29*B*d+9*A*e))/(b^4*d^3*(c*d-b*e)^3*(d+e*x)^(3/2))+1/2*(-A*b*(c*d-b*e)-c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(d+e*x)^(3/2)*(b*x+c*x^2)^2)+1/4*(b*(c*d-b*e)*(12*A*c^2*d^2+b^2*e*(4*B*d-7*A*e)-3*b*c*d*(2*B*d+A*e))+c*(24*A*c^3*d^3-b^3*e^2*(4*B*d-7*A*e)+b^2*c*d*e*(23*B*d-2*A*e)-12*b*c^2*d^2*(B*d+3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*(d+e*x)^(3/2)*(b*x+c*x^2))-1/4*(48*A*c^2*d^2-5*b^2*e*(4*B*d-7*A*e)-12*b*c*d*(2*B*d-5*A*e))*arctanh(sqrt(d+e*x)/sqrt(d))/(b^5*d^(9/2))+1/4*c^(7/2)*(48*A*c^3*d^2-99*b^3*B*e^2-12*b*c^2*d*(2*B*d+13*A*e)+11*b^2*c*e*(8*B*d+13*A*e))*arctanh(sqrt(c)*sqrt(d+e*x)/sqrt(c*d-b*e))/(b^5*(c*d-b*e)^(9/2))+1/4*e*(24*A*c^5*d^5+8*b^4*c*d*e^3*(7*B*d-10*A*e)-5*b^5*e^4*(4*B*d-7*A*e)-6*b^3*c^2*d^2*e^2*(4*B*d-3*A*e)+7*b^2*c^3*d^3*e*(5*B*d+4*A*e)-12*b*c^4*d^4*(B*d+5*A*e))/(b^4*d^4*(c*d-b*e)^4*sqrt(d+e*x))],

# Integrands of the form (d+e x)^(m/2) (A+B x) (b x+c x^2)^(p/2)

# p<0
[(A+B*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2),x,9,2/7*B*(b*x+c*x^2)^(3/2)*sqrt(d+e*x)/c+2/105*(5*c*(3*b*B-7*A*c)*d*e*(2*c*d-b*e)+(B*c*d-4*b*B*e+7*A*c*e)*(8*c^2*d^2-3*b*c*d*e-2*b^2*e^2))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(c^(5/2)*e^3*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2/105*d*(c*d-b*e)*(7*A*c*e*(2*c*d-b*e)-B*(8*c^2*d^2-b*c*d*e-4*b^2*e^2))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(c^(5/2)*e^3*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/105*(7*A*c*e*(c*d+b*e)-B*(4*c^2*d^2-2*b*c*d*e+4*b^2*e^2)+3*c*e*(B*c*d-4*b*B*e+7*A*c*e)*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^2*e^2)],
[(A+B*x)*sqrt(b*x+c*x^2)/sqrt(d+e*x),x,8,-2/15*(5*A*c*e*(2*c*d-b*e)-B*(8*c^2*d^2-3*b*c*d*e-2*b^2*e^2))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(c^(3/2)*e^3*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))-2/15*d*(c*d-b*e)*(8*B*c*d+b*B*e-10*A*c*e)*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(c^(3/2)*e^3*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(4*B*c*d-b*B*e-5*A*c*e-3*B*c*e*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c*e^2)],
[(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(3/2),x,8,-2/3*(8*B*c*d-b*B*e-6*A*c*e)*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(e^3*sqrt(c)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2/3*(B*d*(8*c*d-5*b*e)-3*A*e*(2*c*d-b*e))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(e^3*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*(4*B*d-3*A*e+B*e*x)*sqrt(b*x+c*x^2)/(e^2*sqrt(d+e*x))],
[(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(5/2),x,8,2/3*(B*d*(8*c*d-7*b*e)-A*e*(2*c*d-b*e))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(d*e^3*(c*d-b*e)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))-2/3*(8*B*c*d-3*b*B*e-2*A*c*e)*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(e^3*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*(d^2*(4*B*c*d-3*b*B*e-A*c*e)+e*(B*d*(5*c*d-4*b*e)-A*e*(2*c*d-b*e))*x)*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+e*x)^(3/2))],
[(A+B*x)*sqrt(b*x+c*x^2)/(d+e*x)^(7/2),x,9,-2/15*(2*A*e*(c^2*d^2-b*c*d*e+b^2*e^2)+B*d*(8*c^2*d^2-13*b*c*d*e+3*b^2*e^2))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(d^2*e^3*(c*d-b*e)^2*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2/15*(B*d*(8*c*d-9*b*e)+A*e*(2*c*d-b*e))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(d*e^3*(c*d-b*e)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(d*(B*d*(4*c*d-3*b*e)+A*e*(c*d-2*b*e))+e*(B*d*(7*c*d-6*b*e)-A*e*(2*c*d-b*e))*x)*sqrt(b*x+c*x^2)/(d*e^2*(c*d-b*e)*(d+e*x)^(5/2))+2/15*(2*A*e*(c^2*d^2-b*c*d*e+b^2*e^2)+B*d*(8*c^2*d^2-13*b*c*d*e+3*b^2*e^2))*sqrt(b*x+c*x^2)/(d^2*e^2*(c*d-b*e)^2*sqrt(d+e*x))],
[(A+B*x)*(b*x+c*x^2)^(3/2)/sqrt(d+e*x),x,9,-2/63*(8*B*c*d-3*b*B*e-9*A*c*e-7*B*c*e*x)*(b*x+c*x^2)^(3/2)*sqrt(d+e*x)/(c*e^2)-2/315*(5*b*c*d*e*(2*c*d-b*e)*(8*B*c*d-3*b*B*e-9*A*c*e)+(8*c^2*d^2-3*b*c*d*e-2*b^2*e^2)*(9*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-7*b*c*d*e-4*b^2*e^2)))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(c^(5/2)*e^5*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2/315*d*(c*d-b*e)*(9*A*c*e*(16*c^2*d^2-16*b*c*d*e-b^2*e^2)-B*(128*c^3*d^3-120*b*c^2*d^2*e-9*b^2*c*d*e^2-4*b^3*e^3))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(c^(5/2)*e^5*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/315*(9*A*c*e*(8*c^2*d^2-11*b*c*d*e+b^2*e^2)-2*B*(32*c^3*d^3-42*b*c^2*d^2*e+3*b^2*c*d*e^2+2*b^3*e^3)-3*c*e*(9*A*c*e*(2*c*d-b*e)-B*(16*c^2*d^2-7*b*c*d*e-4*b^2*e^2))*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c^2*e^4)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(3/2),x,9,2/7*(8*B*d-7*A*e+B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+2/35*(5*b*c*e*(8*B*d-7*A*e)*(2*c*d-b*e)-(16*B*c*d-b*B*e-14*A*c*e)*(8*c^2*d^2-3*b*c*d*e-2*b^2*e^2))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(c^(3/2)*e^5*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))-2/35*d*(c*d-b*e)*(56*A*c*e*(2*c*d-b*e)-B*(128*c^2*d^2-72*b*c*d*e-b^2*e^2))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(c^(3/2)*e^5*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/35*(7*A*c*e*(8*c*d-7*b*e)-B*(64*c^2*d^2-60*b*c*d*e+b^2*e^2)+3*c*e*(16*B*c*d-b*B*e-14*A*c*e)*x)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(c*e^4)],
[(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(5/2),x,9,2/15*(8*B*d-5*A*e+3*B*e*x)*(b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-2/15*(40*A*c*e*(2*c*d-b*e)-B*(128*c^2*d^2-88*b*c*d*e+3*b^2*e^2))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(e^5*sqrt(c)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2/15*(5*A*e*(16*c^2*d^2-16*b*c*d*e+3*b^2*e^2)-B*d*(128*c^2*d^2-152*b*c*d*e+39*b^2*e^2))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(e^5*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(4*B*d*(16*c*d-9*b*e)-5*A*e*(8*c*d-3*b*e)+e*(16*B*c*d-3*b*B*e-10*A*c*e)*x)*sqrt(b*x+c*x^2)/(e^4*sqrt(d+e*x))],
[(A+B*x)*(b*x+c*x^2)^(3/2)/(d+e*x)^(7/2),x,9,-2/15*(d^2*(8*B*c*d-5*b*B*e-3*A*c*e)+e*(B*d*(11*c*d-8*b*e)-3*A*e*(2*c*d-b*e))*x)*(b*x+c*x^2)^(3/2)/(d*e^2*(c*d-b*e)*(d+e*x)^(5/2))+2/15*(3*A*e*(16*c^2*d^2-16*b*c*d*e+b^2*e^2)-B*d*(128*c^2*d^2-168*b*c*d*e+43*b^2*e^2))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(d*e^5*(c*d-b*e)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))-2/15*(24*A*c*e*(2*c*d-b*e)-B*(128*c^2*d^2-104*b*c*d*e+15*b^2*e^2))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(e^5*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/15*(d*(3*A*c*e*(8*c*d-7*b*e)-B*(64*c^2*d^2-76*b*c*d*e+15*b^2*e^2))-c*e*(B*d*(16*c*d-13*b*e)-3*A*e*(2*c*d-b*e))*x)*sqrt(b*x+c*x^2)/(d*e^4*(c*d-b*e)*sqrt(d+e*x))],

# p<0
[(A+B*x)*(d+e*x)^(5/2)/sqrt(b*x+c*x^2),x,10,2/105*(7*A*c*e*(23*c^2*d^2-23*b*c*d*e+8*b^2*e^2)+B*(15*c^3*d^3-103*b*c^2*d^2*e+128*b^2*c*d*e^2-48*b^3*e^3))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(c^(7/2)*e*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))-2/105*d*(c*d-b*e)*(28*A*c*e*(2*c*d-b*e)+B*(15*c^2*d^2-43*b*c*d*e+24*b^2*e^2))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(c^(7/2)*e*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/35*(5*B*c*d-6*b*B*e+7*A*c*e)*(d+e*x)^(3/2)*sqrt(b*x+c*x^2)/c^2+2/7*B*(d+e*x)^(5/2)*sqrt(b*x+c*x^2)/c+2/105*(28*A*c*e*(2*c*d-b*e)+B*(15*c^2*d^2-43*b*c*d*e+24*b^2*e^2))*sqrt(d+e*x)*sqrt(b*x+c*x^2)/c^3],
[(A+B*x)*(d+e*x)^(3/2)/sqrt(b*x+c*x^2),x,9,2/15*(10*A*c*e*(2*c*d-b*e)+B*(3*c^2*d^2-13*b*c*d*e+8*b^2*e^2))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(c^(5/2)*e*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))-2/15*d*(c*d-b*e)*(3*B*c*d-4*b*B*e+5*A*c*e)*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(c^(5/2)*e*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/5*B*(d+e*x)^(3/2)*sqrt(b*x+c*x^2)/c+2/15*(3*B*c*d-4*b*B*e+5*A*c*e)*sqrt(d+e*x)*sqrt(b*x+c*x^2)/c^2],
[(A+B*x)*sqrt(d+e*x)/sqrt(b*x+c*x^2),x,8,2/3*(B*c*d-2*b*B*e+3*A*c*e)*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(c^(3/2)*e*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))-2/3*B*d*(c*d-b*e)*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(c^(3/2)*e*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*B*sqrt(d+e*x)*sqrt(b*x+c*x^2)/c],
[(A+B*x)/(sqrt(d+e*x)*sqrt(b*x+c*x^2)),x,7,2*B*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(e*sqrt(c)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))-2*(B*d-A*e)*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(e*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))],
[(A+B*x)/((d+e*x)^(3/2)*sqrt(b*x+c*x^2)),x,8,-2*(B*d-A*e)*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(d*e*(c*d-b*e)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2*B*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(e*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(5/2)*sqrt(b*x+c*x^2)),x,9,2/3*(2*A*e*(2*c*d-b*e)-B*d*(c*d+b*e))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(d^2*e*(c*d-b*e)^2*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2/3*(B*d-A*e)*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(d*e*(c*d-b*e)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)^(3/2))-2/3*(2*A*e*(2*c*d-b*e)-B*d*(c*d+b*e))*sqrt(b*x+c*x^2)/(d^2*(c*d-b*e)^2*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(7/2)*sqrt(b*x+c*x^2)),x,10,-2/15*(B*d*(3*c^2*d^2+7*b*c*d*e-2*b^2*e^2)-A*e*(23*c^2*d^2-23*b*c*d*e+8*b^2*e^2))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/(d^3*e*(c*d-b*e)^3*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))-2/15*(4*A*e*(2*c*d-b*e)-B*d*(3*c*d+b*e))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(-b)*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/(d^2*e*(c*d-b*e)^2*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/5*(B*d-A*e)*sqrt(b*x+c*x^2)/(d*(c*d-b*e)*(d+e*x)^(5/2))-2/15*(4*A*e*(2*c*d-b*e)-B*d*(3*c*d+b*e))*sqrt(b*x+c*x^2)/(d^2*(c*d-b*e)^2*(d+e*x)^(3/2))+2/15*(B*d*(3*c^2*d^2+7*b*c*d*e-2*b^2*e^2)-A*e*(23*c^2*d^2-23*b*c*d*e+8*b^2*e^2))*sqrt(b*x+c*x^2)/(d^3*(c*d-b*e)^3*sqrt(d+e*x))],
[(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^(3/2),x,10,-2*(d+e*x)^(5/2)*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*sqrt(b*x+c*x^2))+2/15*(30*A*c^4*d^3+48*b^4*B*e^3-15*b*c^3*d^2*(B*d+3*A*e)-8*b^3*c*e^2*(16*B*d+5*A*e)+b^2*c^2*d*e*(103*B*d+95*A*e))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/((-b)^(3/2)*c^(7/2)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))-2/15*d*(c*d-b*e)*(30*A*c^3*d^2-24*b^3*B*e^2-15*b*c^2*d*(B*d+2*A*e)+b^2*c*e*(43*B*d+20*A*e))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/((-b)^(3/2)*c^(7/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/5*e*(10*A*c^2*d+6*b^2*B*e-5*b*c*(B*d+A*e))*(d+e*x)^(3/2)*sqrt(b*x+c*x^2)/(b^2*c^2)+2/15*e*(30*A*c^3*d^2-24*b^3*B*e^2-15*b*c^2*d*(B*d+2*A*e)+b^2*c*e*(43*B*d+20*A*e))*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^2*c^3)],
[(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^(3/2),x,9,-2*(d+e*x)^(3/2)*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*sqrt(b*x+c*x^2))+2/3*(6*A*c^3*d^2-8*b^3*B*e^2-3*b*c^2*d*(B*d+2*A*e)+b^2*c*e*(13*B*d+6*A*e))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/((-b)^(3/2)*c^(5/2)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))-2/3*d*(c*d-b*e)*(6*A*c^2*d+4*b^2*B*e-3*b*c*(B*d+A*e))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/((-b)^(3/2)*c^(5/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(6*A*c^2*d+4*b^2*B*e-3*b*c*(B*d+A*e))*sqrt(d+e*x)*sqrt(b*x+c*x^2)/(b^2*c^2)],
[(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^(3/2),x,8,-2*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)*sqrt(d+e*x)/(b^2*c*sqrt(b*x+c*x^2))+2*(2*A*c^2*d+2*b^2*B*e-b*c*(B*d+A*e))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/((-b)^(3/2)*c^(3/2)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2*(b*B-2*A*c)*d*(c*d-b*e)*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/((-b)^(3/2)*c^(3/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))],
[(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^(3/2),x,8,-2*(A*b-(b*B-2*A*c)*x)*sqrt(d+e*x)/(b^2*sqrt(b*x+c*x^2))-2*(b*B-2*A*c)*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/((-b)^(3/2)*sqrt(c)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2*(b*B*d-2*A*c*d+A*b*e)*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/((-b)^(3/2)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))],
[(A+B*x)/((b*x+c*x^2)^(3/2)*sqrt(d+e*x)),x,8,-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)*sqrt(d+e*x)/(b^2*d*(c*d-b*e)*sqrt(b*x+c*x^2))-2*(b*B*d-2*A*c*d+A*b*e)*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/((-b)^(3/2)*d*(c*d-b*e)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2*(b*B-2*A*c)*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/((-b)^(3/2)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))],
[(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^(3/2)),x,9,-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2*(2*A*c^2*d^2-b^2*e*(B*d-2*A*e)-b*c*d*(B*d+2*A*e))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/((-b)^(3/2)*d^2*(c*d-b*e)^2*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2*(b*B*d-2*A*c*d+A*b*e)*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/((-b)^(3/2)*d*(c*d-b*e)*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2*e*(2*A*c^2*d^2-b^2*e*(B*d-2*A*e)-b*c*d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(5/2)*(b*x+c*x^2)^(3/2)),x,10,-2*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(d+e*x)^(3/2)*sqrt(b*x+c*x^2))+2/3*(6*A*c^3*d^3-b^2*c*d*e*(7*B*d-19*A*e)+2*b^3*e^2*(B*d-4*A*e)-3*b*c^2*d^2*(B*d+3*A*e))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/((-b)^(3/2)*d^3*(c*d-b*e)^3*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))-2/3*(6*A*c^2*d^2-b^2*e*(B*d-4*A*e)-3*b*c*d*(B*d+2*A*e))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/((-b)^(3/2)*d^2*(c*d-b*e)^2*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*e*(6*A*c^2*d^2-b^2*e*(B*d-4*A*e)-3*b*c*d*(B*d+2*A*e))*sqrt(b*x+c*x^2)/(b^2*d^2*(c*d-b*e)^2*(d+e*x)^(3/2))-2/3*e*(6*A*c^3*d^3-b^2*c*d*e*(7*B*d-19*A*e)+2*b^3*e^2*(B*d-4*A*e)-3*b*c^2*d^2*(B*d+3*A*e))*sqrt(b*x+c*x^2)/(b^2*d^3*(c*d-b*e)^3*sqrt(d+e*x))],
[(A+B*x)*(d+e*x)^(7/2)/(b*x+c*x^2)^(5/2),x,9,-2/3*(d+e*x)^(5/2)*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*(b*x+c*x^2)^(3/2))+2/3*(b*c*d^2*(8*A*c^2*d+b^2*B*e-b*c*(4*B*d+9*A*e))+(16*A*c^4*d^3-4*b^4*B*e^3+b^3*c*e^2*(4*B*d+A*e)-8*b*c^3*d^2*(B*d+3*A*e)+b^2*c^2*d*e*(5*B*d+6*A*e))*x)*sqrt(d+e*x)/(b^4*c^2*sqrt(b*x+c*x^2))-2/3*(16*A*c^4*d^3-8*b^4*B*e^3+b^3*c*e^2*(5*B*d+2*A*e)-8*b*c^3*d^2*(B*d+3*A*e)+b^2*c^2*d*e*(5*B*d+4*A*e))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/((-b)^(7/2)*c^(5/2)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2/3*d*(c*d-b*e)*(16*A*c^3*d^2+4*b^3*B*e^2+b^2*c*e*(B*d-A*e)-8*b*c^2*d*(B*d+2*A*e))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/((-b)^(7/2)*c^(5/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))],
[(A+B*x)*(d+e*x)^(5/2)/(b*x+c*x^2)^(5/2),x,9,-2/3*(d+e*x)^(3/2)*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)/(b^2*c*(b*x+c*x^2)^(3/2))+2/3*(b*d*(8*A*c^2*d+b^2*B*e-b*c*(4*B*d+7*A*e))+(16*A*c^3*d^2+2*b^3*B*e^2+b^2*c*e*(3*B*d+A*e)-8*b*c^2*d*(B*d+2*A*e))*x)*sqrt(d+e*x)/(b^4*c*sqrt(b*x+c*x^2))-2/3*(16*A*c^3*d^2+2*b^3*B*e^2+b^2*c*e*(3*B*d+A*e)-8*b*c^2*d*(B*d+2*A*e))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/((-b)^(7/2)*c^(3/2)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2/3*d*(c*d-b*e)*(16*A*c^2*d-b^2*B*e-8*b*c*(B*d+A*e))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/((-b)^(7/2)*c^(3/2)*sqrt(d+e*x)*sqrt(b*x+c*x^2))],
[(A+B*x)*(d+e*x)^(3/2)/(b*x+c*x^2)^(5/2),x,9,-2/3*(A*b*c*d+(2*A*c^2*d+b^2*B*e-b*c*(B*d+A*e))*x)*sqrt(d+e*x)/(b^2*c*(b*x+c*x^2)^(3/2))+2/3*(b*(8*A*c^2*d+b^2*B*e-b*c*(4*B*d+5*A*e))+c*(16*A*c^2*d+b^2*B*e-8*b*c*(B*d+A*e))*x)*sqrt(d+e*x)/(b^4*c*sqrt(b*x+c*x^2))-2/3*(16*A*c^2*d+b^2*B*e-8*b*c*(B*d+A*e))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/((-b)^(7/2)*sqrt(c)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2/3*(16*A*c^2*d^2-8*b*c*d*(B*d+2*A*e)+b^2*e*(5*B*d+3*A*e))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/((-b)^(7/2)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))],
[(A+B*x)*sqrt(d+e*x)/(b*x+c*x^2)^(5/2),x,9,-2/3*(A*b-(b*B-2*A*c)*x)*sqrt(d+e*x)/(b^2*(b*x+c*x^2)^(3/2))-2/3*(b*(c*d-b*e)*(4*b*B*d-8*A*c*d+A*b*e)-c*(16*A*c^2*d^2+b^2*e*(7*B*d+A*e)-8*b*c*d*(B*d+2*A*e))*x)*sqrt(d+e*x)/(b^4*d*(c*d-b*e)*sqrt(b*x+c*x^2))-2/3*(16*A*c^2*d^2+b^2*e*(7*B*d+A*e)-8*b*c*d*(B*d+2*A*e))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/((-b)^(7/2)*d*(c*d-b*e)*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2/3*(16*A*c^2*d+3*b^2*B*e-8*b*c*(B*d+A*e))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/((-b)^(7/2)*sqrt(c)*sqrt(d+e*x)*sqrt(b*x+c*x^2))],
[(A+B*x)/((b*x+c*x^2)^(5/2)*sqrt(d+e*x)),x,9,-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)*sqrt(d+e*x)/(b^2*d*(c*d-b*e)*(b*x+c*x^2)^(3/2))+2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+b^2*e*(3*B*d-2*A*e)-b*c*d*(4*B*d+5*A*e))+c*(16*A*c^3*d^3-b^3*e^2*(3*B*d-2*A*e)-8*b*c^2*d^2*(B*d+3*A*e)+b^2*c*d*e*(13*B*d+4*A*e))*x)*sqrt(d+e*x)/(b^4*d^2*(c*d-b*e)^2*sqrt(b*x+c*x^2))-2/3*(16*A*c^3*d^3-b^3*e^2*(3*B*d-2*A*e)-8*b*c^2*d^2*(B*d+3*A*e)+b^2*c*d*e*(13*B*d+4*A*e))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/((-b)^(7/2)*d^2*(c*d-b*e)^2*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2/3*(16*A*c^2*d^2+b^2*e*(9*B*d-A*e)-8*b*c*d*(B*d+2*A*e))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/((-b)^(7/2)*d*(c*d-b*e)*sqrt(d+e*x)*sqrt(b*x+c*x^2))],
[(A+B*x)/((d+e*x)^(3/2)*(b*x+c*x^2)^(5/2)),x,10,-2/3*(A*b*(c*d-b*e)+c*(2*A*c*d-b*(B*d+A*e))*x)/(b^2*d*(c*d-b*e)*(b*x+c*x^2)^(3/2)*sqrt(d+e*x))+2/3*(b*(c*d-b*e)*(8*A*c^2*d^2+b^2*e*(3*B*d-4*A*e)-b*c*d*(4*B*d+3*A*e))+c*(16*A*c^3*d^3+15*b^2*B*c*d^2*e-b^3*e^2*(3*B*d-4*A*e)-8*b*c^2*d^2*(B*d+3*A*e))*x)/(b^4*d^2*(c*d-b*e)^2*sqrt(d+e*x)*sqrt(b*x+c*x^2))-2/3*(16*A*c^4*d^4-b^3*c*d*e^2*(9*B*d-7*A*e)+2*b^4*e^3*(3*B*d-4*A*e)-8*b*c^3*d^3*(B*d+4*A*e)+b^2*c^2*d^2*e*(19*B*d+9*A*e))*EllipticE(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(d+e*x)/((-b)^(7/2)*d^3*(c*d-b*e)^3*sqrt(1+e*x/d)*sqrt(b*x+c*x^2))+2/3*(16*A*c^3*d^3+15*b^2*B*c*d^2*e-b^3*e^2*(3*B*d-4*A*e)-8*b*c^2*d^2*(B*d+3*A*e))*EllipticF(sqrt(c)*sqrt(x)/sqrt(-b),sqrt(b*e/(c*d)))*sqrt(c)*sqrt(x)*sqrt(1+c*x/b)*sqrt(1+e*x/d)/((-b)^(7/2)*d^2*(c*d-b*e)^2*sqrt(d+e*x)*sqrt(b*x+c*x^2))+2/3*e*(16*A*c^4*d^4-b^3*c*d*e^2*(9*B*d-7*A*e)-8*b*c^3*d^3*(B*d+4*A*e)+b^2*c^2*d^2*e*(19*B*d+9*A*e)+b^4*(6*B*d*e^3-8*A*e^4))*sqrt(b*x+c*x^2)/(b^4*d^3*(c*d-b*e)^3*sqrt(d+e*x))],

# Integrands of the form (d+e x)^m (f+g x) (a+b x+c x^2)^p when b=0

# Integrands of the form (d+e x)^m (A+B x) (a+c x^2)^p

# p>0
[(A+B*x)*(d+e*x)^5*(a+c*x^2),x,2,-1/6*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^6/e^4+1/7*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^4-1/8*c*(3*B*d-A*e)*(d+e*x)^8/e^4+1/9*B*c*(d+e*x)^9/e^4],
[(A+B*x)*(d+e*x)^4*(a+c*x^2),x,2,-1/5*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^5/e^4+1/6*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^6/e^4-1/7*c*(3*B*d-A*e)*(d+e*x)^7/e^4+1/8*B*c*(d+e*x)^8/e^4],
[(A+B*x)*(d+e*x)^3*(a+c*x^2),x,2,-1/4*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^4/e^4+1/5*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^5/e^4-1/6*c*(3*B*d-A*e)*(d+e*x)^6/e^4+1/7*B*c*(d+e*x)^7/e^4],
[(A+B*x)*(d+e*x)^2*(a+c*x^2),x,2,-1/3*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^3/e^4+1/4*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^4/e^4-1/5*c*(3*B*d-A*e)*(d+e*x)^5/e^4+1/6*B*c*(d+e*x)^6/e^4],
[(A+B*x)*(d+e*x)*(a+c*x^2),x,2,a*A*d*x+1/2*a*(B*d+A*e)*x^2+1/3*(A*c*d+a*B*e)*x^3+1/4*c*(B*d+A*e)*x^4+1/5*B*c*e*x^5],
[(A+B*x)*(a+c*x^2),x,2,a*A*x+1/3*A*c*x^3+1/4*B*(a+c*x^2)^2/c],
[(A+B*x)*(a+c*x^2)/(d+e*x),x,2,(B*c*d^2-A*c*d*e+a*B*e^2)*x/e^3-1/2*c*(B*d-A*e)*x^2/e^2+1/3*B*c*x^3/e-(B*d-A*e)*(c*d^2+a*e^2)*log(d+e*x)/e^4],
[(A+B*x)*(a+c*x^2)/(d+e*x)^2,x,2,-c*(2*B*d-A*e)*x/e^3+1/2*B*c*x^2/e^2+(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x))+(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^4],
[(A+B*x)*(a+c*x^2)/(d+e*x)^3,x,2,B*c*x/e^3+1/2*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^2)+(-3*B*c*d^2+2*A*c*d*e-a*B*e^2)/(e^4*(d+e*x))-c*(3*B*d-A*e)*log(d+e*x)/e^4],
[(A+B*x)*(a+c*x^2)/(d+e*x)^4,x,2,1/3*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^3)+1/2*(-3*B*c*d^2+2*A*c*d*e-a*B*e^2)/(e^4*(d+e*x)^2)+c*(3*B*d-A*e)/(e^4*(d+e*x))+B*c*log(d+e*x)/e^4],
[(A+B*x)*(a+c*x^2)/(d+e*x)^5,x,2,1/4*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^4)+1/3*(-3*B*c*d^2+2*A*c*d*e-a*B*e^2)/(e^4*(d+e*x)^3)+1/2*c*(3*B*d-A*e)/(e^4*(d+e*x)^2)-B*c/(e^4*(d+e*x))],
[(A+B*x)*(a+c*x^2)/(d+e*x)^6,x,2,1/5*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^5)+1/4*(-3*B*c*d^2+2*A*c*d*e-a*B*e^2)/(e^4*(d+e*x)^4)+1/3*c*(3*B*d-A*e)/(e^4*(d+e*x)^3)-1/2*B*c/(e^4*(d+e*x)^2)],
[(A+B*x)*(a+c*x^2)/(d+e*x)^7,x,2,1/6*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^6)+1/5*(-3*B*c*d^2+2*A*c*d*e-a*B*e^2)/(e^4*(d+e*x)^5)+1/4*c*(3*B*d-A*e)/(e^4*(d+e*x)^4)-1/3*B*c/(e^4*(d+e*x)^3)],
[(A+B*x)*(d+e*x)^5*(a+c*x^2)^2,x,2,-1/6*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^6/e^6+1/7*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^6-1/4*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^8/e^6+2/9*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^9/e^6-1/10*c^2*(5*B*d-A*e)*(d+e*x)^10/e^6+1/11*B*c^2*(d+e*x)^11/e^6],
[(A+B*x)*(d+e*x)^4*(a+c*x^2)^2,x,2,-1/5*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^5/e^6+1/6*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^6/e^6-2/7*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^7/e^6+1/4*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^8/e^6-1/9*c^2*(5*B*d-A*e)*(d+e*x)^9/e^6+1/10*B*c^2*(d+e*x)^10/e^6],
[(A+B*x)*(d+e*x)^3*(a+c*x^2)^2,x,2,-1/4*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^4/e^6+1/5*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^5/e^6-1/3*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^6/e^6+2/7*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^6-1/8*c^2*(5*B*d-A*e)*(d+e*x)^8/e^6+1/9*B*c^2*(d+e*x)^9/e^6],
[(A+B*x)*(d+e*x)^2*(a+c*x^2)^2,x,2,-1/3*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^3/e^6+1/4*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^4/e^6-2/5*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^5/e^6+1/3*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^6/e^6-1/7*c^2*(5*B*d-A*e)*(d+e*x)^7/e^6+1/8*B*c^2*(d+e*x)^8/e^6],
[(A+B*x)*(d+e*x)*(a+c*x^2)^2,x,2,a^2*A*d*x+1/2*a^2*(B*d+A*e)*x^2+1/3*a*(2*A*c*d+a*B*e)*x^3+1/2*a*c*(B*d+A*e)*x^4+1/5*c*(A*c*d+2*a*B*e)*x^5+1/6*c^2*(B*d+A*e)*x^6+1/7*B*c^2*e*x^7],
[(A+B*x)*(a+c*x^2)^2,x,3,a^2*A*x+2/3*a*A*c*x^3+1/5*A*c^2*x^5+1/6*B*(a+c*x^2)^3/c],
[(A+B*x)*(a+c*x^2)^2/(d+e*x),x,2,(B*(c*d^2+a*e^2)^2-A*c*d*e*(c*d^2+2*a*e^2))*x/e^5-1/2*c*(B*d-A*e)*(c*d^2+2*a*e^2)*x^2/e^4+1/3*c*(B*c*d^2-A*c*d*e+2*a*B*e^2)*x^3/e^3-1/4*c^2*(B*d-A*e)*x^4/e^2+1/5*B*c^2*x^5/e-(B*d-A*e)*(c*d^2+a*e^2)^2*log(d+e*x)/e^6],
[(A+B*x)*(a+c*x^2)^2/(d+e*x)^2,x,2,-c*(4*B*c*d^3-3*A*c*d^2*e+4*a*B*d*e^2-2*a*A*e^3)*x/e^5+1/2*c*(3*B*c*d^2-2*A*c*d*e+2*a*B*e^2)*x^2/e^4-1/3*c^2*(2*B*d-A*e)*x^3/e^3+1/4*B*c^2*x^4/e^2+(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x))+(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*log(d+e*x)/e^6],
[(A+B*x)*(a+c*x^2)^2/(d+e*x)^3,x,2,c*(6*B*c*d^2-3*A*c*d*e+2*a*B*e^2)*x/e^5-1/2*c^2*(3*B*d-A*e)*x^2/e^4+1/3*B*c^2*x^3/e^3+1/2*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^2)-(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x))-2*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*log(d+e*x)/e^6],
[(A+B*x)*(a+c*x^2)^2/(d+e*x)^4,x,2,-c^2*(4*B*d-A*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^3)-1/2*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^2)+2*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x))+2*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^6],
[(A+B*x)*(a+c*x^2)^2/(d+e*x)^5,x,2,B*c^2*x/e^5+1/4*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^4)-1/3*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^3)+c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^2)-2*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x))-c^2*(5*B*d-A*e)*log(d+e*x)/e^6],
[(A+B*x)*(a+c*x^2)^2/(d+e*x)^6,x,2,1/5*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^5)-1/4*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^4)+2/3*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^3)-c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^2)+c^2*(5*B*d-A*e)/(e^6*(d+e*x))+B*c^2*log(d+e*x)/e^6],
[(A+B*x)*(a+c*x^2)^2/(d+e*x)^7,x,2,1/6*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^6)-1/5*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^5)+1/2*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^4)-2/3*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^3)+1/2*c^2*(5*B*d-A*e)/(e^6*(d+e*x)^2)-B*c^2/(e^6*(d+e*x))],
[(A+B*x)*(a+c*x^2)^2/(d+e*x)^8,x,2,1/7*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^7)-1/6*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^6)+2/5*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^5)-1/2*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^4)+1/3*c^2*(5*B*d-A*e)/(e^6*(d+e*x)^3)-1/2*B*c^2/(e^6*(d+e*x)^2)],
[(A+B*x)*(a+c*x^2)^2/(d+e*x)^9,x,2,1/8*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^8)-1/7*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^7)+1/3*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^6)-2/5*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^5)+1/4*c^2*(5*B*d-A*e)/(e^6*(d+e*x)^4)-1/3*B*c^2/(e^6*(d+e*x)^3)],
[(A+B*x)*(a+c*x^2)^2/(d+e*x)^10,x,2,1/9*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^9)-1/8*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^8)+2/7*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^7)-1/3*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^6)+1/5*c^2*(5*B*d-A*e)/(e^6*(d+e*x)^5)-1/4*B*c^2/(e^6*(d+e*x)^4)],
[(A+B*x)*(d+e*x)^5*(a+c*x^2)^3,x,2,-1/6*(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^6/e^8+1/7*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^7/e^8-3/8*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^8/e^8-1/9*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^9/e^8-1/10*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^10/e^8+3/11*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^11/e^8-1/12*c^3*(7*B*d-A*e)*(d+e*x)^12/e^8+1/13*B*c^3*(d+e*x)^13/e^8],
[(A+B*x)*(d+e*x)^4*(a+c*x^2)^3,x,2,-1/5*(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^5/e^8+1/6*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^6/e^8-3/7*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^7/e^8-1/8*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^8/e^8-1/9*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^9/e^8+3/10*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^10/e^8-1/11*c^3*(7*B*d-A*e)*(d+e*x)^11/e^8+1/12*B*c^3*(d+e*x)^12/e^8],
[(A+B*x)*(d+e*x)^3*(a+c*x^2)^3,x,2,-1/4*(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^4/e^8+1/5*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^5/e^8-1/2*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^6/e^8-1/7*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^7/e^8-1/8*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^8/e^8+1/3*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^9/e^8-1/10*c^3*(7*B*d-A*e)*(d+e*x)^10/e^8+1/11*B*c^3*(d+e*x)^11/e^8],
[(A+B*x)*(d+e*x)^2*(a+c*x^2)^3,x,2,-1/3*(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^3/e^8+1/4*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^4/e^8-3/5*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^5/e^8-1/6*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^6/e^8-1/7*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^7/e^8+3/8*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^8/e^8-1/9*c^3*(7*B*d-A*e)*(d+e*x)^9/e^8+1/10*B*c^3*(d+e*x)^10/e^8],
[(A+B*x)*(d+e*x)*(a+c*x^2)^3,x,2,a^3*A*d*x+1/2*a^3*(B*d+A*e)*x^2+1/3*a^2*(3*A*c*d+a*B*e)*x^3+3/4*a^2*c*(B*d+A*e)*x^4+3/5*a*c*(A*c*d+a*B*e)*x^5+1/2*a*c^2*(B*d+A*e)*x^6+1/7*c^2*(A*c*d+3*a*B*e)*x^7+1/8*c^3*(B*d+A*e)*x^8+1/9*B*c^3*e*x^9],
[(A+B*x)*(a+c*x^2)^3,x,3,a^3*A*x+a^2*A*c*x^3+3/5*a*A*c^2*x^5+1/7*A*c^3*x^7+1/8*B*(a+c*x^2)^4/c],
[(A+B*x)*(a+c*x^2)^3/(d+e*x),x,2,(B*(c*d^2+a*e^2)^3-A*c*d*e*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4))*x/e^7-1/2*c*(B*d-A*e)*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4)*x^2/e^6-1/3*c*(A*c*d*e*(c*d^2+3*a*e^2)-B*(c^2*d^4+3*a*c*d^2*e^2+3*a^2*e^4))*x^3/e^5-1/4*c^2*(B*d-A*e)*(c*d^2+3*a*e^2)*x^4/e^4+1/5*c^2*(B*c*d^2-A*c*d*e+3*a*B*e^2)*x^5/e^3-1/6*c^3*(B*d-A*e)*x^6/e^2+1/7*B*c^3*x^7/e-(B*d-A*e)*(c*d^2+a*e^2)^3*log(d+e*x)/e^8],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^2,x,2,-c*(6*B*d*(c*d^2+a*e^2)^2-A*e*(5*c^2*d^4+9*a*c*d^2*e^2+3*a^2*e^4))*x/e^7-1/2*c*(2*A*c*d*e*(2*c*d^2+3*a*e^2)-B*(5*c^2*d^4+9*a*c*d^2*e^2+3*a^2*e^4))*x^2/e^6+1/3*c^2*(3*A*e*(c*d^2+a*e^2)-B*(4*c*d^3+6*a*d*e^2))*x^3/e^5-1/4*c^2*(2*A*c*d*e-3*B*(c*d^2+a*e^2))*x^4/e^4-1/5*c^3*(2*B*d-A*e)*x^5/e^3+1/6*B*c^3*x^6/e^2+(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x))+(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)*log(d+e*x)/e^8],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^3,x,2,-c*(A*c*d*e*(10*c*d^2+9*a*e^2)-3*B*(5*c^2*d^4+6*a*c*d^2*e^2+a^2*e^4))*x/e^7-1/2*c^2*(10*B*c*d^3-6*A*c*d^2*e+9*a*B*d*e^2-3*a*A*e^3)*x^2/e^6+c^2*(2*B*c*d^2-A*c*d*e+a*B*e^2)*x^3/e^5-1/4*c^3*(3*B*d-A*e)*x^4/e^4+1/5*B*c^3*x^5/e^3+1/2*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^2)-(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x))-3*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*log(d+e*x)/e^8],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^4,x,2,-c^2*(20*B*c*d^3-10*A*c*d^2*e+12*a*B*d*e^2-3*a*A*e^3)*x/e^7+1/2*c^2*(10*B*c*d^2-4*A*c*d*e+3*a*B*e^2)*x^2/e^6-1/3*c^3*(4*B*d-A*e)*x^3/e^5+1/4*B*c^3*x^4/e^4+1/3*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^3)-1/2*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^2)+3*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x))-c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*log(d+e*x)/e^8],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^5,x,2,-c^2*(5*A*c*d*e-3*B*(5*c*d^2+a*e^2))*x/e^7-1/2*c^3*(5*B*d-A*e)*x^2/e^6+1/3*B*c^3*x^3/e^5+1/4*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^4)-1/3*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^3)+3/2*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^2)+c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x))-c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*log(d+e*x)/e^8],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^6,x,2,-c^3*(6*B*d-A*e)*x/e^7+1/2*B*c^3*x^2/e^6+1/5*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^5)-1/4*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^4)+c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^3)+1/2*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x)^2)+c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)/(e^8*(d+e*x))+3*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*log(d+e*x)/e^8],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^7,x,2,B*c^3*x/e^7+1/6*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^6)-1/5*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^5)+3/4*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^4)+1/3*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x)^3)+1/2*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)/(e^8*(d+e*x)^2)-3*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^8*(d+e*x))-c^3*(7*B*d-A*e)*log(d+e*x)/e^8],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^8,x,2,1/7*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^7)-1/6*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^6)+3/5*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^5)+1/4*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x)^4)+1/3*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)/(e^8*(d+e*x)^3)-3/2*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^2)+c^3*(7*B*d-A*e)/(e^8*(d+e*x))+B*c^3*log(d+e*x)/e^8],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^9,x,2,1/8*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^8)-1/7*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^7)+1/2*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^6)+1/5*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x)^5)+1/4*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)/(e^8*(d+e*x)^4)-c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^3)+1/2*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^2)-B*c^3/(e^8*(d+e*x))],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^10,x,2,1/9*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^9)-1/8*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^8)+3/7*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^7)+1/6*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x)^6)+1/5*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)/(e^8*(d+e*x)^5)-3/4*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^4)+1/3*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^3)-1/2*B*c^3/(e^8*(d+e*x)^2)],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^11,x,2,1/10*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^10)-1/9*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^9)+3/8*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^8)+1/7*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x)^7)+1/6*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)/(e^8*(d+e*x)^6)-3/5*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^5)+1/4*c^3*(7*B*d-A*e)/(e^8*(d+e*x)^4)-1/3*B*c^3/(e^8*(d+e*x)^3)],

# p<0
[(A+B*x)*(d+e*x)^4/(a+c*x^2),x,5,e*(4*B*c*d^3+6*A*c*d^2*e-4*a*B*d*e^2-a*A*e^3)*x/c^2+1/2*e^2*(6*B*c*d^2+4*A*c*d*e-a*B*e^2)*x^2/c^2+1/3*e^3*(4*B*d+A*e)*x^3/c+1/4*B*e^4*x^4/c+1/2*(4*A*c*d*e*(c*d^2-a*e^2)+B*(c^2*d^4-6*a*c*d^2*e^2+a^2*e^4))*log(a+c*x^2)/c^3-(4*a*B*d*e*(c*d^2-a*e^2)-A*(c^2*d^4-6*a*c*d^2*e^2+a^2*e^4))*arctan(x*sqrt(c)/sqrt(a))/(c^(5/2)*sqrt(a))],
[(A+B*x)*(d+e*x)^3/(a+c*x^2),x,5,e*(3*B*c*d^2+3*A*c*d*e-a*B*e^2)*x/c^2+1/2*e^2*(3*B*d+A*e)*x^2/c+1/3*B*e^3*x^3/c+1/2*(B*c*d^3+3*A*c*d^2*e-3*a*B*d*e^2-a*A*e^3)*log(a+c*x^2)/c^2+(A*c*d*(c*d^2-3*a*e^2)-a*B*e*(3*c*d^2-a*e^2))*arctan(x*sqrt(c)/sqrt(a))/(c^(5/2)*sqrt(a))],
[(A+B*x)*(d+e*x)^2/(a+c*x^2),x,5,e*(2*B*d+A*e)*x/c+1/2*B*e^2*x^2/c+1/2*(B*c*d^2+2*A*c*d*e-a*B*e^2)*log(a+c*x^2)/c^2+(A*c*d^2-2*a*B*d*e-a*A*e^2)*arctan(x*sqrt(c)/sqrt(a))/(c^(3/2)*sqrt(a))],
[(A+B*x)*(d+e*x)/(a+c*x^2),x,4,B*e*x/c+1/2*(B*d+A*e)*log(a+c*x^2)/c+(A*c*d-a*B*e)*arctan(x*sqrt(c)/sqrt(a))/(c^(3/2)*sqrt(a))],
[(A+B*x)/(a+c*x^2),x,3,1/2*B*log(a+c*x^2)/c+A*arctan(x*sqrt(c)/sqrt(a))/(sqrt(a)*sqrt(c))],
[(A+B*x)/((d+e*x)*(a+c*x^2)),x,5,-(B*d-A*e)*log(d+e*x)/(c*d^2+a*e^2)+1/2*(B*d-A*e)*log(a+c*x^2)/(c*d^2+a*e^2)+(A*c*d+a*B*e)*arctan(x*sqrt(c)/sqrt(a))/((c*d^2+a*e^2)*sqrt(a)*sqrt(c))],
[(A+B*x)/((d+e*x)^2*(a+c*x^2)),x,5,(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x))-(B*c*d^2-2*A*c*d*e-a*B*e^2)*log(d+e*x)/(c*d^2+a*e^2)^2+1/2*(B*c*d^2-2*A*c*d*e-a*B*e^2)*log(a+c*x^2)/(c*d^2+a*e^2)^2+(A*c*d^2+2*a*B*d*e-a*A*e^2)*arctan(x*sqrt(c)/sqrt(a))*sqrt(c)/((c*d^2+a*e^2)^2*sqrt(a))],
[(A+B*x)/((d+e*x)^3*(a+c*x^2)),x,5,1/2*(B*d-A*e)/((c*d^2+a*e^2)*(d+e*x)^2)+(B*c*d^2-2*A*c*d*e-a*B*e^2)/((c*d^2+a*e^2)^2*(d+e*x))-c*(B*c*d^3-3*A*c*d^2*e-3*a*B*d*e^2+a*A*e^3)*log(d+e*x)/(c*d^2+a*e^2)^3+1/2*c*(B*c*d^3-3*A*c*d^2*e-3*a*B*d*e^2+a*A*e^3)*log(a+c*x^2)/(c*d^2+a*e^2)^3+(A*c*d*(c*d^2-3*a*e^2)+a*B*e*(3*c*d^2-a*e^2))*arctan(x*sqrt(c)/sqrt(a))*sqrt(c)/((c*d^2+a*e^2)^3*sqrt(a))],
[(A+B*x)*(d+e*x)^5/(a+c*x^2)^2,x,6,-1/2*e^2*(3*A*c*d*(2*c*d^2-5*a*e^2)-5*a*B*e*(6*c*d^2-a*e^2))*x/(a*c^3)-e^3*(2*A*c*d^2-5*a*B*d*e-a*A*e^2)*x^2/(a*c^2)-1/6*e^4*(3*A*c*d-5*a*B*e)*x^3/(a*c^2)-1/2*(d+e*x)^4*(a*(B*d+A*e)-(A*c*d-a*B*e)*x)/(a*c*(a+c*x^2))+1/2*(A*c*d*(c^2*d^4+10*a*c*d^2*e^2-15*a^2*e^4)+5*a*B*e*(c^2*d^4-6*a*c*d^2*e^2+a^2*e^4))*arctan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(7/2))+e^2*(5*B*c*d^3+5*A*c*d^2*e-5*a*B*d*e^2-a*A*e^3)*log(a+c*x^2)/c^3],
[(A+B*x)*(d+e*x)^4/(a+c*x^2)^2,x,6,-3/2*e^2*(A*c*d^2-4*a*B*d*e-a*A*e^2)*x/(a*c^2)-1/2*e^3*(A*c*d-2*a*B*e)*x^2/(a*c^2)-1/2*(d+e*x)^3*(a*(B*d+A*e)-(A*c*d-a*B*e)*x)/(a*c*(a+c*x^2))+1/2*(4*a*B*d*e*(c*d^2-3*a*e^2)+A*(c^2*d^4+6*a*c*d^2*e^2-3*a^2*e^4))*arctan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(5/2))+e^2*(3*B*c*d^2+2*A*c*d*e-a*B*e^2)*log(a+c*x^2)/c^3],
[(A+B*x)*(d+e*x)^3/(a+c*x^2)^2,x,5,-1/2*e^2*(A*c*d-3*a*B*e)*x/(a*c^2)-1/2*(d+e*x)^2*(a*(B*d+A*e)-(A*c*d-a*B*e)*x)/(a*c*(a+c*x^2))+1/2*(3*a*B*e*(c*d^2-a*e^2)+A*c*d*(c*d^2+3*a*e^2))*arctan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(5/2))+1/2*e^2*(3*B*d+A*e)*log(a+c*x^2)/c^2],
[(A+B*x)*(d+e*x)^2/(a+c*x^2)^2,x,4,-1/2*(d+e*x)*(a*(B*d+A*e)-(A*c*d-a*B*e)*x)/(a*c*(a+c*x^2))+1/2*(A*c*d^2+a*e*(2*B*d+A*e))*arctan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(3/2))+1/2*B*e^2*log(a+c*x^2)/c^2],
[(A+B*x)*(d+e*x)/(a+c*x^2)^2,x,2,1/2*(-a*(B*d+A*e)+(A*c*d-a*B*e)*x)/(a*c*(a+c*x^2))+1/2*(A*c*d+a*B*e)*arctan(x*sqrt(c)/sqrt(a))/(a^(3/2)*c^(3/2))],
[(A+B*x)/(a+c*x^2)^2,x,2,1/2*(-a*B+A*c*x)/(a*c*(a+c*x^2))+1/2*A*arctan(x*sqrt(c)/sqrt(a))/(a^(3/2)*sqrt(c))],
[(A+B*x)/((d+e*x)*(a+c*x^2)^2),x,6,1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2))-e^2*(B*d-A*e)*log(d+e*x)/(c*d^2+a*e^2)^2+1/2*e^2*(B*d-A*e)*log(a+c*x^2)/(c*d^2+a*e^2)^2-1/2*(a*B*e*(c*d^2-a*e^2)-A*c*d*(c*d^2+3*a*e^2))*arctan(x*sqrt(c)/sqrt(a))/(a^(3/2)*(c*d^2+a*e^2)^2*sqrt(c))],
[(A+B*x)/((d+e*x)^2*(a+c*x^2)^2),x,6,1/2*e*(A*c*d^2+4*a*B*d*e-3*a*A*e^2)/(a*(c*d^2+a*e^2)^2*(d+e*x))+1/2*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(d+e*x)*(a+c*x^2))-e^2*(3*B*c*d^2-4*A*c*d*e-a*B*e^2)*log(d+e*x)/(c*d^2+a*e^2)^3+1/2*e^2*(3*B*c*d^2-4*A*c*d*e-a*B*e^2)*log(a+c*x^2)/(c*d^2+a*e^2)^3-1/2*(2*a*B*d*e*(c*d^2-3*a*e^2)-A*(c^2*d^4+6*a*c*d^2*e^2-3*a^2*e^4))*arctan(x*sqrt(c)/sqrt(a))*sqrt(c)/(a^(3/2)*(c*d^2+a*e^2)^3)],
[(A+B*x)*(d+e*x)^5/(a+c*x^2)^3,x,6,-1/8*e^2*(5*a*B*e*(c*d^2-3*a*e^2)+A*c*d*(3*c*d^2+7*a*e^2))*x/(a^2*c^3)-1/4*(d+e*x)^4*(a*(B*d+A*e)-(A*c*d-a*B*e)*x)/(a*c*(a+c*x^2)^2)-1/8*(d+e*x)^2*(2*a*e*(A*c*d^2+5*a*B*d*e+2*a*A*e^2)-(5*a*B*e*(c*d^2-a*e^2)+A*c*d*(3*c*d^2+5*a*e^2))*x)/(a^2*c^2*(a+c*x^2))+1/8*(5*a*B*e*(c^2*d^4+6*a*c*d^2*e^2-3*a^2*e^4)+A*c*d*(3*c^2*d^4+10*a*c*d^2*e^2+15*a^2*e^4))*arctan(x*sqrt(c)/sqrt(a))/(a^(5/2)*c^(7/2))+1/2*e^4*(5*B*d+A*e)*log(a+c*x^2)/c^3],
[(A+B*x)*(d+e*x)^4/(a+c*x^2)^3,x,5,-1/4*(d+e*x)^3*(a*(B*d+A*e)-(A*c*d-a*B*e)*x)/(a*c*(a+c*x^2)^2)-1/8*(d+e*x)*(a*e*(8*a*B*d*e+3*A*(c*d^2+a*e^2))+(4*a^2*B*e^3-c*d*(3*A*c*d^2+a*e*(4*B*d+3*A*e)))*x)/(a^2*c^2*(a+c*x^2))+1/8*(3*A*(c*d^2+a*e^2)^2+4*a*B*d*e*(c*d^2+3*a*e^2))*arctan(x*sqrt(c)/sqrt(a))/(a^(5/2)*c^(5/2))+1/2*B*e^4*log(a+c*x^2)/c^3],
[(A+B*x)*(d+e*x)^3/(a+c*x^2)^3,x,3,-1/4*(a*B-A*c*x)*(d+e*x)^3/(a*c*(a+c*x^2)^2)-3/8*(A*c*d+a*B*e)*(a*e-c*d*x)*(d+e*x)/(a^2*c^2*(a+c*x^2))+3/8*(A*c*d+a*B*e)*(c*d^2+a*e^2)*arctan(x*sqrt(c)/sqrt(a))/(a^(5/2)*c^(5/2))],
[(A+B*x)*(d+e*x)^2/(a+c*x^2)^3,x,3,-1/4*(a*B-A*c*x)*(d+e*x)^2/(a*c*(a+c*x^2)^2)+1/8*(-2*a*e*(2*A*c*d+a*B*e)+c*(3*A*c*d^2+2*a*B*d*e-a*A*e^2)*x)/(a^2*c^2*(a+c*x^2))+1/8*(3*A*c*d^2+2*a*B*d*e+a*A*e^2)*arctan(x*sqrt(c)/sqrt(a))/(a^(5/2)*c^(3/2))],
[(A+B*x)*(d+e*x)/(a+c*x^2)^3,x,3,1/4*(-a*(B*d+A*e)+(A*c*d-a*B*e)*x)/(a*c*(a+c*x^2)^2)+1/8*(3*A*c*d+a*B*e)*x/(a^2*c*(a+c*x^2))+1/8*(3*A*c*d+a*B*e)*arctan(x*sqrt(c)/sqrt(a))/(a^(5/2)*c^(3/2))],
[(A+B*x)/(a+c*x^2)^3,x,3,1/4*(-a*B+A*c*x)/(a*c*(a+c*x^2)^2)+3/8*A*x/(a^2*(a+c*x^2))+3/8*A*arctan(x*sqrt(c)/sqrt(a))/(a^(5/2)*sqrt(c))],
[(A+B*x)/((d+e*x)*(a+c*x^2)^3),x,7,1/4*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2)^2)+1/8*(-4*a^2*e^2*(B*d-A*e)-(a*B*e*(c*d^2-3*a*e^2)-A*c*d*(3*c*d^2+7*a*e^2))*x)/(a^2*(c*d^2+a*e^2)^2*(a+c*x^2))-e^4*(B*d-A*e)*log(d+e*x)/(c*d^2+a*e^2)^3+1/2*e^4*(B*d-A*e)*log(a+c*x^2)/(c*d^2+a*e^2)^3-1/8*(a*B*e*(c^2*d^4+6*a*c*d^2*e^2-3*a^2*e^4)-A*c*d*(3*c^2*d^4+10*a*c*d^2*e^2+15*a^2*e^4))*arctan(x*sqrt(c)/sqrt(a))/(a^(5/2)*(c*d^2+a*e^2)^3*sqrt(c))],
[(A+B*x)/((d+e*x)^2*(a+c*x^2)^3),x,7,-1/8*e*(2*a*B*d*e*(c*d^2-11*a*e^2)-3*A*(c^2*d^4+4*a*c*d^2*e^2-5*a^2*e^4))/(a^2*(c*d^2+a*e^2)^3*(d+e*x))+1/4*(-a*(B*d-A*e)+(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(d+e*x)*(a+c*x^2)^2)+1/8*(-a*e*(A*c*d^2+6*a*B*d*e-5*a*A*e^2)-(2*a*B*e*(c*d^2-2*a*e^2)-3*A*c*d*(c*d^2+3*a*e^2))*x)/(a^2*(c*d^2+a*e^2)^2*(d+e*x)*(a+c*x^2))-e^4*(5*B*c*d^2-6*A*c*d*e-a*B*e^2)*log(d+e*x)/(c*d^2+a*e^2)^4+1/2*e^4*(5*B*c*d^2-6*A*c*d*e-a*B*e^2)*log(a+c*x^2)/(c*d^2+a*e^2)^4-1/8*(2*a*B*d*e*(c^2*d^4+10*a*c*d^2*e^2-15*a^2*e^4)-3*A*(c^3*d^6+5*a*c^2*d^4*e^2+15*a^2*c*d^2*e^4-5*a^3*e^6))*arctan(x*sqrt(c)/sqrt(a))*sqrt(c)/(a^(5/2)*(c*d^2+a*e^2)^4)],
[(-11+6*x)/((-1+2*x)*(-1+x^2)),x,2,16/3*log(1-2*x)-5/2*log(1-x)-17/6*log(1+x)],
[x*(1+x)^2/(1+x^2)^3,x,3,-1/4*(1+x)^2/(1+x^2)^2+1/4*(-1+x)/(1+x^2)+1/4*arctan(x)],

# Integrands of the form (d+e x)^m (A+B x) (a+c x^2)^(p/2)

# p>0
[(5-x)*(3+2*x)^4*sqrt(2+3*x^2),x,6,923/315*(3+2*x)^2*(2+3*x^2)^(3/2)+29/63*(3+2*x)^3*(2+3*x^2)^(3/2)-1/21*(3+2*x)^4*(2+3*x^2)^(3/2)+2/405*(13781+4599*x)*(2+3*x^2)^(3/2)+2341/9*arcsinh(x*sqrt(3/2))/sqrt(3)+2341/18*x*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^3*sqrt(2+3*x^2),x,5,17/30*(3+2*x)^2*(2+3*x^2)^(3/2)-1/18*(3+2*x)^3*(2+3*x^2)^(3/2)+7/270*(898+267*x)*(2+3*x^2)^(3/2)+1022/9*arcsinh(x*sqrt(3/2))/sqrt(3)+511/9*x*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^2*sqrt(2+3*x^2),x,4,-1/15*(3+2*x)^2*(2+3*x^2)^(3/2)+2/135*(431+99*x)*(2+3*x^2)^(3/2)+131/3*arcsinh(x*sqrt(3/2))/sqrt(3)+131/6*x*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)*sqrt(2+3*x^2),x,3,1/18*(14-3*x)*(2+3*x^2)^(3/2)+46/3*arcsinh(x*sqrt(3/2))/sqrt(3)+23/3*x*sqrt(2+3*x^2)],
[(5-x)*sqrt(2+3*x^2),x,3,-1/9*(2+3*x^2)^(3/2)+5*arcsinh(x*sqrt(3/2))/sqrt(3)+5/2*x*sqrt(2+3*x^2)],
[(5-x)*sqrt(2+3*x^2)/(3+2*x),x,5,-121/8*arcsinh(x*sqrt(3/2))/sqrt(3)-13/8*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+1/4*(13-x)*sqrt(2+3*x^2)],
[(5-x)*sqrt(2+3*x^2)/(3+2*x)^2,x,5,2*arcsinh(x*sqrt(3/2))*sqrt(3)+19*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-1/2*(8+x)*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)*sqrt(2+3*x^2)/(3+2*x)^3,x,5,-1/8*arcsinh(x*sqrt(3/2))*sqrt(3)-471/280*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/140*(53+187*x)*sqrt(2+3*x^2)/(3+2*x)^2],
[(5-x)*sqrt(2+3*x^2)/(3+2*x)^4,x,4,-13/105*(2+3*x^2)^(3/2)/(3+2*x)^3-123/1225*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-41/2450*(4-9*x)*sqrt(2+3*x^2)/(3+2*x)^2],
[(5-x)*sqrt(2+3*x^2)/(3+2*x)^5,x,5,-13/140*(2+3*x^2)^(3/2)/(3+2*x)^4-89/2940*(2+3*x^2)^(3/2)/(3+2*x)^3-198/8575*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-33/8575*(4-9*x)*sqrt(2+3*x^2)/(3+2*x)^2],
[(5-x)*sqrt(2+3*x^2)/(3+2*x)^6,x,6,-13/175*(2+3*x^2)^(3/2)/(3+2*x)^5-23/875*(2+3*x^2)^(3/2)/(3+2*x)^4-43/6125*(2+3*x^2)^(3/2)/(3+2*x)^3-1017/214375*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-339/428750*(4-9*x)*sqrt(2+3*x^2)/(3+2*x)^2],
[(5-x)*sqrt(2+3*x^2)/(3+2*x)^7,x,7,-13/210*(2+3*x^2)^(3/2)/(3+2*x)^6-281/12250*(2+3*x^2)^(3/2)/(3+2*x)^5-111/17500*(2+3*x^2)^(3/2)/(3+2*x)^4-1207/857500*(2+3*x^2)^(3/2)/(3+2*x)^3-6102/7503125*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-1017/7503125*(4-9*x)*sqrt(2+3*x^2)/(3+2*x)^2],
[(5-x)*(3+2*x)^4*(2+3*x^2)^(3/2),x,7,2777/36*x*(2+3*x^2)^(3/2)+4421/2268*(3+2*x)^2*(2+3*x^2)^(5/2)+13/36*(3+2*x)^3*(2+3*x^2)^(5/2)-1/27*(3+2*x)^4*(2+3*x^2)^(5/2)+1/17010*(661583+226755*x)*(2+3*x^2)^(5/2)+2777/6*arcsinh(x*sqrt(3/2))/sqrt(3)+2777/12*x*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^3*(2+3*x^2)^(3/2),x,6,1087/36*x*(2+3*x^2)^(3/2)+71/168*(3+2*x)^2*(2+3*x^2)^(5/2)-1/24*(3+2*x)^3*(2+3*x^2)^(5/2)+1/1260*(16973+5405*x)*(2+3*x^2)^(5/2)+1087/6*arcsinh(x*sqrt(3/2))/sqrt(3)+1087/12*x*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^2*(2+3*x^2)^(3/2),x,5,397/36*x*(2+3*x^2)^(3/2)-1/21*(3+2*x)^2*(2+3*x^2)^(5/2)+2/315*(611+160*x)*(2+3*x^2)^(5/2)+397/6*arcsinh(x*sqrt(3/2))/sqrt(3)+397/12*x*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)*(2+3*x^2)^(3/2),x,4,137/36*x*(2+3*x^2)^(3/2)+1/45*(21-5*x)*(2+3*x^2)^(5/2)+137/6*arcsinh(x*sqrt(3/2))/sqrt(3)+137/12*x*sqrt(2+3*x^2)],
[(5-x)*(2+3*x^2)^(3/2),x,4,5/4*x*(2+3*x^2)^(3/2)-1/15*(2+3*x^2)^(5/2)+5/2*arcsinh(x*sqrt(3/2))*sqrt(3)+15/4*x*sqrt(2+3*x^2)],
[(5-x)*(2+3*x^2)^(3/2)/(3+2*x),x,6,1/24*(26-3*x)*(2+3*x^2)^(3/2)-1529/32*arcsinh(x*sqrt(3/2))*sqrt(3)-455/32*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+1/16*(455-123*x)*sqrt(2+3*x^2)],
[(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^2,x,6,-1/6*(21+x)*(2+3*x^2)^(3/2)/(3+2*x)+663/16*arcsinh(x*sqrt(3/2))*sqrt(3)+193/16*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)-1/8*(193-63*x)*sqrt(2+3*x^2)],
[(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^3,x,6,-1/4*(8+x)*(2+3*x^2)^(3/2)/(3+2*x)^2-111/8*arcsinh(x*sqrt(3/2))*sqrt(3)-1143/8*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+3/4*(37+12*x)*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^4,x,6,1/420*(229+456*x)*(2+3*x^2)^(3/2)/(3+2*x)^3+33/16*arcsinh(x*sqrt(3/2))*sqrt(3)+11727/560*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-3/280*(385+111*x)*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^5,x,6,1/840*(54+491*x)*(2+3*x^2)^(3/2)/(3+2*x)^4-3/32*arcsinh(x*sqrt(3/2))*sqrt(3)-39663/39200*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+3/19600*(2943+4097*x)*sqrt(2+3*x^2)/(3+2*x)^2],
[(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^6,x,5,-41/4900*(4-9*x)*(2+3*x^2)^(3/2)/(3+2*x)^4-13/175*(2+3*x^2)^(5/2)/(3+2*x)^5-1107/85750*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-369/171500*(4-9*x)*sqrt(2+3*x^2)/(3+2*x)^2],
[(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^7,x,6,-1/500*(4-9*x)*(2+3*x^2)^(3/2)/(3+2*x)^4-13/210*(2+3*x^2)^(5/2)/(3+2*x)^6-29/1750*(2+3*x^2)^(5/2)/(3+2*x)^5-27/8750*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-9/17500*(4-9*x)*sqrt(2+3*x^2)/(3+2*x)^2],
[(5-x)*(2+3*x^2)^(3/2)/(3+2*x)^8,x,7,-2689/6002500*(4-9*x)*(2+3*x^2)^(3/2)/(3+2*x)^4-13/245*(2+3*x^2)^(5/2)/(3+2*x)^7-404/25725*(2+3*x^2)^(5/2)/(3+2*x)^6-822/214375*(2+3*x^2)^(5/2)/(3+2*x)^5-72603/105043750*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-24201/210087500*(4-9*x)*sqrt(2+3*x^2)/(3+2*x)^2],
[(5-x)*(3+2*x)^4*(2+3*x^2)^(5/2),x,8,4991/36*x*(2+3*x^2)^(3/2)+4991/90*x*(2+3*x^2)^(5/2)+6433/4455*(3+2*x)^2*(2+3*x^2)^(7/2)+49/165*(3+2*x)^3*(2+3*x^2)^(7/2)-1/33*(3+2*x)^4*(2+3*x^2)^(7/2)+2/13365*(181243+62244*x)*(2+3*x^2)^(7/2)+4991/6*arcsinh(x*sqrt(3/2))/sqrt(3)+4991/12*x*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^3*(2+3*x^2)^(5/2),x,7,3731/72*x*(2+3*x^2)^(3/2)+3731/180*x*(2+3*x^2)^(5/2)+91/270*(3+2*x)^2*(2+3*x^2)^(7/2)-1/30*(3+2*x)^3*(2+3*x^2)^(7/2)+1/1620*(15244+4977*x)*(2+3*x^2)^(7/2)+3731/12*arcsinh(x*sqrt(3/2))/sqrt(3)+3731/24*x*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^2*(2+3*x^2)^(5/2),x,6,665/36*x*(2+3*x^2)^(3/2)+133/18*x*(2+3*x^2)^(5/2)-1/27*(3+2*x)^2*(2+3*x^2)^(7/2)+1/81*(226+63*x)*(2+3*x^2)^(7/2)+665/6*arcsinh(x*sqrt(3/2))/sqrt(3)+665/12*x*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)*(2+3*x^2)^(5/2),x,5,455/72*x*(2+3*x^2)^(3/2)+91/36*x*(2+3*x^2)^(5/2)+1/12*(4-x)*(2+3*x^2)^(7/2)+455/12*arcsinh(x*sqrt(3/2))/sqrt(3)+455/24*x*sqrt(2+3*x^2)],
[(5-x)*(2+3*x^2)^(5/2),x,5,25/12*x*(2+3*x^2)^(3/2)+5/6*x*(2+3*x^2)^(5/2)-1/21*(2+3*x^2)^(7/2)+25/2*arcsinh(x*sqrt(3/2))/sqrt(3)+25/4*x*sqrt(2+3*x^2)],
[(5-x)*(2+3*x^2)^(5/2)/(3+2*x),x,7,7/96*(130-53*x)*(2+3*x^2)^(3/2)+1/60*(39-5*x)*(2+3*x^2)^(5/2)-162673/128*arcsinh(x*sqrt(3/2))/sqrt(3)-15925/128*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+7/64*(2275-691*x)*sqrt(2+3*x^2)],
[(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^2,x,7,-1/24*(310-153*x)*(2+3*x^2)^(3/2)-1/10*(34+x)*(2+3*x^2)^(5/2)/(3+2*x)+18543/32*arcsinh(x*sqrt(3/2))*sqrt(3)+5425/32*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)-7/16*(775-243*x)*sqrt(2+3*x^2)],
[(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^3,x,7,5/32*(178+29*x)*(2+3*x^2)^(3/2)/(3+2*x)-1/16*(29+2*x)*(2+3*x^2)^(5/2)/(3+2*x)^2-43995/128*arcsinh(x*sqrt(3/2))*sqrt(3)-12885/128*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(35)+15/64*(859-267*x)*sqrt(2+3*x^2)],
[(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^4,x,7,5/12*(37+12*x)*(2+3*x^2)^(3/2)/(3+2*x)^2-1/6*(8+x)*(2+3*x^2)^(5/2)/(3+2*x)^3+3657/16*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))*sqrt(5/7)+1785/16*arcsinh(x*sqrt(3/2))*sqrt(3)-15/8*(119+37*x)*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^5,x,7,-1/672*(5003+5517*x)*(2+3*x^2)^(3/2)/(3+2*x)^3-1/16*(19+4*x)*(2+3*x^2)^(5/2)/(3+2*x)^4-2625/128*arcsinh(x*sqrt(3/2))*sqrt(3)-188379/896*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+3/448*(6125+1917*x)*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^6,x,7,1/9800*(6637+8193*x)*(2+3*x^2)^(3/2)/(3+2*x)^3+1/140*(23+76*x)*(2+3*x^2)^(5/2)/(3+2*x)^5+63/32*arcsinh(x*sqrt(3/2))*sqrt(3)+789723/39200*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-9/19600*(8575+2643*x)*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^7,x,7,1/1568*(202+403*x)*(2+3*x^2)^(3/2)/(3+2*x)^4+1/420*(11+159*x)*(2+3*x^2)^(5/2)/(3+2*x)^6-9/128*arcsinh(x*sqrt(3/2))*sqrt(3)-159759/219520*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+9/109760*(4373+5167*x)*sqrt(2+3*x^2)/(3+2*x)^2],
[(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^8,x,6,-41/34300*(4-9*x)*(2+3*x^2)^(3/2)/(3+2*x)^4-41/7350*(4-9*x)*(2+3*x^2)^(5/2)/(3+2*x)^6-13/245*(2+3*x^2)^(7/2)/(3+2*x)^7-1107/600250*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-369/1200500*(4-9*x)*sqrt(2+3*x^2)/(3+2*x)^2],
[(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^9,x,7,-699/2401000*(4-9*x)*(2+3*x^2)^(3/2)/(3+2*x)^4-233/171500*(4-9*x)*(2+3*x^2)^(5/2)/(3+2*x)^6-13/280*(2+3*x^2)^(7/2)/(3+2*x)^8-773/68600*(2+3*x^2)^(7/2)/(3+2*x)^7-18873/42017500*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-6291/84035000*(4-9*x)*sqrt(2+3*x^2)/(3+2*x)^2],
[(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^10,x,8,-2847/42017500*(4-9*x)*(2+3*x^2)^(3/2)/(3+2*x)^4-949/3001250*(4-9*x)*(2+3*x^2)^(5/2)/(3+2*x)^6-13/315*(2+3*x^2)^(7/2)/(3+2*x)^9-27/2450*(2+3*x^2)^(7/2)/(3+2*x)^8-4741/1800750*(2+3*x^2)^(7/2)/(3+2*x)^7-76869/735306250*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-25623/1470612500*(4-9*x)*sqrt(2+3*x^2)/(3+2*x)^2],
[(5-x)*(2+3*x^2)^(5/2)/(3+2*x)^11,x,9,-219699/14706125000*(4-9*x)*(2+3*x^2)^(3/2)/(3+2*x)^4-73233/1050437500*(4-9*x)*(2+3*x^2)^(5/2)/(3+2*x)^6-13/350*(2+3*x^2)^(7/2)/(3+2*x)^10-1171/110250*(2+3*x^2)^(7/2)/(3+2*x)^9-4393/1715000*(2+3*x^2)^(7/2)/(3+2*x)^8-739619/1260525000*(2+3*x^2)^(7/2)/(3+2*x)^7-5931873/257357187500*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-1977291/514714375000*(4-9*x)*sqrt(2+3*x^2)/(3+2*x)^2],

# p<0
[(5-x)*(3+2*x)^4/sqrt(2+3*x^2),x,5,343/3*arcsinh(x*sqrt(3/2))/sqrt(3)+1477/270*(3+2*x)^2*sqrt(2+3*x^2)+19/30*(3+2*x)^3*sqrt(2+3*x^2)-1/15*(3+2*x)^4*sqrt(2+3*x^2)+49/81*(383+99*x)*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^3/sqrt(2+3*x^2),x,4,275/3*arcsinh(x*sqrt(3/2))/sqrt(3)+31/36*(3+2*x)^2*sqrt(2+3*x^2)-1/12*(3+2*x)^3*sqrt(2+3*x^2)+5/54*(809+171*x)*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^2/sqrt(2+3*x^2),x,3,127/3*arcsinh(x*sqrt(3/2))/sqrt(3)-1/9*(3+2*x)^2*sqrt(2+3*x^2)+2/27*(251+36*x)*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)/sqrt(2+3*x^2),x,2,47/3*arcsinh(x*sqrt(3/2))/sqrt(3)+1/3*(7-x)*sqrt(2+3*x^2)],
[(5-x)/sqrt(2+3*x^2),x,2,5*arcsinh(x*sqrt(3/2))/sqrt(3)-1/3*sqrt(2+3*x^2)],
[(5-x)/((3+2*x)*sqrt(2+3*x^2)),x,4,-1/2*arcsinh(x*sqrt(3/2))/sqrt(3)-13/2*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)],
[(5-x)/((3+2*x)^2*sqrt(2+3*x^2)),x,3,-41/35*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-13/35*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^3*sqrt(2+3*x^2)),x,4,-291/1225*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-13/70*sqrt(2+3*x^2)/(3+2*x)^2-281/2450*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^4*sqrt(2+3*x^2)),x,5,-57/1715*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-13/105*sqrt(2+3*x^2)/(3+2*x)^3-16/245*sqrt(2+3*x^2)/(3+2*x)^2-10/343*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^5*sqrt(2+3*x^2)),x,6,27/42875*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-13/140*sqrt(2+3*x^2)/(3+2*x)^4-97/2100*sqrt(2+3*x^2)/(3+2*x)^3-87/4900*sqrt(2+3*x^2)/(3+2*x)^2-991/171500*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^6*sqrt(2+3*x^2)),x,7,19737/7503125*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)-13/175*sqrt(2+3*x^2)/(3+2*x)^5-439/12250*sqrt(2+3*x^2)/(3+2*x)^4-797/61250*sqrt(2+3*x^2)/(3+2*x)^3-1611/428750*sqrt(2+3*x^2)/(3+2*x)^2-10023/15006250*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)*(3+2*x)^4/(2+3*x^2)^(3/2),x,4,880/3*arcsinh(x*sqrt(3/2))/sqrt(3)-7/6*(2-7*x)*(3+2*x)^3/sqrt(2+3*x^2)-151/27*(3+2*x)^2*sqrt(2+3*x^2)-10/81*(185+207*x)*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^3/(2+3*x^2)^(3/2),x,3,134/3*arcsinh(x*sqrt(3/2))/sqrt(3)-7/6*(2-7*x)*(3+2*x)^2/sqrt(2+3*x^2)-2/9*(131+51*x)*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^2/(2+3*x^2)^(3/2),x,3,8/3*arcsinh(x*sqrt(3/2))/sqrt(3)-7/6*(2-7*x)*(3+2*x)/sqrt(2+3*x^2)-53/9*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)/(2+3*x^2)^(3/2),x,2,-2/3*arcsinh(x*sqrt(3/2))/sqrt(3)-7/6*(2-7*x)/sqrt(2+3*x^2)],
[(5-x)/(2+3*x^2)^(3/2),x,1,1/6*(2+15*x)/sqrt(2+3*x^2)],
[(5-x)/((3+2*x)*(2+3*x^2)^(3/2)),x,4,-26/35*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/70*(26+41*x)/sqrt(2+3*x^2)],
[(5-x)/((3+2*x)^2*(2+3*x^2)^(3/2)),x,4,-632/1225*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/70*(26+41*x)/((3+2*x)*sqrt(2+3*x^2))+19/1225*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^3*(2+3*x^2)^(3/2)),x,5,-1962/8575*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/70*(26+41*x)/((3+2*x)^2*sqrt(2+3*x^2))+9/245*sqrt(2+3*x^2)/(3+2*x)^2-331/8575*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^4*(2+3*x^2)^(3/2)),x,6,-3312/42875*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/70*(26+41*x)/((3+2*x)^3*sqrt(2+3*x^2))+23/525*sqrt(2+3*x^2)/(3+2*x)^3-27/1225*sqrt(2+3*x^2)/(3+2*x)^2-1051/42875*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^5*(2+3*x^2)^(3/2)),x,7,-30078/1500625*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/70*(26+41*x)/((3+2*x)^4*sqrt(2+3*x^2))+58/1225*sqrt(2+3*x^2)/(3+2*x)^4-298/18375*sqrt(2+3*x^2)/(3+2*x)^3-708/42875*sqrt(2+3*x^2)/(3+2*x)^2-14944/1500625*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)*(3+2*x)^6/(2+3*x^2)^(5/2),x,5,-7/18*(2-7*x)*(3+2*x)^5/(2+3*x^2)^(3/2)+20720/27*arcsinh(x*sqrt(3/2))/sqrt(3)+1/54*(3+2*x)^3*(158+2427*x)/sqrt(2+3*x^2)-2639/81*(3+2*x)^2*sqrt(2+3*x^2)-70/243*(2167+801*x)*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^5/(2+3*x^2)^(5/2),x,4,-7/18*(2-7*x)*(3+2*x)^4/(2+3*x^2)^(3/2)+1600/27*arcsinh(x*sqrt(3/2))/sqrt(3)-5/54*(16-421*x)*(3+2*x)^2/sqrt(2+3*x^2)-50/81*(299+93*x)*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^4/(2+3*x^2)^(5/2),x,4,-7/18*(2-7*x)*(3+2*x)^3/(2+3*x^2)^(3/2)-16/9*arcsinh(x*sqrt(3/2))/sqrt(3)-1/54*(318-1783*x)*(3+2*x)/sqrt(2+3*x^2)-2027/81*sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^3/(2+3*x^2)^(5/2),x,3,-7/18*(2-7*x)*(3+2*x)^2/(2+3*x^2)^(3/2)-8/9*arcsinh(x*sqrt(3/2))/sqrt(3)+1/54*(-556+1461*x)/sqrt(2+3*x^2)],
[(5-x)*(3+2*x)^2/(2+3*x^2)^(5/2),x,2,1/18*(3+2*x)^2*(2+15*x)/(2+3*x^2)^(3/2)-41/54*(4-9*x)/sqrt(2+3*x^2)],
[(5-x)*(3+2*x)/(2+3*x^2)^(5/2),x,2,-7/18*(2-7*x)/(2+3*x^2)^(3/2)+43/18*x/sqrt(2+3*x^2)],
[(5-x)/(2+3*x^2)^(5/2),x,2,1/18*(2+15*x)/(2+3*x^2)^(3/2)+5/6*x/sqrt(2+3*x^2)],
[(5-x)/((3+2*x)*(2+3*x^2)^(5/2)),x,5,1/210*(26+41*x)/(2+3*x^2)^(3/2)-104/1225*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/7350*(312+2137*x)/sqrt(2+3*x^2)],
[(5-x)/((3+2*x)^2*(2+3*x^2)^(5/2)),x,5,1/210*(26+41*x)/((3+2*x)*(2+3*x^2)^(3/2))-176/1715*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/1470*(34+507*x)/((3+2*x)*sqrt(2+3*x^2))+277/5145*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^3*(2+3*x^2)^(5/2)),x,6,1/210*(26+41*x)/((3+2*x)^2*(2+3*x^2)^(3/2))-3072/42875*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/1050*(4+419*x)/((3+2*x)^2*sqrt(2+3*x^2))+83/1225*sqrt(2+3*x^2)/(3+2*x)^2+857/128625*sqrt(2+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^4*(2+3*x^2)^(5/2)),x,7,1/210*(26+41*x)/((3+2*x)^3*(2+3*x^2)^(3/2))-55344/1500625*arctanh((4-9*x)/(sqrt(35)*sqrt(2+3*x^2)))/sqrt(35)+1/7350*(-114+3331*x)/((3+2*x)^3*sqrt(2+3*x^2))+1471/18375*sqrt(2+3*x^2)/(3+2*x)^3+541/42875*sqrt(2+3*x^2)/(3+2*x)^2-5987/1500625*sqrt(2+3*x^2)/(3+2*x)],

# Integrands of the form (d+e x)^(m/2) (A+B x) (a+c x^2)^p

# p>0
[(A+B*x)*(d+e*x)^(3/2)*(a+c*x^2),x,2,-2/5*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^(5/2)/e^4+2/7*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(7/2)/e^4-2/9*c*(3*B*d-A*e)*(d+e*x)^(9/2)/e^4+2/11*B*c*(d+e*x)^(11/2)/e^4],
[(A+B*x)*(a+c*x^2)*sqrt(d+e*x),x,2,-2/3*(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^(3/2)/e^4+2/5*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^4-2/7*c*(3*B*d-A*e)*(d+e*x)^(7/2)/e^4+2/9*B*c*(d+e*x)^(9/2)/e^4],
[(A+B*x)*(a+c*x^2)/sqrt(d+e*x),x,2,2/3*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^4-2/5*c*(3*B*d-A*e)*(d+e*x)^(5/2)/e^4+2/7*B*c*(d+e*x)^(7/2)/e^4-2*(B*d-A*e)*(c*d^2+a*e^2)*sqrt(d+e*x)/e^4],
[(A+B*x)*(a+c*x^2)/(d+e*x)^(3/2),x,2,-2/3*c*(3*B*d-A*e)*(d+e*x)^(3/2)/e^4+2/5*B*c*(d+e*x)^(5/2)/e^4+2*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*sqrt(d+e*x))+2*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^4],
[(A+B*x)*(a+c*x^2)/(d+e*x)^(5/2),x,2,2/3*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^(3/2))+2/3*B*c*(d+e*x)^(3/2)/e^4-2*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^4*sqrt(d+e*x))-2*c*(3*B*d-A*e)*sqrt(d+e*x)/e^4],
[(A+B*x)*(a+c*x^2)/(d+e*x)^(7/2),x,2,2/5*(B*d-A*e)*(c*d^2+a*e^2)/(e^4*(d+e*x)^(5/2))-2/3*(3*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^4*(d+e*x)^(3/2))+2*c*(3*B*d-A*e)/(e^4*sqrt(d+e*x))+2*B*c*sqrt(d+e*x)/e^4],
[(A+B*x)*(a+c*x^2)^2*sqrt(d+e*x),x,2,-2/3*(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^(3/2)/e^6+2/5*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^6-4/7*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(7/2)/e^6+4/9*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(9/2)/e^6-2/11*c^2*(5*B*d-A*e)*(d+e*x)^(11/2)/e^6+2/13*B*c^2*(d+e*x)^(13/2)/e^6],
[(A+B*x)*(a+c*x^2)^2/sqrt(d+e*x),x,2,2/3*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^6-4/5*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(5/2)/e^6+4/7*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(7/2)/e^6-2/9*c^2*(5*B*d-A*e)*(d+e*x)^(9/2)/e^6+2/11*B*c^2*(d+e*x)^(11/2)/e^6-2*(B*d-A*e)*(c*d^2+a*e^2)^2*sqrt(d+e*x)/e^6],
[(A+B*x)*(a+c*x^2)^2/(d+e*x)^(3/2),x,2,-4/3*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3/2)/e^6+4/5*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^6-2/7*c^2*(5*B*d-A*e)*(d+e*x)^(7/2)/e^6+2/9*B*c^2*(d+e*x)^(9/2)/e^6+2*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*sqrt(d+e*x))+2*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^6],
[(A+B*x)*(a+c*x^2)^2/(d+e*x)^(5/2),x,2,2/3*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(3/2))+4/3*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^6-2/5*c^2*(5*B*d-A*e)*(d+e*x)^(5/2)/e^6+2/7*B*c^2*(d+e*x)^(7/2)/e^6-2*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*sqrt(d+e*x))-4*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*sqrt(d+e*x)/e^6],
[(A+B*x)*(a+c*x^2)^2/(d+e*x)^(7/2),x,2,2/5*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(5/2))-2/3*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^(3/2))-2/3*c^2*(5*B*d-A*e)*(d+e*x)^(3/2)/e^6+2/5*B*c^2*(d+e*x)^(5/2)/e^6+4*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*sqrt(d+e*x))+4*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^6],
[(A+B*x)*(a+c*x^2)^2/(d+e*x)^(9/2),x,2,2/7*(B*d-A*e)*(c*d^2+a*e^2)^2/(e^6*(d+e*x)^(7/2))-2/5*(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)/(e^6*(d+e*x)^(5/2))+4/3*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^6*(d+e*x)^(3/2))+2/3*B*c^2*(d+e*x)^(3/2)/e^6-4*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)/(e^6*sqrt(d+e*x))-2*c^2*(5*B*d-A*e)*sqrt(d+e*x)/e^6],
[(A+B*x)*(a+c*x^2)^3/sqrt(d+e*x),x,2,2/3*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^8-6/5*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(5/2)/e^8-2/7*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(7/2)/e^8-2/9*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(9/2)/e^8+6/11*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(11/2)/e^8-2/13*c^3*(7*B*d-A*e)*(d+e*x)^(13/2)/e^8+2/15*B*c^3*(d+e*x)^(15/2)/e^8-2*(B*d-A*e)*(c*d^2+a*e^2)^3*sqrt(d+e*x)/e^8],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^(3/2),x,2,-2*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3/2)/e^8-2/5*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(5/2)/e^8-2/7*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(7/2)/e^8+2/3*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(9/2)/e^8-2/11*c^3*(7*B*d-A*e)*(d+e*x)^(11/2)/e^8+2/13*B*c^3*(d+e*x)^(13/2)/e^8+2*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*sqrt(d+e*x))+2*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^8],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^(5/2),x,2,2/3*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(3/2))-2/3*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(3/2)/e^8-2/5*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(5/2)/e^8+6/7*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(7/2)/e^8-2/9*c^3*(7*B*d-A*e)*(d+e*x)^(9/2)/e^8+2/11*B*c^3*(d+e*x)^(11/2)/e^8-2*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*sqrt(d+e*x))-6*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*sqrt(d+e*x)/e^8],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^(7/2),x,2,2/5*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(5/2))-2/3*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(3/2))-2/3*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(3/2)/e^8+6/5*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(5/2)/e^8-2/7*c^3*(7*B*d-A*e)*(d+e*x)^(7/2)/e^8+2/9*B*c^3*(d+e*x)^(9/2)/e^8+6*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*sqrt(d+e*x))-2*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*sqrt(d+e*x)/e^8],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^(9/2),x,2,2/7*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(7/2))-2/5*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(5/2))+2*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^(3/2))+2*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(3/2)/e^8-2/5*c^3*(7*B*d-A*e)*(d+e*x)^(5/2)/e^8+2/7*B*c^3*(d+e*x)^(7/2)/e^8+2*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*sqrt(d+e*x))-2*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*sqrt(d+e*x)/e^8],
[(A+B*x)*(a+c*x^2)^3/(d+e*x)^(11/2),x,2,2/9*(B*d-A*e)*(c*d^2+a*e^2)^3/(e^8*(d+e*x)^(9/2))-2/7*(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)/(e^8*(d+e*x)^(7/2))+6/5*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)/(e^8*(d+e*x)^(5/2))+2/3*c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))/(e^8*(d+e*x)^(3/2))-2/3*c^3*(7*B*d-A*e)*(d+e*x)^(3/2)/e^8+2/5*B*c^3*(d+e*x)^(5/2)/e^8+2*c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)/(e^8*sqrt(d+e*x))+6*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/e^8],

# p<0
[(A+B*x)*(d+e*x)^(5/2)/(a-c*x^2),x,7,-2/3*(B*d+A*e)*(d+e*x)^(3/2)/c-2/5*B*(d+e*x)^(5/2)/c+arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(B*sqrt(a)-A*sqrt(c))*(-e*sqrt(a)+d*sqrt(c))^(5/2)/(c^(9/4)*sqrt(a))+arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(B*sqrt(a)+A*sqrt(c))*(e*sqrt(a)+d*sqrt(c))^(5/2)/(c^(9/4)*sqrt(a))-2*(B*c*d^2+2*A*c*d*e+a*B*e^2)*sqrt(d+e*x)/c^2],
[(A+B*x)*(d+e*x)^(3/2)/(a-c*x^2),x,6,-2/3*B*(d+e*x)^(3/2)/c+arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(B*sqrt(a)-A*sqrt(c))*(-e*sqrt(a)+d*sqrt(c))^(3/2)/(c^(7/4)*sqrt(a))+arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(B*sqrt(a)+A*sqrt(c))*(e*sqrt(a)+d*sqrt(c))^(3/2)/(c^(7/4)*sqrt(a))-2*(B*d+A*e)*sqrt(d+e*x)/c],
[(A+B*x)*(d+e*x)^(1/2)/(a-c*x^2),x,5,-2*B*sqrt(d+e*x)/c+arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(B*sqrt(a)-A*sqrt(c))*sqrt(-e*sqrt(a)+d*sqrt(c))/(c^(5/4)*sqrt(a))+arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(B*sqrt(a)+A*sqrt(c))*sqrt(e*sqrt(a)+d*sqrt(c))/(c^(5/4)*sqrt(a))],
[(A+B*x)/((d+e*x)^(1/2)*(a-c*x^2)),x,4,arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(B-A*sqrt(c)/sqrt(a))/(c^(3/4)*sqrt(-e*sqrt(a)+d*sqrt(c)))+arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(B+A*sqrt(c)/sqrt(a))/(c^(3/4)*sqrt(e*sqrt(a)+d*sqrt(c)))],
[(A+B*x)/((d+e*x)^(3/2)*(a-c*x^2)),x,5,arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(B*sqrt(a)-A*sqrt(c))/(c^(1/4)*sqrt(a)*(-e*sqrt(a)+d*sqrt(c))^(3/2))+arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(B*sqrt(a)+A*sqrt(c))/(c^(1/4)*sqrt(a)*(e*sqrt(a)+d*sqrt(c))^(3/2))-2*(B*d-A*e)/((c*d^2-a*e^2)*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(5/2)*(a-c*x^2)),x,6,-2/3*(B*d-A*e)/((c*d^2-a*e^2)*(d+e*x)^(3/2))+c^(1/4)*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(B*sqrt(a)-A*sqrt(c))/(sqrt(a)*(-e*sqrt(a)+d*sqrt(c))^(5/2))+c^(1/4)*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(B*sqrt(a)+A*sqrt(c))/(sqrt(a)*(e*sqrt(a)+d*sqrt(c))^(5/2))-2*(B*c*d^2-2*A*c*d*e+a*B*e^2)/((c*d^2-a*e^2)^2*sqrt(d+e*x))],
[(A+B*x)*(d+e*x)^(5/2)/(a-c*x^2)^2,x,6,1/2*(d+e*x)^(3/2)*(a*(B*d+A*e)+(A*c*d+a*B*e)*x)/(a*c*(a-c*x^2))+1/4*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(e*sqrt(a)+d*sqrt(c))^(3/2)*(2*A*c*d-5*a*B*e-3*A*e*sqrt(a)*sqrt(c))/(a^(3/2)*c^(9/4))-1/4*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(-e*sqrt(a)+d*sqrt(c))^(3/2)*(2*A*c*d-5*a*B*e+3*A*e*sqrt(a)*sqrt(c))/(a^(3/2)*c^(9/4))+1/2*e*(A*c*d+5*a*B*e)*sqrt(d+e*x)/(a*c^2)],
[(A+B*x)*(d+e*x)^(3/2)/(a-c*x^2)^2,x,5,1/2*(a*(B*d+A*e)+(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*c*(a-c*x^2))-1/4*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(2*A*c*d-3*a*B*e+A*e*sqrt(a)*sqrt(c))*sqrt(-e*sqrt(a)+d*sqrt(c))/(a^(3/2)*c^(7/4))+1/4*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(2*A*c*d-3*a*B*e-A*e*sqrt(a)*sqrt(c))*sqrt(e*sqrt(a)+d*sqrt(c))/(a^(3/2)*c^(7/4))],
[(A+B*x)*(d+e*x)^(1/2)/(a-c*x^2)^2,x,5,1/2*(a*B+A*c*x)*sqrt(d+e*x)/(a*c*(a-c*x^2))-1/4*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(2*A*c*d-a*B*e-A*e*sqrt(a)*sqrt(c))/(a^(3/2)*c^(5/4)*sqrt(-e*sqrt(a)+d*sqrt(c)))+1/4*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(2*A*c*d-a*B*e+A*e*sqrt(a)*sqrt(c))/(a^(3/2)*c^(5/4)*sqrt(e*sqrt(a)+d*sqrt(c)))],
[(A+B*x)/((d+e*x)^(1/2)*(a-c*x^2)^2),x,5,-1/4*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(2*A*c*d+a*B*e-3*A*e*sqrt(a)*sqrt(c))/(a^(3/2)*c^(3/4)*(-e*sqrt(a)+d*sqrt(c))^(3/2))+1/4*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(2*A*c*d+a*B*e+3*A*e*sqrt(a)*sqrt(c))/(a^(3/2)*c^(3/4)*(e*sqrt(a)+d*sqrt(c))^(3/2))+1/2*(a*(B*d-A*e)+(A*c*d-a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2-a*e^2)*(a-c*x^2))],
[(A+B*x)/((d+e*x)^(3/2)*(a-c*x^2)^2),x,6,-1/4*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(2*A*c*d+3*a*B*e-5*A*e*sqrt(a)*sqrt(c))/(a^(3/2)*c^(1/4)*(-e*sqrt(a)+d*sqrt(c))^(5/2))+1/4*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(2*A*c*d+3*a*B*e+5*A*e*sqrt(a)*sqrt(c))/(a^(3/2)*c^(1/4)*(e*sqrt(a)+d*sqrt(c))^(5/2))-1/2*e*(A*c*d^2-6*a*B*d*e+5*a*A*e^2)/(a*(c*d^2-a*e^2)^2*sqrt(d+e*x))+1/2*(a*(B*d-A*e)+(A*c*d-a*B*e)*x)/(a*(c*d^2-a*e^2)*(a-c*x^2)*sqrt(d+e*x))],
[(A+B*x)*(d+e*x)^(7/2)/(a-c*x^2)^3,x,6,1/4*(d+e*x)^(5/2)*(a*(B*d+A*e)+(A*c*d+a*B*e)*x)/(a*c*(a-c*x^2)^2)-1/32*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(e*sqrt(a)+d*sqrt(c))^(3/2)*(7*a*B*e*(-3*e*sqrt(a)+2*d*sqrt(c))-A*(12*c^(3/2)*d^2-18*c*d*e*sqrt(a)+5*a*e^2*sqrt(c)))/(a^(5/2)*c^(11/4))+1/32*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(-e*sqrt(a)+d*sqrt(c))^(3/2)*(7*a*B*e*(3*e*sqrt(a)+2*d*sqrt(c))-A*(12*c^(3/2)*d^2+18*c*d*e*sqrt(a)+5*a*e^2*sqrt(c)))/(a^(5/2)*c^(11/4))+1/16*(a*e*(7*A*c*d^2-14*a*B*d*e-5*a*A*e^2)+(2*A*c*d*(3*c*d^2-2*a*e^2)-7*a*B*e*(c*d^2+a*e^2))*x)*sqrt(d+e*x)/(a^2*c^2*(a-c*x^2))],
[(A+B*x)*(d+e*x)^(5/2)/(a-c*x^2)^3,x,6,1/4*(d+e*x)^(3/2)*(a*(B*d+A*e)+(A*c*d+a*B*e)*x)/(a*c*(a-c*x^2)^2)+1/16*(a*e*(3*A*c*d-5*a*B*e)+c*(6*A*c*d^2-a*e*(5*B*d+3*A*e))*x)*sqrt(d+e*x)/(a^2*c^2*(a-c*x^2))+1/32*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(5*a*B*e*(e*sqrt(a)+2*d*sqrt(c))-3*A*(4*c^(3/2)*d^2+2*c*d*e*sqrt(a)-a*e^2*sqrt(c)))*sqrt(-e*sqrt(a)+d*sqrt(c))/(a^(5/2)*c^(9/4))-1/32*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(5*a*B*e*(-e*sqrt(a)+2*d*sqrt(c))-A*(12*c^(3/2)*d^2-6*c*d*e*sqrt(a)-3*a*e^2*sqrt(c)))*sqrt(e*sqrt(a)+d*sqrt(c))/(a^(5/2)*c^(9/4))],
[(A+B*x)*(d+e*x)^(3/2)/(a-c*x^2)^3,x,6,1/4*(a*(B*d+A*e)+(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*c*(a-c*x^2)^2)-1/16*(a*A*e-3*(2*A*c*d-a*B*e)*x)*sqrt(d+e*x)/(a^2*c*(a-c*x^2))+3/32*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(a*B*e*(-e*sqrt(a)+2*d*sqrt(c))-A*(4*c^(3/2)*d^2-2*c*d*e*sqrt(a)-a*e^2*sqrt(c)))/(a^(5/2)*c^(7/4)*sqrt(-e*sqrt(a)+d*sqrt(c)))-3/32*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(a*B*e*(e*sqrt(a)+2*d*sqrt(c))-A*(4*c^(3/2)*d^2+2*c*d*e*sqrt(a)-a*e^2*sqrt(c)))/(a^(5/2)*c^(7/4)*sqrt(e*sqrt(a)+d*sqrt(c)))],
[(A+B*x)*(d+e*x)^(1/2)/(a-c*x^2)^3,x,6,1/32*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(a*B*e*(-3*e*sqrt(a)+2*d*sqrt(c))-A*(12*c^(3/2)*d^2-18*c*d*e*sqrt(a)+5*a*e^2*sqrt(c)))/(a^(5/2)*c^(5/4)*(-e*sqrt(a)+d*sqrt(c))^(3/2))-1/32*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(a*B*e*(3*e*sqrt(a)+2*d*sqrt(c))-A*(12*c^(3/2)*d^2+18*c*d*e*sqrt(a)+5*a*e^2*sqrt(c)))/(a^(5/2)*c^(5/4)*(e*sqrt(a)+d*sqrt(c))^(3/2))+1/4*(a*B+A*c*x)*sqrt(d+e*x)/(a*c*(a-c*x^2)^2)-1/16*(a*e*(A*c*d-a*B*e)-c*(6*A*c*d^2-a*B*d*e-5*a*A*e^2)*x)*sqrt(d+e*x)/(a^2*c*(c*d^2-a*e^2)*(a-c*x^2))],
[(A+B*x)/((d+e*x)^(1/2)*(a-c*x^2)^3),x,6,-1/32*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(-e*sqrt(a)+d*sqrt(c)))*(a*B*e*(-5*e*sqrt(a)+2*d*sqrt(c))+3*A*(4*c^(3/2)*d^2-10*c*d*e*sqrt(a)+7*a*e^2*sqrt(c)))/(a^(5/2)*c^(3/4)*(-e*sqrt(a)+d*sqrt(c))^(5/2))+1/32*arctanh(c^(1/4)*sqrt(d+e*x)/sqrt(e*sqrt(a)+d*sqrt(c)))*(a*B*e*(5*e*sqrt(a)+2*d*sqrt(c))+3*A*(4*c^(3/2)*d^2+10*c*d*e*sqrt(a)+7*a*e^2*sqrt(c)))/(a^(5/2)*c^(3/4)*(e*sqrt(a)+d*sqrt(c))^(5/2))+1/4*(a*(B*d-A*e)+(A*c*d-a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2-a*e^2)*(a-c*x^2)^2)-1/16*(a*e*(A*c*d^2+6*a*B*d*e-7*a*A*e^2)-(6*A*c*d*(c*d^2-2*a*e^2)+a*B*e*(c*d^2+5*a*e^2))*x)*sqrt(d+e*x)/(a^2*(c*d^2-a*e^2)^2*(a-c*x^2))],
[(A+B*x)/((2*A*B*d-A^2*e-B^2*e*x^2)*sqrt(d+e*x)),x,4,-log(B*d-A*e+B*(d+e*x)-sqrt(2)*sqrt(B)*sqrt(2*B*d-A*e)*sqrt(d+e*x))/(e*sqrt(2)*sqrt(B)*sqrt(2*B*d-A*e))+log(B*d-A*e+B*(d+e*x)+sqrt(2)*sqrt(B)*sqrt(2*B*d-A*e)*sqrt(d+e*x))/(e*sqrt(2)*sqrt(B)*sqrt(2*B*d-A*e))],
[(A+B*x)/((1+x^2)*sqrt(1/2*(A^2*e-B^2*e)/(A*B)+e*x)),x,6,-arctan(A/B-sqrt(A)*sqrt(e*(A/B-B/A+2*x))/(sqrt(B)*sqrt(e)))*sqrt(2)*sqrt(A)*sqrt(B)/sqrt(e)+arctan(A/B+sqrt(A)*sqrt(e*(A/B-B/A+2*x))/(sqrt(B)*sqrt(e)))*sqrt(2)*sqrt(A)*sqrt(B)/sqrt(e)],
[(A+B*x)/((1-x^2)*sqrt(d+e*x)),x,4,-(A-B)*arctanh(sqrt(d+e*x)/sqrt(d-e))/sqrt(d-e)+(A+B)*arctanh(sqrt(d+e*x)/sqrt(d+e))/sqrt(d+e)],
[(A+B*x)/((1+x^2)*sqrt(d+e*x)),x,10,arctanh((-sqrt(2)*sqrt(d+e*x)+sqrt(d+sqrt(d^2+e^2)))/sqrt(d-sqrt(d^2+e^2)))*(A*e-B*(d-sqrt(d^2+e^2)))/(sqrt(2)*sqrt(d^2+e^2)*sqrt(d-sqrt(d^2+e^2)))-arctanh((sqrt(2)*sqrt(d+e*x)+sqrt(d+sqrt(d^2+e^2)))/sqrt(d-sqrt(d^2+e^2)))*(A*e-B*(d-sqrt(d^2+e^2)))/(sqrt(2)*sqrt(d^2+e^2)*sqrt(d-sqrt(d^2+e^2)))-1/2*log(d+e*x+sqrt(d^2+e^2)-sqrt(2)*sqrt(d+e*x)*sqrt(d+sqrt(d^2+e^2)))*(A*e-B*(d+sqrt(d^2+e^2)))/(sqrt(2)*sqrt(d^2+e^2)*sqrt(d+sqrt(d^2+e^2)))+1/2*log(d+e*x+sqrt(d^2+e^2)+sqrt(2)*sqrt(d+e*x)*sqrt(d+sqrt(d^2+e^2)))*(A*e-B*(d+sqrt(d^2+e^2)))/(sqrt(2)*sqrt(d^2+e^2)*sqrt(d+sqrt(d^2+e^2)))],
[(1-x)*sqrt(1+x)/(1+x^2),x,12,-2*sqrt(1+x)-1/2*log(1+x+sqrt(2)-sqrt(1+x)*sqrt(2*(1+sqrt(2))))/sqrt(1+sqrt(2))+1/2*log(1+x+sqrt(2)+sqrt(1+x)*sqrt(2*(1+sqrt(2))))/sqrt(1+sqrt(2))-arctan((-2*sqrt(1+x)+sqrt(2*(1+sqrt(2))))/sqrt(2*(-1+sqrt(2))))*sqrt(1+sqrt(2))+arctan((2*sqrt(1+x)+sqrt(2*(1+sqrt(2))))/sqrt(2*(-1+sqrt(2))))*sqrt(1+sqrt(2))],
[(3+x)/((1+x^2)*sqrt(4+3*x)),x,6,-arctan(3-sqrt(2)*sqrt(4+3*x))*sqrt(2)+arctan(3+sqrt(8+6*x))*sqrt(2)],
[(1-3*x)/((1+x^2)*sqrt(4+3*x)),x,4,-log(3+x-sqrt(2)*sqrt(4+3*x))/sqrt(2)+log(3+x+sqrt(2)*sqrt(4+3*x))/sqrt(2)],
[(2+x)/((1+x^2)*sqrt(3+4*x)),x,6,-arctan(2-sqrt(3+4*x))+arctan(2+sqrt(3+4*x))],
[(-2+x)/((-8+x^2)*sqrt(-3+x)),x,4,arctan((-1+sqrt(2))*sqrt(-3+x))/sqrt(2)+arctan((1+sqrt(2))*sqrt(-3+x))/sqrt(2),arctan(sqrt(-3+x)/sqrt(3-2*sqrt(2)))/sqrt(2)+arctan(sqrt(-3+x)/sqrt(3+2*sqrt(2)))/sqrt(2)],

# Integrands of the form (d+e x)^(m/2) (A+B x) (a+c x^2)^(p/2)

# p>0
[(A+B*x)*sqrt(d+e*x)*sqrt(a+c*x^2),x,7,2/7*B*(a+c*x^2)^(3/2)*sqrt(d+e*x)/c-2/105*(4*B*c*d^2-7*A*c*d*e+5*a*B*e^2-3*c*e*(B*d+7*A*e)*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/(c*e^2)-4/105*(4*B*c*d^3-7*A*c*d^2*e+8*a*B*d*e^2+21*a*A*e^3)*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(e^3*sqrt(c)*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))+4/105*(c*d^2+a*e^2)*(4*B*c*d^2-7*A*c*d*e+5*a*B*e^2)*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(c^(3/2)*e^3*sqrt(d+e*x)*sqrt(a+c*x^2))],
[(A+B*x)*sqrt(a+c*x^2)/sqrt(d+e*x),x,6,-2/15*(4*B*d-5*A*e-3*B*e*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/e^2-4/15*(4*B*c*d^2-5*A*c*d*e+3*a*B*e^2)*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(e^3*sqrt(c)*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))+4/15*(4*B*d-5*A*e)*(c*d^2+a*e^2)*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(e^3*sqrt(c)*sqrt(d+e*x)*sqrt(a+c*x^2))],
[(A+B*x)*sqrt(a+c*x^2)/(d+e*x)^(3/2),x,6,2/3*(4*B*d-3*A*e+B*e*x)*sqrt(a+c*x^2)/(e^2*sqrt(d+e*x))+4/3*(4*B*d-3*A*e)*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(c)*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(e^3*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))-4/3*(4*B*c*d^2-3*A*c*d*e+a*B*e^2)*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(e^3*sqrt(c)*sqrt(d+e*x)*sqrt(a+c*x^2))],
[(A+B*x)*sqrt(a+c*x^2)/(d+e*x)^(5/2),x,6,-2/3*(4*B*c*d^3-A*c*d^2*e+2*a*B*d*e^2+a*A*e^3+e*(5*B*c*d^2-2*A*c*d*e+3*a*B*e^2)*x)*sqrt(a+c*x^2)/(e^2*(c*d^2+a*e^2)*(d+e*x)^(3/2))-4/3*(4*B*c*d^2-A*c*d*e+3*a*B*e^2)*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(c)*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(e^3*(c*d^2+a*e^2)*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))+4/3*(4*B*d-A*e)*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(c)*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(e^3*sqrt(d+e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(3/2)/sqrt(d+e*x),x,7,-2/63*(8*B*d-9*A*e-7*B*e*x)*(a+c*x^2)^(3/2)*sqrt(d+e*x)/e^2-4/315*(32*B*c*d^3-36*A*c*d^2*e+33*a*B*d*e^2-45*a*A*e^3-3*e*(8*B*c*d^2-9*A*c*d*e+7*a*B*e^2)*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/e^4+8/315*(36*A*c*d*e*(c*d^2+2*a*e^2)-B*(32*c^2*d^4+57*a*c*d^2*e^2+21*a^2*e^4))*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(e^5*sqrt(c)*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))+8/315*(c*d^2+a*e^2)*(32*B*c*d^3-36*A*c*d^2*e+33*a*B*d*e^2-45*a*A*e^3)*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(e^5*sqrt(c)*sqrt(d+e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(3/2),x,7,2/7*(8*B*d-7*A*e+B*e*x)*(a+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+4/35*(5*a*B*e^2+4*c*d*(8*B*d-7*A*e)-3*c*e*(8*B*d-7*A*e)*x)*sqrt(d+e*x)*sqrt(a+c*x^2)/e^4+8/35*(32*B*c*d^3-28*A*c*d^2*e+29*a*B*d*e^2-21*a*A*e^3)*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(c)*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(e^5*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))-8/35*(c*d^2+a*e^2)*(32*B*c*d^2-28*A*c*d*e+5*a*B*e^2)*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(e^5*sqrt(c)*sqrt(d+e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(5/2),x,7,2/15*(8*B*d-5*A*e+3*B*e*x)*(a+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-4/15*(9*a*B*e^2+4*c*d*(8*B*d-5*A*e)+c*e*(8*B*d-5*A*e)*x)*sqrt(a+c*x^2)/(e^4*sqrt(d+e*x))-8/15*(9*a*B*e^2+4*c*d*(8*B*d-5*A*e))*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(c)*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(e^5*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))+8/15*(32*B*c*d^3-20*A*c*d^2*e+17*a*B*d*e^2-5*a*A*e^3)*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(c)*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(e^5*sqrt(d+e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(a+c*x^2)^(3/2)/(d+e*x)^(7/2),x,7,-2/15*(2*B*(4*c*d^3+a*d*e^2)-3*A*(c*d^2*e-a*e^3)+e*(11*B*c*d^2-6*A*c*d*e+5*a*B*e^2)*x)*(a+c*x^2)^(3/2)/(e^2*(c*d^2+a*e^2)*(d+e*x)^(5/2))+4/15*c*(32*B*c*d^3-12*A*c*d^2*e+29*a*B*d*e^2-9*a*A*e^3+e*(8*B*c*d^2-3*A*c*d*e+5*a*B*e^2)*x)*sqrt(a+c*x^2)/(e^4*(c*d^2+a*e^2)*sqrt(d+e*x))+8/15*c^(3/2)*(32*B*c*d^3-12*A*c*d^2*e+29*a*B*d*e^2-9*a*A*e^3)*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(e^5*(c*d^2+a*e^2)*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))-8/15*(32*B*c*d^2-12*A*c*d*e+5*a*B*e^2)*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(c)*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(e^5*sqrt(d+e*x)*sqrt(a+c*x^2))],

# p<0
[(A+B*x)*(d+e*x)^(3/2)/sqrt(a+c*x^2),x,7,2/5*B*(d+e*x)^(3/2)*sqrt(a+c*x^2)/c+2/15*(3*B*d+5*A*e)*sqrt(d+e*x)*sqrt(a+c*x^2)/c-2/15*(3*B*c*d^2+20*A*c*d*e-9*a*B*e^2)*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(c^(3/2)*e*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))+2/15*(3*B*d+5*A*e)*(c*d^2+a*e^2)*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(c^(3/2)*e*sqrt(d+e*x)*sqrt(a+c*x^2))],
[(A+B*x)*sqrt(d+e*x)/sqrt(a+c*x^2),x,6,2/3*B*sqrt(d+e*x)*sqrt(a+c*x^2)/c-2/3*(B*d+3*A*e)*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(e*sqrt(c)*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))+2/3*B*(c*d^2+a*e^2)*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(c^(3/2)*e*sqrt(d+e*x)*sqrt(a+c*x^2))],
[(A+B*x)/(sqrt(d+e*x)*sqrt(a+c*x^2)),x,5,-2*B*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(e*sqrt(c)*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))+2*(B*d-A*e)*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(e*sqrt(c)*sqrt(d+e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((d+e*x)^(3/2)*sqrt(a+c*x^2)),x,6,2*(B*d-A*e)*sqrt(a+c*x^2)/((c*d^2+a*e^2)*sqrt(d+e*x))+2*(B*d-A*e)*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(c)*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(e*(c*d^2+a*e^2)*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))-2*B*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(-a)*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(e*sqrt(c)*sqrt(d+e*x)*sqrt(a+c*x^2))],
[(A+B*x)*(d+e*x)^(3/2)/(a+c*x^2)^(3/2),x,6,-(a*(B*d+A*e)-(A*c*d-a*B*e)*x)*sqrt(d+e*x)/(a*c*sqrt(a+c*x^2))-(A*c*d-3*a*B*e)*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(c^(3/2)*sqrt(-a)*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))+A*(c*d^2+a*e^2)*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(c^(3/2)*sqrt(-a)*sqrt(d+e*x)*sqrt(a+c*x^2))],
[(A+B*x)*sqrt(d+e*x)/(a+c*x^2)^(3/2),x,6,-(a*B-A*c*x)*sqrt(d+e*x)/(a*c*sqrt(a+c*x^2))-A*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(d+e*x)*sqrt(1+c*x^2/a)/(sqrt(-a)*sqrt(c)*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))+(A*c*d+a*B*e)*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(c^(3/2)*sqrt(-a)*sqrt(d+e*x)*sqrt(a+c*x^2))],
[(A+B*x)/((a+c*x^2)^(3/2)*sqrt(d+e*x)),x,6,-(a*(B*d-A*e)-(A*c*d+a*B*e)*x)*sqrt(d+e*x)/(a*(c*d^2+a*e^2)*sqrt(a+c*x^2))-(A*c*d+a*B*e)*EllipticE(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(d+e*x)*sqrt(1+c*x^2/a)/((c*d^2+a*e^2)*sqrt(-a)*sqrt(c)*sqrt(a+c*x^2)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c))))+A*EllipticF(sqrt(1-x*sqrt(c)/sqrt(-a))/sqrt(2),sqrt(-2*a*e/(-a*e+d*sqrt(-a)*sqrt(c))))*sqrt(1+c*x^2/a)*sqrt((d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))/(sqrt(-a)*sqrt(c)*sqrt(d+e*x)*sqrt(a+c*x^2))],

# Integrands of the form (d+e x)^m (A+B x) (a+c x^2)^p when m is symbolic
[(A+B*x)*(d+e*x)^m*(a+c*x^2)^3,x,2,-(B*d-A*e)*(c*d^2+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))+(c*d^2+a*e^2)^2*(7*B*c*d^2-6*A*c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^8*(2+m))-3*c*(c*d^2+a*e^2)*(7*B*c*d^3-5*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3+m)/(e^8*(3+m))-c*(4*A*c*d*e*(5*c*d^2+3*a*e^2)-B*(35*c^2*d^4+30*a*c*d^2*e^2+3*a^2*e^4))*(d+e*x)^(4+m)/(e^8*(4+m))-c^2*(35*B*c*d^3-15*A*c*d^2*e+15*a*B*d*e^2-3*a*A*e^3)*(d+e*x)^(5+m)/(e^8*(5+m))+3*c^2*(7*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(6+m)/(e^8*(6+m))-c^3*(7*B*d-A*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*(d+e*x)^(8+m)/(e^8*(8+m))],
[(A+B*x)*(d+e*x)^m*(a+c*x^2)^2,x,2,-(B*d-A*e)*(c*d^2+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))+(c*d^2+a*e^2)*(5*B*c*d^2-4*A*c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^6*(2+m))-2*c*(5*B*c*d^3-3*A*c*d^2*e+3*a*B*d*e^2-a*A*e^3)*(d+e*x)^(3+m)/(e^6*(3+m))+2*c*(5*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(4+m)/(e^6*(4+m))-c^2*(5*B*d-A*e)*(d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*(d+e*x)^(6+m)/(e^6*(6+m))],
[(A+B*x)*(d+e*x)^m*(a+c*x^2),x,2,-(B*d-A*e)*(c*d^2+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(3*B*c*d^2-2*A*c*d*e+a*B*e^2)*(d+e*x)^(2+m)/(e^4*(2+m))-c*(3*B*d-A*e)*(d+e*x)^(3+m)/(e^4*(3+m))+B*c*(d+e*x)^(4+m)/(e^4*(4+m))],
[(A+B*x)*(d+e*x)^m/(a+c*x^2),x,4,-1/2*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],(d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))*(A+B*sqrt(-a)/sqrt(c))/((1+m)*sqrt(-a)*(e*sqrt(-a)+d*sqrt(c)))-1/2*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],(d+e*x)*sqrt(c)/(-e*sqrt(-a)+d*sqrt(c)))*(a*B+A*sqrt(-a)*sqrt(c))/(a*(1+m)*sqrt(c)*(-e*sqrt(-a)+d*sqrt(c)))],
[(A+B*x)*(d+e*x)^m/(a+c*x^2)^2,x,5,-1/2*(d+e*x)^(1+m)*(a*(B*d-A*e)-(A*c*d+a*B*e)*x)/(a*(c*d^2+a*e^2)*(a+c*x^2))+1/4*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],(d+e*x)*sqrt(c)/(-e*sqrt(-a)+d*sqrt(c)))*(a*e*(A*c*d+a*B*e)*m-(A*(c*d^2+a*e^2*(1-m))+a*B*d*e*m)*sqrt(-a)*sqrt(c))/(a^2*(c*d^2+a*e^2)*(1+m)*sqrt(c)*(-e*sqrt(-a)+d*sqrt(c)))+1/4*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],(d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))*(a*e*(A*c*d+a*B*e)*m+(A*(c*d^2+a*e^2*(1-m))+a*B*d*e*m)*sqrt(-a)*sqrt(c))/(a^2*(c*d^2+a*e^2)*(1+m)*sqrt(c)*(e*sqrt(-a)+d*sqrt(c)))],
[(A+B*x)*(d+e*x)^(1+m)/(a+c*x^2),x,4,-1/2*(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],(d+e*x)*sqrt(c)/(e*sqrt(-a)+d*sqrt(c)))*(A+B*sqrt(-a)/sqrt(c))/((2+m)*sqrt(-a)*(e*sqrt(-a)+d*sqrt(c)))-1/2*(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],(d+e*x)*sqrt(c)/(-e*sqrt(-a)+d*sqrt(c)))*(a*B+A*sqrt(-a)*sqrt(c))/(a*(2+m)*sqrt(c)*(-e*sqrt(-a)+d*sqrt(c)))],

# Integrands of the form (d+e x)^m (A+B x) (a+c x^2)^p when p is symbolic
[(-a*e+c*d*x)*(d+e*x)^(-3-2*p)*(a+c*x^2)^p,x,1,1/2*(a+c*x^2)^(1+p)/((1+p)*(d+e*x)^(2*(1+p)))],

# Integrands of the form (d+e x)^m (f+g x) (a+b x+c x^2)^p when 2 c f-b g=0

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

# p>0
[(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2),x,2,-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4+1/6*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^6/e^4-3/7*c*(2*c*d-b*e)*(d+e*x)^7/e^4+1/4*c^2*(d+e*x)^8/e^4],
[(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2),x,2,-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^4/e^4+1/5*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^5/e^4-1/2*c*(2*c*d-b*e)*(d+e*x)^6/e^4+2/7*c^2*(d+e*x)^7/e^4],
[(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2),x,2,-1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3/e^4+1/4*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^4/e^4-3/5*c*(2*c*d-b*e)*(d+e*x)^5/e^4+1/3*c^2*(d+e*x)^6/e^4],
[(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2),x,2,a*b*d*x+1/2*(b^2*d+2*a*c*d+a*b*e)*x^2+1/3*(3*b*c*d+b^2*e+2*a*c*e)*x^3+1/4*c*(2*c*d+3*b*e)*x^4+2/5*c^2*e*x^5],
[(b+2*c*x)*(a+b*x+c*x^2),x,1,1/2*(a+b*x+c*x^2)^2],
[(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x),x,2,(2*c^2*d^2+b^2*e^2-c*e*(3*b*d-2*a*e))*x/e^3-1/2*c*(2*c*d-3*b*e)*x^2/e^2+2/3*c^2*x^3/e-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4],
[(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^2,x,2,-c*(4*c*d-3*b*e)*x/e^3+c^2*x^2/e^2+(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x))+(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*log(d+e*x)/e^4],
[(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^3,x,2,2*c^2*x/e^3+1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+(-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x))-3*c*(2*c*d-b*e)*log(d+e*x)/e^4],
[(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^4,x,2,1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+1/2*(-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x)^2)+3*c*(2*c*d-b*e)/(e^4*(d+e*x))+2*c^2*log(d+e*x)/e^4],
[(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^5,x,2,1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+1/3*(-6*c^2*d^2-b^2*e^2+2*c*e*(3*b*d-a*e))/(e^4*(d+e*x)^3)+3/2*c*(2*c*d-b*e)/(e^4*(d+e*x)^2)-2*c^2/(e^4*(d+e*x))],
[(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2)^2,x,2,-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^5/e^6+1/3*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^6/e^6-1/7*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^7/e^6+1/2*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^8/e^6-5/9*c^2*(2*c*d-b*e)*(d+e*x)^9/e^6+1/5*c^3*(d+e*x)^10/e^6],
[(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^2,x,2,-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^4/e^6+2/5*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^5/e^6-1/6*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^6/e^6+4/7*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^7/e^6-5/8*c^2*(2*c*d-b*e)*(d+e*x)^8/e^6+2/9*c^3*(d+e*x)^9/e^6],
[(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^2,x,2,-1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^3/e^6+1/2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^4/e^6-1/5*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^5/e^6+2/3*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^6/e^6-5/7*c^2*(2*c*d-b*e)*(d+e*x)^7/e^6+1/4*c^3*(d+e*x)^8/e^6],
[(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^2,x,2,a^2*b*d*x+1/2*a*(2*b^2*d+2*a*c*d+a*b*e)*x^2+1/3*(b^3*d+6*a*b*c*d+2*a*b^2*e+2*a^2*c*e)*x^3+1/4*(4*b^2*c*d+4*a*c^2*d+b^3*e+6*a*b*c*e)*x^4+1/5*c*(5*b*c*d+4*b^2*e+4*a*c*e)*x^5+1/6*c^2*(2*c*d+5*b*e)*x^6+2/7*c^3*e*x^7],
[(b+2*c*x)*(a+b*x+c*x^2)^2,x,1,1/3*(a+b*x+c*x^2)^3],
[(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x),x,2,2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*x/e^5-1/2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^2/e^6+4/3*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^3/e^6-5/4*c^2*(2*c*d-b*e)*(d+e*x)^4/e^6+2/5*c^3*(d+e*x)^5/e^6-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/e^6],
[(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^2,x,2,-(8*c^3*d^3-b^3*e^3-c^2*d*e*(15*b*d-8*a*e)+2*b*c*e^2*(4*b*d-3*a*e))*x/e^5+c*(3*c^2*d^2+2*b^2*e^2-c*e*(5*b*d-2*a*e))*x^2/e^4-1/3*c^2*(4*c*d-5*b*e)*x^3/e^3+1/2*c^3*x^4/e^2+(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x))+2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*log(d+e*x)/e^6],
[(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^3,x,2,c*(12*c^2*d^2+4*b^2*e^2-c*e*(15*b*d-4*a*e))*x/e^5-1/2*c^2*(6*c*d-5*b*e)*x^2/e^4+2/3*c^3*x^3/e^3+1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^2)-2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/(e^6*(d+e*x))-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*log(d+e*x)/e^6],
[(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^4,x,2,-c^2*(8*c*d-5*b*e)*x/e^5+c^3*x^2/e^4+1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^3)-(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/(e^6*(d+e*x)^2)+(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))/(e^6*(d+e*x))+4*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*log(d+e*x)/e^6],
[(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^5,x,2,2*c^3*x/e^5+1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^4)-2/3*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/(e^6*(d+e*x)^3)+1/2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))/(e^6*(d+e*x)^2)-4*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/(e^6*(d+e*x))-5*c^2*(2*c*d-b*e)*log(d+e*x)/e^6],
[(b+2*c*x)*(d+e*x)^4*(a+b*x+c*x^2)^3,x,2,-1/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^5/e^8+1/6*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^6/e^8-3/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^7/e^8+1/8*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^8/e^8-5/9*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^9/e^8+3/10*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^10/e^8-7/11*c^3*(2*c*d-b*e)*(d+e*x)^11/e^8+1/6*c^4*(d+e*x)^12/e^8],
[(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^3,x,2,-1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^4/e^8+1/5*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^5/e^8-1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^6/e^8+1/7*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^7/e^8-5/8*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^8/e^8+1/3*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^9/e^8-7/10*c^3*(2*c*d-b*e)*(d+e*x)^10/e^8+2/11*c^4*(d+e*x)^11/e^8],
[(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^3,x,2,-1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^3/e^8+1/4*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^4/e^8-3/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^5/e^8+1/6*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^6/e^8-5/7*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^7/e^8+3/8*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^8/e^8-7/9*c^3*(2*c*d-b*e)*(d+e*x)^9/e^8+1/5*c^4*(d+e*x)^10/e^8],
[(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^3,x,2,a^3*b*d*x+1/2*a^2*(3*b^2*d+2*a*c*d+a*b*e)*x^2+1/3*a*(3*b^3*d+9*a*b*c*d+3*a*b^2*e+2*a^2*c*e)*x^3+1/4*(b^4*d+12*a*b^2*c*d+6*a^2*c^2*d+3*a*b^3*e+9*a^2*b*c*e)*x^4+1/5*(5*b^3*c*d+15*a*b*c^2*d+b^4*e+12*a*b^2*c*e+6*a^2*c^2*e)*x^5+1/6*c*(9*b^2*c*d+6*a*c^2*d+5*b^3*e+15*a*b*c*e)*x^6+1/7*c^2*(7*b*c*d+9*b^2*e+6*a*c*e)*x^7+1/8*c^3*(2*c*d+7*b*e)*x^8+2/9*c^4*e*x^9],
[(b+2*c*x)*(a+b*x+c*x^2)^3,x,1,1/4*(a+b*x+c*x^2)^4],
[(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x),x,2,(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*x/e^7-3/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^2/e^8+1/3*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^3/e^8-5/4*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^4/e^8+3/5*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^5/e^8-7/6*c^3*(2*c*d-b*e)*(d+e*x)^6/e^8+2/7*c^4*(d+e*x)^7/e^8-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/e^8],
[(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^2,x,2,-3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*x/e^7+(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x))+1/2*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^2/e^8-5/3*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^3/e^8+3/4*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^4/e^8-7/5*c^3*(2*c*d-b*e)*(d+e*x)^5/e^8+1/3*c^4*(d+e*x)^6/e^8+(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*log(d+e*x)/e^8],
[(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^3,x,2,(30*c^4*d^4+b^4*e^4-2*c^3*d^2*e*(35*b*d-18*a*e)-3*b^2*c*e^3*(5*b*d-4*a*e)+3*c^2*e^2*(18*b^2*d^2-15*a*b*d*e+2*a^2*e^2))*x/e^7-1/2*c*(20*c^3*d^3-5*b^3*e^3+3*b*c*e^2*(9*b*d-5*a*e)-6*c^2*d*e*(7*b*d-3*a*e))*x^2/e^6+c^2*(4*c^2*d^2+3*b^2*e^2-c*e*(7*b*d-2*a*e))*x^3/e^5-1/4*c^3*(6*c*d-7*b*e)*x^4/e^4+2/5*c^4*x^5/e^3+1/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^2)-(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x))-3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*log(d+e*x)/e^8],
[(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^4,x,2,-c*(40*c^3*d^3-5*b^3*e^3-2*c^2*d*e*(35*b*d-12*a*e)+3*b*c*e^2*(12*b*d-5*a*e))*x/e^7+1/2*c^2*(20*c^2*d^2-28*b*c*d*e+9*b^2*e^2+6*a*c*e^2)*x^2/e^6-1/3*c^3*(8*c*d-7*b*e)*x^3/e^5+1/2*c^4*x^4/e^4+1/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^3)-1/2*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x)^2)+3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))/(e^8*(d+e*x))+(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*log(d+e*x)/e^8],
[(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^5,x,2,c^2*(30*c^2*d^2+9*b^2*e^2-c*e*(35*b*d-6*a*e))*x/e^7-1/2*c^3*(10*c*d-7*b*e)*x^2/e^6+2/3*c^4*x^3/e^5+1/4*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^4)-1/3*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*(d+e*x)^3)+3/2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))/(e^8*(d+e*x)^2)+(-70*c^4*d^4-b^4*e^4+4*b^2*c*e^3*(5*b*d-3*a*e)+20*c^3*d^2*e*(7*b*d-3*a*e)-6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))/(e^8*(d+e*x))-5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*log(d+e*x)/e^8],

# p<0
[(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2),x,6,e*(8*c^3*d^3-b^3*e^3+b*c*e^2*(4*b*d+3*a*e)-2*c^2*d*e*(3*b*d+4*a*e))*x/c^3+1/2*e^2*(12*c^2*d^2+b^2*e^2-2*c*e*(2*b*d+a*e))*x^2/c^2+1/3*e^3*(8*c*d-b*e)*x^3/c+1/2*e^4*x^4+1/2*(2*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(b*d+a*e)-4*c^3*d^2*e*(b*d+3*a*e)+2*c^2*e^2*(3*b^2*d^2+6*a*b*d*e+a^2*e^2))*log(a+b*x+c*x^2)/c^4-e*(2*c*d-b*e)*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c^4],
[(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2),x,6,e*(6*c^2*d^2+b^2*e^2-c*e*(3*b*d+2*a*e))*x/c^2+1/2*e^2*(6*c*d-b*e)*x^2/c+2/3*e^3*x^3+1/2*(2*c*d-b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*log(a+b*x+c*x^2)/c^3-e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c^3],
[(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2),x,6,e*(4*d-b*e/c)*x+e^2*x^2+1/2*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*log(a+b*x+c*x^2)/c^2-e*(2*c*d-b*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c^2],
[(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2),x,5,2*e*x+1/2*(2*c*d-b*e)*log(a+b*x+c*x^2)/c-e*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/c],
[(b+2*c*x)/(a+b*x+c*x^2),x,1,log(a+b*x+c*x^2)],
[(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)),x,6,-(2*c*d-b*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)+1/2*(2*c*d-b*e)*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)+e*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/(c*d^2-b*d*e+a*e^2)],
[(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)),x,6,(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x))-(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^2+1/2*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^2+e*(2*c*d-b*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/(c*d^2-b*d*e+a*e^2)^2],
[(b+2*c*x)/((d+e*x)^3*(a+b*x+c*x^2)),x,6,1/2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))-(2*c*d-b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+1/2*(2*c*d-b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^3+e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))*sqrt(b^2-4*a*c)/(c*d^2-b*d*e+a*e^2)^3],
[(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^2,x,7,4*e^3*(3*c*d-b*e)*x/c^2+2*e^4*x^2/c-(d+e*x)^4/(a+b*x+c*x^2)+2*e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*log(a+b*x+c*x^2)/c^3-4*e*(2*c*d-b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*sqrt(b^2-4*a*c))],
[(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^2,x,7,3*e^3*x/c-(d+e*x)^3/(a+b*x+c*x^2)+3/2*e^2*(2*c*d-b*e)*log(a+b*x+c*x^2)/c^2-3*e*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^2*sqrt(b^2-4*a*c))],
[(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^2,x,5,-(d+e*x)^2/(a+b*x+c*x^2)+e^2*log(a+b*x+c*x^2)/c-2*e*(2*c*d-b*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c*sqrt(b^2-4*a*c))],
[(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^2,x,3,(-d-e*x)/(a+b*x+c*x^2)-2*e*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c)],
[(b+2*c*x)/(a+b*x+c*x^2)^2,x,1,(-1)/(a+b*x+c*x^2)],
[(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^2),x,7,(-(b^2-4*a*c)*(c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2))-e^2*(2*c*d-b*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^2+1/2*e^2*(2*c*d-b*e)*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^2+e*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c))],
[(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^2),x,7,2*e^2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))+(-(b^2-4*a*c)*(c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*(a+b*x+c*x^2))-2*e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+e^2*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^3+2*e*(2*c*d-b*e)*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^3*sqrt(b^2-4*a*c))],
[(b+2*c*x)*(d+e*x)^5/(a+b*x+c*x^2)^3,x,8,5*e^3*(3*c^2*d^2+b^2*e^2-c*e*(2*b*d+3*a*e))*x/(c^2*(b^2-4*a*c))+5/2*e^4*(2*c*d-b*e)*x^2/(c*(b^2-4*a*c))-1/2*(d+e*x)^5/(a+b*x+c*x^2)^2-5/2*e*(d+e*x)^3*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+5*e*(2*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(b*d-3*a*e)-6*a*c^2*e^3*(2*b*d+a*e)+2*b^2*c*e^3*(b*d+3*a*e))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*(b^2-4*a*c)^(3/2))+5/2*e^4*(2*c*d-b*e)*log(a+b*x+c*x^2)/c^3],
[(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^3,x,7,2*e^3*(2*c*d-b*e)*x/(c*(b^2-4*a*c))-1/2*(d+e*x)^4/(a+b*x+c*x^2)^2-2*e*(d+e*x)^2*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+2*e*(2*c*d-b*e)*(2*c^2*d^2-b^2*e^2-2*c*e*(b*d-3*a*e))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^2*(b^2-4*a*c)^(3/2))+e^4*log(a+b*x+c*x^2)/c^2],
[(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^3,x,4,-1/2*(d+e*x)^3/(a+b*x+c*x^2)^2-3/2*e*(d+e*x)*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+6*e*(c*d^2-b*d*e+a*e^2)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(b^2-4*a*c)^(3/2)],
[(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^3,x,4,-1/2*(d+e*x)^2/(a+b*x+c*x^2)^2-e*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+2*e*(2*c*d-b*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(b^2-4*a*c)^(3/2)],
[(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^3,x,4,1/2*(-d-e*x)/(a+b*x+c*x^2)^2-1/2*e*(b+2*c*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+2*c*e*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(b^2-4*a*c)^(3/2)],
[(b+2*c*x)/(a+b*x+c*x^2)^3,x,1,(-1/2)/(a+b*x+c*x^2)^2],
[(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^3),x,8,1/2*(-(b^2-4*a*c)*(c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^2)-1/2*e*(3*b^2*c*d*e-8*a*c^2*d*e-2*b^3*e^2-b*c*(c*d^2-7*a*e^2)-2*c*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*(a+b*x+c*x^2))-e*(2*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(b*d-3*a*e)-6*a*c^2*e^3*(2*b*d+a*e)+2*b^2*c*e^3*(b*d+3*a*e))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)^3)-e^4*(2*c*d-b*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+1/2*e^4*(2*c*d-b*e)*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^3],

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

# p>0
[(b+2*c*x)*(d+e*x)^4*sqrt(a+b*x+c*x^2),x,7,1/35*(4*c^2*d^2+3*b^2*e^2-4*c*e*(b*d+2*a*e))*(d+e*x)^2*(a+b*x+c*x^2)^(3/2)/c^2+2/21*(2*c*d-b*e)*(d+e*x)^3*(a+b*x+c*x^2)^(3/2)/c+2/7*(d+e*x)^4*(a+b*x+c*x^2)^(3/2)+1/1680*(128*c^4*d^4+105*b^4*e^4-14*b^2*c*e^3*(35*b*d+34*a*e)-16*c^3*d^2*e*(13*b*d+144*a*e)+8*c^2*e^2*(87*b^2*d^2+231*a*b*d*e+32*a^2*e^2)+6*c*e*(2*c*d-b*e)*(8*c^2*d^2+21*b^2*e^2-4*c*e*(2*b*d+19*a*e))*x)*(a+b*x+c*x^2)^(3/2)/c^4-1/256*(b^2-4*a*c)^2*e*(2*c*d-b*e)*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(11/2)+1/128*(b^2-4*a*c)*e*(2*c*d-b*e)*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5],
[(b+2*c*x)*(d+e*x)^3*sqrt(a+b*x+c*x^2),x,6,1/10*(2*c*d-b*e)*(d+e*x)^2*(a+b*x+c*x^2)^(3/2)/c+1/3*(d+e*x)^3*(a+b*x+c*x^2)^(3/2)+1/480*(64*c^3*d^3-35*b^3*e^3+12*b*c*e^2*(10*b*d+11*a*e)-24*c^2*d*e*(3*b*d+16*a*e)+6*c*e*(8*c^2*d^2+7*b^2*e^2-4*c*e*(2*b*d+5*a*e))*x)*(a+b*x+c*x^2)^(3/2)/c^3-1/512*(b^2-4*a*c)^2*e*(24*c^2*d^2+7*b^2*e^2-4*c*e*(6*b*d+a*e))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)+1/256*(b^2-4*a*c)*e*(24*c^2*d^2+7*b^2*e^2-4*c*e*(6*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4],
[(b+2*c*x)*(d+e*x)^2*sqrt(a+b*x+c*x^2),x,5,2/5*(d+e*x)^2*(a+b*x+c*x^2)^(3/2)+1/60*(16*c^2*d^2+5*b^2*e^2-2*c*e*(5*b*d+8*a*e)+6*c*e*(2*c*d-b*e)*x)*(a+b*x+c*x^2)^(3/2)/c^2-1/64*(b^2-4*a*c)^2*e*(2*c*d-b*e)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+1/32*(b^2-4*a*c)*e*(2*c*d-b*e)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^3],
[(b+2*c*x)*(d+e*x)*sqrt(a+b*x+c*x^2),x,4,1/12*(8*c*d-b*e+6*c*e*x)*(a+b*x+c*x^2)^(3/2)/c-1/64*(b^2-4*a*c)^2*e*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)+1/32*(b^2-4*a*c)*e*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^2],
[(b+2*c*x)*sqrt(a+b*x+c*x^2),x,1,2/3*(a+b*x+c*x^2)^(3/2)],
[(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x),x,6,1/4*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(e^3*sqrt(c))-(2*c*d-b*e)*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/e^3-1/2*(4*c*d-3*b*e-2*c*e*x)*sqrt(a+b*x+c*x^2)/e^2],
[(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^2,x,6,-2*(2*c*d-b*e)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/e^3+1/2*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^3*sqrt(c*d^2-b*d*e+a*e^2))+(4*c*d-b*e+2*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*(d+e*x))],
[(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^3,x,6,2*c^(3/2)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/e^3-1/8*(2*c*d-b*e)*(8*c^2*d^2-b^2*e^2-4*c*e*(2*b*d-3*a*e))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^3*(c*d^2-b*d*e+a*e^2)^(3/2))-1/4*(8*c^2*d^3-b*e^2*(b*d-2*a*e)-2*c*d*e*(3*b*d-2*a*e)+e*(12*c^2*d^2+b^2*e^2-4*c*e*(3*b*d-2*a*e))*x)*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^2)],
[(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^4,x,4,1/3*(2*c*d-b*e)*(a+b*x+c*x^2)^(3/2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^3)+1/16*(b^2-4*a*c)^2*e*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)-1/8*(b^2-4*a*c)*e*(b*d-2*a*e+(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x)^2)],
[(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^5,x,5,1/4*(2*c*d-b*e)*(a+b*x+c*x^2)^(3/2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^4)+1/24*(4*c^2*d^2+5*b^2*e^2-4*c*e*(b*d+4*a*e))*(a+b*x+c*x^2)^(3/2)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x)^3)+5/128*(b^2-4*a*c)^2*e*(2*c*d-b*e)*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)-5/64*(b^2-4*a*c)*e*(2*c*d-b*e)*(b*d-2*a*e+(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^3*(d+e*x)^2)],
[(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^6,x,6,1/5*(2*c*d-b*e)*(a+b*x+c*x^2)^(3/2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^5)+1/40*(8*c^2*d^2+7*b^2*e^2-4*c*e*(2*b*d+5*a*e))*(a+b*x+c*x^2)^(3/2)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x)^4)+1/240*(2*c*d-b*e)*(8*c^2*d^2+35*b^2*e^2-4*c*e*(2*b*d+33*a*e))*(a+b*x+c*x^2)^(3/2)/((c*d^2-b*d*e+a*e^2)^3*(d+e*x)^3)+1/256*(b^2-4*a*c)^2*e*(24*c^2*d^2+7*b^2*e^2-4*c*e*(6*b*d+a*e))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(9/2)-1/128*(b^2-4*a*c)*e*(24*c^2*d^2+7*b^2*e^2-4*c*e*(6*b*d+a*e))*(b*d-2*a*e+(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^4*(d+e*x)^2)],
[(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^(3/2),x,7,1/1024*(b^2-4*a*c)*e*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^4+3/56*(2*c*d-b*e)*(d+e*x)^2*(a+b*x+c*x^2)^(5/2)/c+1/4*(d+e*x)^3*(a+b*x+c*x^2)^(5/2)+1/2240*(96*c^3*d^3-63*b^3*e^3+4*b*c*e^2*(56*b*d+61*a*e)-8*c^2*d*e*(13*b*d+96*a*e)+10*c*e*(8*c^2*d^2+9*b^2*e^2-4*c*e*(2*b*d+7*a*e))*x)*(a+b*x+c*x^2)^(5/2)/c^3+3/16384*(b^2-4*a*c)^3*e*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(11/2)-3/8192*(b^2-4*a*c)^2*e*(32*c^2*d^2+9*b^2*e^2-4*c*e*(8*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5],
[(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^(3/2),x,6,1/96*(b^2-4*a*c)*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^3+2/7*(d+e*x)^2*(a+b*x+c*x^2)^(5/2)+1/210*(24*c^2*d^2+7*b^2*e^2-2*c*e*(7*b*d+12*a*e)+10*c*e*(2*c*d-b*e)*x)*(a+b*x+c*x^2)^(5/2)/c^2+1/512*(b^2-4*a*c)^3*e*(2*c*d-b*e)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)-1/256*(b^2-4*a*c)^2*e*(2*c*d-b*e)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4],
[(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^(3/2),x,5,1/96*(b^2-4*a*c)*e*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^2+1/30*(12*c*d-b*e+10*c*e*x)*(a+b*x+c*x^2)^(5/2)/c+1/512*(b^2-4*a*c)^3*e*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)-1/256*(b^2-4*a*c)^2*e*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^3],
[(b+2*c*x)*(a+b*x+c*x^2)^(3/2),x,1,2/5*(a+b*x+c*x^2)^(5/2)],
[(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x),x,7,-1/12*(8*c*d-7*b*e-6*c*e*x)*(a+b*x+c*x^2)^(3/2)/e^2+1/64*(128*c^4*d^4-b^4*e^4-8*b^2*c*e^3*(2*b*d-3*a*e)-64*c^3*d^2*e*(4*b*d-3*a*e)+48*c^2*e^2*(3*b^2*d^2-4*a*b*d*e+a^2*e^2))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*e^5)-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^(3/2)*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/e^5-1/32*(64*c^3*d^3-b^3*e^3+4*b*c*e^2*(12*b*d-11*a*e)-16*c^2*d*e*(7*b*d-4*a*e)-2*c*e*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*x)*sqrt(a+b*x+c*x^2)/(c*e^4)],
[(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^2,x,7,1/3*(8*c*d-3*b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x))-1/4*(2*c*d-b*e)*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(e^5*sqrt(c))+1/2*(16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/e^5+1/2*(16*c^2*d^2+5*b^2*e^2-4*c*e*(5*b*d-a*e)-4*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/e^4],
[(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^3,x,7,1/2*(4*c*d-b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^2)+3/4*(16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/e^5-3/8*(2*c*d-b*e)*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*sqrt(c*d^2-b*d*e+a*e^2))-3/4*(16*c^2*d^2+b^2*e^2-4*c*e*(3*b*d-a*e)+4*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/(e^4*(d+e*x))],
[(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^4,x,7,-1/12*(16*c^2*d^3-b*e^2*(b*d-4*a*e)-4*c*d*e*(3*b*d-a*e)+3*e*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3)-4*c^(3/2)*(2*c*d-b*e)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/e^5+1/16*(128*c^4*d^4-b^4*e^4-8*b^2*c*e^3*(2*b*d-3*a*e)-64*c^3*d^2*e*(4*b*d-3*a*e)+48*c^2*e^2*(3*b^2*d^2-4*a*b*d*e+a^2*e^2))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^5*(c*d^2-b*d*e+a*e^2)^(3/2))+1/8*(64*c^3*d^3+b^3*e^3+4*b*c*e^2*(4*b*d-5*a*e)-16*c^2*d*e*(5*b*d-4*a*e)+2*c*e*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*x)*sqrt(a+b*x+c*x^2)/(e^4*(c*d^2-b*d*e+a*e^2)*(d+e*x))],
[(b+2*c*x)*(d+e*x)^3*(a+b*x+c*x^2)^(5/2),x,8,-1/8192*(b^2-4*a*c)^2*e*(40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^5+1/2560*(b^2-4*a*c)*e*(40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^4+1/30*(2*c*d-b*e)*(d+e*x)^2*(a+b*x+c*x^2)^(7/2)/c+1/5*(d+e*x)^3*(a+b*x+c*x^2)^(7/2)+1/6720*(128*c^3*d^3-99*b^3*e^3+4*b*c*e^2*(90*b*d+97*a*e)-8*c^2*d*e*(17*b*d+160*a*e)+14*c*e*(8*c^2*d^2+11*b^2*e^2-4*c*e*(2*b*d+9*a*e))*x)*(a+b*x+c*x^2)^(7/2)/c^3-3/131072*(b^2-4*a*c)^4*e*(40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(13/2)+3/65536*(b^2-4*a*c)^3*e*(40*c^2*d^2+11*b^2*e^2-4*c*e*(10*b*d+a*e))*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^6],
[(b+2*c*x)*(d+e*x)^2*(a+b*x+c*x^2)^(5/2),x,7,-5/3072*(b^2-4*a*c)^2*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^4+1/192*(b^2-4*a*c)*e*(2*c*d-b*e)*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^3+2/9*(d+e*x)^2*(a+b*x+c*x^2)^(7/2)+1/504*(32*c^2*d^2+9*b^2*e^2-2*c*e*(9*b*d+16*a*e)+14*c*e*(2*c*d-b*e)*x)*(a+b*x+c*x^2)^(7/2)/c^2-5/16384*(b^2-4*a*c)^4*e*(2*c*d-b*e)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(11/2)+5/8192*(b^2-4*a*c)^3*e*(2*c*d-b*e)*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^5],
[(b+2*c*x)*(d+e*x)*(a+b*x+c*x^2)^(5/2),x,6,-5/3072*(b^2-4*a*c)^2*e*(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/c^3+1/192*(b^2-4*a*c)*e*(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/c^2+1/56*(16*c*d-b*e+14*c*e*x)*(a+b*x+c*x^2)^(7/2)/c-5/16384*(b^2-4*a*c)^4*e*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)+5/8192*(b^2-4*a*c)^3*e*(b+2*c*x)*sqrt(a+b*x+c*x^2)/c^4],
[(b+2*c*x)*(a+b*x+c*x^2)^(5/2),x,1,2/7*(a+b*x+c*x^2)^(7/2)],
[(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x),x,8,-1/96*(64*c^3*d^3-b^3*e^3+4*b*c*e^2*(14*b*d-13*a*e)-8*c^2*d*e*(15*b*d-8*a*e)-2*c*e*(24*c^2*d^2+b^2*e^2-4*c*e*(6*b*d-5*a*e))*x)*(a+b*x+c*x^2)^(3/2)/(c*e^4)-1/30*(12*c*d-11*b*e-10*c*e*x)*(a+b*x+c*x^2)^(5/2)/e^2+1/512*(1024*c^6*d^6+b^6*e^6+4*b^4*c*e^5*(2*b*d-5*a*e)-512*c^5*d^4*e*(6*b*d-5*a*e)-320*c^3*e^3*(b*d-a*e)^2*(4*b*d-a*e)+640*c^4*d^2*e^2*(5*b^2*d^2-8*a*b*d*e+3*a^2*e^2)+40*b^2*c^2*e^4*(3*b^2*d^2-8*a*b*d*e+6*a^2*e^2))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(5/2)*e^7)-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^(5/2)*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/e^7-1/256*(512*c^5*d^5+b^5*e^5-128*c^4*d^3*e*(11*b*d-8*a*e)+8*b^3*c*e^4*(b*d-2*a*e)+32*c^3*d*e^2*(40*b^2*d^2-55*a*b*d*e+16*a^2*e^2)-8*b*c^2*e^3*(49*b^2*d^2-92*a*b*d*e+42*a^2*e^2)-2*c*e*(16*c^2*d^2-b^2*e^2-4*c*e*(4*b*d-5*a*e))*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*x)*sqrt(a+b*x+c*x^2)/(c^2*e^6)],
[(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^2,x,8,1/12*(48*c^2*d^2-66*b*c*d*e+19*b^2*e^2+8*a*c*e^2-18*c*e*(2*c*d-b*e)*x)*(a+b*x+c*x^2)^(3/2)/e^4+1/5*(12*c*d-5*b*e+2*c*e*x)*(a+b*x+c*x^2)^(5/2)/(e^2*(d+e*x))-1/64*(2*c*d-b*e)*(384*c^4*d^4-b^4*e^4-8*b^2*c*e^3*(4*b*d-5*a*e)-128*c^3*d^2*e*(6*b*d-5*a*e)+16*c^2*e^2*(26*b^2*d^2-40*a*b*d*e+15*a^2*e^2))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(c^(3/2)*e^7)+1/2*(c*d^2-b*d*e+a*e^2)^(3/2)*(24*c^2*d^2+5*b^2*e^2-4*c*e*(6*b*d-a*e))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/e^7+1/32*(384*c^4*d^4+b^4*e^4-2*b^2*c*e^3*(65*b*d-62*a*e)-32*c^3*d^2*e*(27*b*d-14*a*e)+8*c^2*e^2*(76*b^2*d^2-67*a*b*d*e+8*a^2*e^2)-2*c*e*(2*c*d-b*e)*(48*c^2*d^2-48*b*c*d*e+b^2*e^2+44*a*c*e^2)*x)*sqrt(a+b*x+c*x^2)/(c*e^6)],
[(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^3,x,8,-5/4*(8*c^2*d^2+b^2*e^2-c*e*(7*b*d-2*a*e)+c*e*(2*c*d-b*e)*x)*(a+b*x+c*x^2)^(3/2)/(e^4*(d+e*x))+1/2*(3*c*d-b*e+c*e*x)*(a+b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^2)+15/64*(128*c^4*d^4+b^4*e^4-8*b^2*c*e^3*(4*b*d-3*a*e)-128*c^3*d^2*e*(2*b*d-a*e)+16*c^2*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(e^7*sqrt(c))-15/8*(2*c*d-b*e)*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))*sqrt(c*d^2-b*d*e+a*e^2)/e^7-15/32*(64*c^3*d^3-7*b^3*e^3+4*b*c*e^2*(14*b*d-5*a*e)-16*c^2*d*e*(7*b*d-2*a*e)-2*c*e*(16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*x)*sqrt(a+b*x+c*x^2)/e^6],
[(b+2*c*x)*(a+b*x+c*x^2)^(5/2)/(d+e*x)^4,x,8,-5/12*(16*c^2*d^2+b^2*e^2-4*c*e*(3*b*d-a*e)+4*c*e*(2*c*d-b*e)*x)*(a+b*x+c*x^2)^(3/2)/(e^4*(d+e*x)^2)+1/3*(4*c*d-b*e+2*c*e*x)*(a+b*x+c*x^2)^(5/2)/(e^2*(d+e*x)^3)-5/2*(2*c*d-b*e)*(8*c^2*d^2+b^2*e^2-4*c*e*(2*b*d-a*e))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/e^7+5/16*(128*c^4*d^4+b^4*e^4-8*b^2*c*e^3*(4*b*d-3*a*e)-128*c^3*d^2*e*(2*b*d-a*e)+16*c^2*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e^7*sqrt(c*d^2-b*d*e+a*e^2))+5/8*(64*c^3*d^3-b^3*e^3-16*c^2*d*e*(5*b*d-2*a*e)+12*b*c*e^2*(2*b*d-a*e)+2*c*e*(16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*x)*sqrt(a+b*x+c*x^2)/(e^6*(d+e*x))],

# p<0
[(b+2*c*x)*(d+e*x)^3/sqrt(a+b*x+c*x^2),x,5,3/64*(b^2-4*a*c)*e*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+1/4*(2*c*d-b*e)*(d+e*x)^2*sqrt(a+b*x+c*x^2)/c+1/2*(d+e*x)^3*sqrt(a+b*x+c*x^2)+1/32*(32*c^3*d^3-15*b^3*e^3+4*b*c*e^2*(12*b*d+13*a*e)-8*c^2*d*e*(5*b*d+16*a*e)+2*c*e*(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*x)*sqrt(a+b*x+c*x^2)/c^3],
[(b+2*c*x)*(d+e*x)^2/sqrt(a+b*x+c*x^2),x,4,1/4*(b^2-4*a*c)*e*(2*c*d-b*e)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)+2/3*(d+e*x)^2*sqrt(a+b*x+c*x^2)+1/6*(8*c^2*d^2+3*b^2*e^2-2*c*e*(3*b*d+4*a*e)+2*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/c^2],
[(b+2*c*x)*(d+e*x)/sqrt(a+b*x+c*x^2),x,3,1/4*(b^2-4*a*c)*e*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)+1/2*(4*c*d-b*e+2*c*e*x)*sqrt(a+b*x+c*x^2)/c],
[(b+2*c*x)/sqrt(a+b*x+c*x^2),x,1,2*sqrt(a+b*x+c*x^2)],
[(b+2*c*x)/((d+e*x)*sqrt(a+b*x+c*x^2)),x,5,2*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))*sqrt(c)/e-(2*c*d-b*e)*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e*sqrt(c*d^2-b*d*e+a*e^2))],
[(b+2*c*x)/((d+e*x)^2*sqrt(a+b*x+c*x^2)),x,3,-1/2*(b^2-4*a*c)*e*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(3/2)+(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x))],
[(b+2*c*x)/((d+e*x)^3*sqrt(a+b*x+c*x^2)),x,4,-3/8*(b^2-4*a*c)*e*(2*c*d-b*e)*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)+1/2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+1/4*(4*c^2*d^2+3*b^2*e^2-4*c*e*(b*d+2*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))],
[(b+2*c*x)/((d+e*x)^4*sqrt(a+b*x+c*x^2)),x,5,-1/16*(b^2-4*a*c)*e*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)+1/3*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^3)+1/12*(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x)^2)+1/24*(2*c*d-b*e)*(8*c^2*d^2+15*b^2*e^2-4*c*e*(2*b*d+13*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^3*(d+e*x))],
[(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^(3/2),x,5,1/2*e*(2*c*d-b*e)*(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)-2*(d+e*x)^4/sqrt(a+b*x+c*x^2)+8/3*e^2*(d+e*x)^2*sqrt(a+b*x+c*x^2)/c+1/3*e^2*(64*c^2*d^2+15*b^2*e^2-2*c*e*(27*b*d+8*a*e)+10*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/c^3],
[(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^(3/2),x,5,3/4*e*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-2*(d+e*x)^3/sqrt(a+b*x+c*x^2)+9/2*e^2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/c^2+3*e^2*(d+e*x)*sqrt(a+b*x+c*x^2)/c],
[(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^(3/2),x,4,2*e*(2*c*d-b*e)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-2*(d+e*x)^2/sqrt(a+b*x+c*x^2)+4*e^2*sqrt(a+b*x+c*x^2)/c],
[(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^(3/2),x,3,2*e*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/sqrt(c)-2*(d+e*x)/sqrt(a+b*x+c*x^2)],
[(b+2*c*x)/(a+b*x+c*x^2)^(3/2),x,1,(-2)/sqrt(a+b*x+c*x^2)],
[(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^(3/2)),x,4,-e*(2*c*d-b*e)*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(3/2)-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^(3/2)),x,4,-1/2*e*(8*c^2*d^2+3*b^2*e^2-4*c*e*(2*b*d+a*e))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*sqrt(a+b*x+c*x^2))+3*e^2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))],
[(b+2*c*x)*(d+e*x)^4/(a+b*x+c*x^2)^(5/2),x,5,-2/3*(d+e*x)^4/(a+b*x+c*x^2)^(3/2)+4*e^3*(2*c*d-b*e)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-16/3*e*(d+e*x)^2*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+8/3*e^2*(8*c^2*d^2+3*b^2*e^2-2*c*e*(3*b*d+4*a*e)+2*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/(c^2*(b^2-4*a*c))],
[(b+2*c*x)*(d+e*x)^3/(a+b*x+c*x^2)^(5/2),x,5,-2/3*(d+e*x)^3/(a+b*x+c*x^2)^(3/2)+2*e^3*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)-4*e*(d+e*x)*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+4*e^2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/(c*(b^2-4*a*c))],
[(b+2*c*x)*(d+e*x)^2/(a+b*x+c*x^2)^(5/2),x,2,-2/3*(d+e*x)^2/(a+b*x+c*x^2)^(3/2)-8/3*e*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*(d+e*x)/(a+b*x+c*x^2)^(5/2),x,2,-2/3*(d+e*x)/(a+b*x+c*x^2)^(3/2)-4/3*e*(b+2*c*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)/(a+b*x+c*x^2)^(5/2),x,1,(-2/3)/(a+b*x+c*x^2)^(3/2)],
[(b+2*c*x)/((d+e*x)*(a+b*x+c*x^2)^(5/2)),x,5,-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2))-e^3*(2*c*d-b*e)*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)-2/3*e*(5*b^2*c*d*e-12*a*c^2*d*e-3*b^3*e^2-2*b*c*(c*d^2-5*a*e^2)-c*(4*c^2*d^2+3*b^2*e^2-4*c*e*(b*d+2*a*e))*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)/((d+e*x)^2*(a+b*x+c*x^2)^(5/2)),x,5,-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*(a+b*x+c*x^2)^(3/2))-1/2*e^3*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)-2/3*e*(9*b^2*c*d*e-20*a*c^2*d*e-5*b^3*e^2-4*b*c*(c*d^2-4*a*e^2)-c*(8*c^2*d^2+5*b^2*e^2-4*c*e*(2*b*d+3*a*e))*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)*sqrt(a+b*x+c*x^2))+1/3*e^2*(2*c*d-b*e)*(8*c^2*d^2+15*b^2*e^2-4*c*e*(2*b*d+13*a*e))*sqrt(a+b*x+c*x^2)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x))],

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

# p>0
[(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2),x,2,-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(7/2)/e^4+2/9*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(9/2)/e^4-6/11*c*(2*c*d-b*e)*(d+e*x)^(11/2)/e^4+4/13*c^2*(d+e*x)^(13/2)/e^4],
[(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2),x,2,-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(5/2)/e^4+2/7*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(7/2)/e^4-2/3*c*(2*c*d-b*e)*(d+e*x)^(9/2)/e^4+4/11*c^2*(d+e*x)^(11/2)/e^4],
[(b+2*c*x)*(a+b*x+c*x^2)*sqrt(d+e*x),x,2,-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2)/e^4+2/5*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(5/2)/e^4-6/7*c*(2*c*d-b*e)*(d+e*x)^(7/2)/e^4+4/9*c^2*(d+e*x)^(9/2)/e^4],
[(b+2*c*x)*(a+b*x+c*x^2)/sqrt(d+e*x),x,2,2/3*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(3/2)/e^4-6/5*c*(2*c*d-b*e)*(d+e*x)^(5/2)/e^4+4/7*c^2*(d+e*x)^(7/2)/e^4-2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x)/e^4],
[(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^(3/2),x,2,-2*c*(2*c*d-b*e)*(d+e*x)^(3/2)/e^4+4/5*c^2*(d+e*x)^(5/2)/e^4+2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*sqrt(d+e*x))+2*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*sqrt(d+e*x)/e^4],
[(b+2*c*x)*(a+b*x+c*x^2)/(d+e*x)^(5/2),x,2,2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^(3/2))+4/3*c^2*(d+e*x)^(3/2)/e^4-2*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))/(e^4*sqrt(d+e*x))-6*c*(2*c*d-b*e)*sqrt(d+e*x)/e^4],
[(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2)^2,x,2,-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(7/2)/e^6+4/9*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(9/2)/e^6-2/11*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^(11/2)/e^6+8/13*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(13/2)/e^6-2/3*c^2*(2*c*d-b*e)*(d+e*x)^(15/2)/e^6+4/17*c^3*(d+e*x)^(17/2)/e^6],
[(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2)^2,x,2,-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(5/2)/e^6+4/7*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(7/2)/e^6-2/9*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^(9/2)/e^6+8/11*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(11/2)/e^6-10/13*c^2*(2*c*d-b*e)*(d+e*x)^(13/2)/e^6+4/15*c^3*(d+e*x)^(15/2)/e^6],
[(b+2*c*x)*(a+b*x+c*x^2)^2*sqrt(d+e*x),x,2,-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(3/2)/e^6+4/5*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(5/2)/e^6-2/7*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^(7/2)/e^6+8/9*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(9/2)/e^6-10/11*c^2*(2*c*d-b*e)*(d+e*x)^(11/2)/e^6+4/13*c^3*(d+e*x)^(13/2)/e^6],
[(b+2*c*x)*(a+b*x+c*x^2)^2/sqrt(d+e*x),x,2,4/3*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(3/2)/e^6-2/5*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^(5/2)/e^6+8/7*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(7/2)/e^6-10/9*c^2*(2*c*d-b*e)*(d+e*x)^(9/2)/e^6+4/11*c^3*(d+e*x)^(11/2)/e^6-2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x)/e^6],
[(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^(3/2),x,2,-2/3*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^(3/2)/e^6+8/5*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(5/2)/e^6-10/7*c^2*(2*c*d-b*e)*(d+e*x)^(7/2)/e^6+4/9*c^3*(d+e*x)^(9/2)/e^6+2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*sqrt(d+e*x))+4*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*sqrt(d+e*x)/e^6],
[(b+2*c*x)*(a+b*x+c*x^2)^2/(d+e*x)^(5/2),x,2,2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^(3/2))+8/3*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(3/2)/e^6-2*c^2*(2*c*d-b*e)*(d+e*x)^(5/2)/e^6+4/7*c^3*(d+e*x)^(7/2)/e^6-4*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))/(e^6*sqrt(d+e*x))-2*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*sqrt(d+e*x)/e^6],
[(b+2*c*x)*(d+e*x)^(5/2)*(a+b*x+c*x^2)^3,x,2,-2/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(7/2)/e^8+2/9*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(9/2)/e^8-6/11*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(11/2)/e^8+2/13*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(13/2)/e^8-2/3*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(15/2)/e^8+6/17*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(17/2)/e^8-14/19*c^3*(2*c*d-b*e)*(d+e*x)^(19/2)/e^8+4/21*c^4*(d+e*x)^(21/2)/e^8],
[(b+2*c*x)*(d+e*x)^(3/2)*(a+b*x+c*x^2)^3,x,2,-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(5/2)/e^8+2/7*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(7/2)/e^8-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(9/2)/e^8+2/11*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(11/2)/e^8-10/13*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(13/2)/e^8+2/5*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(15/2)/e^8-14/17*c^3*(2*c*d-b*e)*(d+e*x)^(17/2)/e^8+4/19*c^4*(d+e*x)^(19/2)/e^8],
[(b+2*c*x)*(a+b*x+c*x^2)^3*sqrt(d+e*x),x,2,-2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(3/2)/e^8+2/5*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(5/2)/e^8-6/7*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(7/2)/e^8+2/9*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(9/2)/e^8-10/11*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(11/2)/e^8+6/13*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(13/2)/e^8-14/15*c^3*(2*c*d-b*e)*(d+e*x)^(15/2)/e^8+4/17*c^4*(d+e*x)^(17/2)/e^8],
[(b+2*c*x)*(a+b*x+c*x^2)^3/sqrt(d+e*x),x,2,2/3*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(3/2)/e^8-6/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(5/2)/e^8+2/7*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(7/2)/e^8-10/9*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(9/2)/e^8+6/11*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(11/2)/e^8-14/13*c^3*(2*c*d-b*e)*(d+e*x)^(13/2)/e^8+4/15*c^4*(d+e*x)^(15/2)/e^8-2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*sqrt(d+e*x)/e^8],
[(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^(3/2),x,2,-2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(3/2)/e^8+2/5*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(5/2)/e^8-10/7*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(7/2)/e^8+2/3*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(9/2)/e^8-14/11*c^3*(2*c*d-b*e)*(d+e*x)^(11/2)/e^8+4/13*c^4*(d+e*x)^(13/2)/e^8+2*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*sqrt(d+e*x))+2*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*sqrt(d+e*x)/e^8],
[(b+2*c*x)*(a+b*x+c*x^2)^3/(d+e*x)^(5/2),x,2,2/3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^(3/2))+2/3*(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(3/2)/e^8-2*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(5/2)/e^8+6/7*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(7/2)/e^8-14/9*c^3*(2*c*d-b*e)*(d+e*x)^(9/2)/e^8+4/11*c^4*(d+e*x)^(11/2)/e^8-2*(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))/(e^8*sqrt(d+e*x))-6*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*sqrt(d+e*x)/e^8],

# p<0
[(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2),x,6,4/3*(d+e*x)^(3/2)+2*(2*c*d-b*e)*sqrt(d+e*x)/c+arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(b^2*e^2*(b-sqrt(b^2-4*a*c))-2*c^2*d*(-4*a*e+d*sqrt(b^2-4*a*c))-2*c*e*(b^2*d+2*a*b*e-b*d*sqrt(b^2-4*a*c)-a*e*sqrt(b^2-4*a*c)))/(c^(3/2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(b^2*e^2*(b+sqrt(b^2-4*a*c))+2*c^2*d*(4*a*e+d*sqrt(b^2-4*a*c))-2*c*e*(b^2*d+2*a*b*e+b*d*sqrt(b^2-4*a*c)+a*e*sqrt(b^2-4*a*c)))/(c^(3/2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2),x,5,4*sqrt(d+e*x)-arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*(b*e*(b-sqrt(b^2-4*a*c))+2*c*(-2*a*e+d*sqrt(b^2-4*a*c)))/(sqrt(c)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))+arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*(b*e*(b+sqrt(b^2-4*a*c))-2*c*(2*a*e+d*sqrt(b^2-4*a*c)))/(sqrt(c)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(b+2*c*x)/((a+b*x+c*x^2)*sqrt(d+e*x)),x,4,-2*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))-2*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))],
[(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)),x,5,2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))+arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*(b*e*(b+sqrt(b^2-4*a*c))-2*c*(2*a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*(b*e*(b-sqrt(b^2-4*a*c))+2*c*(-2*a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(b+2*c*x)/((d+e*x)^(5/2)*(a+b*x+c*x^2)),x,6,2/3*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))+2*(2*c^2*d^2+b^2*e^2-2*c*e*(b*d+a*e))/((c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))-arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*(b^2*e^2*(b+sqrt(b^2-4*a*c))+2*c^2*d*(4*a*e+d*sqrt(b^2-4*a*c))-2*c*e*(b^2*d+2*a*b*e+b*d*sqrt(b^2-4*a*c)+a*e*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))+arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)*(b^2*e^2*(b-sqrt(b^2-4*a*c))-2*c^2*d*(-4*a*e+d*sqrt(b^2-4*a*c))-2*c*e*(b^2*d+2*a*b*e-b*d*sqrt(b^2-4*a*c)-a*e*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^2,x,6,-(d+e*x)^(5/2)/(a+b*x+c*x^2)+5*e^2*sqrt(d+e*x)/c-5*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c^2*d^2+b*e^2*(b-sqrt(b^2-4*a*c))-2*c*e*(b*d+a*e-d*sqrt(b^2-4*a*c)))/(c^(3/2)*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))+5*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c^2*d^2+b*e^2*(b+sqrt(b^2-4*a*c))-2*c*e*(b*d+a*e+d*sqrt(b^2-4*a*c)))/(c^(3/2)*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^2,x,5,-(d+e*x)^(3/2)/(a+b*x+c*x^2)-3*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c)))/(sqrt(2)*sqrt(c)*sqrt(b^2-4*a*c))+3*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c)))/(sqrt(2)*sqrt(c)*sqrt(b^2-4*a*c))],
[(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^2,x,5,-sqrt(d+e*x)/(a+b*x+c*x^2)-e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)/(sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))+e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(2)*sqrt(c)/(sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(b+2*c*x)/((a+b*x+c*x^2)^2*sqrt(d+e*x)),x,5,-((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2))+e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^2),x,6,3*e^2*(2*c*d-b*e)/((c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))+(-(b^2-4*a*c)*(c*d-b*e)+c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)*sqrt(d+e*x))+3*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(2*c^2*d^2+b*e^2*(b+sqrt(b^2-4*a*c))-2*c*e*(b*d+a*e+d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-3*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(2*c^2*d^2+b*e^2*(b-sqrt(b^2-4*a*c))-2*c*e*(b*d+a*e-d*sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)^2*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^3,x,7,-1/2*(d+e*x)^(7/2)/(a+b*x+c*x^2)^2-7/4*e*(d+e*x)^(3/2)*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+7/4*e^2*(2*c*d-b*e)*sqrt(d+e*x)/(c*(b^2-4*a*c))+7/4*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(8*c^3*d^3+b^2*e^3*(b-sqrt(b^2-4*a*c))-2*c^2*d*e*(6*b*d-8*a*e-d*sqrt(b^2-4*a*c))+2*c*e^2*(b^2*d-4*a*b*e-b*d*sqrt(b^2-4*a*c)+3*a*e*sqrt(b^2-4*a*c)))/(c^(3/2)*(b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-7/4*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(8*c^3*d^3+b^2*e^3*(b+sqrt(b^2-4*a*c))-2*c^2*d*e*(6*b*d-8*a*e+d*sqrt(b^2-4*a*c))+2*c*e^2*(b^2*d-4*a*b*e+b*d*sqrt(b^2-4*a*c)-3*a*e*sqrt(b^2-4*a*c)))/(c^(3/2)*(b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^3,x,6,-1/2*(d+e*x)^(5/2)/(a+b*x+c*x^2)^2-5/4*e*(b*d-2*a*e+(2*c*d-b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+5/4*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(8*c^2*d^2+b*e^2*(b-sqrt(b^2-4*a*c))-2*c*e*(4*b*d-2*a*e-d*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(c)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-5/4*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(8*c^2*d^2+b*e^2*(b+sqrt(b^2-4*a*c))-2*c*e*(4*b*d-2*a*e+d*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(c)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^3,x,6,-1/2*(d+e*x)^(3/2)/(a+b*x+c*x^2)^2-3/4*e*(b+2*c*x)*sqrt(d+e*x)/((b^2-4*a*c)*(a+b*x+c*x^2))+3/2*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(4*c*d-e*(2*b-sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-3/2*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(4*c*d-e*(2*b+sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^3,x,6,-1/2*sqrt(d+e*x)/(a+b*x+c*x^2)^2-1/4*e*(b*c*d-b^2*e+2*a*c*e+c*(2*c*d-b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2))+1/4*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^2*d^2-b*e^2*(b+sqrt(b^2-4*a*c))-2*c*e*(4*b*d-6*a*e-d*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))-1/4*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^2*d^2-b*e^2*(b-sqrt(b^2-4*a*c))-2*c*e*(4*b*d-6*a*e+d*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)*sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(b+2*c*x)/((a+b*x+c*x^2)^3*sqrt(d+e*x)),x,6,-1/2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^2)+1/4*e*(5*a*c*e*(2*c*d-b*e)+(c*d-3*b*e)*(b*c*d-b^2*e+2*a*c*e)+c*(2*c^2*d^2+3*b^2*e^2-2*c*e*(b*d+5*a*e))*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*(a+b*x+c*x^2))-1/4*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^3*d^3+3*b^2*e^3*(b+sqrt(b^2-4*a*c))-2*c^2*d*e*(6*b*d-16*a*e-d*sqrt(b^2-4*a*c))-2*c*e^2*(b^2*d+8*a*b*e+b*d*sqrt(b^2-4*a*c)+5*a*e*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)^2*sqrt(2)*sqrt(2*c*d-e*(b-sqrt(b^2-4*a*c))))+1/4*e*arctanh(sqrt(2)*sqrt(c)*sqrt(d+e*x)/sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))*sqrt(c)*(8*c^3*d^3+3*b^2*e^3*(b-sqrt(b^2-4*a*c))-2*c^2*d*e*(6*b*d-16*a*e+d*sqrt(b^2-4*a*c))-2*c*e^2*(b^2*d+8*a*b*e-b*d*sqrt(b^2-4*a*c)-5*a*e*sqrt(b^2-4*a*c)))/((b^2-4*a*c)^(3/2)*(c*d^2-b*d*e+a*e^2)^2*sqrt(2)*sqrt(2*c*d-e*(b+sqrt(b^2-4*a*c))))],

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

# p>0
[(b+2*c*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2),x,7,4/7*(a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)-2/105*(8*c^2*d^2+b^2*e^2-c*e*(11*b*d-10*a*e)-3*c*e*(2*c*d-b*e)*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/(c*e^2)+2/105*(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c^2*e^3*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-2/105*(c*d^2-b*d*e+a*e^2)*(16*c^2*d^2-b^2*e^2-4*c*e*(4*b*d-5*a*e))*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^2*e^3*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*sqrt(a+b*x+c*x^2)/sqrt(d+e*x),x,6,-2/15*(8*c*d-7*b*e-6*c*e*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/e^2+1/15*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c*e^3*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-16/15*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c*e^3*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(3/2),x,6,2/3*(8*c*d-3*b*e+2*c*e*x)*sqrt(a+b*x+c*x^2)/(e^2*sqrt(d+e*x))-8/3*(2*c*d-b*e)*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(e^3*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+2/3*(16*c^2*d^2+3*b^2*e^2-4*c*e*(4*b*d-a*e))*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c*e^3*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(5/2),x,6,-2/3*(8*c^2*d^3+a*b*e^3-c*d*e*(7*b*d-4*a*e)+e*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*x)*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))+1/3*(16*c^2*d^2+b^2*e^2-4*c*e*(4*b*d-3*a*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(e^3*(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-16/3*(2*c*d-b*e)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e^3*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*sqrt(a+b*x+c*x^2)/(d+e*x)^(7/2),x,7,-2/15*(8*c^2*d^3-c*d*e*(5*b*d-4*a*e)-b*e^2*(2*b*d-3*a*e)+e*(14*c^2*d^2+b^2*e^2-2*c*e*(7*b*d-5*a*e))*x)*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(5/2))+4/15*(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*sqrt(a+b*x+c*x^2)/(e^2*(c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))-2/15*(2*c*d-b*e)*(4*c^2*d^2-b^2*e^2-4*c*e*(b*d-2*a*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(e^3*(c*d^2-b*d*e+a*e^2)^2*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+2/15*(16*c^2*d^2-b^2*e^2-4*c*e*(4*b*d-5*a*e))*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e^3*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/sqrt(d+e*x),x,7,-2/63*(16*c*d-15*b*e-14*c*e*x)*(a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)/e^2-2/315*(128*c^3*d^3-b^3*e^3+3*b*c*e^2*(37*b*d-36*a*e)-12*c^2*d*e*(20*b*d-11*a*e)-3*c*e*(32*c^2*d^2+b^2*e^2-4*c*e*(8*b*d-7*a*e))*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/(c*e^4)+2/315*(128*c^4*d^4-b^4*e^4-4*c^3*d^2*e*(64*b*d-57*a*e)-b^2*c*e^3*(7*b*d-15*a*e)+3*c^2*e^2*(45*b^2*d^2-76*a*b*d*e+28*a^2*e^2))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c^2*e^5*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-2/315*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(128*c^2*d^2-b^2*e^2-4*c*e*(32*b*d-33*a*e))*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^2*e^5*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(3/2),x,7,2/7*(16*c*d-7*b*e+2*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*sqrt(d+e*x))+2/35*(128*c^2*d^2+51*b^2*e^2-4*c*e*(44*b*d-5*a*e)-48*c*e*(2*c*d-b*e)*x)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/e^4-1/35*(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c*e^5*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+4/35*(c*d^2-b*d*e+a*e^2)*(128*c^2*d^2+27*b^2*e^2-4*c*e*(32*b*d-5*a*e))*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c*e^5*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(5/2),x,7,2/15*(16*c*d-5*b*e+6*c*e*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-2/15*(128*c^2*d^2+15*b^2*e^2-4*c*e*(28*b*d-9*a*e)+16*c*e*(2*c*d-b*e)*x)*sqrt(a+b*x+c*x^2)/(e^4*sqrt(d+e*x))+2/15*(128*c^2*d^2+23*b^2*e^2-4*c*e*(32*b*d-9*a*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(e^5*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-2/15*(2*c*d-b*e)*(128*c^2*d^2+15*b^2*e^2-4*c*e*(32*b*d-17*a*e))*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c*e^5*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*(a+b*x+c*x^2)^(3/2)/(d+e*x)^(7/2),x,7,-2/15*(16*c^2*d^3+3*a*b*e^3-c*d*e*(13*b*d-4*a*e)+e*(22*c^2*d^2+3*b^2*e^2-2*c*e*(11*b*d-5*a*e))*x)*(a+b*x+c*x^2)^(3/2)/(e^2*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(5/2))+2/15*c*(128*c^2*d^3-4*c*d*e*(44*b*d-29*a*e)+3*b*e^2*(17*b*d-16*a*e)+e*(32*c^2*d^2+3*b^2*e^2-4*c*e*(8*b*d-5*a*e))*x)*sqrt(a+b*x+c*x^2)/(e^4*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))-1/15*(2*c*d-b*e)*(128*c^2*d^2+3*b^2*e^2-4*c*e*(32*b*d-29*a*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(e^5*(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+4/15*(128*c^2*d^2+27*b^2*e^2-4*c*e*(32*b*d-5*a*e))*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e^5*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
#  {((b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(d + e*x)^(5/2), x, 7, -((2*Sqrt[d + e*x]*(1024*c^3*d^3 + 1056*b^2*c*d*e^2 - b*(155*b^2 + 276*a*c)*e^3 - 384*c^2*d*e*(5*b*d - a*e) - 6*c*e*(128*c^2*d^2 - 128*b*c*d*e + (25*b^2 + 28*a*c)*e^2)*x)*Sqrt[a + b*x + c*x^2])/(63*e^6)) - (10*(128*c^2*d^2 - 120*b*c*d*e + 7*(3*b^2 + 4*a*c)*e^2 + 8*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(63*e^4*Sqrt[d + e*x]) + (2*(8*c*d - 3*b*e + 2*c*e*x)*(a + b*x + c*x^2)^(5/2))/(9*e^2*(d + e*x)^(3/2)) - (1/(63*Sqrt[2]*c^(3/2)*e^8*Sqrt[a + b*x + c*x^2]))*((2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(2048*c^4*d^4 - 448*b^3*c*d*e^3 + b^2*(5*b^2 + 408*a*c)*e^4 - 256*c^3*d^2*e*(16*b*d - 9*a*e) + 48*c^2*e^2*(52*b^2*d^2 - 48*a*b*d*e + 7*a^2*e^2))*Sqrt[-((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e))]*Sqrt[-((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e))]*EllipticE[ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]], (2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e)/(2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e)]) - (1/(63*Sqrt[2]*c^(3/2)*e^7*Sqrt[a + b*x + c*x^2]))*(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*((b - Sqrt[b^2 - 4*a*c])*(2048*c^4*d^4 - 448*b^3*c*d*e^3 + b^2*(5*b^2 + 408*a*c)*e^4 - 256*c^3*d^2*e*(16*b*d - 9*a*e) + 48*c^2*e^2*(52*b^2*d^2 - 48*a*b*d*e + 7*a^2*e^2)) + 2*c*(5*b^2*(31*b^2 + 264*a*c)*d*e^3 - 384*a^2*b*c*e^4 - 512*c^3*d^3*(2*b*d - a*e) - 32*b^3*e^2*(33*c*d^2 + 5*a*e^2) + 48*c^2*d*e*(40*b^2*d^2 - 40*a*b*d*e + 9*a^2*e^2)))*Sqrt[-((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e))]*Sqrt[-((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e))]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]], (2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e)/(2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e)])}
# {((b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(d + e*x)^(7/2), x, 7, (2*(3072*c^3*d^3 + 1504*b^2*c*d*e^2 - 3*b*(35*b^2 + 244*a*c)*e^3 - 128*c^2*d*e*(33*b*d - 13*a*e) + 2*c*e*(384*c^2*d^2 - 384*b*c*d*e + (71*b^2 + 100*a*c)*e^2)*x)*Sqrt[a + b*x + c*x^2])/(105*e^6*Sqrt[d + e*x]) - (2*(384*c^2*d^2 - 312*b*c*d*e + 5*(7*b^2 + 20*a*c)*e^2 + 72*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(105*e^4*(d + e*x)^(3/2)) + (2*(24*c*d - 7*b*e + 10*c*e*x)*(a + b*x + c*x^2)^(5/2))/(35*e^2*(d + e*x)^(5/2)) + (1/(105*Sqrt[c]*e^8*Sqrt[a + b*x + c*x^2]))*(16*Sqrt[2]*(2*c*d - b*e)*(2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(96*c^2*d^2 - 96*b*c*d*e + (11*b^2 + 52*a*c)*e^2)*Sqrt[-((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e))]*Sqrt[-((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e))]*EllipticE[ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]], (2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e)/(2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e)]) + (1/(105*Sqrt[c]*e^7*Sqrt[a + b*x + c*x^2]))*(Sqrt[2]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(32*c*(12*b^3 - 59*b^2*Sqrt[b^2 - 4*a*c] - 4*a*c*(12*b + 13*Sqrt[b^2 - 4*a*c]))*d*e^2 - (71*b^4 - 184*a*b^2*c - 400*a^2*c^2 - 16*b*Sqrt[b^2 - 4*a*c]*(11*b^2 + 52*a*c))*e^3 - 384*c^2*d^2*(b*(b - 12*Sqrt[b^2 - 4*a*c])*e + 4*c*(2*Sqrt[b^2 - 4*a*c]*d - a*e)))*Sqrt[-((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e))]*Sqrt[-((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e))]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]], (2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e)/(2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e)])}

# {((b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(d + e*x)^(9/2), x, 8, -((2*(2048*c^4*d^4 - 448*b^3*c*d*e^3 + b^2*(5*b^2 + 408*a*c)*e^4 - 256*c^3*d^2*e*(16*b*d - 9*a*e) + 48*c^2*e^2*(52*b^2*d^2 - 48*a*b*d*e + 7*a^2*e^2))*Sqrt[a + b*x + c*x^2])/(35*e^6*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x])) + (2*(1024*c^3*d^3 + 288*b^2*c*d*e^2 - b*(5*b^2 + 108*a*c)*e^3 - 384*c^2*d*e*(3*b*d - a*e) + 6*c*e*(128*c^2*d^2 - 128*b*c*d*e + (25*b^2 + 28*a*c)*e^2)*x)*Sqrt[a + b*x + c*x^2])/(35*e^6*(d + e*x)^(3/2)) - (2*(128*c^2*d^2 - 88*b*c*d*e + (5*b^2 + 28*a*c)*e^2 + 40*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(35*e^4*(d + e*x)^(5/2)) + (2*(24*c*d - 5*b*e + 14*c*e*x)*(a + b*x + c*x^2)^(5/2))/(35*e^2*(d + e*x)^(7/2)) - (1/(35*Sqrt[2]*Sqrt[c]*e^8*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]))*((2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(2048*c^4*d^4 - 448*b^3*c*d*e^3 + b^2*(5*b^2 + 408*a*c)*e^4 - 256*c^3*d^2*e*(16*b*d - 9*a*e) + 48*c^2*e^2*(52*b^2*d^2 - 48*a*b*d*e + 7*a^2*e^2))*Sqrt[-((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e))]*Sqrt[-((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e))]*EllipticE[ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]], (2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e)/(2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e)]) - (1/(35*Sqrt[2]*Sqrt[c]*e^7*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]))*(Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*((b - Sqrt[b^2 - 4*a*c])*(2048*c^4*d^4 + 5*b^4*e^4 - 8*b^2*c*e^3*(56*b*d - 51*a*e) - 256*c^3*d^2*e*(16*b*d - 9*a*e) + 48*c^2*e^2*(52*b^2*d^2 - 48*a*b*d*e + 7*a^2*e^2)) + 2*c*(5*b^2*(31*b^2 + 264*a*c)*d*e^3 - 384*a^2*b*c*e^4 - 512*c^3*d^3*(2*b*d - a*e) - 32*b^3*e^2*(33*c*d^2 + 5*a*e^2) + 48*c^2*d*e*(40*b^2*d^2 - 40*a*b*d*e + 9*a^2*e^2)))*Sqrt[-((e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e))]*Sqrt[-((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e))]*EllipticF[ArcSin[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]], (2*c*d - b*e + Sqrt[b^2 - 4*a*c]*e)/(2*c*d - b*e - Sqrt[b^2 - 4*a*c]*e)])} 

# p<0
[(b+2*c*x)*(d+e*x)^(5/2)/sqrt(a+b*x+c*x^2),x,8,2/7*(2*c*d-b*e)*(d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)/c+4/7*(d+e*x)^(5/2)*sqrt(a+b*x+c*x^2)+4/21*(3*c^2*d^2+2*b^2*e^2-c*e*(3*b*d+5*a*e))*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c^2+1/21*(2*c*d-b*e)*(3*c^2*d^2+8*b^2*e^2-c*e*(3*b*d+29*a*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c^3*e*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-4/21*(c*d^2-b*d*e+a*e^2)*(3*c^2*d^2+2*b^2*e^2-c*e*(3*b*d+5*a*e))*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^3*e*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*(d+e*x)^(3/2)/sqrt(a+b*x+c*x^2),x,7,4/5*(d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)+2/5*(2*c*d-b*e)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c+2/5*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c^2*e*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-2/5*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^2*e*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*sqrt(d+e*x)/sqrt(a+b*x+c*x^2),x,6,4/3*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)+1/3*(2*c*d-b*e)*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c*e*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-4/3*(c*d^2-b*d*e+a*e^2)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c*e*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)/(sqrt(d+e*x)*sqrt(a+b*x+c*x^2)),x,5,2*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(e*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-2*(2*c*d-b*e)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c*e*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)/((d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)),x,6,2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))-(2*c*d-b*e)*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(e*(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+4*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)/((d+e*x)^(5/2)*sqrt(a+b*x+c*x^2)),x,7,2/3*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))+4/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))-2/3*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(e*(c*d^2-b*d*e+a*e^2)^2*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+2/3*(2*c*d-b*e)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(3/2),x,8,-2*(d+e*x)^(7/2)/sqrt(a+b*x+c*x^2)+14/5*e^2*(d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)/c+56/15*e^2*(2*c*d-b*e)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c^2+7/15*e*(23*c^2*d^2+8*b^2*e^2-c*e*(23*b*d+9*a*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c^3*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-56/15*e*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^3*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(3/2),x,7,-2*(d+e*x)^(5/2)/sqrt(a+b*x+c*x^2)+10/3*e^2*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c+10/3*e*(2*c*d-b*e)*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c^2*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-10/3*e*(c*d^2-b*d*e+a*e^2)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^2*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2),x,3,-2*(d+e*x)^(3/2)/sqrt(a+b*x+c*x^2)+3*e*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))],
[(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^(3/2),x,3,-2*sqrt(d+e*x)/sqrt(a+b*x+c*x^2)+2*e*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)/((a+b*x+c*x^2)^(3/2)*sqrt(d+e*x)),x,4,-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2))-e*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))],
[(b+2*c*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^(3/2)),x,7,-2*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))+4*e^2*(2*c*d-b*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))-2*e*(2*c*d-b*e)*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+2*e*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(5/2),x,8,-2/3*(d+e*x)^(7/2)/(a+b*x+c*x^2)^(3/2)-14/3*e*(d+e*x)^(3/2)*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+14/3*e^2*(2*c*d-b*e)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/(c*(b^2-4*a*c))+14/3*e*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c^2*sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-14/3*e*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^2*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(5/2),x,7,-2/3*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(3/2)-10/3*e*(b*d-2*a*e+(2*c*d-b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+5/3*e*(2*c*d-b*e)*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c*sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-20/3*e*(c*d^2-b*d*e+a*e^2)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(5/2),x,7,-2/3*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2)-2*e*(b+2*c*x)*sqrt(d+e*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))+2*e*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-2*e*(2*c*d-b*e)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)*sqrt(d+e*x)/(a+b*x+c*x^2)^(5/2),x,7,-2/3*sqrt(d+e*x)/(a+b*x+c*x^2)^(3/2)-2/3*e*(b*c*d-b^2*e+2*a*c*e+c*(2*c*d-b*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2))+1/3*e*(2*c*d-b*e)*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)*sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-4/3*e*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(b+2*c*x)/((a+b*x+c*x^2)^(5/2)*sqrt(d+e*x)),x,7,-2/3*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2))-2/3*e*(3*b^2*c*d*e-8*a*c^2*d*e-2*b^3*e^2-b*c*(c*d^2-7*a*e^2)-2*c*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*sqrt(a+b*x+c*x^2))-2/3*e*(c^2*d^2+b^2*e^2-c*e*(b*d+3*a*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+2/3*e*(2*c*d-b*e)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/((c*d^2-b*d*e+a*e^2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],

# Integrands of the form (d+e x)^m (b+2 c x) (a+b x+c x^2)^p with m symbolic
[(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2)^3,x,2,-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))+(c*d^2-b*d*e+a*e^2)^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(2+m)/(e^8*(2+m))-3*(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(3+m)/(e^8*(3+m))+(70*c^4*d^4+b^4*e^4-4*b^2*c*e^3*(5*b*d-3*a*e)-20*c^3*d^2*e*(7*b*d-3*a*e)+6*c^2*e^2*(15*b^2*d^2-10*a*b*d*e+a^2*e^2))*(d+e*x)^(4+m)/(e^8*(4+m))-5*c*(2*c*d-b*e)*(7*c^2*d^2+b^2*e^2-c*e*(7*b*d-3*a*e))*(d+e*x)^(5+m)/(e^8*(5+m))+3*c^2*(14*c^2*d^2+3*b^2*e^2-2*c*e*(7*b*d-a*e))*(d+e*x)^(6+m)/(e^8*(6+m))-7*c^3*(2*c*d-b*e)*(d+e*x)^(7+m)/(e^8*(7+m))+2*c^4*(d+e*x)^(8+m)/(e^8*(8+m))],
[(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2)^2,x,2,-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))+2*(c*d^2-b*d*e+a*e^2)*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(2+m)/(e^6*(2+m))-(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))*(d+e*x)^(3+m)/(e^6*(3+m))+4*c*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e))*(d+e*x)^(4+m)/(e^6*(4+m))-5*c^2*(2*c*d-b*e)*(d+e*x)^(5+m)/(e^6*(5+m))+2*c^3*(d+e*x)^(6+m)/(e^6*(6+m))],
[(b+2*c*x)*(d+e*x)^m*(a+b*x+c*x^2),x,2,-(2*c*d-b*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e))*(d+e*x)^(2+m)/(e^4*(2+m))-3*c*(2*c*d-b*e)*(d+e*x)^(3+m)/(e^4*(3+m))+2*c^2*(d+e*x)^(4+m)/(e^4*(4+m))],
[(b+2*c*x)*(d+e*x)^m/(a+b*x+c*x^2),x,4,-2*c*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],2*c*(d+e*x)/(2*c*d-e*(b-sqrt(b^2-4*a*c))))/((1+m)*(2*c*d-e*(b-sqrt(b^2-4*a*c))))-2*c*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],2*c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/((1+m)*(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(b+2*c*x)*(d+e*x)^m/(a+b*x+c*x^2)^2,x,5,-(d+e*x)^(1+m)*((b^2-4*a*c)*(c*d-b*e)-c*(b^2-4*a*c)*e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2))+c*e*m*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],2*c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(2*c*d-e*(b-sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*(1+m)*sqrt(b^2-4*a*c)*(2*c*d-e*(b+sqrt(b^2-4*a*c))))-c*e*m*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],2*c*(d+e*x)/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(2*c*d-e*(b+sqrt(b^2-4*a*c)))/((c*d^2-b*d*e+a*e^2)*(1+m)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*sqrt(b^2-4*a*c))],

# Integrands of the form (d+e x)^m (f+g x) (a+b x+c x^2)^p when b^2-4 a c=0

# Integrands of the form (d+e x)^m (A+B x) (a^2+2 a b x+b^2 x^2)^p

# p>0
[(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2),x,3,-1/6*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^6/e^4+1/7*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^7/e^4-1/8*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^8/e^4+1/9*b^2*B*(d+e*x)^9/e^4],
[(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2),x,3,-1/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^5/e^4+1/6*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^6/e^4-1/7*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^7/e^4+1/8*b^2*B*(d+e*x)^8/e^4],
[(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2),x,3,-1/4*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^4/e^4+1/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^5/e^4-1/6*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^6/e^4+1/7*b^2*B*(d+e*x)^7/e^4],
[(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2),x,3,1/3*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^3/b^4+1/4*(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^4/b^4+1/5*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^5/b^4+1/6*B*e^2*(a+b*x)^6/b^4],
[(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2),x,3,1/3*(A*b-a*B)*(b*d-a*e)*(a+b*x)^3/b^3+1/4*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^4/b^3+1/5*B*e*(a+b*x)^5/b^3],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2),x,3,1/3*(A*b-a*B)*(a+b*x)^3/b^2+1/4*B*(a+b*x)^4/b^2],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x),x,3,b*(b*d-a*e)*(B*d-A*e)*x/e^3-1/2*(B*d-A*e)*(a+b*x)^2/e^2+1/3*B*(a+b*x)^3/(b*e)-(b*d-a*e)^2*(B*d-A*e)*log(d+e*x)/e^4],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2,x,3,-b*(2*b*B*d-A*b*e-2*a*B*e)*x/e^3+1/2*b^2*B*x^2/e^2+(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x))+(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*log(d+e*x)/e^4],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3,x,3,b^2*B*x/e^3+1/2*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^2)-(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x))-b*(3*b*B*d-A*b*e-2*a*B*e)*log(d+e*x)/e^4],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4,x,4,-1/3*(B*d-A*e)*(a+b*x)^3/(e*(b*d-a*e)*(d+e*x)^3)-1/2*B*(b*d-a*e)^2/(e^4*(d+e*x)^2)+2*b*B*(b*d-a*e)/(e^4*(d+e*x))+b^2*B*log(d+e*x)/e^4],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5,x,3,-1/4*(B*d-A*e)*(a+b*x)^3/(e*(b*d-a*e)*(d+e*x)^4)+1/12*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^3/(e*(b*d-a*e)^2*(d+e*x)^3)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6,x,3,1/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^5)-1/4*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^4)+1/3*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^3)-1/2*b^2*B/(e^4*(d+e*x)^2)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7,x,3,1/6*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^6)-1/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^5)+1/4*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^4)-1/3*b^2*B/(e^4*(d+e*x)^3)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^8,x,3,1/7*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^7)-1/6*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^6)+1/5*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*(d+e*x)^5)-1/4*b^2*B/(e^4*(d+e*x)^4)],
[(A+B*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^2,x,3,-1/8*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^8/e^6+1/9*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^9/e^6-1/5*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^10/e^6+2/11*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^11/e^6-1/12*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^12/e^6+1/13*b^4*B*(d+e*x)^13/e^6],
[(A+B*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^2,x,3,-1/7*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^7/e^6+1/8*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^8/e^6-2/9*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^9/e^6+1/5*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^10/e^6-1/11*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^11/e^6+1/12*b^4*B*(d+e*x)^12/e^6],
[(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^2,x,3,-1/6*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^6/e^6+1/7*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^7/e^6-1/4*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^8/e^6+2/9*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^9/e^6-1/10*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^10/e^6+1/11*b^4*B*(d+e*x)^11/e^6],
[(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/5*(A*b-a*B)*(b*d-a*e)^4*(a+b*x)^5/b^6+1/6*(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)*(a+b*x)^6/b^6+2/7*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)^7/b^6+1/4*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^8/b^6+1/9*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^9/b^6+1/10*B*e^4*(a+b*x)^10/b^6],
[(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/5*(A*b-a*B)*(b*d-a*e)^3*(a+b*x)^5/b^5+1/6*(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*(a+b*x)^6/b^5+3/7*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^7/b^5+1/8*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^8/b^5+1/9*B*e^3*(a+b*x)^9/b^5],
[(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/5*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^5/b^4+1/6*(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^6/b^4+1/7*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^7/b^4+1/8*B*e^2*(a+b*x)^8/b^4],
[(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/5*(A*b-a*B)*(b*d-a*e)*(a+b*x)^5/b^3+1/6*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^6/b^3+1/7*B*e*(a+b*x)^7/b^3],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/5*(A*b-a*B)*(a+b*x)^5/b^2+1/6*B*(a+b*x)^6/b^2],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x),x,3,b*(b*d-a*e)^3*(B*d-A*e)*x/e^5-1/2*(b*d-a*e)^2*(B*d-A*e)*(a+b*x)^2/e^4+1/3*(b*d-a*e)*(B*d-A*e)*(a+b*x)^3/e^3-1/4*(B*d-A*e)*(a+b*x)^4/e^2+1/5*B*(a+b*x)^5/(b*e)-(b*d-a*e)^4*(B*d-A*e)*log(d+e*x)/e^6],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^2,x,3,-2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*x/e^5+(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x))+b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^2/e^6-1/3*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^3/e^6+1/4*b^4*B*(d+e*x)^4/e^6+(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*log(d+e*x)/e^6],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^3,x,3,2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*x/e^5+1/2*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^2)-(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x))-1/2*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^2/e^6+1/3*b^4*B*(d+e*x)^3/e^6-2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*log(d+e*x)/e^6],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^4,x,3,-b^3*(4*b*B*d-A*b*e-4*a*B*e)*x/e^5+1/2*b^4*B*x^2/e^4+1/3*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^3)-1/2*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^2)+2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*(d+e*x))+2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*log(d+e*x)/e^6],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^5,x,3,b^4*B*x/e^5+1/4*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^4)-1/3*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^3)+b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*(d+e*x)^2)-2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/(e^6*(d+e*x))-b^3*(5*b*B*d-A*b*e-4*a*B*e)*log(d+e*x)/e^6],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^6,x,4,-1/5*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^5)-1/4*B*(b*d-a*e)^4/(e^6*(d+e*x)^4)+4/3*b*B*(b*d-a*e)^3/(e^6*(d+e*x)^3)-3*b^2*B*(b*d-a*e)^2/(e^6*(d+e*x)^2)+4*b^3*B*(b*d-a*e)/(e^6*(d+e*x))+b^4*B*log(d+e*x)/e^6],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^7,x,3,-1/6*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^6)+1/30*(5*b*B*d+A*b*e-6*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^5)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^8,x,4,-1/7*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^7)+1/42*(5*b*B*d+2*A*b*e-7*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^6)+1/210*b*(5*b*B*d+2*A*b*e-7*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^3*(d+e*x)^5)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^9,x,5,-1/8*(B*d-A*e)*(a+b*x)^5/(e*(b*d-a*e)*(d+e*x)^8)+1/56*(5*b*B*d+3*A*b*e-8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^2*(d+e*x)^7)+1/168*b*(5*b*B*d+3*A*b*e-8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^3*(d+e*x)^6)+1/840*b^2*(5*b*B*d+3*A*b*e-8*a*B*e)*(a+b*x)^5/(e*(b*d-a*e)^4*(d+e*x)^5)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^10,x,3,1/9*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^9)-1/8*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^8)+2/7*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*(d+e*x)^7)-1/3*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/(e^6*(d+e*x)^6)+1/5*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^5)-1/4*b^4*B/(e^6*(d+e*x)^4)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^11,x,3,1/10*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^10)-1/9*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^9)+1/4*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*(d+e*x)^8)-2/7*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/(e^6*(d+e*x)^7)+1/6*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^6)-1/5*b^4*B/(e^6*(d+e*x)^5)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^12,x,3,1/11*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^11)-1/10*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^10)+2/9*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*(d+e*x)^9)-1/4*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)/(e^6*(d+e*x)^8)+1/7*b^3*(5*b*B*d-A*b*e-4*a*B*e)/(e^6*(d+e*x)^7)-1/6*b^4*B/(e^6*(d+e*x)^6)],

# p<0
[(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2),x,3,2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*x/b^5-(A*b-a*B)*(b*d-a*e)^4/(b^6*(a+b*x))+e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^2/b^6+1/3*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^3/b^6+1/4*B*e^4*(a+b*x)^4/b^6+(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)*log(a+b*x)/b^6],
[(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2),x,3,3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*x/b^4-(A*b-a*B)*(b*d-a*e)^3/(b^5*(a+b*x))+1/2*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^2/b^5+1/3*B*e^3*(a+b*x)^3/b^5+(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*log(a+b*x)/b^5],
[(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2),x,3,e*(2*b*B*d+A*b*e-2*a*B*e)*x/b^3+1/2*B*e^2*x^2/b^2-(A*b-a*B)*(b*d-a*e)^2/(b^4*(a+b*x))+(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*log(a+b*x)/b^4],
[(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2),x,3,B*e*x/b^2-(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x))+(b*B*d+A*b*e-2*a*B*e)*log(a+b*x)/b^3],
[(A+B*x)/(a^2+2*a*b*x+b^2*x^2),x,3,(-A*b+a*B)/(b^2*(a+b*x))+B*log(a+b*x)/b^2],
[(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)),x,3,(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x))+(B*d-A*e)*log(a+b*x)/(b*d-a*e)^2-(B*d-A*e)*log(d+e*x)/(b*d-a*e)^2],
[(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)),x,3,(-A*b+a*B)/((b*d-a*e)^2*(a+b*x))+(B*d-A*e)/((b*d-a*e)^2*(d+e*x))+(b*B*d-2*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^3-(b*B*d-2*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^3],
[(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)),x,3,-b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x))+1/2*(B*d-A*e)/((b*d-a*e)^2*(d+e*x)^2)+(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^3*(d+e*x))+b*(b*B*d-3*A*b*e+2*a*B*e)*log(a+b*x)/(b*d-a*e)^4-b*(b*B*d-3*A*b*e+2*a*B*e)*log(d+e*x)/(b*d-a*e)^4],
[(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^2,x,3,e^3*(4*b*B*d+A*b*e-4*a*B*e)*x/b^5+1/2*B*e^4*x^2/b^4-1/3*(A*b-a*B)*(b*d-a*e)^4/(b^6*(a+b*x)^3)-1/2*(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)/(b^6*(a+b*x)^2)-2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)/(b^6*(a+b*x))+2*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*log(a+b*x)/b^6],
[(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^2,x,3,B*e^3*x/b^4-1/3*(A*b-a*B)*(b*d-a*e)^3/(b^5*(a+b*x)^3)-1/2*(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)/(b^5*(a+b*x)^2)-3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)/(b^5*(a+b*x))+e^2*(3*b*B*d+A*b*e-4*a*B*e)*log(a+b*x)/b^5],
[(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^2,x,4,-1/2*B*(b*d-a*e)^2/(b^4*(a+b*x)^2)-2*B*e*(b*d-a*e)/(b^4*(a+b*x))-1/3*(A*b-a*B)*(d+e*x)^3/(b*(b*d-a*e)*(a+b*x)^3)+B*e^2*log(a+b*x)/b^4],
[(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,3,-1/3*(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x)^3)+1/2*(-b*B*d-A*b*e+2*a*B*e)/(b^3*(a+b*x)^2)-B*e/(b^3*(a+b*x))],
[(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/3*(-A*b+a*B)/(b^2*(a+b*x)^3)-1/2*B/(b^2*(a+b*x)^2)],
[(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2),x,3,1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3)+1/2*(-B*d+A*e)/((b*d-a*e)^2*(a+b*x)^2)+e*(B*d-A*e)/((b*d-a*e)^3*(a+b*x))+e^2*(B*d-A*e)*log(a+b*x)/(b*d-a*e)^4-e^2*(B*d-A*e)*log(d+e*x)/(b*d-a*e)^4],
[(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2),x,3,1/3*(-A*b+a*B)/((b*d-a*e)^2*(a+b*x)^3)+1/2*(-b*B*d+2*A*b*e-a*B*e)/((b*d-a*e)^3*(a+b*x)^2)+e*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^4*(a+b*x))+e^2*(B*d-A*e)/((b*d-a*e)^4*(d+e*x))+e^2*(3*b*B*d-4*A*b*e+a*B*e)*log(a+b*x)/(b*d-a*e)^5-e^2*(3*b*B*d-4*A*b*e+a*B*e)*log(d+e*x)/(b*d-a*e)^5],

# Integrands of the form (d+e x)^m (A+B x) (a^2+2 a b x+b^2 x^2)^(p/2)

# p>0
[(A+B*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,1/5*(b*d-a*e)*(B*d-A*e)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-1/6*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+1/7*b*B*(d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(A+B*x)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,1/4*(b*d-a*e)*(B*d-A*e)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-1/5*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+1/6*b*B*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(A+B*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,1/3*(b*d-a*e)*(B*d-A*e)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-1/4*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+1/5*b*B*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(A+B*x)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,a*A*d*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/2*(A*b*d+a*B*d+a*A*e)*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/3*(b*B*d+A*b*e+a*B*e)*x^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)+1/4*b*B*e*x^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(a+b*x)],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,2,1/3*B*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/2*(A*b-a*B)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x),x,3,-b*(B*d-A*e)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(a+b*x))+1/2*B*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e)+(b*d-a*e)*(B*d-A*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2,x,3,b*B*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(a+b*x))-(b*d-a*e)*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x))-(2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3,x,3,-1/2*(b*d-a*e)*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^2)+(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x))+b*B*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4,x,3,1/3*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)^2*(d+e*x)^3)+1/2*(A*b-a*B)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^2*(d+e*x)^2)],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5,x,3,-1/4*(b*d-a*e)*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^4)+1/3*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^3)-1/2*b*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^2)],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6,x,3,-1/5*(b*d-a*e)*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^5)+1/4*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^4)-1/3*b*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^3)],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7,x,3,-1/6*(b*d-a*e)*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^6)+1/5*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^5)-1/4*b*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^4)],
[(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,1/6*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-1/7*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+3/8*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-1/9*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/10*b^3*B*(d+e*x)^10*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,1/5*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-1/6*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+3/7*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-1/8*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/9*b^3*B*(d+e*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,1/4*(A*b-a*B)*(b*d-a*e)^3*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/5*(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/2*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/7*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/8*B*e^3*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5],
[(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,1/4*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+1/5*(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+1/6*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+1/7*B*e^2*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4],
[(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,1/4*(A*b-a*B)*(b*d-a*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/5*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/6*B*e*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,2,1/4*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b^2+1/5*B*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x),x,3,-b*(b*d-a*e)^2*(B*d-A*e)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(a+b*x))+1/2*(b*d-a*e)*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3-1/3*(B*d-A*e)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/4*B*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e)+(b*d-a*e)^3*(B*d-A*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^2,x,3,3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(a+b*x))-(b*d-a*e)^3*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x))-1/2*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/3*b^3*B*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^3,x,3,-b^2*(3*b*B*d-A*b*e-3*a*B*e)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(a+b*x))+1/2*b^3*B*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-1/2*(b*d-a*e)^3*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^2)+(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x))+3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^4,x,3,b^3*B*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(a+b*x))-1/3*(b*d-a*e)^3*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^3)+1/2*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^2)-3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x))-b^2*(4*b*B*d-A*b*e-3*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^5,x,4,-1/4*(B*d-A*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*(d+e*x)^4)+1/3*B*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^3)-3/2*b*B*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^2)+3*b^2*B*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x))+b^3*B*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^6,x,3,1/5*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)^2*(d+e*x)^5)+1/4*(A*b-a*B)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^2*(d+e*x)^4)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^7,x,4,-1/6*(B*d-A*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*(d+e*x)^6)+1/15*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)^2*(d+e*x)^5)+1/60*b*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)^3*(d+e*x)^4)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^8,x,3,-1/7*(b*d-a*e)^3*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7)+1/6*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^6)-3/5*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^5)+1/4*b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^4)-1/3*b^3*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^3)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^9,x,3,-1/8*(b*d-a*e)^3*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8)+1/7*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7)-1/2*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^6)+1/5*b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^5)-1/4*b^3*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^4)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^10,x,3,-1/9*(b*d-a*e)^3*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^9)+1/8*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8)-3/7*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7)+1/6*b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^6)-1/5*b^3*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^5)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^11,x,3,-1/10*(b*d-a*e)^3*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^10)+1/9*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^9)-3/8*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8)+1/7*b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7)-1/6*b^3*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^6)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^12,x,3,-1/11*(b*d-a*e)^3*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^11)+1/10*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^10)-1/3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^9)+1/8*b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8)-1/7*b^3*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7)],
[(A+B*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,1/7*(b*d-a*e)^5*(B*d-A*e)*(d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-1/8*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*(d+e*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+5/9*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^10*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+5/11*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^11*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-1/12*b^4*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^12*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/13*b^5*B*(d+e*x)^13*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,1/6*(A*b-a*B)*(b*d-a*e)^5*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7+1/7*(b*d-a*e)^4*(b*B*d+5*A*b*e-6*a*B*e)*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7+5/8*e*(b*d-a*e)^3*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7+10/9*e^2*(b*d-a*e)^2*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7+1/2*e^3*(b*d-a*e)*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7+1/11*e^4*(5*b*B*d+A*b*e-6*a*B*e)*(a+b*x)^10*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7+1/12*B*e^5*(a+b*x)^11*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7],
[(A+B*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,1/6*(A*b-a*B)*(b*d-a*e)^4*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6+1/7*(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6+1/4*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6+2/9*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)*(a+b*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6+1/10*e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6+1/11*B*e^4*(a+b*x)^10*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6],
[(A+B*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,1/6*(A*b-a*B)*(b*d-a*e)^3*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/7*(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+3/8*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/9*e^2*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/10*B*e^3*(a+b*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5],
[(A+B*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,1/6*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+1/7*(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+1/8*e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+1/9*B*e^2*(a+b*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4],
[(A+B*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,1/6*(A*b-a*B)*(b*d-a*e)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/7*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/8*B*e*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,2,1/6*(A*b-a*B)*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b^2+1/7*B*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b^2],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x),x,3,-b*(b*d-a*e)^4*(B*d-A*e)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(a+b*x))+1/2*(b*d-a*e)^3*(B*d-A*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-1/3*(b*d-a*e)^2*(B*d-A*e)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/4*(b*d-a*e)*(B*d-A*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3-1/5*(B*d-A*e)*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/6*B*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(b*e)+(b*d-a*e)^5*(B*d-A*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^2,x,3,5*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(a+b*x))-(b*d-a*e)^5*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))-5*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+5/3*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-1/4*b^4*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/5*b^5*B*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^3,x,3,-10*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(a+b*x))-1/2*(b*d-a*e)^5*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^2)+(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))+5/2*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-1/3*b^4*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/4*b^5*B*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+5*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^4,x,3,5*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(a+b*x))-1/3*(b*d-a*e)^5*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^3)+1/2*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^2)-5*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))-1/2*b^4*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/3*b^5*B*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-10*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^5,x,3,-b^4*(5*b*B*d-A*b*e-5*a*B*e)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(a+b*x))+1/2*b^5*B*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-1/4*(b*d-a*e)^5*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^4)+1/3*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^3)-5/2*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^2)+10*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))+5*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^6,x,3,b^5*B*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(a+b*x))-1/5*(b*d-a*e)^5*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^5)+1/4*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^4)-5/3*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^3)+5*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^2)-5*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))-b^4*(6*b*B*d-A*b*e-5*a*B*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^7,x,4,-1/6*(B*d-A*e)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*(d+e*x)^6)+1/5*B*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^5)-5/4*b*B*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^4)+10/3*b^2*B*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^3)-5*b^3*B*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^2)+5*b^4*B*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))+b^5*B*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^8,x,3,1/7*(B*d-A*e)*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)^2*(d+e*x)^7)+1/6*(A*b-a*B)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^2*(d+e*x)^6)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^9,x,4,-1/8*(B*d-A*e)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*(d+e*x)^8)+1/28*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)^2*(d+e*x)^7)+1/168*b*(3*b*B*d+A*b*e-4*a*B*e)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)^3*(d+e*x)^6)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^10,x,5,-1/9*(B*d-A*e)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)*(d+e*x)^9)+1/24*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)^2*(d+e*x)^8)+1/84*b*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)^3*(d+e*x)^7)+1/504*b^2*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e*(b*d-a*e)^4*(d+e*x)^6)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^11,x,3,-1/10*(b*d-a*e)^5*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^10)+1/9*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^9)-5/8*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^8)+10/7*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^7)-5/6*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^6)+1/5*b^4*(6*b*B*d-A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^5)-1/4*b^5*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^4)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^12,x,3,-1/11*(b*d-a*e)^5*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^11)+1/10*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^10)-5/9*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^9)+5/4*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^8)-5/7*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^7)+1/6*b^4*(6*b*B*d-A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^6)-1/5*b^5*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^5)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^13,x,3,-1/12*(b*d-a*e)^5*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^12)+1/11*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^11)-1/2*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^10)+10/9*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^9)-5/8*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^8)+1/7*b^4*(6*b*B*d-A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^7)-1/6*b^5*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^6)],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^14,x,3,-1/13*(b*d-a*e)^5*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^13)+1/12*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^12)-5/11*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^11)+b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^10)-5/9*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^9)+1/8*b^4*(6*b*B*d-A*b*e-5*a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^8)-1/7*b^5*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^7)],

# p<0
[(A+B*x)*(d+e*x)^3/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,(A*b-a*B)*e*(b*d-a*e)^2*x*(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-a*B)*(b*d-a*e)*(a+b*x)*(d+e*x)^2/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*(A*b-a*B)*(a+b*x)*(d+e*x)^3/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*B*(a+b*x)*(d+e*x)^4/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*(b*d-a*e)^3*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^2/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,(A*b-a*B)*e*(b*d-a*e)*x*(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-a*B)*(a+b*x)*(d+e*x)^2/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*B*(a+b*x)*(d+e*x)^3/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*(b*d-a*e)^2*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,B*(b*d-a*e)*x*(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*e*(a+b*x)*(A+B*x)^2/(b*B*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*(b*d-a*e)*(a+b*x)*log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,(A*b-a*B)*(a+b*x)*log(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+B*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2],
[(A+B*x)/((d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,(A*b-a*B)*(a+b*x)*log(a+b*x)/(b*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))+(B*d-A*e)*(a+b*x)*log(d+e*x)/(e*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)),x,5,(A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-(A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^2*(d+e*x))],
[(A+B*x)/((d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,-1/2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+(A*b-a*B)*(a+b*x)/((b*d-a*e)^2*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+b*(A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-b*(A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,-1/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(A*b-a*B)*(a+b*x)/((b*d-a*e)^2*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+b*(A*b-a*B)*(a+b*x)/((b*d-a*e)^3*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+b^2*(A*b-a*B)*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-b^2*(A*b-a*B)*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,-(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*(A*b-a*B)*(b*d-a*e)^4/(b^6*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+e^2*(6*a^2*B*e^2-3*a*b*e*(4*B*d+A*e)+2*b^2*d*(3*B*d+2*A*e))*x*(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*e^3*(4*b*B*d+A*b*e-3*a*B*e)*x^2*(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*B*e^4*x^3*(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)*(a+b*x)*log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,-(b*d-a*e)^2*(b*B*d+3*A*b*e-4*a*B*e)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*(A*b-a*B)*(b*d-a*e)^3/(b^5*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+e^2*(3*b*B*d+A*b*e-3*a*B*e)*x*(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*B*e^3*x^2*(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e*(b*d-a*e)*(b*B*d+A*b*e-2*a*B*e)*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,-(b*d-a*e)*(b*B*d+2*A*b*e-3*a*B*e)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*(A*b-a*B)*(b*d-a*e)^2/(b^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+B*e^2*x*(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,(-b*B*d-A*b*e+2*a*B*e)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+B*e*(a+b*x)*log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,2,-B/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(-A*b+a*B)/(b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,3,(-B*d+A*e)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(B*d-A*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(B*d-A*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,3,(-b*B*d+2*A*b*e-a*B*e)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(-A*b+a*B)/((b*d-a*e)^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(B*d-A*e)*(a+b*x)/((b*d-a*e)^3*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,3,-b*(b*B*d-3*A*b*e+2*a*B*e)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*e*(B*d-A*e)*(a+b*x)/((b*d-a*e)^3*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)/((b*d-a*e)^4*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-3*b*e*(b*B*d-2*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))+3*b*e*(b*B*d-2*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^5/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,-10*e^2*(b*d-a*e)^2*(b*B*d+A*b*e-2*a*B*e)/(b^7*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(A*b-a*B)*(b*d-a*e)^5/(b^7*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-1/3*(b*d-a*e)^4*(b*B*d+5*A*b*e-6*a*B*e)/(b^7*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-5/2*e*(b*d-a*e)^3*(b*B*d+2*A*b*e-3*a*B*e)/(b^7*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+e^4*(5*b*B*d+A*b*e-5*a*B*e)*x*(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*B*e^5*x^2*(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+5*e^3*(b*d-a*e)*(2*b*B*d+A*b*e-3*a*B*e)*(a+b*x)*log(a+b*x)/(b^7*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,-2*e^2*(b*d-a*e)*(3*b*B*d+2*A*b*e-5*a*B*e)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(A*b-a*B)*(b*d-a*e)^4/(b^6*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-1/3*(b*d-a*e)^3*(b*B*d+4*A*b*e-5*a*B*e)/(b^6*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(b*d-a*e)^2*(2*b*B*d+3*A*b*e-5*a*B*e)/(b^6*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+B*e^4*x*(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,-3*B*e^2*(b*d-a*e)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))-1/3*B*(b*d-a*e)^3/(b^5*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-3/2*B*e*(b*d-a*e)^2/(b^5*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(A*b-a*B)*(d+e*x)^4/(b*(b*d-a*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+B*e^3*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,-1/3*(B*d-A*e)*(d+e*x)^3/((b*d-a*e)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/4*(A*b-a*B)*(d+e*x)^4/((b*d-a*e)^2*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,-1/4*(A*b-a*B)*(b*d-a*e)/(b^3*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*(-b*B*d-A*b*e+2*a*B*e)/(b^3*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*B*e/(b^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,2,-1/3*B/(b^2*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/4*(-A*b+a*B)/(b^2*(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2))],
[(A+B*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,3,-e^2*(B*d-A*e)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*(-B*d+A*e)/((b*d-a*e)^2*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*e*(B*d-A*e)/((b*d-a*e)^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(B*d-A*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(B*d-A*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,3,-e^2*(3*b*B*d-4*A*b*e+a*B*e)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(-A*b+a*B)/((b*d-a*e)^2*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/3*(-b*B*d+2*A*b*e-a*B*e)/((b*d-a*e)^3*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*e*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(B*d-A*e)*(a+b*x)/((b*d-a*e)^5*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,3,-2*b*e^2*(3*b*B*d-5*A*b*e+2*a*B*e)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*b*(A*b-a*B)/((b*d-a*e)^3*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-1/3*b*(b*B*d-3*A*b*e+2*a*B*e)/((b*d-a*e)^4*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+3/2*b*e*(b*B*d-2*A*b*e+a*B*e)/((b*d-a*e)^5*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*e^3*(B*d-A*e)*(a+b*x)/((b*d-a*e)^5*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)/((b*d-a*e)^6*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-5*b*e^3*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*log(a+b*x)/((b*d-a*e)^7*sqrt(a^2+2*a*b*x+b^2*x^2))+5*b*e^3*(2*b*B*d-3*A*b*e+a*B*e)*(a+b*x)*log(d+e*x)/((b*d-a*e)^7*sqrt(a^2+2*a*b*x+b^2*x^2))],

# Integrands of the form (d+e x)^(m/2) (A+B x) (a^2+2 a b x+b^2 x^2)^p

# p>0
[(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2),x,3,-2/9*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(9/2)/e^4+2/11*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^4-2/13*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(13/2)/e^4+2/15*b^2*B*(d+e*x)^(15/2)/e^4],
[(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2),x,3,-2/7*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(7/2)/e^4+2/9*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^4-2/11*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(11/2)/e^4+2/13*b^2*B*(d+e*x)^(13/2)/e^4],
[(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2),x,3,-2/5*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(5/2)/e^4+2/7*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^4-2/9*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(9/2)/e^4+2/11*b^2*B*(d+e*x)^(11/2)/e^4],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x),x,3,-2/3*(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(3/2)/e^4+2/5*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^4-2/7*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(7/2)/e^4+2/9*b^2*B*(d+e*x)^(9/2)/e^4],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x),x,3,2/3*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^4-2/5*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^4+2/7*b^2*B*(d+e*x)^(7/2)/e^4-2*(b*d-a*e)^2*(B*d-A*e)*sqrt(d+e*x)/e^4],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2),x,3,-2/3*b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^4+2/5*b^2*B*(d+e*x)^(5/2)/e^4+2*(b*d-a*e)^2*(B*d-A*e)/(e^4*sqrt(d+e*x))+2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(d+e*x)/e^4],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2),x,3,2/3*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(3/2))+2/3*b^2*B*(d+e*x)^(3/2)/e^4-2*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*sqrt(d+e*x))-2*b*(3*b*B*d-A*b*e-2*a*B*e)*sqrt(d+e*x)/e^4],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2),x,3,2/5*(b*d-a*e)^2*(B*d-A*e)/(e^4*(d+e*x)^(5/2))-2/3*(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)/(e^4*(d+e*x)^(3/2))+2*b*(3*b*B*d-A*b*e-2*a*B*e)/(e^4*sqrt(d+e*x))+2*b^2*B*sqrt(d+e*x)/e^4],
[(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,-2/9*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(9/2)/e^6+2/11*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^6-4/13*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(13/2)/e^6+4/15*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(15/2)/e^6-2/17*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(17/2)/e^6+2/19*b^4*B*(d+e*x)^(19/2)/e^6],
[(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,-2/7*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(7/2)/e^6+2/9*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^6-4/11*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(11/2)/e^6+4/13*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(13/2)/e^6-2/15*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(15/2)/e^6+2/17*b^4*B*(d+e*x)^(17/2)/e^6],
[(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,-2/5*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(5/2)/e^6+2/7*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^6-4/9*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(9/2)/e^6+4/11*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(11/2)/e^6-2/13*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(13/2)/e^6+2/15*b^4*B*(d+e*x)^(15/2)/e^6],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x),x,3,-2/3*(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(3/2)/e^6+2/5*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^6-4/7*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(7/2)/e^6+4/9*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(9/2)/e^6-2/11*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(11/2)/e^6+2/13*b^4*B*(d+e*x)^(13/2)/e^6],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/sqrt(d+e*x),x,3,2/3*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^6-4/5*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^6+4/7*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(7/2)/e^6-2/9*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(9/2)/e^6+2/11*b^4*B*(d+e*x)^(11/2)/e^6-2*(b*d-a*e)^4*(B*d-A*e)*sqrt(d+e*x)/e^6],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(3/2),x,3,-4/3*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^6+4/5*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(5/2)/e^6-2/7*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(7/2)/e^6+2/9*b^4*B*(d+e*x)^(9/2)/e^6+2*(b*d-a*e)^4*(B*d-A*e)/(e^6*sqrt(d+e*x))+2*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*sqrt(d+e*x)/e^6],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(5/2),x,3,2/3*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^(3/2))+4/3*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(3/2)/e^6-2/5*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(5/2)/e^6+2/7*b^4*B*(d+e*x)^(7/2)/e^6-2*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*sqrt(d+e*x))-4*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*sqrt(d+e*x)/e^6],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(7/2),x,3,2/5*(b*d-a*e)^4*(B*d-A*e)/(e^6*(d+e*x)^(5/2))-2/3*(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)/(e^6*(d+e*x)^(3/2))-2/3*b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(3/2)/e^6+2/5*b^4*B*(d+e*x)^(5/2)/e^6+4*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)/(e^6*sqrt(d+e*x))+4*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*sqrt(d+e*x)/e^6],
[(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,-2/9*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^(9/2)/e^8+2/11*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(11/2)/e^8-6/13*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(13/2)/e^8+2/3*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(15/2)/e^8-10/17*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(17/2)/e^8+6/19*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(19/2)/e^8-2/21*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(21/2)/e^8+2/23*b^6*B*(d+e*x)^(23/2)/e^8],
[(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,-2/7*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^(7/2)/e^8+2/9*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(9/2)/e^8-6/11*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(11/2)/e^8+10/13*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(13/2)/e^8-2/3*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(15/2)/e^8+6/17*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(17/2)/e^8-2/19*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(19/2)/e^8+2/21*b^6*B*(d+e*x)^(21/2)/e^8],
[(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,-2/5*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^(5/2)/e^8+2/7*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(7/2)/e^8-2/3*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(9/2)/e^8+10/11*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(11/2)/e^8-10/13*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(13/2)/e^8+2/5*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(15/2)/e^8-2/17*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(17/2)/e^8+2/19*b^6*B*(d+e*x)^(19/2)/e^8],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x),x,3,-2/3*(b*d-a*e)^6*(B*d-A*e)*(d+e*x)^(3/2)/e^8+2/5*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(5/2)/e^8-6/7*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(7/2)/e^8+10/9*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(9/2)/e^8-10/11*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(11/2)/e^8+6/13*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(13/2)/e^8-2/15*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(15/2)/e^8+2/17*b^6*B*(d+e*x)^(17/2)/e^8],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/sqrt(d+e*x),x,3,2/3*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*(d+e*x)^(3/2)/e^8-6/5*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(5/2)/e^8+10/7*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(7/2)/e^8-10/9*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(9/2)/e^8+6/11*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(11/2)/e^8-2/13*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(13/2)/e^8+2/15*b^6*B*(d+e*x)^(15/2)/e^8-2*(b*d-a*e)^6*(B*d-A*e)*sqrt(d+e*x)/e^8],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(3/2),x,3,-2*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*(d+e*x)^(3/2)/e^8+2*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(5/2)/e^8-10/7*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(7/2)/e^8+2/3*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(9/2)/e^8-2/11*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(11/2)/e^8+2/13*b^6*B*(d+e*x)^(13/2)/e^8+2*(b*d-a*e)^6*(B*d-A*e)/(e^8*sqrt(d+e*x))+2*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)*sqrt(d+e*x)/e^8],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(5/2),x,3,2/3*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^(3/2))+10/3*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*(d+e*x)^(3/2)/e^8-2*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(5/2)/e^8+6/7*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(7/2)/e^8-2/9*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(9/2)/e^8+2/11*b^6*B*(d+e*x)^(11/2)/e^8-2*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*sqrt(d+e*x))-6*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)*sqrt(d+e*x)/e^8],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(7/2),x,3,2/5*(b*d-a*e)^6*(B*d-A*e)/(e^8*(d+e*x)^(5/2))-2/3*(b*d-a*e)^5*(7*b*B*d-6*A*b*e-a*B*e)/(e^8*(d+e*x)^(3/2))-10/3*b^3*(b*d-a*e)^2*(7*b*B*d-3*A*b*e-4*a*B*e)*(d+e*x)^(3/2)/e^8+6/5*b^4*(b*d-a*e)*(7*b*B*d-2*A*b*e-5*a*B*e)*(d+e*x)^(5/2)/e^8-2/7*b^5*(7*b*B*d-A*b*e-6*a*B*e)*(d+e*x)^(7/2)/e^8+2/9*b^6*B*(d+e*x)^(9/2)/e^8+6*b*(b*d-a*e)^4*(7*b*B*d-5*A*b*e-2*a*B*e)/(e^8*sqrt(d+e*x))+10*b^2*(b*d-a*e)^3*(7*b*B*d-4*A*b*e-3*a*B*e)*sqrt(d+e*x)/e^8],

# p<0
[(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2),x,8,1/3*(b*d-a*e)*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(3/2)/b^4+1/5*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(5/2)/b^3+1/7*(2*b*B*d+7*A*b*e-9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x))-(b*d-a*e)^(5/2)*(2*b*B*d+7*A*b*e-9*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+(b*d-a*e)^2*(2*b*B*d+7*A*b*e-9*a*B*e)*sqrt(d+e*x)/b^5],
[(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2),x,7,1/3*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/b^3+1/5*(2*b*B*d+5*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x))-(b*d-a*e)^(3/2)*(2*b*B*d+5*A*b*e-7*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+(b*d-a*e)*(2*b*B*d+5*A*b*e-7*a*B*e)*sqrt(d+e*x)/b^4],
[(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2),x,6,1/3*(2*b*B*d+3*A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e))-(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x))-(2*b*B*d+3*A*b*e-5*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(7/2)+(2*b*B*d+3*A*b*e-5*a*B*e)*sqrt(d+e*x)/b^3],
[(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2),x,5,-(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x))-(2*b*B*d+A*b*e-3*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*sqrt(b*d-a*e))+(2*b*B*d+A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e))],
[(A+B*x)/((a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x)),x,4,-(2*b*B*d-A*b*e-a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(3/2))-(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x))],
[(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)),x,5,-(2*b*B*d-3*A*b*e+a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(5/2)*sqrt(b))+(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^2*sqrt(d+e*x))+(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)),x,6,1/3*(2*b*B*d-5*A*b*e+3*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(3/2))+(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2))-(2*b*B*d-5*A*b*e+3*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(7/2)+(2*b*B*d-5*A*b*e+3*a*B*e)/((b*d-a*e)^3*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)),x,7,1/5*(2*b*B*d-7*A*b*e+5*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(5/2))+(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(5/2))+1/3*(2*b*B*d-7*A*b*e+5*a*B*e)/((b*d-a*e)^3*(d+e*x)^(3/2))-b^(3/2)*(2*b*B*d-7*A*b*e+5*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(9/2)+b*(2*b*B*d-7*A*b*e+5*a*B*e)/((b*d-a*e)^4*sqrt(d+e*x))],
[(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^2,x,9,7/8*e^2*(6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(3/2)/b^5+21/40*e^2*(6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(5/2)/(b^4*(b*d-a*e))-3/8*e*(6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(7/2)/(b^3*(b*d-a*e)*(a+b*x))-1/12*(6*b*B*d+5*A*b*e-11*a*B*e)*(d+e*x)^(9/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-1/3*(A*b-a*B)*(d+e*x)^(11/2)/(b*(b*d-a*e)*(a+b*x)^3)-21/8*e^2*(b*d-a*e)^(3/2)*(6*b*B*d+5*A*b*e-11*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(13/2)+21/8*e^2*(b*d-a*e)*(6*b*B*d+5*A*b*e-11*a*B*e)*sqrt(d+e*x)/b^6],
[(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^2,x,8,35/24*e^2*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(3/2)/(b^4*(b*d-a*e))-7/8*e*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(5/2)/(b^3*(b*d-a*e)*(a+b*x))-1/4*(2*b*B*d+A*b*e-3*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-1/3*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^3)-35/8*e^2*(2*b*B*d+A*b*e-3*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(11/2)+35/8*e^2*(2*b*B*d+A*b*e-3*a*B*e)*sqrt(d+e*x)/b^5],
[(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^2,x,7,-5/24*e*(6*b*B*d+A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e)*(a+b*x))-1/12*(6*b*B*d+A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-1/3*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^3)-5/8*e^2*(6*b*B*d+A*b*e-7*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*sqrt(b*d-a*e))+5/8*e^2*(6*b*B*d+A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e))],
[(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^2,x,6,-1/12*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x)^2)-1/3*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^3)-1/8*e^2*(6*b*B*d-A*b*e-5*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*(b*d-a*e)^(3/2))-1/8*e*(6*b*B*d-A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)*(a+b*x))],
[(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,6,-1/3*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^3)+1/8*e^2*(2*b*B*d-A*b*e-a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(5/2))-1/4*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)*(a+b*x)^2)-1/8*e*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^2*(a+b*x))],
[(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x)),x,6,-1/8*e^2*(6*b*B*d-5*A*b*e-a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(7/2))-1/3*(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)^3)-1/12*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^2*(a+b*x)^2)+1/8*e*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^3*(a+b*x))],
[(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2),x,7,-5/8*e^2*(6*b*B*d-7*A*b*e+a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*sqrt(b))+5/8*e^2*(6*b*B*d-7*A*b*e+a*B*e)/(b*(b*d-a*e)^4*sqrt(d+e*x))+1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*sqrt(d+e*x))+1/12*(-6*b*B*d+7*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*sqrt(d+e*x))+5/24*e*(6*b*B*d-7*A*b*e+a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2),x,8,35/24*e^2*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^4*(d+e*x)^(3/2))+1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*(d+e*x)^(3/2))+1/4*(-2*b*B*d+3*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*(d+e*x)^(3/2))+7/8*e*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*(d+e*x)^(3/2))-35/8*e^2*(2*b*B*d-3*A*b*e+a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(11/2)+35/8*e^2*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^5*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2),x,9,21/40*e^2*(6*b*B*d-11*A*b*e+5*a*B*e)/(b*(b*d-a*e)^4*(d+e*x)^(5/2))+1/3*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*(d+e*x)^(5/2))+1/12*(-6*b*B*d+11*A*b*e-5*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*(d+e*x)^(5/2))+3/8*e*(6*b*B*d-11*A*b*e+5*a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*(d+e*x)^(5/2))+7/8*e^2*(6*b*B*d-11*A*b*e+5*a*B*e)/((b*d-a*e)^5*(d+e*x)^(3/2))-21/8*b^(3/2)*e^2*(6*b*B*d-11*A*b*e+5*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(13/2)+21/8*b*e^2*(6*b*B*d-11*A*b*e+5*a*B*e)/((b*d-a*e)^6*sqrt(d+e*x))],
[(A+B*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^3,x,10,77/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(3/2)/(b^6*(b*d-a*e))-231/640*e^3*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(5/2)/(b^5*(b*d-a*e)*(a+b*x))-33/320*e^2*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(7/2)/(b^4*(b*d-a*e)*(a+b*x)^2)-11/240*e*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(9/2)/(b^3*(b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d+3*A*b*e-13*a*B*e)*(d+e*x)^(11/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(13/2)/(b*(b*d-a*e)*(a+b*x)^5)-231/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(15/2)+231/128*e^4*(10*b*B*d+3*A*b*e-13*a*B*e)*sqrt(d+e*x)/b^7],
[(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^3,x,9,-21/128*e^3*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(3/2)/(b^5*(b*d-a*e)*(a+b*x))-21/320*e^2*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(5/2)/(b^4*(b*d-a*e)*(a+b*x)^2)-3/80*e*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(7/2)/(b^3*(b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d+A*b*e-11*a*B*e)*(d+e*x)^(9/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(11/2)/(b*(b*d-a*e)*(a+b*x)^5)-63/128*e^4*(10*b*B*d+A*b*e-11*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(13/2)*sqrt(b*d-a*e))+63/128*e^4*(10*b*B*d+A*b*e-11*a*B*e)*sqrt(d+e*x)/(b^6*(b*d-a*e))],
[(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^3,x,8,-7/192*e^2*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(3/2)/(b^4*(b*d-a*e)*(a+b*x)^2)-7/240*e*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(5/2)/(b^3*(b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d-A*b*e-9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^5)-7/128*e^4*(10*b*B*d-A*b*e-9*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(11/2)*(b*d-a*e)^(3/2))-7/128*e^3*(10*b*B*d-A*b*e-9*a*B*e)*sqrt(d+e*x)/(b^5*(b*d-a*e)*(a+b*x))],
[(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^3,x,8,-1/48*e*(10*b*B*d-3*A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e)*(a+b*x)^3)-1/40*(10*b*B*d-3*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^5)+1/128*e^4*(10*b*B*d-3*A*b*e-7*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*(b*d-a*e)^(5/2))-1/64*e^2*(10*b*B*d-3*A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)*(a+b*x)^2)-1/128*e^3*(10*b*B*d-3*A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)^2*(a+b*x))],
[(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^3,x,8,-1/8*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/5*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^5)-3/128*e^4*(2*b*B*d-A*b*e-a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*(b*d-a*e)^(7/2))-1/16*e*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)*(a+b*x)^3)-1/64*e^2*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)^2*(a+b*x)^2)+3/128*e^3*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)^3*(a+b*x))],
[(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,8,-1/5*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^5)+1/128*e^4*(10*b*B*d-7*A*b*e-3*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(9/2))-1/40*(10*b*B*d-7*A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)*(a+b*x)^4)-1/240*e*(10*b*B*d-7*A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^2*(a+b*x)^3)+1/192*e^2*(10*b*B*d-7*A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^3*(a+b*x)^2)-1/128*e^3*(10*b*B*d-7*A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^4*(a+b*x))],
[(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x)),x,8,-7/128*e^4*(10*b*B*d-9*A*b*e-a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(11/2))-1/5*(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)^5)-1/40*(10*b*B*d-9*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^2*(a+b*x)^4)+7/240*e*(10*b*B*d-9*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^3*(a+b*x)^3)-7/192*e^2*(10*b*B*d-9*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^4*(a+b*x)^2)+7/128*e^3*(10*b*B*d-9*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^5*(a+b*x))],
[(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3),x,9,-63/128*e^4*(10*b*B*d-11*A*b*e+a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(13/2)*sqrt(b))+63/128*e^4*(10*b*B*d-11*A*b*e+a*B*e)/(b*(b*d-a*e)^6*sqrt(d+e*x))+1/5*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^5*sqrt(d+e*x))+1/40*(-10*b*B*d+11*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^4*sqrt(d+e*x))+3/80*e*(10*b*B*d-11*A*b*e+a*B*e)/(b*(b*d-a*e)^3*(a+b*x)^3*sqrt(d+e*x))-21/320*e^2*(10*b*B*d-11*A*b*e+a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*sqrt(d+e*x))+21/128*e^3*(10*b*B*d-11*A*b*e+a*B*e)/(b*(b*d-a*e)^5*(a+b*x)*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3),x,10,77/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^6*(d+e*x)^(3/2))+1/5*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^5*(d+e*x)^(3/2))+1/40*(-10*b*B*d+13*A*b*e-3*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^4*(d+e*x)^(3/2))+11/240*e*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^3*(a+b*x)^3*(d+e*x)^(3/2))-33/320*e^2*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*(d+e*x)^(3/2))+231/640*e^3*(10*b*B*d-13*A*b*e+3*a*B*e)/(b*(b*d-a*e)^5*(a+b*x)*(d+e*x)^(3/2))-231/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(15/2)+231/128*e^4*(10*b*B*d-13*A*b*e+3*a*B*e)/((b*d-a*e)^7*sqrt(d+e*x))],
[(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3),x,11,3003/640*e^4*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^6*(d+e*x)^(5/2))+1/5*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^5*(d+e*x)^(5/2))+1/8*(-2*b*B*d+3*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^4*(d+e*x)^(5/2))+13/48*e*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^3*(a+b*x)^3*(d+e*x)^(5/2))-143/192*e^2*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^4*(a+b*x)^2*(d+e*x)^(5/2))+429/128*e^3*(2*b*B*d-3*A*b*e+a*B*e)/(b*(b*d-a*e)^5*(a+b*x)*(d+e*x)^(5/2))+1001/128*e^4*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^7*(d+e*x)^(3/2))-3003/128*b^(3/2)*e^4*(2*b*B*d-3*A*b*e+a*B*e)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(17/2)+3003/128*b*e^4*(2*b*B*d-3*A*b*e+a*B*e)/((b*d-a*e)^8*sqrt(d+e*x))],

# Integrands of the form (d+e x)^(m/2) (A+B x) (a^2+2 a b x+b^2 x^2)^(p/2)

# p>0
[(A+B*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,2/9*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-2/11*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/13*b*B*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(A+B*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,2/7*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-2/9*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/11*b*B*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(A+B*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,2/5*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-2/7*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/9*b*B*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(A+B*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,3,2/3*(b*d-a*e)*(B*d-A*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-2/5*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/7*b*B*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x),x,3,-2/3*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/5*b*B*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2*(b*d-a*e)*(B*d-A*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2),x,3,2/3*b*B*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-2*(b*d-a*e)*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x))-2*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2),x,3,-2/3*(b*d-a*e)*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(3/2))+2*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x))+2*b*B*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(A+B*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2),x,3,-2/5*(b*d-a*e)*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(5/2))+2/3*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(3/2))-2*b*B*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x))],
[(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,2/9*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-2/11*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+6/13*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-2/15*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/17*b^3*B*(d+e*x)^(17/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,2/7*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-2/9*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+6/11*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-2/13*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/15*b^3*B*(d+e*x)^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,2/5*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-2/7*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-2/11*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/13*b^3*B*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x),x,3,2/3*(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-2/5*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+6/7*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-2/9*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/11*b^3*B*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/sqrt(d+e*x),x,3,-2/3*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+6/5*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-2/7*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/9*b^3*B*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2*(b*d-a*e)^3*(B*d-A*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(3/2),x,3,2*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-2/5*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/7*b^3*B*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-2*(b*d-a*e)^3*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*sqrt(d+e*x))-2*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(5/2),x,3,-2/3*(b*d-a*e)^3*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(3/2))-2/3*b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/5*b^3*B*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*sqrt(d+e*x))+6*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(7/2),x,3,-2/5*(b*d-a*e)^3*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(5/2))+2/3*(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(3/2))+2/3*b^3*B*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-6*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*sqrt(d+e*x))-2*b^2*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(A+B*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,2/9*(b*d-a*e)^5*(B*d-A*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/11*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+10/13*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-4/3*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+10/17*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(17/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/19*b^4*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(19/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/21*b^5*B*(d+e*x)^(21/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,2/7*(b*d-a*e)^5*(B*d-A*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/9*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+10/11*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-20/13*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/3*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/17*b^4*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(17/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/19*b^5*B*(d+e*x)^(19/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,2/5*(b*d-a*e)^5*(B*d-A*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/7*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+10/9*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-20/11*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+10/13*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/15*b^4*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/17*b^5*B*(d+e*x)^(17/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x),x,3,2/3*(b*d-a*e)^5*(B*d-A*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/5*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+10/7*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-20/9*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+10/11*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/13*b^4*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/15*b^5*B*(d+e*x)^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/sqrt(d+e*x),x,3,-2/3*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-20/7*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+10/9*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/11*b^4*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/13*b^5*B*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2*(b*d-a*e)^5*(B*d-A*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(3/2),x,3,10/3*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-4*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+10/7*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/9*b^4*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/11*b^5*B*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2*(b*d-a*e)^5*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x))-2*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(5/2),x,3,-2/3*(b*d-a*e)^5*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(3/2))-20/3*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/7*b^4*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/9*b^5*B*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x))+10*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(A+B*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(7/2),x,3,-2/5*(b*d-a*e)^5*(B*d-A*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(5/2))+2/3*(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(3/2))+10/3*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/5*b^4*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/7*b^5*B*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-10*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x))-20*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],

# p<0
[(A+B*x)*(d+e*x)^(5/2)/sqrt(a^2+2*a*b*x+b^2*x^2),x,7,2/3*(A*b-a*B)*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2/5*(A*b-a*B)*(a+b*x)*(d+e*x)^(5/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+2/7*B*(a+b*x)*(d+e*x)^(7/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-2*(A*b-a*B)*(b*d-a*e)^(5/2)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*(b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^(3/2)/sqrt(a^2+2*a*b*x+b^2*x^2),x,6,2/3*(A*b-a*B)*(a+b*x)*(d+e*x)^(3/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))+2/5*B*(a+b*x)*(d+e*x)^(5/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-2*(A*b-a*B)*(b*d-a*e)^(3/2)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*sqrt(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,5,2/3*B*(a+b*x)*(d+e*x)^(3/2)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))-2*(A*b-a*B)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*(a+b*x)*sqrt(d+e*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/(sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,4,-2*(A*b-a*B)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*B*(a+b*x)*sqrt(d+e*x)/(b*e*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,4,-2*(A*b-a*B)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(3/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-2*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,5,-2/3*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-2*(A*b-a*B)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/((b*d-a*e)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*(A*b-a*B)*(a+b*x)/((b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,6,-2/5*(B*d-A*e)*(a+b*x)/(e*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2/3*(A*b-a*B)*(a+b*x)/((b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-2*b^(3/2)*(A*b-a*B)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+2*b*(A*b-a*B)*(a+b*x)/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,8,7/12*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+7/20*e*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*(d+e*x)^(5/2)/(b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(4*b*B*d+5*A*b*e-9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/4*e*(b*d-a*e)^(3/2)*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/4*e*(b*d-a*e)*(4*b*B*d+5*A*b*e-9*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,7,5/12*e*(4*b*B*d+3*A*b*e-7*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(4*b*B*d+3*A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5/4*e*(4*b*B*d+3*A*b*e-7*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,6,-1/4*(4*b*B*d+A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-3/4*e*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))+3/4*e*(4*b*B*d+A*b*e-5*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,5,-1/2*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*e*(4*b*B*d-A*b*e-3*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(4*b*B*d-A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)),x,5,1/4*e*(4*b*B*d-3*A*b*e-a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(4*b*B*d-3*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,6,3/4*e*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(-4*b*B*d+5*A*b*e-a*B*e)/(b*(b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-3/4*e*(4*b*B*d-5*A*b*e+a*B*e)*(a+b*x)/(b*(b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,7,1/4*(-4*b*B*d+7*A*b*e-3*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/12*e*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)/(b*(b*d-a*e)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5/4*e*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/((b*d-a*e)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/4*e*(4*b*B*d-7*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^4*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,8,1/4*(-4*b*B*d+9*A*b*e-5*a*B*e)/(b*(b*d-a*e)^2*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/20*e*(4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)/(b*(b*d-a*e)^3*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/12*e*(4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^4*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/4*b^(3/2)*e*(4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/4*b*e*(4*b*B*d-9*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,10,77/64*e^3*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))+231/320*e^3*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*(d+e*x)^(5/2)/(b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-33/64*e^2*(8*b*B*d+5*A*b*e-13*a*B*e)*(d+e*x)^(7/2)/(b^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-11/96*e*(8*b*B*d+5*A*b*e-13*a*B*e)*(d+e*x)^(9/2)/(b^3*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/24*(8*b*B*d+5*A*b*e-13*a*B*e)*(d+e*x)^(11/2)/(b^2*(b*d-a*e)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(A*b-a*B)*(d+e*x)^(13/2)/(b*(b*d-a*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-231/64*e^3*(b*d-a*e)^(3/2)*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+231/64*e^3*(b*d-a*e)*(8*b*B*d+5*A*b*e-13*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^7*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,9,35/64*e^3*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*(d+e*x)^(3/2)/(b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-21/64*e^2*(8*b*B*d+3*A*b*e-11*a*B*e)*(d+e*x)^(5/2)/(b^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-3/32*e*(8*b*B*d+3*A*b*e-11*a*B*e)*(d+e*x)^(7/2)/(b^3*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/24*(8*b*B*d+3*A*b*e-11*a*B*e)*(d+e*x)^(9/2)/(b^2*(b*d-a*e)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(A*b-a*B)*(d+e*x)^(11/2)/(b*(b*d-a*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-105/64*e^3*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+105/64*e^3*(8*b*B*d+3*A*b*e-11*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,8,-35/192*e^2*(8*b*B*d+A*b*e-9*a*B*e)*(d+e*x)^(3/2)/(b^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/96*e*(8*b*B*d+A*b*e-9*a*B*e)*(d+e*x)^(5/2)/(b^3*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/24*(8*b*B*d+A*b*e-9*a*B*e)*(d+e*x)^(7/2)/(b^2*(b*d-a*e)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(A*b-a*B)*(d+e*x)^(9/2)/(b*(b*d-a*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^3*(8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(11/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))+35/64*e^3*(8*b*B*d+A*b*e-9*a*B*e)*(a+b*x)*sqrt(d+e*x)/(b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,7,-5/96*e*(8*b*B*d-A*b*e-7*a*B*e)*(d+e*x)^(3/2)/(b^3*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/24*(8*b*B*d-A*b*e-7*a*B*e)*(d+e*x)^(5/2)/(b^2*(b*d-a*e)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(A*b-a*B)*(d+e*x)^(7/2)/(b*(b*d-a*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-5/64*e^3*(8*b*B*d-A*b*e-7*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*(b*d-a*e)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/64*e^2*(8*b*B*d-A*b*e-7*a*B*e)*sqrt(d+e*x)/(b^4*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,7,-1/24*(8*b*B*d-3*A*b*e-5*a*B*e)*(d+e*x)^(3/2)/(b^2*(b*d-a*e)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(A*b-a*B)*(d+e*x)^(5/2)/(b*(b*d-a*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+1/64*e^3*(8*b*B*d-3*A*b*e-5*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*(b*d-a*e)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/64*e^2*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-1/32*e*(8*b*B*d-3*A*b*e-5*a*B*e)*sqrt(d+e*x)/(b^3*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,7,-1/4*(A*b-a*B)*(d+e*x)^(3/2)/(b*(b*d-a*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-1/64*e^3*(8*b*B*d-5*A*b*e-3*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/64*e^2*(8*b*B*d-5*A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-1/24*(8*b*B*d-5*A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-1/96*e*(8*b*B*d-5*A*b*e-3*a*B*e)*sqrt(d+e*x)/(b^2*(b*d-a*e)^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)),x,7,5/64*e^3*(8*b*B*d-7*A*b*e-a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/64*e^2*(8*b*B*d-7*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*(A*b-a*B)*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-1/24*(8*b*B*d-7*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^2*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+5/96*e*(8*b*B*d-7*A*b*e-a*B*e)*sqrt(d+e*x)/(b*(b*d-a*e)^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,8,35/64*e^3*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(11/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/192*e^2*(8*b*B*d-9*A*b*e+a*B*e)/(b*(b*d-a*e)^4*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/24*(-8*b*B*d+9*A*b*e-a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/96*e*(8*b*B*d-9*A*b*e+a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^3*(8*b*B*d-9*A*b*e+a*B*e)*(a+b*x)/(b*(b*d-a*e)^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,9,-21/64*e^2*(8*b*B*d-11*A*b*e+3*a*B*e)/(b*(b*d-a*e)^4*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/24*(-8*b*B*d+11*A*b*e-3*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+3/32*e*(8*b*B*d-11*A*b*e+3*a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/64*e^3*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/(b*(b*d-a*e)^5*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+105/64*e^3*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/((b*d-a*e)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-105/64*e^3*(8*b*B*d-11*A*b*e+3*a*B*e)*(a+b*x)/((b*d-a*e)^6*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,10,-33/64*e^2*(8*b*B*d-13*A*b*e+5*a*B*e)/(b*(b*d-a*e)^4*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/4*(-A*b+a*B)/(b*(b*d-a*e)*(a+b*x)^3*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/24*(-8*b*B*d+13*A*b*e-5*a*B*e)/(b*(b*d-a*e)^2*(a+b*x)^2*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+11/96*e*(8*b*B*d-13*A*b*e+5*a*B*e)/(b*(b*d-a*e)^3*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-231/320*e^3*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/(b*(b*d-a*e)^5*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-77/64*e^3*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^6*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+231/64*b^(3/2)*e^3*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-231/64*b*e^3*(8*b*B*d-13*A*b*e+5*a*B*e)*(a+b*x)/((b*d-a*e)^7*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],

# Integrands of the form (d+e x)^m (A+B x) (a^2+2 a b x+b^2 x^2)^p when m symbolic
[(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^2,x,3,-(b*d-a*e)^4*(B*d-A*e)*(d+e*x)^(1+m)/(e^6*(1+m))+(b*d-a*e)^3*(5*b*B*d-4*A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^6*(2+m))-2*b*(b*d-a*e)^2*(5*b*B*d-3*A*b*e-2*a*B*e)*(d+e*x)^(3+m)/(e^6*(3+m))+2*b^2*(b*d-a*e)*(5*b*B*d-2*A*b*e-3*a*B*e)*(d+e*x)^(4+m)/(e^6*(4+m))-b^3*(5*b*B*d-A*b*e-4*a*B*e)*(d+e*x)^(5+m)/(e^6*(5+m))+b^4*B*(d+e*x)^(6+m)/(e^6*(6+m))],
[(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2),x,3,-(b*d-a*e)^2*(B*d-A*e)*(d+e*x)^(1+m)/(e^4*(1+m))+(b*d-a*e)*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(2+m)/(e^4*(2+m))-b*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(3+m)/(e^4*(3+m))+b^2*B*(d+e*x)^(4+m)/(e^4*(4+m))],
[(A+B*x)*(d+e*x)^m/(a^2+2*a*b*x+b^2*x^2),x,3,-(A*b-a*B)*(d+e*x)^(1+m)/(b*(b*d-a*e)*(a+b*x))+(a*B*e*(1+m)-b*(B*d+A*e*m))*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],b*(d+e*x)/(b*d-a*e))/(b*(b*d-a*e)^2*(1+m))],
[(A+B*x)*(d+e*x)^m/(a^2+2*a*b*x+b^2*x^2)^2,x,3,-1/3*(A*b-a*B)*(d+e*x)^(1+m)/(b*(b*d-a*e)*(a+b*x)^3)-1/3*e^2*(b*(3*B*d-A*e*(2-m))-a*B*e*(1+m))*(d+e*x)^(1+m)*hypergeom([3,1+m],[2+m],b*(d+e*x)/(b*d-a*e))/(b*(b*d-a*e)^4*(1+m))],
[(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,(b*d-a*e)^5*(B*d-A*e)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(1+m)*(a+b*x))-(b*d-a*e)^4*(6*b*B*d-5*A*b*e-a*B*e)*(d+e*x)^(2+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(2+m)*(a+b*x))+5*b*(b*d-a*e)^3*(3*b*B*d-2*A*b*e-a*B*e)*(d+e*x)^(3+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(3+m)*(a+b*x))-10*b^2*(b*d-a*e)^2*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(4+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(4+m)*(a+b*x))+5*b^3*(b*d-a*e)*(3*b*B*d-A*b*e-2*a*B*e)*(d+e*x)^(5+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(5+m)*(a+b*x))-b^4*(6*b*B*d-A*b*e-5*a*B*e)*(d+e*x)^(6+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(6+m)*(a+b*x))+b^5*B*(d+e*x)^(7+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(7+m)*(a+b*x))],
[(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,(b*d-a*e)^3*(B*d-A*e)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(1+m)*(a+b*x))-(b*d-a*e)^2*(4*b*B*d-3*A*b*e-a*B*e)*(d+e*x)^(2+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(2+m)*(a+b*x))+3*b*(b*d-a*e)*(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(3+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(3+m)*(a+b*x))-b^2*(4*b*B*d-A*b*e-3*a*B*e)*(d+e*x)^(4+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(4+m)*(a+b*x))+b^3*B*(d+e*x)^(5+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(5+m)*(a+b*x))],
[(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(1/2),x,3,(b*d-a*e)*(B*d-A*e)*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(1+m)*(a+b*x))-(2*b*B*d-A*b*e-a*B*e)*(d+e*x)^(2+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(2+m)*(a+b*x))+b*B*(d+e*x)^(3+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(3+m)*(a+b*x))],
[(A+B*x)*(d+e*x)^m/(a^2+2*a*b*x+b^2*x^2)^(1/2),x,3,B*(a+b*x)*(d+e*x)^(1+m)/(b*e*(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2))-(A*b-a*B)*(a+b*x)*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],b*(d+e*x)/(b*d-a*e))/(b*(b*d-a*e)*(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(A+B*x)*(d+e*x)^m/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,-1/2*(A*b-a*B)*(d+e*x)^(1+m)/(b*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*e*(b*(2*B*d-A*e*(1-m))-a*B*e*(1+m))*(a+b*x)*(d+e*x)^(1+m)*hypergeom([2,1+m],[2+m],b*(d+e*x)/(b*d-a*e))/(b*(b*d-a*e)^3*(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2))],

# Integrands of the form (d+e x)^m (A+B x) (a^2+2 a b x+b^2 x^2)^p when p symbolic
[(A+B*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^p,x,4,B*(a+b*x)*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b*e*(2+m+2*p))+(A*b*e*(2+m+2*p)-B*(a*e*(1+m)+b*(d+2*d*p)))*(d+e*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^p*hypergeom([1+m,-2*p],[2+m],b*(d+e*x)/(b*d-a*e))/(b*e^2*(1+m)*(2+m+2*p)*(-e*(a+b*x)/(b*d-a*e))^(2*p))],
[(d+e*x)^(-3-2*p)*(f+g*x)*(a^2+2*a*b*x+b^2*x^2)^p,x,3,(b*f-a*g)*(a+b*x)*(d+e*x)^(-1-2*p)*(a^2+2*a*b*x+b^2*x^2)^p/((b*d-a*e)^2*(1+2*p))-1/2*(e*f-d*g)*(a^2+2*a*b*x+b^2*x^2)^(1+p)/((b*d-a*e)^2*(1+p)*(d+e*x)^(2*(1+p)))],

# Integrands of the form (d+e x)^m (f+g x) (a+b x+c x^2)^p when b^2-4 a c=0 and 2 c f-b g=0

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

# p>0
[(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2),x,3,-1/6*(b*d-a*e)^3*(d+e*x)^6/e^4+3/7*b*(b*d-a*e)^2*(d+e*x)^7/e^4-3/8*b^2*(b*d-a*e)*(d+e*x)^8/e^4+1/9*b^3*(d+e*x)^9/e^4],
[(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2),x,3,-1/5*(b*d-a*e)^3*(d+e*x)^5/e^4+1/2*b*(b*d-a*e)^2*(d+e*x)^6/e^4-3/7*b^2*(b*d-a*e)*(d+e*x)^7/e^4+1/8*b^3*(d+e*x)^8/e^4],
[(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2),x,3,1/4*(b*d-a*e)^3*(a+b*x)^4/b^4+3/5*e*(b*d-a*e)^2*(a+b*x)^5/b^4+1/2*e^2*(b*d-a*e)*(a+b*x)^6/b^4+1/7*e^3*(a+b*x)^7/b^4],
[(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2),x,3,1/4*(b*d-a*e)^2*(a+b*x)^4/b^3+2/5*e*(b*d-a*e)*(a+b*x)^5/b^3+1/6*e^2*(a+b*x)^6/b^3],
[(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2),x,3,1/4*(b*d-a*e)*(a+b*x)^4/b^2+1/5*e*(a+b*x)^5/b^2],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2),x,2,1/4*(a+b*x)^4/b],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x),x,3,b*(b*d-a*e)^2*x/e^3-1/2*(b*d-a*e)*(a+b*x)^2/e^2+1/3*(a+b*x)^3/e-(b*d-a*e)^3*log(d+e*x)/e^4],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2,x,3,-b^2*(2*b*d-3*a*e)*x/e^3+1/2*b^3*x^2/e^2+(b*d-a*e)^3/(e^4*(d+e*x))+3*b*(b*d-a*e)^2*log(d+e*x)/e^4],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3,x,3,b^3*x/e^3+1/2*(b*d-a*e)^3/(e^4*(d+e*x)^2)-3*b*(b*d-a*e)^2/(e^4*(d+e*x))-3*b^2*(b*d-a*e)*log(d+e*x)/e^4],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4,x,3,1/3*(b*d-a*e)^3/(e^4*(d+e*x)^3)-3/2*b*(b*d-a*e)^2/(e^4*(d+e*x)^2)+3*b^2*(b*d-a*e)/(e^4*(d+e*x))+b^3*log(d+e*x)/e^4],
[(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^2,x,3,-1/7*(b*d-a*e)^5*(d+e*x)^7/e^6+5/8*b*(b*d-a*e)^4*(d+e*x)^8/e^6-10/9*b^2*(b*d-a*e)^3*(d+e*x)^9/e^6+b^3*(b*d-a*e)^2*(d+e*x)^10/e^6-5/11*b^4*(b*d-a*e)*(d+e*x)^11/e^6+1/12*b^5*(d+e*x)^12/e^6],
[(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/6*(b*d-a*e)^5*(a+b*x)^6/b^6+5/7*e*(b*d-a*e)^4*(a+b*x)^7/b^6+5/4*e^2*(b*d-a*e)^3*(a+b*x)^8/b^6+10/9*e^3*(b*d-a*e)^2*(a+b*x)^9/b^6+1/2*e^4*(b*d-a*e)*(a+b*x)^10/b^6+1/11*e^5*(a+b*x)^11/b^6],
[(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/6*(b*d-a*e)^4*(a+b*x)^6/b^5+4/7*e*(b*d-a*e)^3*(a+b*x)^7/b^5+3/4*e^2*(b*d-a*e)^2*(a+b*x)^8/b^5+4/9*e^3*(b*d-a*e)*(a+b*x)^9/b^5+1/10*e^4*(a+b*x)^10/b^5],
[(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/6*(b*d-a*e)^3*(a+b*x)^6/b^4+3/7*e*(b*d-a*e)^2*(a+b*x)^7/b^4+3/8*e^2*(b*d-a*e)*(a+b*x)^8/b^4+1/9*e^3*(a+b*x)^9/b^4],
[(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/6*(b*d-a*e)^2*(a+b*x)^6/b^3+2/7*e*(b*d-a*e)*(a+b*x)^7/b^3+1/8*e^2*(a+b*x)^8/b^3],
[(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,1/6*(b*d-a*e)*(a+b*x)^6/b^2+1/7*e*(a+b*x)^7/b^2],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2,x,2,1/6*(a+b*x)^6/b],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x),x,3,b*(b*d-a*e)^4*x/e^5-1/2*(b*d-a*e)^3*(a+b*x)^2/e^4+1/3*(b*d-a*e)^2*(a+b*x)^3/e^3-1/4*(b*d-a*e)*(a+b*x)^4/e^2+1/5*(a+b*x)^5/e-(b*d-a*e)^5*log(d+e*x)/e^6],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^2,x,3,-10*b^2*(b*d-a*e)^3*x/e^5+(b*d-a*e)^5/(e^6*(d+e*x))+5*b^3*(b*d-a*e)^2*(d+e*x)^2/e^6-5/3*b^4*(b*d-a*e)*(d+e*x)^3/e^6+1/4*b^5*(d+e*x)^4/e^6+5*b*(b*d-a*e)^4*log(d+e*x)/e^6],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^3,x,3,10*b^3*(b*d-a*e)^2*x/e^5+1/2*(b*d-a*e)^5/(e^6*(d+e*x)^2)-5*b*(b*d-a*e)^4/(e^6*(d+e*x))-5/2*b^4*(b*d-a*e)*(d+e*x)^2/e^6+1/3*b^5*(d+e*x)^3/e^6-10*b^2*(b*d-a*e)^3*log(d+e*x)/e^6],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^4,x,3,-b^4*(4*b*d-5*a*e)*x/e^5+1/2*b^5*x^2/e^4+1/3*(b*d-a*e)^5/(e^6*(d+e*x)^3)-5/2*b*(b*d-a*e)^4/(e^6*(d+e*x)^2)+10*b^2*(b*d-a*e)^3/(e^6*(d+e*x))+10*b^3*(b*d-a*e)^2*log(d+e*x)/e^6],
[(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/8*(b*d-a*e)^6*(a+b*x)^8/b^7+2/3*e*(b*d-a*e)^5*(a+b*x)^9/b^7+3/2*e^2*(b*d-a*e)^4*(a+b*x)^10/b^7+20/11*e^3*(b*d-a*e)^3*(a+b*x)^11/b^7+5/4*e^4*(b*d-a*e)^2*(a+b*x)^12/b^7+6/13*e^5*(b*d-a*e)*(a+b*x)^13/b^7+1/14*e^6*(a+b*x)^14/b^7],
[(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/8*(b*d-a*e)^5*(a+b*x)^8/b^6+5/9*e*(b*d-a*e)^4*(a+b*x)^9/b^6+e^2*(b*d-a*e)^3*(a+b*x)^10/b^6+10/11*e^3*(b*d-a*e)^2*(a+b*x)^11/b^6+5/12*e^4*(b*d-a*e)*(a+b*x)^12/b^6+1/13*e^5*(a+b*x)^13/b^6],
[(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/8*(b*d-a*e)^4*(a+b*x)^8/b^5+4/9*e*(b*d-a*e)^3*(a+b*x)^9/b^5+3/5*e^2*(b*d-a*e)^2*(a+b*x)^10/b^5+4/11*e^3*(b*d-a*e)*(a+b*x)^11/b^5+1/12*e^4*(a+b*x)^12/b^5],
[(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/8*(b*d-a*e)^3*(a+b*x)^8/b^4+1/3*e*(b*d-a*e)^2*(a+b*x)^9/b^4+3/10*e^2*(b*d-a*e)*(a+b*x)^10/b^4+1/11*e^3*(a+b*x)^11/b^4],
[(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/8*(b*d-a*e)^2*(a+b*x)^8/b^3+2/9*e*(b*d-a*e)*(a+b*x)^9/b^3+1/10*e^2*(a+b*x)^10/b^3],
[(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/8*(b*d-a*e)*(a+b*x)^8/b^2+1/9*e*(a+b*x)^9/b^2],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3,x,2,1/8*(a+b*x)^8/b],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x),x,3,b*(b*d-a*e)^6*x/e^7-1/2*(b*d-a*e)^5*(a+b*x)^2/e^6+1/3*(b*d-a*e)^4*(a+b*x)^3/e^5-1/4*(b*d-a*e)^3*(a+b*x)^4/e^4+1/5*(b*d-a*e)^2*(a+b*x)^5/e^3-1/6*(b*d-a*e)*(a+b*x)^6/e^2+1/7*(a+b*x)^7/e-(b*d-a*e)^7*log(d+e*x)/e^8],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^2,x,3,-21*b^2*(b*d-a*e)^5*x/e^7+(b*d-a*e)^7/(e^8*(d+e*x))+35/2*b^3*(b*d-a*e)^4*(d+e*x)^2/e^8-35/3*b^4*(b*d-a*e)^3*(d+e*x)^3/e^8+21/4*b^5*(b*d-a*e)^2*(d+e*x)^4/e^8-7/5*b^6*(b*d-a*e)*(d+e*x)^5/e^8+1/6*b^7*(d+e*x)^6/e^8+7*b*(b*d-a*e)^6*log(d+e*x)/e^8],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^3,x,3,35*b^3*(b*d-a*e)^4*x/e^7+1/2*(b*d-a*e)^7/(e^8*(d+e*x)^2)-7*b*(b*d-a*e)^6/(e^8*(d+e*x))-35/2*b^4*(b*d-a*e)^3*(d+e*x)^2/e^8+7*b^5*(b*d-a*e)^2*(d+e*x)^3/e^8-7/4*b^6*(b*d-a*e)*(d+e*x)^4/e^8+1/5*b^7*(d+e*x)^5/e^8-21*b^2*(b*d-a*e)^5*log(d+e*x)/e^8],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^4,x,3,-35*b^4*(b*d-a*e)^3*x/e^7+1/3*(b*d-a*e)^7/(e^8*(d+e*x)^3)-7/2*b*(b*d-a*e)^6/(e^8*(d+e*x)^2)+21*b^2*(b*d-a*e)^5/(e^8*(d+e*x))+21/2*b^5*(b*d-a*e)^2*(d+e*x)^2/e^8-7/3*b^6*(b*d-a*e)*(d+e*x)^3/e^8+1/4*b^7*(d+e*x)^4/e^8+35*b^3*(b*d-a*e)^4*log(d+e*x)/e^8],

# p<0
[(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2),x,3,e*(b*d-a*e)^3*x/b^4+1/2*(b*d-a*e)^2*(d+e*x)^2/b^3+1/3*(b*d-a*e)*(d+e*x)^3/b^2+1/4*(d+e*x)^4/b+(b*d-a*e)^4*log(a+b*x)/b^5],
[(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2),x,3,e*(b*d-a*e)^2*x/b^3+1/2*(b*d-a*e)*(d+e*x)^2/b^2+1/3*(d+e*x)^3/b+(b*d-a*e)^3*log(a+b*x)/b^4],
[(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2),x,3,e*(b*d-a*e)*x/b^2+1/2*(d+e*x)^2/b+(b*d-a*e)^2*log(a+b*x)/b^3],
[(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2),x,3,e*x/b+(b*d-a*e)*log(a+b*x)/b^2],
[(a+b*x)/(a^2+2*a*b*x+b^2*x^2),x,2,log(a+b*x)/b],
[(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)),x,4,log(a+b*x)/(b*d-a*e)-log(d+e*x)/(b*d-a*e)],
[(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)),x,3,1/((b*d-a*e)*(d+e*x))+b*log(a+b*x)/(b*d-a*e)^2-b*log(d+e*x)/(b*d-a*e)^2],
[(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)),x,3,1/2/((b*d-a*e)*(d+e*x)^2)+b/((b*d-a*e)^2*(d+e*x))+b^2*log(a+b*x)/(b*d-a*e)^3-b^2*log(d+e*x)/(b*d-a*e)^3],
[(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)),x,3,1/3/((b*d-a*e)*(d+e*x)^3)+1/2*b/((b*d-a*e)^2*(d+e*x)^2)+b^2/((b*d-a*e)^3*(d+e*x))+b^3*log(a+b*x)/(b*d-a*e)^4-b^3*log(d+e*x)/(b*d-a*e)^4],
[(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^2,x,3,e^3*(4*b*d-3*a*e)*x/b^4+1/2*e^4*x^2/b^3-1/2*(b*d-a*e)^4/(b^5*(a+b*x)^2)-4*e*(b*d-a*e)^3/(b^5*(a+b*x))+6*e^2*(b*d-a*e)^2*log(a+b*x)/b^5],
[(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^2,x,3,e^3*x/b^3-1/2*(b*d-a*e)^3/(b^4*(a+b*x)^2)-3*e*(b*d-a*e)^2/(b^4*(a+b*x))+3*e^2*(b*d-a*e)*log(a+b*x)/b^4],
[(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^2,x,3,-1/2*(b*d-a*e)^2/(b^3*(a+b*x)^2)-2*e*(b*d-a*e)/(b^3*(a+b*x))+e^2*log(a+b*x)/b^3],
[(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,2,-1/2*(d+e*x)^2/((b*d-a*e)*(a+b*x)^2)],
[(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,2,(-1/2)/(b*(a+b*x)^2)],
[(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^2),x,3,(-1/2)/((b*d-a*e)*(a+b*x)^2)+e/((b*d-a*e)^2*(a+b*x))+e^2*log(a+b*x)/(b*d-a*e)^3-e^2*log(d+e*x)/(b*d-a*e)^3],
[(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^2),x,3,-1/2*b/((b*d-a*e)^2*(a+b*x)^2)+2*b*e/((b*d-a*e)^3*(a+b*x))+e^2/((b*d-a*e)^3*(d+e*x))+3*b*e^2*log(a+b*x)/(b*d-a*e)^4-3*b*e^2*log(d+e*x)/(b*d-a*e)^4],
[(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^2),x,3,-1/2*b^2/((b*d-a*e)^3*(a+b*x)^2)+3*b^2*e/((b*d-a*e)^4*(a+b*x))+1/2*e^2/((b*d-a*e)^3*(d+e*x)^2)+3*b*e^2/((b*d-a*e)^4*(d+e*x))+6*b^2*e^2*log(a+b*x)/(b*d-a*e)^5-6*b^2*e^2*log(d+e*x)/(b*d-a*e)^5],
[(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^2),x,3,-1/2*b^3/((b*d-a*e)^4*(a+b*x)^2)+4*b^3*e/((b*d-a*e)^5*(a+b*x))+1/3*e^2/((b*d-a*e)^3*(d+e*x)^3)+3/2*b*e^2/((b*d-a*e)^4*(d+e*x)^2)+6*b^2*e^2/((b*d-a*e)^5*(d+e*x))+10*b^3*e^2*log(a+b*x)/(b*d-a*e)^6-10*b^3*e^2*log(d+e*x)/(b*d-a*e)^6],
[(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^3,x,3,-1/4*(b*d-a*e)^4/(b^5*(a+b*x)^4)-4/3*e*(b*d-a*e)^3/(b^5*(a+b*x)^3)-3*e^2*(b*d-a*e)^2/(b^5*(a+b*x)^2)-4*e^3*(b*d-a*e)/(b^5*(a+b*x))+e^4*log(a+b*x)/b^5],
[(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^3,x,2,-1/4*(d+e*x)^4/((b*d-a*e)*(a+b*x)^4)],
[(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^3,x,3,-1/4*(b*d-a*e)^2/(b^3*(a+b*x)^4)-2/3*e*(b*d-a*e)/(b^3*(a+b*x)^3)-1/2*e^2/(b^3*(a+b*x)^2)],
[(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,3,1/4*(-b*d+a*e)/(b^2*(a+b*x)^4)-1/3*e/(b^2*(a+b*x)^3)],
[(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,2,(-1/4)/(b*(a+b*x)^4)],
[(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^3),x,3,(-1/4)/((b*d-a*e)*(a+b*x)^4)+1/3*e/((b*d-a*e)^2*(a+b*x)^3)-1/2*e^2/((b*d-a*e)^3*(a+b*x)^2)+e^3/((b*d-a*e)^4*(a+b*x))+e^4*log(a+b*x)/(b*d-a*e)^5-e^4*log(d+e*x)/(b*d-a*e)^5],
[(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^3),x,3,-1/4*b/((b*d-a*e)^2*(a+b*x)^4)+2/3*b*e/((b*d-a*e)^3*(a+b*x)^3)-3/2*b*e^2/((b*d-a*e)^4*(a+b*x)^2)+4*b*e^3/((b*d-a*e)^5*(a+b*x))+e^4/((b*d-a*e)^5*(d+e*x))+5*b*e^4*log(a+b*x)/(b*d-a*e)^6-5*b*e^4*log(d+e*x)/(b*d-a*e)^6],
[(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^3),x,3,-1/4*b^2/((b*d-a*e)^3*(a+b*x)^4)+b^2*e/((b*d-a*e)^4*(a+b*x)^3)-3*b^2*e^2/((b*d-a*e)^5*(a+b*x)^2)+10*b^2*e^3/((b*d-a*e)^6*(a+b*x))+1/2*e^4/((b*d-a*e)^5*(d+e*x)^2)+5*b*e^4/((b*d-a*e)^6*(d+e*x))+15*b^2*e^4*log(a+b*x)/(b*d-a*e)^7-15*b^2*e^4*log(d+e*x)/(b*d-a*e)^7],
[(a+b*x)/((d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^3),x,3,-1/4*b^3/((b*d-a*e)^4*(a+b*x)^4)+4/3*b^3*e/((b*d-a*e)^5*(a+b*x)^3)-5*b^3*e^2/((b*d-a*e)^6*(a+b*x)^2)+20*b^3*e^3/((b*d-a*e)^7*(a+b*x))+1/3*e^4/((b*d-a*e)^5*(d+e*x)^3)+5/2*b*e^4/((b*d-a*e)^6*(d+e*x)^2)+15*b^2*e^4/((b*d-a*e)^7*(d+e*x))+35*b^3*e^4*log(a+b*x)/(b*d-a*e)^8-35*b^3*e^4*log(d+e*x)/(b*d-a*e)^8],

# Integrands of the form (d+e x)^m (a+b x) (a^2+2 a b x+b^2 x^2)^(p/2)

# p>0
[(a+b*x)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2),x,4,1/6*(b*d-a*e)^2*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-2/7*b*(b*d-a*e)*(d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+1/8*b^2*(d+e*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(a+b*x)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2),x,4,1/5*(b*d-a*e)^2*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-1/3*b*(b*d-a*e)*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+1/7*b^2*(d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(a+b*x)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2),x,4,1/4*(b*d-a*e)^2*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-2/5*b*(b*d-a*e)*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+1/6*b^2*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(a+b*x)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2),x,4,1/3*(b*d-a*e)^2*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/2*e*(b*d-a*e)*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/5*e^2*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3],
[(a+b*x)*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,4,1/3*(b*d-a*e)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2+1/4*e*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2],
[(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,1,1/3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/b],
[(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x),x,4,-b*(b*d-a*e)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(a+b*x))+1/2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e+(b*d-a*e)^2*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^2,x,4,b^2*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^2*(a+b*x))-(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x))-2*b*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^3,x,4,-1/2*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^2)+2*b*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x))+b^2*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^4,x,1,1/3*(a^2+2*a*b*x+b^2*x^2)^(3/2)/((b*d-a*e)*(d+e*x)^3)],
[(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^5,x,4,-1/4*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^4)+2/3*b*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^3)-1/2*b^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^2)],
[(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^6,x,4,-1/5*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^5)+1/2*b*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^4)-1/3*b^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^3)],
[(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^7,x,4,-1/6*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^6)+2/5*b*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^5)-1/4*b^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^4)],
[(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^8,x,4,-1/7*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^7)+1/3*b*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^6)-1/5*b^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^5)],
[(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,1/8*(b*d-a*e)^4*(d+e*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-4/9*b*(b*d-a*e)^3*(d+e*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+3/5*b^2*(b*d-a*e)^2*(d+e*x)^10*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-4/11*b^3*(b*d-a*e)*(d+e*x)^11*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/12*b^4*(d+e*x)^12*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,1/7*(b*d-a*e)^4*(d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-1/2*b*(b*d-a*e)^3*(d+e*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/3*b^2*(b*d-a*e)^2*(d+e*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-2/5*b^3*(b*d-a*e)*(d+e*x)^10*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/11*b^4*(d+e*x)^11*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,1/6*(b*d-a*e)^4*(d+e*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-4/7*b*(b*d-a*e)^3*(d+e*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+3/4*b^2*(b*d-a*e)^2*(d+e*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-4/9*b^3*(b*d-a*e)*(d+e*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/10*b^4*(d+e*x)^10*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,1/5*(b*d-a*e)^4*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+2/3*e*(b*d-a*e)^3*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+6/7*e^2*(b*d-a*e)^2*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/2*e^3*(b*d-a*e)*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/9*e^4*(a+b*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5],
[(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,1/5*(b*d-a*e)^3*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+1/2*e*(b*d-a*e)^2*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+3/7*e^2*(b*d-a*e)*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+1/8*e^3*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4],
[(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,1/5*(b*d-a*e)^2*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/3*e*(b*d-a*e)*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/7*e^2*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3],
[(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,1/5*(b*d-a*e)*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2+1/6*e*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,1,1/5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/b],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x),x,4,-b*(b*d-a*e)^3*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(a+b*x))+1/2*(b*d-a*e)^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3-1/3*(b*d-a*e)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/4*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/e+(b*d-a*e)^4*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^2,x,4,6*b^2*(b*d-a*e)^2*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(a+b*x))-(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x))-2*b^3*(b*d-a*e)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+1/3*b^4*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-4*b*(b*d-a*e)^3*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^3,x,4,-b^3*(3*b*d-4*a*e)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(a+b*x))+1/2*b^4*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-1/2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^2)+4*b*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x))+6*b^2*(b*d-a*e)^2*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^4,x,4,b^4*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^4*(a+b*x))-1/3*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^3)+2*b*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^2)-6*b^2*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x))-4*b^3*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^5,x,4,-1/4*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^4)+4/3*b*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^3)-3*b^2*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^2)+4*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x))+b^4*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^6,x,1,1/5*(a^2+2*a*b*x+b^2*x^2)^(5/2)/((b*d-a*e)*(d+e*x)^5)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^7,x,4,1/6*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)*(d+e*x)^6)+1/30*b*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^2*(d+e*x)^5)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^8,x,5,1/7*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)*(d+e*x)^7)+1/21*b*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^2*(d+e*x)^6)+1/105*b^2*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^3*(d+e*x)^5)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^9,x,4,-1/8*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8)+4/7*b*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7)-b^2*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^6)+4/5*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^5)-1/4*b^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^4)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^10,x,4,-1/9*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^9)+1/2*b*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8)-6/7*b^2*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7)+2/3*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^6)-1/5*b^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^5)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^11,x,4,-1/10*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^10)+4/9*b*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^9)-3/4*b^2*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8)+4/7*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7)-1/6*b^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^6)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^12,x,4,-1/11*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^11)+2/5*b*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^10)-2/3*b^2*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^9)+1/2*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^8)-1/7*b^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^7)],
[(a+b*x)*(d+e*x)^9*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,1/10*(b*d-a*e)^6*(d+e*x)^10*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-6/11*b*(b*d-a*e)^5*(d+e*x)^11*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+5/4*b^2*(b*d-a*e)^4*(d+e*x)^12*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-20/13*b^3*(b*d-a*e)^3*(d+e*x)^13*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+15/14*b^4*(b*d-a*e)^2*(d+e*x)^14*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/5*b^5*(b*d-a*e)*(d+e*x)^15*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/16*b^6*(d+e*x)^16*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(d+e*x)^8*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,1/9*(b*d-a*e)^6*(d+e*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-3/5*b*(b*d-a*e)^5*(d+e*x)^10*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+15/11*b^2*(b*d-a*e)^4*(d+e*x)^11*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-5/3*b^3*(b*d-a*e)^3*(d+e*x)^12*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+15/13*b^4*(b*d-a*e)^2*(d+e*x)^13*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-3/7*b^5*(b*d-a*e)*(d+e*x)^14*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/15*b^6*(d+e*x)^15*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(d+e*x)^7*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,1/8*(b*d-a*e)^6*(d+e*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2/3*b*(b*d-a*e)^5*(d+e*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+3/2*b^2*(b*d-a*e)^4*(d+e*x)^10*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-20/11*b^3*(b*d-a*e)^3*(d+e*x)^11*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+5/4*b^4*(b*d-a*e)^2*(d+e*x)^12*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-6/13*b^5*(b*d-a*e)*(d+e*x)^13*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/14*b^6*(d+e*x)^14*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(d+e*x)^6*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,1/7*(b*d-a*e)^6*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7+3/4*e*(b*d-a*e)^5*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7+5/3*e^2*(b*d-a*e)^4*(a+b*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7+2*e^3*(b*d-a*e)^3*(a+b*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7+15/11*e^4*(b*d-a*e)^2*(a+b*x)^10*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7+1/2*e^5*(b*d-a*e)*(a+b*x)^11*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7+1/13*e^6*(a+b*x)^12*sqrt(a^2+2*a*b*x+b^2*x^2)/b^7],
[(a+b*x)*(d+e*x)^5*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,1/7*(b*d-a*e)^5*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6+5/8*e*(b*d-a*e)^4*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6+10/9*e^2*(b*d-a*e)^3*(a+b*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6+e^3*(b*d-a*e)^2*(a+b*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6+5/11*e^4*(b*d-a*e)*(a+b*x)^10*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6+1/12*e^5*(a+b*x)^11*sqrt(a^2+2*a*b*x+b^2*x^2)/b^6],
[(a+b*x)*(d+e*x)^4*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,1/7*(b*d-a*e)^4*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/2*e*(b*d-a*e)^3*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+2/3*e^2*(b*d-a*e)^2*(a+b*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+2/5*e^3*(b*d-a*e)*(a+b*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5+1/11*e^4*(a+b*x)^10*sqrt(a^2+2*a*b*x+b^2*x^2)/b^5],
[(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,1/7*(b*d-a*e)^3*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+3/8*e*(b*d-a*e)^2*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+1/3*e^2*(b*d-a*e)*(a+b*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4+1/10*e^3*(a+b*x)^9*sqrt(a^2+2*a*b*x+b^2*x^2)/b^4],
[(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,1/7*(b*d-a*e)^2*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/4*e*(b*d-a*e)*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3+1/9*e^2*(a+b*x)^8*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3],
[(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,1/7*(b*d-a*e)*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2+1/8*e*(a+b*x)^7*sqrt(a^2+2*a*b*x+b^2*x^2)/b^2],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,1,1/7*(a^2+2*a*b*x+b^2*x^2)^(7/2)/b],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x),x,4,-b*(b*d-a*e)^5*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(a+b*x))+1/2*(b*d-a*e)^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/e^5-1/3*(b*d-a*e)^3*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/e^4+1/4*(b*d-a*e)^2*(a+b*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/e^3-1/5*(b*d-a*e)*(a+b*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/e^2+1/6*(a+b*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/e+(b*d-a*e)^6*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^2,x,4,15*b^2*(b*d-a*e)^4*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(a+b*x))-(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))-10*b^3*(b*d-a*e)^3*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+5*b^4*(b*d-a*e)^2*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-3/2*b^5*(b*d-a*e)*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/5*b^6*(d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-6*b*(b*d-a*e)^5*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^3,x,4,-20*b^3*(b*d-a*e)^3*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(a+b*x))-1/2*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^2)+6*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))+15/2*b^4*(b*d-a*e)^2*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2*b^5*(b*d-a*e)*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/4*b^6*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+15*b^2*(b*d-a*e)^4*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^4,x,4,15*b^4*(b*d-a*e)^2*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(a+b*x))-1/3*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^3)+3*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^2)-15*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))-3*b^5*(b*d-a*e)*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+1/3*b^6*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-20*b^3*(b*d-a*e)^3*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^5,x,4,-b^5*(5*b*d-6*a*e)*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(a+b*x))+1/2*b^6*x^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-1/4*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^4)+2*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^3)-15/2*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^2)+20*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))+15*b^4*(b*d-a*e)^2*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^6,x,4,b^6*x*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^6*(a+b*x))-1/5*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^5)+3/2*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^4)-5*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^3)+10*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^2)-15*b^4*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))-6*b^5*(b*d-a*e)*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^7,x,4,-1/6*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^6)+6/5*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^5)-15/4*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^4)+20/3*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^3)-15/2*b^4*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^2)+6*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x))+b^6*log(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^8,x,1,1/7*(a^2+2*a*b*x+b^2*x^2)^(7/2)/((b*d-a*e)*(d+e*x)^7)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^9,x,4,1/8*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)*(d+e*x)^8)+1/56*b*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^2*(d+e*x)^7)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^10,x,5,1/9*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)*(d+e*x)^9)+1/36*b*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^2*(d+e*x)^8)+1/252*b^2*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^3*(d+e*x)^7)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^11,x,6,1/10*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)*(d+e*x)^10)+1/30*b*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^2*(d+e*x)^9)+1/120*b^2*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^3*(d+e*x)^8)+1/840*b^3*(a+b*x)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)^4*(d+e*x)^7)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^12,x,4,-1/11*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^11)+3/5*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^10)-5/3*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^9)+5/2*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^8)-15/7*b^4*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^7)+b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^6)-1/5*b^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^5)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^13,x,4,-1/12*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^12)+6/11*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^11)-3/2*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^10)+20/9*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^9)-15/8*b^4*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^8)+6/7*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^7)-1/6*b^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^6)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^14,x,4,-1/13*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^13)+1/2*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^12)-15/11*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^11)+2*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^10)-5/3*b^4*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^9)+3/4*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^8)-1/7*b^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^7)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^15,x,4,-1/14*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^14)+6/13*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^13)-5/4*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^12)+20/11*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^11)-3/2*b^4*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^10)+2/3*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^9)-1/8*b^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^8)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^16,x,4,-1/15*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^15)+3/7*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^14)-15/13*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^13)+5/3*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^12)-15/11*b^4*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^11)+3/5*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^10)-1/9*b^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^9)],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^17,x,4,-1/16*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^16)+2/5*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^15)-15/14*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^14)+20/13*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^13)-5/4*b^4*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^12)+6/11*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^11)-1/10*b^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^10)],

# p<0
[(a+b*x)*(d+e*x)^4/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,1/5*(a+b*x)*(d+e*x)^5/(e*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^3/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,1/4*(a+b*x)*(d+e*x)^4/(e*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^2/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,1/3*(a+b*x)*(d+e*x)^3/(e*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,d*x*(a+b*x)/sqrt(a^2+2*a*b*x+b^2*x^2)+1/2*e*x^2*(a+b*x)/sqrt(a^2+2*a*b*x+b^2*x^2)],
[(a+b*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,1,sqrt(a^2+2*a*b*x+b^2*x^2)/b],
[(a+b*x)/((d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,(a+b*x)*log(d+e*x)/(e*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2)),x,1,sqrt(a^2+2*a*b*x+b^2*x^2)/((b*d-a*e)*(d+e*x))],
[(a+b*x)/((d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,1/2*(-a-b*x)/(e*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,1/3*(-a-b*x)/(e*(d+e*x)^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^5*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,1/4*(-a-b*x)/(e*(d+e*x)^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,4*e^2*(b*d-a*e)^2*x*(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e*(b*d-a*e)*(a+b*x)*(d+e*x)^2/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+4/3*e*(a+b*x)*(d+e*x)^3/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-(d+e*x)^4/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+4*e*(b*d-a*e)^3*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,3*e^2*(b*d-a*e)*x*(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+3/2*e*(a+b*x)*(d+e*x)^2/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-(d+e*x)^3/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e*(b*d-a*e)^2*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,-(d+e*x)^2/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e*(b*d-a*e)*(a+b*x)*log(a+b*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2*e^2*sqrt(a^2+2*a*b*x+b^2*x^2)/b^3],
[(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,(-d-e*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(a+b*x)*log(a+b*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,1,(-1)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,4,(-1)/((b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(a+b*x)*log(a+b*x)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+e*(a+b*x)*log(d+e*x)/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,4,-b/((b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-e*(a+b*x)/((b*d-a*e)^2*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-2*b*e*(a+b*x)*log(a+b*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+2*b*e*(a+b*x)*log(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,4,-b^2/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*e*(a+b*x)/((b*d-a*e)^2*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-2*b*e*(a+b*x)/((b*d-a*e)^3*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-3*b^2*e*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))+3*b^2*e*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^5/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,-1/3*(d+e*x)^5/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-20/3*e^2*(b*d-a*e)^3/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))-5/6*e*(b*d-a*e)^4/(b^6*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+5/3*e^4*(4*b*d-3*a*e)*x*(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))+5/6*e^5*x^2*(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+10*e^3*(b*d-a*e)^2*(a+b*x)*log(a+b*x)/(b^6*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^4/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,-1/3*(d+e*x)^4/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-4*e^2*(b*d-a*e)^2/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))-2/3*e*(b*d-a*e)^3/(b^5*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+4/3*e^4*x*(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))+4*e^3*(b*d-a*e)*(a+b*x)*log(a+b*x)/(b^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^3/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,-1/3*(d+e*x)^3/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-2*e^2*(b*d-a*e)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*e*(b*d-a*e)^2/(b^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(a+b*x)*log(a+b*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^2/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,1,-1/3*(d+e*x)^3/((b*d-a*e)*(a^2+2*a*b*x+b^2*x^2)^(3/2))],
[(a+b*x)*(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,2,1/3*(-d-e*x)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/6*e/(b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,1,(-1/3)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))],
[(a+b*x)/((d+e*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,4,-e^2/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))+(-1/3)/((b*d-a*e)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+1/2*e/((b*d-a*e)^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))+e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,4,-3*b*e^2/((b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2))-1/3*b/((b*d-a*e)^2*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+b*e/((b*d-a*e)^3*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-e^3*(a+b*x)/((b*d-a*e)^4*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-4*b*e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))+4*b*e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,4,-6*b^2*e^2/((b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2))-1/3*b^2/((b*d-a*e)^3*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+3/2*b^2*e/((b*d-a*e)^4*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/2*e^3*(a+b*x)/((b*d-a*e)^4*(d+e*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-4*b*e^3*(a+b*x)/((b*d-a*e)^5*(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-10*b^2*e^3*(a+b*x)*log(a+b*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2))+10*b^2*e^3*(a+b*x)*log(d+e*x)/((b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2))],

# Integrands of the form (d+e x)^(m/2) (a+b x) (a^2+2 a b x+b^2 x^2)^p

# p>0
[(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2),x,3,-2/9*(b*d-a*e)^3*(d+e*x)^(9/2)/e^4+6/11*b*(b*d-a*e)^2*(d+e*x)^(11/2)/e^4-6/13*b^2*(b*d-a*e)*(d+e*x)^(13/2)/e^4+2/15*b^3*(d+e*x)^(15/2)/e^4],
[(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2),x,3,-2/7*(b*d-a*e)^3*(d+e*x)^(7/2)/e^4+2/3*b*(b*d-a*e)^2*(d+e*x)^(9/2)/e^4-6/11*b^2*(b*d-a*e)*(d+e*x)^(11/2)/e^4+2/13*b^3*(d+e*x)^(13/2)/e^4],
[(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2),x,3,-2/5*(b*d-a*e)^3*(d+e*x)^(5/2)/e^4+6/7*b*(b*d-a*e)^2*(d+e*x)^(7/2)/e^4-2/3*b^2*(b*d-a*e)*(d+e*x)^(9/2)/e^4+2/11*b^3*(d+e*x)^(11/2)/e^4],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x),x,3,-2/3*(b*d-a*e)^3*(d+e*x)^(3/2)/e^4+6/5*b*(b*d-a*e)^2*(d+e*x)^(5/2)/e^4-6/7*b^2*(b*d-a*e)*(d+e*x)^(7/2)/e^4+2/9*b^3*(d+e*x)^(9/2)/e^4],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x),x,3,2*b*(b*d-a*e)^2*(d+e*x)^(3/2)/e^4-6/5*b^2*(b*d-a*e)*(d+e*x)^(5/2)/e^4+2/7*b^3*(d+e*x)^(7/2)/e^4-2*(b*d-a*e)^3*sqrt(d+e*x)/e^4],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2),x,3,-2*b^2*(b*d-a*e)*(d+e*x)^(3/2)/e^4+2/5*b^3*(d+e*x)^(5/2)/e^4+2*(b*d-a*e)^3/(e^4*sqrt(d+e*x))+6*b*(b*d-a*e)^2*sqrt(d+e*x)/e^4],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2),x,3,2/3*(b*d-a*e)^3/(e^4*(d+e*x)^(3/2))+2/3*b^3*(d+e*x)^(3/2)/e^4-6*b*(b*d-a*e)^2/(e^4*sqrt(d+e*x))-6*b^2*(b*d-a*e)*sqrt(d+e*x)/e^4],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2),x,3,2/5*(b*d-a*e)^3/(e^4*(d+e*x)^(5/2))-2*b*(b*d-a*e)^2/(e^4*(d+e*x)^(3/2))+6*b^2*(b*d-a*e)/(e^4*sqrt(d+e*x))+2*b^3*sqrt(d+e*x)/e^4],
[(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,-2/9*(b*d-a*e)^5*(d+e*x)^(9/2)/e^6+10/11*b*(b*d-a*e)^4*(d+e*x)^(11/2)/e^6-20/13*b^2*(b*d-a*e)^3*(d+e*x)^(13/2)/e^6+4/3*b^3*(b*d-a*e)^2*(d+e*x)^(15/2)/e^6-10/17*b^4*(b*d-a*e)*(d+e*x)^(17/2)/e^6+2/19*b^5*(d+e*x)^(19/2)/e^6],
[(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,-2/7*(b*d-a*e)^5*(d+e*x)^(7/2)/e^6+10/9*b*(b*d-a*e)^4*(d+e*x)^(9/2)/e^6-20/11*b^2*(b*d-a*e)^3*(d+e*x)^(11/2)/e^6+20/13*b^3*(b*d-a*e)^2*(d+e*x)^(13/2)/e^6-2/3*b^4*(b*d-a*e)*(d+e*x)^(15/2)/e^6+2/17*b^5*(d+e*x)^(17/2)/e^6],
[(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2,x,3,-2/5*(b*d-a*e)^5*(d+e*x)^(5/2)/e^6+10/7*b*(b*d-a*e)^4*(d+e*x)^(7/2)/e^6-20/9*b^2*(b*d-a*e)^3*(d+e*x)^(9/2)/e^6+20/11*b^3*(b*d-a*e)^2*(d+e*x)^(11/2)/e^6-10/13*b^4*(b*d-a*e)*(d+e*x)^(13/2)/e^6+2/15*b^5*(d+e*x)^(15/2)/e^6],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x),x,3,-2/3*(b*d-a*e)^5*(d+e*x)^(3/2)/e^6+2*b*(b*d-a*e)^4*(d+e*x)^(5/2)/e^6-20/7*b^2*(b*d-a*e)^3*(d+e*x)^(7/2)/e^6+20/9*b^3*(b*d-a*e)^2*(d+e*x)^(9/2)/e^6-10/11*b^4*(b*d-a*e)*(d+e*x)^(11/2)/e^6+2/13*b^5*(d+e*x)^(13/2)/e^6],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/sqrt(d+e*x),x,3,10/3*b*(b*d-a*e)^4*(d+e*x)^(3/2)/e^6-4*b^2*(b*d-a*e)^3*(d+e*x)^(5/2)/e^6+20/7*b^3*(b*d-a*e)^2*(d+e*x)^(7/2)/e^6-10/9*b^4*(b*d-a*e)*(d+e*x)^(9/2)/e^6+2/11*b^5*(d+e*x)^(11/2)/e^6-2*(b*d-a*e)^5*sqrt(d+e*x)/e^6],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(3/2),x,3,-20/3*b^2*(b*d-a*e)^3*(d+e*x)^(3/2)/e^6+4*b^3*(b*d-a*e)^2*(d+e*x)^(5/2)/e^6-10/7*b^4*(b*d-a*e)*(d+e*x)^(7/2)/e^6+2/9*b^5*(d+e*x)^(9/2)/e^6+2*(b*d-a*e)^5/(e^6*sqrt(d+e*x))+10*b*(b*d-a*e)^4*sqrt(d+e*x)/e^6],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(5/2),x,3,2/3*(b*d-a*e)^5/(e^6*(d+e*x)^(3/2))+20/3*b^3*(b*d-a*e)^2*(d+e*x)^(3/2)/e^6-2*b^4*(b*d-a*e)*(d+e*x)^(5/2)/e^6+2/7*b^5*(d+e*x)^(7/2)/e^6-10*b*(b*d-a*e)^4/(e^6*sqrt(d+e*x))-20*b^2*(b*d-a*e)^3*sqrt(d+e*x)/e^6],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^2/(d+e*x)^(7/2),x,3,2/5*(b*d-a*e)^5/(e^6*(d+e*x)^(5/2))-10/3*b*(b*d-a*e)^4/(e^6*(d+e*x)^(3/2))-10/3*b^4*(b*d-a*e)*(d+e*x)^(3/2)/e^6+2/5*b^5*(d+e*x)^(5/2)/e^6+20*b^2*(b*d-a*e)^3/(e^6*sqrt(d+e*x))+20*b^3*(b*d-a*e)^2*sqrt(d+e*x)/e^6],
[(a+b*x)*(d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,-2/9*(b*d-a*e)^7*(d+e*x)^(9/2)/e^8+14/11*b*(b*d-a*e)^6*(d+e*x)^(11/2)/e^8-42/13*b^2*(b*d-a*e)^5*(d+e*x)^(13/2)/e^8+14/3*b^3*(b*d-a*e)^4*(d+e*x)^(15/2)/e^8-70/17*b^4*(b*d-a*e)^3*(d+e*x)^(17/2)/e^8+42/19*b^5*(b*d-a*e)^2*(d+e*x)^(19/2)/e^8-2/3*b^6*(b*d-a*e)*(d+e*x)^(21/2)/e^8+2/23*b^7*(d+e*x)^(23/2)/e^8],
[(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,-2/7*(b*d-a*e)^7*(d+e*x)^(7/2)/e^8+14/9*b*(b*d-a*e)^6*(d+e*x)^(9/2)/e^8-42/11*b^2*(b*d-a*e)^5*(d+e*x)^(11/2)/e^8+70/13*b^3*(b*d-a*e)^4*(d+e*x)^(13/2)/e^8-14/3*b^4*(b*d-a*e)^3*(d+e*x)^(15/2)/e^8+42/17*b^5*(b*d-a*e)^2*(d+e*x)^(17/2)/e^8-14/19*b^6*(b*d-a*e)*(d+e*x)^(19/2)/e^8+2/21*b^7*(d+e*x)^(21/2)/e^8],
[(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3,x,3,-2/5*(b*d-a*e)^7*(d+e*x)^(5/2)/e^8+2*b*(b*d-a*e)^6*(d+e*x)^(7/2)/e^8-14/3*b^2*(b*d-a*e)^5*(d+e*x)^(9/2)/e^8+70/11*b^3*(b*d-a*e)^4*(d+e*x)^(11/2)/e^8-70/13*b^4*(b*d-a*e)^3*(d+e*x)^(13/2)/e^8+14/5*b^5*(b*d-a*e)^2*(d+e*x)^(15/2)/e^8-14/17*b^6*(b*d-a*e)*(d+e*x)^(17/2)/e^8+2/19*b^7*(d+e*x)^(19/2)/e^8],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x),x,3,-2/3*(b*d-a*e)^7*(d+e*x)^(3/2)/e^8+14/5*b*(b*d-a*e)^6*(d+e*x)^(5/2)/e^8-6*b^2*(b*d-a*e)^5*(d+e*x)^(7/2)/e^8+70/9*b^3*(b*d-a*e)^4*(d+e*x)^(9/2)/e^8-70/11*b^4*(b*d-a*e)^3*(d+e*x)^(11/2)/e^8+42/13*b^5*(b*d-a*e)^2*(d+e*x)^(13/2)/e^8-14/15*b^6*(b*d-a*e)*(d+e*x)^(15/2)/e^8+2/17*b^7*(d+e*x)^(17/2)/e^8],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/sqrt(d+e*x),x,3,14/3*b*(b*d-a*e)^6*(d+e*x)^(3/2)/e^8-42/5*b^2*(b*d-a*e)^5*(d+e*x)^(5/2)/e^8+10*b^3*(b*d-a*e)^4*(d+e*x)^(7/2)/e^8-70/9*b^4*(b*d-a*e)^3*(d+e*x)^(9/2)/e^8+42/11*b^5*(b*d-a*e)^2*(d+e*x)^(11/2)/e^8-14/13*b^6*(b*d-a*e)*(d+e*x)^(13/2)/e^8+2/15*b^7*(d+e*x)^(15/2)/e^8-2*(b*d-a*e)^7*sqrt(d+e*x)/e^8],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(3/2),x,3,-14*b^2*(b*d-a*e)^5*(d+e*x)^(3/2)/e^8+14*b^3*(b*d-a*e)^4*(d+e*x)^(5/2)/e^8-10*b^4*(b*d-a*e)^3*(d+e*x)^(7/2)/e^8+14/3*b^5*(b*d-a*e)^2*(d+e*x)^(9/2)/e^8-14/11*b^6*(b*d-a*e)*(d+e*x)^(11/2)/e^8+2/13*b^7*(d+e*x)^(13/2)/e^8+2*(b*d-a*e)^7/(e^8*sqrt(d+e*x))+14*b*(b*d-a*e)^6*sqrt(d+e*x)/e^8],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(5/2),x,3,2/3*(b*d-a*e)^7/(e^8*(d+e*x)^(3/2))+70/3*b^3*(b*d-a*e)^4*(d+e*x)^(3/2)/e^8-14*b^4*(b*d-a*e)^3*(d+e*x)^(5/2)/e^8+6*b^5*(b*d-a*e)^2*(d+e*x)^(7/2)/e^8-14/9*b^6*(b*d-a*e)*(d+e*x)^(9/2)/e^8+2/11*b^7*(d+e*x)^(11/2)/e^8-14*b*(b*d-a*e)^6/(e^8*sqrt(d+e*x))-42*b^2*(b*d-a*e)^5*sqrt(d+e*x)/e^8],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^3/(d+e*x)^(7/2),x,3,2/5*(b*d-a*e)^7/(e^8*(d+e*x)^(5/2))-14/3*b*(b*d-a*e)^6/(e^8*(d+e*x)^(3/2))-70/3*b^4*(b*d-a*e)^3*(d+e*x)^(3/2)/e^8+42/5*b^5*(b*d-a*e)^2*(d+e*x)^(5/2)/e^8-2*b^6*(b*d-a*e)*(d+e*x)^(7/2)/e^8+2/9*b^7*(d+e*x)^(9/2)/e^8+42*b^2*(b*d-a*e)^5/(e^8*sqrt(d+e*x))+70*b^3*(b*d-a*e)^4*sqrt(d+e*x)/e^8],

# p<0
[(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2),x,7,2/3*(b*d-a*e)^2*(d+e*x)^(3/2)/b^3+2/5*(b*d-a*e)*(d+e*x)^(5/2)/b^2+2/7*(d+e*x)^(7/2)/b-2*(b*d-a*e)^(7/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+2*(b*d-a*e)^3*sqrt(d+e*x)/b^4],
[(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2),x,6,2/3*(b*d-a*e)*(d+e*x)^(3/2)/b^2+2/5*(d+e*x)^(5/2)/b-2*(b*d-a*e)^(5/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(7/2)+2*(b*d-a*e)^2*sqrt(d+e*x)/b^3],
[(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2),x,5,2/3*(d+e*x)^(3/2)/b-2*(b*d-a*e)^(3/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(5/2)+2*(b*d-a*e)*sqrt(d+e*x)/b^2],
[(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2),x,4,-2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(3/2)+2*sqrt(d+e*x)/b],
[(a+b*x)/((a^2+2*a*b*x+b^2*x^2)*sqrt(d+e*x)),x,3,-2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(sqrt(b)*sqrt(b*d-a*e))],
[(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)),x,4,-2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(3/2)+2/((b*d-a*e)*sqrt(d+e*x))],
[(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)),x,5,2/3/((b*d-a*e)*(d+e*x)^(3/2))-2*b^(3/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(5/2)+2*b/((b*d-a*e)^2*sqrt(d+e*x))],
[(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)),x,6,2/5/((b*d-a*e)*(d+e*x)^(5/2))+2/3*b/((b*d-a*e)^2*(d+e*x)^(3/2))-2*b^(5/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(7/2)+2*b^2/((b*d-a*e)^3*sqrt(d+e*x))],
[(a+b*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^2,x,8,21/4*e^2*(b*d-a*e)*(d+e*x)^(3/2)/b^4+63/20*e^2*(d+e*x)^(5/2)/b^3-9/4*e*(d+e*x)^(7/2)/(b^2*(a+b*x))-1/2*(d+e*x)^(9/2)/(b*(a+b*x)^2)-63/4*e^2*(b*d-a*e)^(5/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(11/2)+63/4*e^2*(b*d-a*e)^2*sqrt(d+e*x)/b^5],
[(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^2,x,7,35/12*e^2*(d+e*x)^(3/2)/b^3-7/4*e*(d+e*x)^(5/2)/(b^2*(a+b*x))-1/2*(d+e*x)^(7/2)/(b*(a+b*x)^2)-35/4*e^2*(b*d-a*e)^(3/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(9/2)+35/4*e^2*(b*d-a*e)*sqrt(d+e*x)/b^4],
[(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^2,x,6,-5/4*e*(d+e*x)^(3/2)/(b^2*(a+b*x))-1/2*(d+e*x)^(5/2)/(b*(a+b*x)^2)-15/4*e^2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(7/2)+15/4*e^2*sqrt(d+e*x)/b^3],
[(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^2,x,5,-1/2*(d+e*x)^(3/2)/(b*(a+b*x)^2)-3/4*e^2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*sqrt(b*d-a*e))-3/4*e*sqrt(d+e*x)/(b^2*(a+b*x))],
[(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^2,x,5,1/4*e^2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(3/2))-1/2*sqrt(d+e*x)/(b*(a+b*x)^2)-1/4*e*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x))],
[(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^2*sqrt(d+e*x)),x,5,-3/4*e^2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(5/2)*sqrt(b))-1/2*sqrt(d+e*x)/((b*d-a*e)*(a+b*x)^2)+3/4*e*sqrt(d+e*x)/((b*d-a*e)^2*(a+b*x))],
[(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^2),x,6,-15/4*e^2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(7/2)+15/4*e^2/((b*d-a*e)^3*sqrt(d+e*x))+(-1/2)/((b*d-a*e)*(a+b*x)^2*sqrt(d+e*x))+5/4*e/((b*d-a*e)^2*(a+b*x)*sqrt(d+e*x))],
[(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^2),x,7,35/12*e^2/((b*d-a*e)^3*(d+e*x)^(3/2))+(-1/2)/((b*d-a*e)*(a+b*x)^2*(d+e*x)^(3/2))+7/4*e/((b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2))-35/4*b^(3/2)*e^2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(9/2)+35/4*b*e^2/((b*d-a*e)^4*sqrt(d+e*x))],
[(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^2),x,8,63/20*e^2/((b*d-a*e)^3*(d+e*x)^(5/2))+(-1/2)/((b*d-a*e)*(a+b*x)^2*(d+e*x)^(5/2))+9/4*e/((b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2))+21/4*b*e^2/((b*d-a*e)^4*(d+e*x)^(3/2))-63/4*b^(5/2)*e^2*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(11/2)+63/4*b^2*e^2/((b*d-a*e)^5*sqrt(d+e*x))],
[(a+b*x)*(d+e*x)^(11/2)/(a^2+2*a*b*x+b^2*x^2)^3,x,9,385/64*e^4*(d+e*x)^(3/2)/b^5-231/64*e^3*(d+e*x)^(5/2)/(b^4*(a+b*x))-33/32*e^2*(d+e*x)^(7/2)/(b^3*(a+b*x)^2)-11/24*e*(d+e*x)^(9/2)/(b^2*(a+b*x)^3)-1/4*(d+e*x)^(11/2)/(b*(a+b*x)^4)-1155/64*e^4*(b*d-a*e)^(3/2)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/b^(13/2)+1155/64*e^4*(b*d-a*e)*sqrt(d+e*x)/b^6],
[(a+b*x)*(d+e*x)^(9/2)/(a^2+2*a*b*x+b^2*x^2)^3,x,8,-105/64*e^3*(d+e*x)^(3/2)/(b^4*(a+b*x))-21/32*e^2*(d+e*x)^(5/2)/(b^3*(a+b*x)^2)-3/8*e*(d+e*x)^(7/2)/(b^2*(a+b*x)^3)-1/4*(d+e*x)^(9/2)/(b*(a+b*x)^4)-315/64*e^4*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/b^(11/2)+315/64*e^4*sqrt(d+e*x)/b^5],
[(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^3,x,7,-35/96*e^2*(d+e*x)^(3/2)/(b^3*(a+b*x)^2)-7/24*e*(d+e*x)^(5/2)/(b^2*(a+b*x)^3)-1/4*(d+e*x)^(7/2)/(b*(a+b*x)^4)-35/64*e^4*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*sqrt(b*d-a*e))-35/64*e^3*sqrt(d+e*x)/(b^4*(a+b*x))],
[(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^3,x,7,-5/24*e*(d+e*x)^(3/2)/(b^2*(a+b*x)^3)-1/4*(d+e*x)^(5/2)/(b*(a+b*x)^4)+5/64*e^4*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*(b*d-a*e)^(3/2))-5/32*e^2*sqrt(d+e*x)/(b^3*(a+b*x)^2)-5/64*e^3*sqrt(d+e*x)/(b^3*(b*d-a*e)*(a+b*x))],
[(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^3,x,7,-1/4*(d+e*x)^(3/2)/(b*(a+b*x)^4)-3/64*e^4*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(5/2))-1/8*e*sqrt(d+e*x)/(b^2*(a+b*x)^3)-1/32*e^2*sqrt(d+e*x)/(b^2*(b*d-a*e)*(a+b*x)^2)+3/64*e^3*sqrt(d+e*x)/(b^2*(b*d-a*e)^2*(a+b*x))],
[(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^3,x,7,5/64*e^4*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(7/2))-1/4*sqrt(d+e*x)/(b*(a+b*x)^4)-1/24*e*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)^3)+5/96*e^2*sqrt(d+e*x)/(b*(b*d-a*e)^2*(a+b*x)^2)-5/64*e^3*sqrt(d+e*x)/(b*(b*d-a*e)^3*(a+b*x))],
[(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^3*sqrt(d+e*x)),x,7,-35/64*e^4*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*sqrt(b))-1/4*sqrt(d+e*x)/((b*d-a*e)*(a+b*x)^4)+7/24*e*sqrt(d+e*x)/((b*d-a*e)^2*(a+b*x)^3)-35/96*e^2*sqrt(d+e*x)/((b*d-a*e)^3*(a+b*x)^2)+35/64*e^3*sqrt(d+e*x)/((b*d-a*e)^4*(a+b*x))],
[(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^3),x,8,-315/64*e^4*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/(b*d-a*e)^(11/2)+315/64*e^4/((b*d-a*e)^5*sqrt(d+e*x))+(-1/4)/((b*d-a*e)*(a+b*x)^4*sqrt(d+e*x))+3/8*e/((b*d-a*e)^2*(a+b*x)^3*sqrt(d+e*x))-21/32*e^2/((b*d-a*e)^3*(a+b*x)^2*sqrt(d+e*x))+105/64*e^3/((b*d-a*e)^4*(a+b*x)*sqrt(d+e*x))],
[(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^3),x,9,385/64*e^4/((b*d-a*e)^5*(d+e*x)^(3/2))+(-1/4)/((b*d-a*e)*(a+b*x)^4*(d+e*x)^(3/2))+11/24*e/((b*d-a*e)^2*(a+b*x)^3*(d+e*x)^(3/2))-33/32*e^2/((b*d-a*e)^3*(a+b*x)^2*(d+e*x)^(3/2))+231/64*e^3/((b*d-a*e)^4*(a+b*x)*(d+e*x)^(3/2))-1155/64*b^(3/2)*e^4*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b*d-a*e)^(13/2)+1155/64*b*e^4/((b*d-a*e)^6*sqrt(d+e*x))],

# Integrands of the form (d+e x)^(m/2) (a+b x) (a^2+2 a b x+b^2 x^2)^(p/2)

# p>0
[(a+b*x)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2),x,4,2/9*(b*d-a*e)^2*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-4/11*b*(b*d-a*e)*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/13*b^2*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2),x,4,2/7*(b*d-a*e)^2*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-4/9*b*(b*d-a*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/11*b^2*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2),x,4,2/5*(b*d-a*e)^2*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-4/7*b*(b*d-a*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/9*b^2*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2),x,4,2/3*(b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-4/5*b*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/7*b^2*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/sqrt(d+e*x),x,4,-4/3*b*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2/5*b^2*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))+2*(b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(3/2),x,4,2/3*b^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))-2*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x))-4*b*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(5/2),x,4,-2/3*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(3/2))+4*b*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x))+2*b^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x))],
[(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(d+e*x)^(7/2),x,4,-2/5*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(5/2))+4/3*b*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*(d+e*x)^(3/2))-2*b^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(a+b*x)*sqrt(d+e*x))],
[(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,2/7*(b*d-a*e)^4*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-8/9*b*(b*d-a*e)^3*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+12/11*b^2*(b*d-a*e)^2*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-8/13*b^3*(b*d-a*e)*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/15*b^4*(d+e*x)^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,2/5*(b*d-a*e)^4*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-8/7*b*(b*d-a*e)^3*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+4/3*b^2*(b*d-a*e)^2*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-8/11*b^3*(b*d-a*e)*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/13*b^4*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x),x,4,2/3*(b*d-a*e)^4*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-8/5*b*(b*d-a*e)^3*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+12/7*b^2*(b*d-a*e)^2*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-8/9*b^3*(b*d-a*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/11*b^4*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/sqrt(d+e*x),x,4,-8/3*b*(b*d-a*e)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+12/5*b^2*(b*d-a*e)^2*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-8/7*b^3*(b*d-a*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/9*b^4*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2*(b*d-a*e)^4*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(3/2),x,4,4*b^2*(b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-8/5*b^3*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/7*b^4*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*sqrt(d+e*x))-8*b*(b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(5/2),x,4,-2/3*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(3/2))-8/3*b^3*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+2/5*b^4*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))+8*b*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*sqrt(d+e*x))+12*b^2*(b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(7/2),x,4,-2/5*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(5/2))+8/3*b*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(3/2))+2/3*b^4*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))-12*b^2*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*sqrt(d+e*x))-8*b^3*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(9/2),x,4,-2/7*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(7/2))+8/5*b*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(5/2))-4*b^2*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(3/2))+8*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*sqrt(d+e*x))+2*b^4*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(11/2),x,4,-2/9*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(9/2))+8/7*b*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(7/2))-12/5*b^2*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(5/2))+8/3*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(3/2))-2*b^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*sqrt(d+e*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(3/2)/(d+e*x)^(13/2),x,4,-2/11*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(11/2))+8/9*b*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(9/2))-12/7*b^2*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(7/2))+8/5*b^3*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(5/2))-2/3*b^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(a+b*x)*(d+e*x)^(3/2))],
[(a+b*x)*(d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,2/7*(b*d-a*e)^6*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-4/3*b*(b*d-a*e)^5*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+30/11*b^2*(b*d-a*e)^4*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-40/13*b^3*(b*d-a*e)^3*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2*b^4*(b*d-a*e)^2*(d+e*x)^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-12/17*b^5*(b*d-a*e)*(d+e*x)^(17/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/19*b^6*(d+e*x)^(19/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,2/5*(b*d-a*e)^6*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-12/7*b*(b*d-a*e)^5*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+10/3*b^2*(b*d-a*e)^4*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-40/11*b^3*(b*d-a*e)^3*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+30/13*b^4*(b*d-a*e)^2*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-4/5*b^5*(b*d-a*e)*(d+e*x)^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/17*b^6*(d+e*x)^(17/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x),x,4,2/3*(b*d-a*e)^6*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-12/5*b*(b*d-a*e)^5*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+30/7*b^2*(b*d-a*e)^4*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-40/9*b^3*(b*d-a*e)^3*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+30/11*b^4*(b*d-a*e)^2*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-12/13*b^5*(b*d-a*e)*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/15*b^6*(d+e*x)^(15/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/sqrt(d+e*x),x,4,-4*b*(b*d-a*e)^5*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+6*b^2*(b*d-a*e)^4*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-40/7*b^3*(b*d-a*e)^3*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+10/3*b^4*(b*d-a*e)^2*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-12/11*b^5*(b*d-a*e)*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/13*b^6*(d+e*x)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2*(b*d-a*e)^6*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(3/2),x,4,10*b^2*(b*d-a*e)^4*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-8*b^3*(b*d-a*e)^3*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+30/7*b^4*(b*d-a*e)^2*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-4/3*b^5*(b*d-a*e)*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/11*b^6*(d+e*x)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-2*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x))-12*b*(b*d-a*e)^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(5/2),x,4,-2/3*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(3/2))-40/3*b^3*(b*d-a*e)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+6*b^4*(b*d-a*e)^2*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-12/7*b^5*(b*d-a*e)*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/9*b^6*(d+e*x)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+12*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x))+30*b^2*(b*d-a*e)^4*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(7/2),x,4,-2/5*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(5/2))+4*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(3/2))+10*b^4*(b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-12/5*b^5*(b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/7*b^6*(d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-30*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x))-40*b^3*(b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(9/2),x,4,-2/7*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(7/2))+12/5*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(5/2))-10*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(3/2))-4*b^5*(b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+2/5*b^6*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))+40*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x))+30*b^4*(b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(11/2),x,4,-2/9*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(9/2))+12/7*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(7/2))-6*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(5/2))+40/3*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(3/2))+2/3*b^6*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))-30*b^4*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x))-12*b^5*(b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(13/2),x,4,-2/11*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(11/2))+4/3*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(9/2))-30/7*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(7/2))+8*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(5/2))-10*b^4*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(3/2))+12*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x))+2*b^6*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(15/2),x,4,-2/13*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(13/2))+12/11*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(11/2))-10/3*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(9/2))+40/7*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(7/2))-6*b^4*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(5/2))+4*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(3/2))-2*b^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*sqrt(d+e*x))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^(5/2)/(d+e*x)^(17/2),x,4,-2/15*(b*d-a*e)^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(15/2))+12/13*b*(b*d-a*e)^5*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(13/2))-30/11*b^2*(b*d-a*e)^4*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(11/2))+40/9*b^3*(b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(9/2))-30/7*b^4*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(7/2))+12/5*b^5*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(5/2))-2/3*b^6*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(a+b*x)*(d+e*x)^(3/2))],

# p<0
[(a+b*x)*(d+e*x)^(7/2)/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,2/9*(a+b*x)*(d+e*x)^(9/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^(5/2)/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,2/7*(a+b*x)*(d+e*x)^(7/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^(3/2)/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,2/5*(a+b*x)*(d+e*x)^(5/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*sqrt(d+e*x)/sqrt(a^2+2*a*b*x+b^2*x^2),x,3,2/3*(a+b*x)*(d+e*x)^(3/2)/(e*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/(sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,2*(a+b*x)*sqrt(d+e*x)/(e*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,-2*(a+b*x)/(e*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,-2/3*(a+b*x)/(e*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2)),x,3,-2/5*(a+b*x)/(e*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,7,7/3*e*(b*d-a*e)*(a+b*x)*(d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))+7/5*e*(a+b*x)*(d+e*x)^(5/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-(d+e*x)^(7/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-7*e*(b*d-a*e)^(5/2)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7*e*(b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,6,5/3*e*(a+b*x)*(d+e*x)^(3/2)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))-(d+e*x)^(5/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-5*e*(b*d-a*e)^(3/2)*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5*e*(b*d-a*e)*(a+b*x)*sqrt(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,5,-(d+e*x)^(3/2)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))-3*e*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+3*e*(a+b*x)*sqrt(d+e*x)/(b^2*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,-e*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-sqrt(d+e*x)/(b*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^(3/2)*sqrt(d+e*x)),x,5,e*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(3/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-sqrt(d+e*x)/((b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,6,3*e*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/((b*d-a*e)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+(-1)/((b*d-a*e)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-3*e*(a+b*x)/((b*d-a*e)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,7,(-1)/((b*d-a*e)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/3*e*(a+b*x)/((b*d-a*e)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+5*b^(3/2)*e*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-5*b*e*(a+b*x)/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(3/2)),x,8,(-1)/((b*d-a*e)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/5*e*(a+b*x)/((b*d-a*e)^2*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-7/3*b*e*(a+b*x)/((b*d-a*e)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+7*b^(5/2)*e*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-7*b^2*e*(a+b*x)/((b*d-a*e)^4*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^(7/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,7,-1/3*(d+e*x)^(7/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-35/24*e^2*(d+e*x)^(3/2)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))-7/12*e*(d+e*x)^(5/2)/(b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/8*e^3*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b*d-a*e)/(b^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+35/8*e^3*(a+b*x)*sqrt(d+e*x)/(b^4*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^(5/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,6,-1/3*(d+e*x)^(5/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-5/12*e*(d+e*x)^(3/2)/(b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/8*e^3*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(7/2)*sqrt(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/8*e^2*sqrt(d+e*x)/(b^3*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^(3/2)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,6,-1/3*(d+e*x)^(3/2)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))+1/8*e^3*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(5/2)*(b*d-a*e)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/8*e^2*sqrt(d+e*x)/(b^2*(b*d-a*e)*sqrt(a^2+2*a*b*x+b^2*x^2))-1/4*e*sqrt(d+e*x)/(b^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*sqrt(d+e*x)/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,6,-1/3*sqrt(d+e*x)/(b*(a^2+2*a*b*x+b^2*x^2)^(3/2))-1/8*e^3*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/(b^(3/2)*(b*d-a*e)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+1/8*e^2*sqrt(d+e*x)/(b*(b*d-a*e)^2*sqrt(a^2+2*a*b*x+b^2*x^2))-1/12*e*sqrt(d+e*x)/(b*(b*d-a*e)*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((a^2+2*a*b*x+b^2*x^2)^(5/2)*sqrt(d+e*x)),x,7,5/8*e^3*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(7/2)*sqrt(b)*sqrt(a^2+2*a*b*x+b^2*x^2))-5/8*e^2*sqrt(d+e*x)/((b*d-a*e)^3*sqrt(a^2+2*a*b*x+b^2*x^2))-1/3*sqrt(d+e*x)/((b*d-a*e)*(a+b*x)^2*sqrt(a^2+2*a*b*x+b^2*x^2))+5/12*e*sqrt(d+e*x)/((b*d-a*e)^2*(a+b*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^(3/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,8,35/8*e^3*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))*sqrt(b)/((b*d-a*e)^(9/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/24*e^2/((b*d-a*e)^3*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+(-1/3)/((b*d-a*e)*(a+b*x)^2*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))+7/12*e/((b*d-a*e)^2*(a+b*x)*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/8*e^3*(a+b*x)/((b*d-a*e)^4*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^(5/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,9,-21/8*e^2/((b*d-a*e)^3*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+(-1/3)/((b*d-a*e)*(a+b*x)^2*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+3/4*e/((b*d-a*e)^2*(a+b*x)*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-35/8*e^3*(a+b*x)/((b*d-a*e)^4*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+105/8*b^(3/2)*e^3*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(11/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-105/8*b*e^3*(a+b*x)/((b*d-a*e)^5*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)/((d+e*x)^(7/2)*(a^2+2*a*b*x+b^2*x^2)^(5/2)),x,10,-33/8*e^2/((b*d-a*e)^3*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+(-1/3)/((b*d-a*e)*(a+b*x)^2*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+11/12*e/((b*d-a*e)^2*(a+b*x)*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-231/40*e^3*(a+b*x)/((b*d-a*e)^4*(d+e*x)^(5/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-77/8*b*e^3*(a+b*x)/((b*d-a*e)^5*(d+e*x)^(3/2)*sqrt(a^2+2*a*b*x+b^2*x^2))+231/8*b^(5/2)*e^3*(a+b*x)*arctanh(sqrt(b)*sqrt(d+e*x)/sqrt(b*d-a*e))/((b*d-a*e)^(13/2)*sqrt(a^2+2*a*b*x+b^2*x^2))-231/8*b^2*e^3*(a+b*x)/((b*d-a*e)^6*sqrt(d+e*x)*sqrt(a^2+2*a*b*x+b^2*x^2))],

# Integrands of the form (d+e x)^m (a+b x) (a^2+2 a b x+b^2 x^2)^p when m symbolic
[(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^3,x,3,-(b*d-a*e)^7*(d+e*x)^(1+m)/(e^8*(1+m))+7*b*(b*d-a*e)^6*(d+e*x)^(2+m)/(e^8*(2+m))-21*b^2*(b*d-a*e)^5*(d+e*x)^(3+m)/(e^8*(3+m))+35*b^3*(b*d-a*e)^4*(d+e*x)^(4+m)/(e^8*(4+m))-35*b^4*(b*d-a*e)^3*(d+e*x)^(5+m)/(e^8*(5+m))+21*b^5*(b*d-a*e)^2*(d+e*x)^(6+m)/(e^8*(6+m))-7*b^6*(b*d-a*e)*(d+e*x)^(7+m)/(e^8*(7+m))+b^7*(d+e*x)^(8+m)/(e^8*(8+m))],
[(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^2,x,3,-(b*d-a*e)^5*(d+e*x)^(1+m)/(e^6*(1+m))+5*b*(b*d-a*e)^4*(d+e*x)^(2+m)/(e^6*(2+m))-10*b^2*(b*d-a*e)^3*(d+e*x)^(3+m)/(e^6*(3+m))+10*b^3*(b*d-a*e)^2*(d+e*x)^(4+m)/(e^6*(4+m))-5*b^4*(b*d-a*e)*(d+e*x)^(5+m)/(e^6*(5+m))+b^5*(d+e*x)^(6+m)/(e^6*(6+m))],
[(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2),x,3,-(b*d-a*e)^3*(d+e*x)^(1+m)/(e^4*(1+m))+3*b*(b*d-a*e)^2*(d+e*x)^(2+m)/(e^4*(2+m))-3*b^2*(b*d-a*e)*(d+e*x)^(3+m)/(e^4*(3+m))+b^3*(d+e*x)^(4+m)/(e^4*(4+m))],
[(a+b*x)*(d+e*x)^m/(a^2+2*a*b*x+b^2*x^2),x,2,-(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],b*(d+e*x)/(b*d-a*e))/((b*d-a*e)*(1+m))],
[(a+b*x)*(d+e*x)^m/(a^2+2*a*b*x+b^2*x^2)^2,x,2,-e^2*(d+e*x)^(1+m)*hypergeom([3,1+m],[2+m],b*(d+e*x)/(b*d-a*e))/((b*d-a*e)^3*(1+m))],
[(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(5/2),x,4,(b*d-a*e)^6*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(1+m)*(a+b*x))-6*b*(b*d-a*e)^5*(d+e*x)^(2+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(2+m)*(a+b*x))+15*b^2*(b*d-a*e)^4*(d+e*x)^(3+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(3+m)*(a+b*x))-20*b^3*(b*d-a*e)^3*(d+e*x)^(4+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(4+m)*(a+b*x))+15*b^4*(b*d-a*e)^2*(d+e*x)^(5+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(5+m)*(a+b*x))-6*b^5*(b*d-a*e)*(d+e*x)^(6+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(6+m)*(a+b*x))+b^6*(d+e*x)^(7+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^7*(7+m)*(a+b*x))],
[(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,(b*d-a*e)^4*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(1+m)*(a+b*x))-4*b*(b*d-a*e)^3*(d+e*x)^(2+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(2+m)*(a+b*x))+6*b^2*(b*d-a*e)^2*(d+e*x)^(3+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(3+m)*(a+b*x))-4*b^3*(b*d-a*e)*(d+e*x)^(4+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(4+m)*(a+b*x))+b^4*(d+e*x)^(5+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^5*(5+m)*(a+b*x))],
[(a+b*x)*(d+e*x)^m*(a^2+2*a*b*x+b^2*x^2)^(1/2),x,4,(b*d-a*e)^2*(d+e*x)^(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(1+m)*(a+b*x))-2*b*(b*d-a*e)*(d+e*x)^(2+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(2+m)*(a+b*x))+b^2*(d+e*x)^(3+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(e^3*(3+m)*(a+b*x))],
[(a+b*x)*(d+e*x)^m/(a^2+2*a*b*x+b^2*x^2)^(1/2),x,3,(a+b*x)*(d+e*x)^(1+m)/(e*(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^m/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,3,e*(a+b*x)*(d+e*x)^(1+m)*hypergeom([2,1+m],[2+m],b*(d+e*x)/(b*d-a*e))/((b*d-a*e)^2*(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2))],
[(a+b*x)*(d+e*x)^m/(a^2+2*a*b*x+b^2*x^2)^(5/2),x,3,e^3*(a+b*x)*(d+e*x)^(1+m)*hypergeom([4,1+m],[2+m],b*(d+e*x)/(b*d-a*e))/((b*d-a*e)^4*(1+m)*sqrt(a^2+2*a*b*x+b^2*x^2))],

# Integrands of the form (d+e x)^m (a+b x) (a^2+2 a b x+b^2 x^2)^p when p symbolic
[(a*c+b*c*x)*(d+e*x)^(-3-2*p)*(a^2+2*a*b*x+b^2*x^2)^p,x,1,1/2*c*(a^2+2*a*b*x+b^2*x^2)^(1+p)/((b*d-a*e)*(1+p)*(d+e*x)^(2*(1+p)))],
[(a+b*x)*(d+e*x)^3*(a^2+2*a*b*x+b^2*x^2)^p,x,4,1/2*(b*d-a*e)^3*(a+b*x)^2*(a^2+2*a*b*x+b^2*x^2)^p/(b^4*(1+p))+3*e*(b*d-a*e)^2*(a+b*x)^3*(a^2+2*a*b*x+b^2*x^2)^p/(b^4*(3+2*p))+3/2*e^2*(b*d-a*e)*(a+b*x)^4*(a^2+2*a*b*x+b^2*x^2)^p/(b^4*(2+p))+e^3*(a+b*x)^5*(a^2+2*a*b*x+b^2*x^2)^p/(b^4*(5+2*p))],
[(a+b*x)*(d+e*x)^2*(a^2+2*a*b*x+b^2*x^2)^p,x,4,1/2*(b*d-a*e)^2*(a+b*x)^2*(a^2+2*a*b*x+b^2*x^2)^p/(b^3*(1+p))+2*e*(b*d-a*e)*(a+b*x)^3*(a^2+2*a*b*x+b^2*x^2)^p/(b^3*(3+2*p))+1/2*e^2*(a+b*x)^4*(a^2+2*a*b*x+b^2*x^2)^p/(b^3*(2+p))],
[(a+b*x)*(d+e*x)*(a^2+2*a*b*x+b^2*x^2)^p,x,4,1/2*(b*d-a*e)*(a+b*x)^2*(a^2+2*a*b*x+b^2*x^2)^p/(b^2*(1+p))+e*(a+b*x)^3*(a^2+2*a*b*x+b^2*x^2)^p/(b^2*(3+2*p))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p,x,1,1/2*(a^2+2*a*b*x+b^2*x^2)^(1+p)/(b*(1+p))],
[(a+b*x)*(a^2+2*a*b*x+b^2*x^2)^p/(d+e*x),x,3,1/2*(a+b*x)^2*(a^2+2*a*b*x+b^2*x^2)^p*hypergeom([1,2*(1+p)],[3+2*p],-e*(a+b*x)/(b*d-a*e))/((b*d-a*e)*(1+p))],

# Integrands of the form (d+e x)^m (f+g x) (a+b x+c x^2)^p when b^2-4 a c=0 and 2 c d-b e=0

# Integrands of the form (a c+b c x)^m (A+B x) (a^2+2 a b x+b^2 x^2)^p

# p>0
[(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^3,x,4,(A*b-a*B)*(a*c+b*c*x)^(7+m)/(b^2*c^7*(7+m))+B*(a*c+b*c*x)^(8+m)/(b^2*c^8*(8+m))],

# p<0
[(A+B*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^3,x,4,-(A*b-a*B)*c^5*(a*c+b*c*x)^(-5+m)/(b^2*(5-m))-B*c^4*(a*c+b*c*x)^(-4+m)/(b^2*(4-m))],

# Integrands of the form (a c+b c x)^m (A+B x) (a^2+2 a b x+b^2 x^2)^(p/2)

# p>0
[(A+B*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,(A*b-a*B)*(a*c+b*c*x)^(4+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b^2*c^4*(4+m)*(a+b*x))+B*(a*c+b*c*x)^(5+m)*sqrt(a^2+2*a*b*x+b^2*x^2)/(b^2*c^5*(5+m)*(a+b*x))],

# p<0
[(A+B*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^(3/2),x,4,-(A*b-a*B)*c^2*(a+b*x)*(a*c+b*c*x)^(-2+m)/(b^2*(2-m)*sqrt(a^2+2*a*b*x+b^2*x^2))-B*c*(a+b*x)*(a*c+b*c*x)^(-1+m)/(b^2*(1-m)*sqrt(a^2+2*a*b*x+b^2*x^2))],

# Integrands of the form (a c+b c x)^m (A+B x) (a^2+2 a b x+b^2 x^2)^p when p symbolic
[(a*c+b*c*x)^m*(f+g*x)*(a^2+2*a*b*x+b^2*x^2)^p,x,4,(b*f-a*g)*(a*c+b*c*x)^(1+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b^2*c*(1+m+2*p))+g*(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b^2*c^2*(2+m+2*p))],
[(a*c+b*c*x)^(-3-2*p)*(f+g*x)*(a^2+2*a*b*x+b^2*x^2)^p,x,3,-1/2*(f+g*x)^2*(a^2+2*a*b*x+b^2*x^2)^p/(c^3*(b*f-a*g)*(a+b*x)^2*(a*c+b*c*x)^(2*p))],

# Integrands of the form (d+e x)^m (f+g x) (a+b x+c x^2)^p when b^2-4 a c=0, 2 c f-b g=0 and 2 c d-b e=0
[(a+b*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^p,x,3,(a*c+b*c*x)^(2+m)*(a^2+2*a*b*x+b^2*x^2)^p/(b*c^2*(2+m+2*p))],
[(a+b*x)*(a*c+b*c*x)^m*(a^2+2*a*b*x+b^2*x^2)^3,x,4,(a*c+b*c*x)^(8+m)/(b*c^8*(8+m))],
[(a+b*x)*(a*c+b*c*x)^m/(a^2+2*a*b*x+b^2*x^2)^3,x,4,-c^4*(a*c+b*c*x)^(-4+m)/(b*(4-m))],

# Integrands of the form (d+e x)^m (f+g x) (a+b x+c x^2)^p when c d^2-b d e+a e^2=0

# Integrands of the form (d+e x)^m (A+B x) (c d^2-b d e-b e^2 x-c e^2 x^2)^(p/2)

# p>0
[(d+e*x)^3*(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,7,-7/192*(2*c*d-b*e)^2*(4*c*e*f+2*c*d*g-3*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^4*e^2)-7/160*(2*c*d-b*e)*(4*c*e*f+2*c*d*g-3*b*e*g)*(d+e*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^3*e^2)-1/20*(4*c*e*f+2*c*d*g-3*b*e*g)*(d+e*x)^2*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^2*e^2)-1/6*g*(d+e*x)^3*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c*e^2)+7/1024*(2*c*d-b*e)^5*(4*c*e*f+2*c*d*g-3*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(11/2)*e^2)+7/512*(2*c*d-b*e)^3*(4*c*e*f+2*c*d*g-3*b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^5*e)],
[(d+e*x)^2*(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,7,-1/48*(2*c*d-b*e)*(10*c*e*f+4*c*d*g-7*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^3*e^2)-1/40*(10*c*e*f+4*c*d*g-7*b*e*g)*(d+e*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^2*e^2)-1/5*g*(d+e*x)^2*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c*e^2)+1/256*(2*c*d-b*e)^4*(10*c*e*f+4*c*d*g-7*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(9/2)*e^2)+1/128*(2*c*d-b*e)^2*(10*c*e*f+4*c*d*g-7*b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^4*e)],
[(d+e*x)*(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,4,1/24*(5*b*e*g-8*c*(e*f+d*g)-6*c*e*g*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^2*e^2)+1/128*(2*c*d-b*e)^3*(8*c*e*f+2*c*d*g-5*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(7/2)*e^2)+1/64*(2*c*d-b*e)*(8*c*e*f+2*c*d*g-5*b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^3*e)],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x),x,4,-1/2*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c*e^2*(d+e*x))+1/8*(2*c*d-b*e)*(4*c*e*f-2*c*d*g-b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(3/2)*e^2)+1/4*(4*c*e*f-2*c*d*g-b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c*e^2)],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x)^2,x,4,-2*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^2)-1/2*(2*c*e*f-4*c*d*g+b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(e^2*sqrt(c))-(2*c*e*f-4*c*d*g+b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e))],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x)^3,x,4,-2/3*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^3)-g*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))*sqrt(c)/e^2-2*g*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(d+e*x))],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x)^4,x,2,-2/5*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^4)-2/15*(2*c*e*f+8*c*d*g-5*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^3)],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x)^5,x,3,-2/7*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^5)-2/35*(4*c*e*f+10*c*d*g-7*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^4)-4/105*c*(4*c*e*f+10*c*d*g-7*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^3*(d+e*x)^3)],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x)^6,x,4,-2/9*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^6)-2/21*(2*c*e*f+4*c*d*g-3*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^5)-8/105*c*(2*c*e*f+4*c*d*g-3*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^3*(d+e*x)^4)-16/315*c^2*(2*c*e*f+4*c*d*g-3*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^4*(d+e*x)^3)],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x)^7,x,5,-2/11*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^7)-2/99*(8*c*e*f+14*c*d*g-11*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^6)-4/231*c*(8*c*e*f+14*c*d*g-11*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^3*(d+e*x)^5)-16/1155*c^2*(8*c*e*f+14*c*d*g-11*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^4*(d+e*x)^4)-32/3465*c^3*(8*c*e*f+14*c*d*g-11*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^5*(d+e*x)^3)],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x)^8,x,6,-2/13*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^8)-2/143*(10*c*e*f+16*c*d*g-13*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^7)+16/1287*c*(13*b*e*g-2*c*(5*e*f+8*d*g))*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^3*(d+e*x)^6)-32/3003*c^2*(10*c*e*f+16*c*d*g-13*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^4*(d+e*x)^5)+128/15015*c^3*(13*b*e*g-2*c*(5*e*f+8*d*g))*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^5*(d+e*x)^4)-256/45045*c^4*(10*c*e*f+16*c*d*g-13*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)^6*(d+e*x)^3)],
[(d+e*x)^3*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,8,3/2048*(2*c*d-b*e)^3*(16*c*e*f+6*c*d*g-11*b*e*g)*(b+2*c*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^5*e)-3/640*(2*c*d-b*e)^2*(16*c*e*f+6*c*d*g-11*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^4*e^2)-3/448*(2*c*d-b*e)*(16*c*e*f+6*c*d*g-11*b*e*g)*(d+e*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^3*e^2)-1/112*(16*c*e*f+6*c*d*g-11*b*e*g)*(d+e*x)^2*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^2*e^2)-1/8*g*(d+e*x)^3*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c*e^2)+9/32768*(2*c*d-b*e)^7*(16*c*e*f+6*c*d*g-11*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(13/2)*e^2)+9/16384*(2*c*d-b*e)^5*(16*c*e*f+6*c*d*g-11*b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^6*e)],
[(d+e*x)^2*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,8,1/384*(2*c*d-b*e)^2*(14*c*e*f+4*c*d*g-9*b*e*g)*(b+2*c*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^4*e)-1/120*(2*c*d-b*e)*(14*c*e*f+4*c*d*g-9*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^3*e^2)-1/84*(14*c*e*f+4*c*d*g-9*b*e*g)*(d+e*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^2*e^2)-1/7*g*(d+e*x)^2*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c*e^2)+1/2048*(2*c*d-b*e)^6*(14*c*e*f+4*c*d*g-9*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(11/2)*e^2)+1/1024*(2*c*d-b*e)^4*(14*c*e*f+4*c*d*g-9*b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^5*e)],
[(d+e*x)*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,5,1/192*(2*c*d-b*e)*(12*c*e*f+2*c*d*g-7*b*e*g)*(b+2*c*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^3*e)+1/60*(7*b*e*g-12*c*(e*f+d*g)-10*c*e*g*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^2*e^2)+1/1024*(2*c*d-b*e)^5*(12*c*e*f+2*c*d*g-7*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(9/2)*e^2)+1/512*(2*c*d-b*e)^3*(12*c*e*f+2*c*d*g-7*b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^4*e)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x),x,5,1/24*(8*c*e*f-2*c*d*g-3*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c*e^2)-1/4*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c*e^2*(d+e*x))+1/128*(2*c*d-b*e)^3*(8*c*e*f-2*c*d*g-3*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(5/2)*e^2)+1/64*(2*c*d-b*e)*(8*c*e*f-2*c*d*g-3*b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^2,x,5,1/3*(6*c*e*f-4*c*d*g-b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e))+2*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^2)+1/16*(2*c*d-b*e)^2*(6*c*e*f-4*c*d*g-b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(3/2)*e^2)+1/8*(6*c*e*f-4*c*d*g-b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c*e)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^3,x,5,-1/2*(4*c*e*f-6*c*d*g+b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x))-2*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^3)-3/8*(2*c*d-b*e)*(4*c*e*f-6*c*d*g+b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(e^2*sqrt(c))-3/4*(4*c*e*f-6*c*d*g+b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/e^2],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^4,x,5,2/3*(2*c*e*f-8*c*d*g+3*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^2)-2/3*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^4)+1/2*(2*c*e*f-8*c*d*g+3*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))*sqrt(c)/e^2+c*(2*c*e*f-8*c*d*g+3*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^5,x,5,-2/3*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(d+e*x)^3)-2/5*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^5)+c^(3/2)*g*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/e^2+2*c*g*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(d+e*x))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^6,x,2,-2/7*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^6)+2/35*(7*b*e*g-2*c*(e*f+6*d*g))*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^5)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^7,x,3,-2/9*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^7)-2/63*(4*c*e*f+14*c*d*g-9*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^6)-4/315*c*(4*c*e*f+14*c*d*g-9*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)^3*(d+e*x)^5)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^8,x,4,-2/11*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^8)-2/99*(6*c*e*f+16*c*d*g-11*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^7)-8/693*c*(6*c*e*f+16*c*d*g-11*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)^3*(d+e*x)^6)-16/3465*c^2*(6*c*e*f+16*c*d*g-11*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)^4*(d+e*x)^5)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^9,x,5,-2/13*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^9)-2/143*(8*c*e*f+18*c*d*g-13*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^8)-4/429*c*(8*c*e*f+18*c*d*g-13*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)^3*(d+e*x)^7)-16/3003*c^2*(8*c*e*f+18*c*d*g-13*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)^4*(d+e*x)^6)-32/15015*c^3*(8*c*e*f+18*c*d*g-13*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)^5*(d+e*x)^5)],
[(d+e*x)^3*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,9,11/49152*(2*c*d-b*e)^5*(20*c*e*f+6*c*d*g-13*b*e*g)*(b+2*c*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^6*e)+11/15360*(2*c*d-b*e)^3*(20*c*e*f+6*c*d*g-13*b*e*g)*(b+2*c*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^5*e)-11/4480*(2*c*d-b*e)^2*(20*c*e*f+6*c*d*g-13*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^4*e^2)-11/2880*(2*c*d-b*e)*(20*c*e*f+6*c*d*g-13*b*e*g)*(d+e*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^3*e^2)-1/180*(20*c*e*f+6*c*d*g-13*b*e*g)*(d+e*x)^2*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^2*e^2)-1/10*g*(d+e*x)^3*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c*e^2)+11/262144*(2*c*d-b*e)^9*(20*c*e*f+6*c*d*g-13*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(15/2)*e^2)+11/131072*(2*c*d-b*e)^7*(20*c*e*f+6*c*d*g-13*b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^7*e)],
[(d+e*x)^2*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,9,5/12288*(2*c*d-b*e)^4*(18*c*e*f+4*c*d*g-11*b*e*g)*(b+2*c*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^5*e)+1/768*(2*c*d-b*e)^2*(18*c*e*f+4*c*d*g-11*b*e*g)*(b+2*c*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^4*e)-1/224*(2*c*d-b*e)*(18*c*e*f+4*c*d*g-11*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^3*e^2)-1/144*(18*c*e*f+4*c*d*g-11*b*e*g)*(d+e*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^2*e^2)-1/9*g*(d+e*x)^2*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c*e^2)+5/65536*(2*c*d-b*e)^8*(18*c*e*f+4*c*d*g-11*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(13/2)*e^2)+5/32768*(2*c*d-b*e)^6*(18*c*e*f+4*c*d*g-11*b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^6*e)],
[(d+e*x)*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,6,5/6144*(2*c*d-b*e)^3*(16*c*e*f+2*c*d*g-9*b*e*g)*(b+2*c*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^4*e)+1/384*(2*c*d-b*e)*(16*c*e*f+2*c*d*g-9*b*e*g)*(b+2*c*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^3*e)+1/112*(9*b*e*g-16*c*(e*f+d*g)-14*c*e*g*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^2*e^2)+5/32768*(2*c*d-b*e)^7*(16*c*e*f+2*c*d*g-9*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(11/2)*e^2)+5/16384*(2*c*d-b*e)^5*(16*c*e*f+2*c*d*g-9*b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^5*e)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x),x,6,-1/192*(2*c*d-b*e)*(5*b*e*g-2*c*(6*e*f-d*g))*(b+2*c*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^2*e)+1/60*(12*c*e*f-2*c*d*g-5*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c*e^2)-1/6*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c*e^2*(d+e*x))-1/1024*(2*c*d-b*e)^5*(5*b*e*g-2*c*(6*e*f-d*g))*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(7/2)*e^2)-1/512*(2*c*d-b*e)^3*(5*b*e*g-2*c*(6*e*f-d*g))*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^3*e)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^2,x,6,1/48*(10*c*e*f-4*c*d*g-3*b*e*g)*(b+2*c*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c*e)+1/15*(10*c*e*f-4*c*d*g-3*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e))+2/3*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^2)+1/256*(2*c*d-b*e)^4*(10*c*e*f-4*c*d*g-3*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(5/2)*e^2)+1/128*(2*c*d-b*e)^2*(10*c*e*f-4*c*d*g-3*b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^3,x,7,5/24*(8*c*e*f-6*c*d*g-b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/e^2+1/4*(8*c*e*f-6*c*d*g-b*e*g)*(c*d-b*e-c*e*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e))+2*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^3)+5/128*(2*c*d-b*e)^3*(8*c*e*f-6*c*d*g-b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(3/2)*e^2)+5/64*(2*c*d-b*e)*(8*c*e*f-6*c*d*g-b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c*e)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^4,x,6,-5/3*c*(6*c*e*f-8*c*d*g+b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e))-2*(6*c*e*f-8*c*d*g+b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^2)-2*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^4)-5/16*(2*c*d-b*e)^2*(6*c*e*f-8*c*d*g+b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(e^2*sqrt(c))-5/8*(6*c*e*f-8*c*d*g+b*e*g)*(b+2*c*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/e],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^5,x,6,5/6*c*(4*c*e*f-10*c*d*g+3*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x))+2/3*(4*c*e*f-10*c*d*g+3*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^3)-2/3*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^5)+5/8*(2*c*d-b*e)*(4*c*e*f-10*c*d*g+3*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))*sqrt(c)/e^2+5/4*c*(4*c*e*f-10*c*d*g+3*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/e^2],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^6,x,6,-2/3*c*(2*c*e*f-12*c*d*g+5*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^2)+2/15*(2*c*e*f-12*c*d*g+5*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^4)-2/5*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^6)-1/2*c^(3/2)*(2*c*e*f-12*c*d*g+5*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/e^2-c^2*(2*c*e*f-12*c*d*g+5*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^7,x,6,2/3*c*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(d+e*x)^3)-2/5*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(d+e*x)^5)-2/7*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^7)-c^(5/2)*g*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/e^2-2*c^2*g*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(d+e*x))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^8,x,2,-2/9*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^8)+2/63*(9*b*e*g-2*c*(e*f+8*d*g))*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^7)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^9,x,3,-2/11*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^9)-2/99*(4*c*e*f+18*c*d*g-11*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^8)-4/693*c*(4*c*e*f+18*c*d*g-11*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)^3*(d+e*x)^7)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^10,x,4,-2/13*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^10)-2/143*(6*c*e*f+20*c*d*g-13*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^9)-8/1287*c*(6*c*e*f+20*c*d*g-13*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)^3*(d+e*x)^8)-16/9009*c^2*(6*c*e*f+20*c*d*g-13*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)^4*(d+e*x)^7)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^11,x,5,-2/15*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^11)-2/195*(8*c*e*f+22*c*d*g-15*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^10)-4/715*c*(8*c*e*f+22*c*d*g-15*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)^3*(d+e*x)^9)-16/6435*c^2*(8*c*e*f+22*c*d*g-15*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)^4*(d+e*x)^8)-32/45045*c^3*(8*c*e*f+22*c*d*g-15*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)^5*(d+e*x)^7)],

# p<0
[(d+e*x)^3*(f+g*x)/sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,6,5/128*(2*c*d-b*e)^3*(8*c*e*f+6*c*d*g-7*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(9/2)*e^2)-5/64*(2*c*d-b*e)^2*(8*c*e*f+6*c*d*g-7*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^4*e^2)-5/96*(2*c*d-b*e)*(8*c*e*f+6*c*d*g-7*b*e*g)*(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^3*e^2)-1/24*(8*c*e*f+6*c*d*g-7*b*e*g)*(d+e*x)^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e^2)-1/4*g*(d+e*x)^3*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c*e^2)],
[(d+e*x)^2*(f+g*x)/sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,6,1/16*(2*c*d-b*e)^2*(6*c*e*f+4*c*d*g-5*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(7/2)*e^2)-1/8*(2*c*d-b*e)*(6*c*e*f+4*c*d*g-5*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^3*e^2)-1/12*(6*c*e*f+4*c*d*g-5*b*e*g)*(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e^2)-1/3*g*(d+e*x)^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c*e^2)],
[(d+e*x)*(f+g*x)/sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,3,1/8*(2*c*d-b*e)*(4*c*e*f+2*c*d*g-3*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(5/2)*e^2)+1/4*(3*b*e*g-4*c*(e*f+d*g)-2*c*e*g*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e^2)],
[(f+g*x)/((d+e*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)),x,3,g*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(e^2*sqrt(c))-2*(e*f-d*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x))],
[(f+g*x)/((d+e*x)^2*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)),x,2,-2/3*(e*f-d*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x)^2)-2/3*(2*c*e*f+4*c*d*g-3*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^2*(d+e*x))],
[(f+g*x)/((d+e*x)^3*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)),x,3,-2/5*(e*f-d*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x)^3)-2/15*(4*c*e*f+6*c*d*g-5*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^2)-4/15*c*(4*c*e*f+6*c*d*g-5*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^3*(d+e*x))],
[(f+g*x)/((d+e*x)^4*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)),x,4,-2/7*(e*f-d*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x)^4)-2/35*(6*c*e*f+8*c*d*g-7*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^3)-8/105*c*(6*c*e*f+8*c*d*g-7*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^3*(d+e*x)^2)-16/105*c^2*(6*c*e*f+8*c*d*g-7*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^4*(d+e*x))],
[(f+g*x)/((d+e*x)^5*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)),x,5,-2/9*(e*f-d*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x)^5)-2/63*(8*c*e*f+10*c*d*g-9*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^4)-4/105*c*(8*c*e*f+10*c*d*g-9*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^3*(d+e*x)^3)-16/315*c^2*(8*c*e*f+10*c*d*g-9*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^4*(d+e*x)^2)-32/315*c^3*(8*c*e*f+10*c*d*g-9*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^5*(d+e*x))],
[(d+e*x)^3*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,5,-3/8*(2*c*d-b*e)*(4*c*e*f+6*c*d*g-5*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(7/2)*e^2)+2*(c*e*f+c*d*g-b*e*g)*(d+e*x)^3/(c*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+3/4*(4*c*e*f+6*c*d*g-5*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^3*e^2)+1/2*(4*c*e*f+6*c*d*g-5*b*e*g)*(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e^2*(2*c*d-b*e))],
[(d+e*x)^2*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,4,-1/2*(2*c*e*f+4*c*d*g-3*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(5/2)*e^2)+2*(c*e*f+c*d*g-b*e*g)*(d+e*x)^2/(c*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+(2*c*e*f+4*c*d*g-3*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e^2*(2*c*d-b*e))],
[(d+e*x)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,3,-g*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(3/2)*e^2)+2*(c*e*f+c*d*g-b*e*g)*(d+e*x)/(c*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)),-g*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(3/2)*e^2)+2*(c*e*f+c*d*g-b*e*g)*(d*(2*c*d-b*e)+e*(2*c*d-b*e)*x)/(c*e^2*(2*c*d-b*e)^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(f+g*x)/((d+e*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)),x,2,2/3*(4*c*e*f+2*c*d*g-3*b*e*g)*(b+2*c*x)/(e*(2*c*d-b*e)^3*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-2/3*(e*f-d*g)/(e^2*(2*c*d-b*e)*(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(f+g*x)/((d+e*x)^2*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)),x,3,8/15*c*(6*c*e*f+4*c*d*g-5*b*e*g)*(b+2*c*x)/(e*(2*c*d-b*e)^4*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-2/5*(e*f-d*g)/(e^2*(2*c*d-b*e)*(d+e*x)^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-2/15*(6*c*e*f+4*c*d*g-5*b*e*g)/(e^2*(2*c*d-b*e)^2*(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(f+g*x)/((d+e*x)^3*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)),x,4,16/35*c^2*(8*c*e*f+6*c*d*g-7*b*e*g)*(b+2*c*x)/(e*(2*c*d-b*e)^5*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-2/7*(e*f-d*g)/(e^2*(2*c*d-b*e)*(d+e*x)^3*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-2/35*(8*c*e*f+6*c*d*g-7*b*e*g)/(e^2*(2*c*d-b*e)^2*(d+e*x)^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-4/35*c*(8*c*e*f+6*c*d*g-7*b*e*g)/(e^2*(2*c*d-b*e)^3*(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(d+e*x)^5*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,6,2/3*(c*e*f+c*d*g-b*e*g)*(d+e*x)^5/(c*e^2*(2*c*d-b*e)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+5/8*(2*c*d-b*e)*(4*c*e*f+10*c*d*g-7*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(9/2)*e^2)-2/3*(4*c*e*f+10*c*d*g-7*b*e*g)*(d+e*x)^3/(c^2*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-5/4*(4*c*e*f+10*c*d*g-7*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^4*e^2)-5/6*(4*c*e*f+10*c*d*g-7*b*e*g)*(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^3*e^2*(2*c*d-b*e))],
[(d+e*x)^4*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,5,2/3*(c*e*f+c*d*g-b*e*g)*(d+e*x)^4/(c*e^2*(2*c*d-b*e)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+1/2*(2*c*e*f+8*c*d*g-5*b*e*g)*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(7/2)*e^2)-2/3*(2*c*e*f+8*c*d*g-5*b*e*g)*(d+e*x)^2/(c^2*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-(2*c*e*f+8*c*d*g-5*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^3*e^2*(2*c*d-b*e))],
[(d+e*x)^3*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,4,2/3*(c*e*f+c*d*g-b*e*g)*(d+e*x)^3/(c*e^2*(2*c*d-b*e)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+g*arctan(1/2*e*(b+2*c*x)/(sqrt(c)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)))/(c^(5/2)*e^2)-2*g*(d+e*x)/(c^2*e^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(d+e*x)^2*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,2,2/3*(c*e*f+c*d*g-b*e*g)*(d+e*x)^2/(c*e^2*(2*c*d-b*e)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+2/3*(2*c*e*f-4*c*d*g+b*e*g)*(d+e*x)/(c*e^2*(2*c*d-b*e)^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(d+e*x)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,2,2/3*(c*e*f+c*d*g-b*e*g)*(d*(2*c*d-b*e)+e*(2*c*d-b*e)*x)/(c*e^2*(2*c*d-b*e)^2*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+2/3*(4*c*e*f-2*c*d*g-b*e*g)*(b+2*c*x)/(c*e*(2*c*d-b*e)^3*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(f+g*x)/((d+e*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)),x,3,2/15*(8*c*e*f+2*c*d*g-5*b*e*g)*(b+2*c*x)/(e*(2*c*d-b*e)^3*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))-2/5*(e*f-d*g)/(e^2*(2*c*d-b*e)*(d+e*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+16/15*c*(8*c*e*f+2*c*d*g-5*b*e*g)*(b+2*c*x)/(e*(2*c*d-b*e)^5*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(f+g*x)/((d+e*x)^2*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)),x,4,16/105*c*(10*c*e*f+4*c*d*g-7*b*e*g)*(b+2*c*x)/(e*(2*c*d-b*e)^4*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))-2/7*(e*f-d*g)/(e^2*(2*c*d-b*e)*(d+e*x)^2*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))-2/35*(10*c*e*f+4*c*d*g-7*b*e*g)/(e^2*(2*c*d-b*e)^2*(d+e*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+128/105*c^2*(10*c*e*f+4*c*d*g-7*b*e*g)*(b+2*c*x)/(e*(2*c*d-b*e)^6*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(f+g*x)/((d+e*x)^3*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)),x,5,32/63*c^2*(4*c*e*f+2*c*d*g-3*b*e*g)*(b+2*c*x)/(e*(2*c*d-b*e)^5*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))-2/9*(e*f-d*g)/(e^2*(2*c*d-b*e)*(d+e*x)^3*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))-2/21*(4*c*e*f+2*c*d*g-3*b*e*g)/(e^2*(2*c*d-b*e)^2*(d+e*x)^2*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))-4/21*c*(4*c*e*f+2*c*d*g-3*b*e*g)/(e^2*(2*c*d-b*e)^3*(d+e*x)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+256/63*c^3*(4*c*e*f+2*c*d*g-3*b*e*g)*(b+2*c*x)/(e*(2*c*d-b*e)^7*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],

# Integrands of the form (d+e x)^(m/2) (A+B x) (c d^2-b d e-b e^2 x-c e^2 x^2)^(p/2)

# p>0
[(d+e*x)^(5/2)*(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,5,-32/3465*(2*c*d-b*e)^3*(11*c*e*f+5*c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^5*e^2*(d+e*x)^(3/2))-2/99*(11*c*e*f+5*c*d*g-8*b*e*g)*(d+e*x)^(3/2)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^2*e^2)-2/11*g*(d+e*x)^(5/2)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c*e^2)-16/1155*(2*c*d-b*e)^2*(11*c*e*f+5*c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^4*e^2*sqrt(d+e*x))-4/231*(2*c*d-b*e)*(11*c*e*f+5*c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)*sqrt(d+e*x)/(c^3*e^2)],
[(d+e*x)^(3/2)*(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,4,-16/315*(2*c*d-b*e)^2*(3*c*e*f+c*d*g-2*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^4*e^2*(d+e*x)^(3/2))-2/9*g*(d+e*x)^(3/2)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c*e^2)-8/105*(2*c*d-b*e)*(3*c*e*f+c*d*g-2*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^3*e^2*sqrt(d+e*x))-2/21*(3*c*e*f+c*d*g-2*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)*sqrt(d+e*x)/(c^2*e^2)],
[(d+e*x)^(1/2)*(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,3,-4/105*(2*c*d-b*e)*(7*c*e*f+c*d*g-4*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^3*e^2*(d+e*x)^(3/2))-2/35*(7*c*e*f+c*d*g-4*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^2*e^2*sqrt(d+e*x))-2/7*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)*sqrt(d+e*x)/(c*e^2)],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x)^(1/2),x,2,-2/15*(5*c*e*f-c*d*g-2*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c^2*e^2*(d+e*x)^(3/2))-2/5*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c*e^2*sqrt(d+e*x))],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x)^(3/2),x,4,-2/3*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c*e^2*(d+e*x)^(3/2))-2*(e*f-d*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))*sqrt(2*c*d-b*e)/e^2+2*(e*f-d*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*sqrt(d+e*x))],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x)^(5/2),x,4,-(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(5/2))+(c*e*f-5*c*d*g+2*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*sqrt(2*c*d-b*e))-(c*e*f-5*c*d*g+2*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*sqrt(d+e*x))],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x)^(7/2),x,4,-1/2*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(7/2))+1/4*c*(c*e*f+7*c*d*g-4*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(3/2))-1/4*(c*e*f+7*c*d*g-4*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x)^(3/2))],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x)^(9/2),x,5,-1/3*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(9/2))+1/8*c^2*(c*e*f+3*c*d*g-2*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(5/2))-1/4*(c*e*f+3*c*d*g-2*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x)^(5/2))+1/8*c*(c*e*f+3*c*d*g-2*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^(3/2))],
[(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)/(d+e*x)^(11/2),x,6,-1/4*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(11/2))+1/64*c^3*(5*c*e*f+11*c*d*g-8*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(7/2))-1/24*(5*c*e*f+11*c*d*g-8*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x)^(7/2))+1/96*c*(5*c*e*f+11*c*d*g-8*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^(5/2))+1/64*c^2*(5*c*e*f+11*c*d*g-8*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^3*(d+e*x)^(3/2))],
[(d+e*x)^(5/2)*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,6,-256/45045*(2*c*d-b*e)^4*(3*c*e*f+c*d*g-2*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^6*e^2*(d+e*x)^(5/2))-128/9009*(2*c*d-b*e)^3*(3*c*e*f+c*d*g-2*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^5*e^2*(d+e*x)^(3/2))-2/39*(3*c*e*f+c*d*g-2*b*e*g)*(d+e*x)^(3/2)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^2*e^2)-2/15*g*(d+e*x)^(5/2)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c*e^2)-32/1287*(2*c*d-b*e)^2*(3*c*e*f+c*d*g-2*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^4*e^2*sqrt(d+e*x))-16/429*(2*c*d-b*e)*(3*c*e*f+c*d*g-2*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)*sqrt(d+e*x)/(c^3*e^2)],
[(d+e*x)^(3/2)*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,5,-32/15015*(2*c*d-b*e)^3*(13*c*e*f+3*c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^5*e^2*(d+e*x)^(5/2))-16/3003*(2*c*d-b*e)^2*(13*c*e*f+3*c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^4*e^2*(d+e*x)^(3/2))-2/13*g*(d+e*x)^(3/2)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c*e^2)-4/429*(2*c*d-b*e)*(13*c*e*f+3*c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^3*e^2*sqrt(d+e*x))-2/143*(13*c*e*f+3*c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)*sqrt(d+e*x)/(c^2*e^2)],
[(d+e*x)^(1/2)*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,4,-16/3465*(2*c*d-b*e)^2*(11*c*e*f+c*d*g-6*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^4*e^2*(d+e*x)^(5/2))-8/693*(2*c*d-b*e)*(11*c*e*f+c*d*g-6*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^3*e^2*(d+e*x)^(3/2))-2/99*(11*c*e*f+c*d*g-6*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^2*e^2*sqrt(d+e*x))-2/11*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)*sqrt(d+e*x)/(c*e^2)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^(1/2),x,3,-4/315*(2*c*d-b*e)*(9*c*e*f-c*d*g-4*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^3*e^2*(d+e*x)^(5/2))-2/63*(9*c*e*f-c*d*g-4*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^2*e^2*(d+e*x)^(3/2))-2/9*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c*e^2*sqrt(d+e*x))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^(3/2),x,2,-2/35*(7*c*e*f-3*c*d*g-2*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c^2*e^2*(d+e*x)^(5/2))-2/7*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c*e^2*(d+e*x)^(3/2))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^(5/2),x,5,2/3*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-2/5*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c*e^2*(d+e*x)^(5/2))-2*(2*c*d-b*e)^(3/2)*(e*f-d*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/e^2+2*(2*c*d-b*e)*(e*f-d*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*sqrt(d+e*x))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^(7/2),x,5,-1/3*(3*c*e*f-7*c*d*g+2*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(3/2))-(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(7/2))+(3*c*e*f-7*c*d*g+2*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))*sqrt(2*c*d-b*e)/e^2-(3*c*e*f-7*c*d*g+2*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*sqrt(d+e*x))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^(9/2),x,5,1/4*(c*e*f-9*c*d*g+4*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(5/2))-1/2*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(9/2))-3/4*c*(c*e*f-9*c*d*g+4*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*sqrt(2*c*d-b*e))+3/4*c*(c*e*f-9*c*d*g+4*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*sqrt(d+e*x))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^(11/2),x,5,-1/12*(c*e*f+11*c*d*g-6*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(7/2))-1/3*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(11/2))-1/8*c^2*(c*e*f+11*c*d*g-6*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(3/2))+1/8*c*(c*e*f+11*c*d*g-6*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x)^(3/2))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)/(d+e*x)^(13/2),x,6,-1/24*(3*c*e*f+13*c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(9/2))-1/4*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(13/2))-1/64*c^3*(3*c*e*f+13*c*d*g-8*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(5/2))+1/32*c*(3*c*e*f+13*c*d*g-8*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x)^(5/2))-1/64*c^2*(3*c*e*f+13*c*d*g-8*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^(3/2))],
[(d+e*x)^(5/2)*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,7,-512/2909907*(2*c*d-b*e)^5*(19*c*e*f+5*c*d*g-12*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^7*e^2*(d+e*x)^(7/2))-256/415701*(2*c*d-b*e)^4*(19*c*e*f+5*c*d*g-12*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^6*e^2*(d+e*x)^(5/2))-64/46189*(2*c*d-b*e)^3*(19*c*e*f+5*c*d*g-12*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^5*e^2*(d+e*x)^(3/2))-2/323*(19*c*e*f+5*c*d*g-12*b*e*g)*(d+e*x)^(3/2)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^2*e^2)-2/19*g*(d+e*x)^(5/2)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c*e^2)-32/12597*(2*c*d-b*e)^2*(19*c*e*f+5*c*d*g-12*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^4*e^2*sqrt(d+e*x))-4/969*(2*c*d-b*e)*(19*c*e*f+5*c*d*g-12*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)*sqrt(d+e*x)/(c^3*e^2)],
[(d+e*x)^(3/2)*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,6,-256/765765*(2*c*d-b*e)^4*(17*c*e*f+3*c*d*g-10*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^6*e^2*(d+e*x)^(7/2))-128/109395*(2*c*d-b*e)^3*(17*c*e*f+3*c*d*g-10*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^5*e^2*(d+e*x)^(5/2))-32/12155*(2*c*d-b*e)^2*(17*c*e*f+3*c*d*g-10*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^4*e^2*(d+e*x)^(3/2))-2/17*g*(d+e*x)^(3/2)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c*e^2)-16/3315*(2*c*d-b*e)*(17*c*e*f+3*c*d*g-10*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^3*e^2*sqrt(d+e*x))-2/255*(17*c*e*f+3*c*d*g-10*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)*sqrt(d+e*x)/(c^2*e^2)],
[(d+e*x)^(1/2)*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,5,-32/45045*(2*c*d-b*e)^3*(15*c*e*f+c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^5*e^2*(d+e*x)^(7/2))-16/6435*(2*c*d-b*e)^2*(15*c*e*f+c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^4*e^2*(d+e*x)^(5/2))-4/715*(2*c*d-b*e)*(15*c*e*f+c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^3*e^2*(d+e*x)^(3/2))-2/195*(15*c*e*f+c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^2*e^2*sqrt(d+e*x))-2/15*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)*sqrt(d+e*x)/(c*e^2)],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^(1/2),x,4,-16/9009*(2*c*d-b*e)^2*(13*c*e*f-c*d*g-6*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^4*e^2*(d+e*x)^(7/2))-8/1287*(2*c*d-b*e)*(13*c*e*f-c*d*g-6*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^3*e^2*(d+e*x)^(5/2))-2/143*(13*c*e*f-c*d*g-6*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^2*e^2*(d+e*x)^(3/2))-2/13*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c*e^2*sqrt(d+e*x))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^(3/2),x,3,-4/693*(2*c*d-b*e)*(11*c*e*f-3*c*d*g-4*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^3*e^2*(d+e*x)^(7/2))-2/99*(11*c*e*f-3*c*d*g-4*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^2*e^2*(d+e*x)^(5/2))-2/11*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c*e^2*(d+e*x)^(3/2))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^(5/2),x,2,-2/63*(9*c*e*f-5*c*d*g-2*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c^2*e^2*(d+e*x)^(7/2))-2/9*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c*e^2*(d+e*x)^(5/2))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^(7/2),x,6,2/3*(2*c*d-b*e)*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))+2/5*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(d+e*x)^(5/2))-2/7*g*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c*e^2*(d+e*x)^(7/2))-2*(2*c*d-b*e)^(5/2)*(e*f-d*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/e^2+2*(2*c*d-b*e)^2*(e*f-d*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*sqrt(d+e*x))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^(9/2),x,6,-1/3*(5*c*e*f-9*c*d*g+2*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(d+e*x)^(3/2))-1/5*(5*c*e*f-9*c*d*g+2*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(5/2))-(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(9/2))+(2*c*d-b*e)^(3/2)*(5*c*e*f-9*c*d*g+2*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/e^2-(2*c*d-b*e)*(5*c*e*f-9*c*d*g+2*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*sqrt(d+e*x))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^(11/2),x,6,5/12*c*(3*c*e*f-11*c*d*g+4*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(3/2))+1/4*(3*c*e*f-11*c*d*g+4*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(7/2))-1/2*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(11/2))-5/4*c*(3*c*e*f-11*c*d*g+4*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))*sqrt(2*c*d-b*e)/e^2+5/4*c*(3*c*e*f-11*c*d*g+4*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*sqrt(d+e*x))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^(13/2),x,6,-5/24*c*(c*e*f-13*c*d*g+6*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(5/2))+1/12*(c*e*f-13*c*d*g+6*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(9/2))-1/3*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(13/2))+5/8*c^2*(c*e*f-13*c*d*g+6*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*sqrt(2*c*d-b*e))-5/8*c^2*(c*e*f-13*c*d*g+6*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*sqrt(d+e*x))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^(15/2),x,6,5/96*c*(c*e*f+15*c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(7/2))-1/24*(c*e*f+15*c*d*g-8*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(11/2))-1/4*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(15/2))+5/64*c^3*(c*e*f+15*c*d*g-8*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(3/2))-5/64*c^2*(c*e*f+15*c*d*g-8*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x)^(3/2))],
[(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)/(d+e*x)^(17/2),x,7,1/48*c*(3*c*e*f+17*c*d*g-10*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(9/2))-1/40*(3*c*e*f+17*c*d*g-10*b*e*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(13/2))-1/5*(e*f-d*g)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(e^2*(2*c*d-b*e)*(d+e*x)^(17/2))+1/128*c^4*(3*c*e*f+17*c*d*g-10*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(5/2))-1/64*c^2*(3*c*e*f+17*c*d*g-10*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x)^(5/2))+1/128*c^3*(3*c*e*f+17*c*d*g-10*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^(3/2))],

# p<0
[(d+e*x)^(5/2)*(f+g*x)/sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,4,-2/35*(7*c*e*f+5*c*d*g-6*b*e*g)*(d+e*x)^(3/2)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e^2)-2/7*g*(d+e*x)^(5/2)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c*e^2)-16/105*(2*c*d-b*e)^2*(7*c*e*f+5*c*d*g-6*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^4*e^2*sqrt(d+e*x))-8/105*(2*c*d-b*e)*(7*c*e*f+5*c*d*g-6*b*e*g)*sqrt(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^3*e^2)],
[(d+e*x)^(3/2)*(f+g*x)/sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,3,-2/5*g*(d+e*x)^(3/2)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c*e^2)-4/15*(2*c*d-b*e)*(5*c*e*f+3*c*d*g-4*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^3*e^2*sqrt(d+e*x))-2/15*(5*c*e*f+3*c*d*g-4*b*e*g)*sqrt(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e^2)],
[(d+e*x)^(1/2)*(f+g*x)/sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,2,-2/3*(3*c*e*f+c*d*g-2*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e^2*sqrt(d+e*x))-2/3*g*sqrt(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c*e^2)],
[(f+g*x)/((d+e*x)^(1/2)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)),x,3,-2*(e*f-d*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*sqrt(2*c*d-b*e))-2*g*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c*e^2*sqrt(d+e*x))],
[(f+g*x)/((d+e*x)^(3/2)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)),x,3,-(c*e*f+3*c*d*g-2*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(3/2))-(e*f-d*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x)^(3/2))],
[(f+g*x)/((d+e*x)^(5/2)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)),x,4,-1/4*c*(3*c*e*f+5*c*d*g-4*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(5/2))-1/2*(e*f-d*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)*(d+e*x)^(5/2))-1/4*(3*c*e*f+5*c*d*g-4*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(e^2*(2*c*d-b*e)^2*(d+e*x)^(3/2))],
[(d+e*x)^(9/2)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,5,2*(c*e*f+c*d*g-b*e*g)*(d+e*x)^(9/2)/(c*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+12/35*(7*c*e*f+9*c*d*g-8*b*e*g)*(d+e*x)^(3/2)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^3*e^2)+2/7*(7*c*e*f+9*c*d*g-8*b*e*g)*(d+e*x)^(5/2)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e^2*(2*c*d-b*e))+32/35*(2*c*d-b*e)^2*(7*c*e*f+9*c*d*g-8*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^5*e^2*sqrt(d+e*x))+16/35*(2*c*d-b*e)*(7*c*e*f+9*c*d*g-8*b*e*g)*sqrt(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^4*e^2)],
[(d+e*x)^(7/2)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,4,2*(c*e*f+c*d*g-b*e*g)*(d+e*x)^(7/2)/(c*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+2/5*(5*c*e*f+7*c*d*g-6*b*e*g)*(d+e*x)^(3/2)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e^2*(2*c*d-b*e))+16/15*(2*c*d-b*e)*(5*c*e*f+7*c*d*g-6*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^4*e^2*sqrt(d+e*x))+8/15*(5*c*e*f+7*c*d*g-6*b*e*g)*sqrt(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^3*e^2)],
[(d+e*x)^(5/2)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,3,2*(c*e*f+c*d*g-b*e*g)*(d+e*x)^(5/2)/(c*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+4/3*(3*c*e*f+5*c*d*g-4*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^3*e^2*sqrt(d+e*x))+2/3*(3*c*e*f+5*c*d*g-4*b*e*g)*sqrt(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e^2*(2*c*d-b*e))],
[(d+e*x)^(3/2)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,2,2*(c*e*f+c*d*g-b*e*g)*(d+e*x)^(3/2)/(c*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+2*(c*e*f+3*c*d*g-2*b*e*g)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e^2*(2*c*d-b*e)*sqrt(d+e*x))],
[(d+e*x)^(1/2)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,3,-2*(e*f-d*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(3/2))+2*(c*e*f+c*d*g-b*e*g)*sqrt(d+e*x)/(c*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(f+g*x)/((d+e*x)^(1/2)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)),x,4,-(3*c*e*f+c*d*g-2*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(5/2))+(-e*f+d*g)/(e^2*(2*c*d-b*e)*sqrt(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+(3*c*e*f+c*d*g-2*b*e*g)*sqrt(d+e*x)/(e^2*(2*c*d-b*e)^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(f+g*x)/((d+e*x)^(3/2)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)),x,5,-3/4*c*(5*c*e*f+3*c*d*g-4*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(7/2))+1/2*(-e*f+d*g)/(e^2*(2*c*d-b*e)*(d+e*x)^(3/2)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+1/4*(-5*c*e*f-3*c*d*g+4*b*e*g)/(e^2*(2*c*d-b*e)^2*sqrt(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+3/4*c*(5*c*e*f+3*c*d*g-4*b*e*g)*sqrt(d+e*x)/(e^2*(2*c*d-b*e)^3*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(f+g*x)/((d+e*x)^(5/2)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2)),x,6,-5/8*c^2*(7*c*e*f+5*c*d*g-6*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(9/2))+1/3*(-e*f+d*g)/(e^2*(2*c*d-b*e)*(d+e*x)^(5/2)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+1/12*(-7*c*e*f-5*c*d*g+6*b*e*g)/(e^2*(2*c*d-b*e)^2*(d+e*x)^(3/2)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-5/24*c*(7*c*e*f+5*c*d*g-6*b*e*g)/(e^2*(2*c*d-b*e)^3*sqrt(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+5/8*c^2*(7*c*e*f+5*c*d*g-6*b*e*g)*sqrt(d+e*x)/(e^2*(2*c*d-b*e)^4*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(d+e*x)^(13/2)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,6,2/3*(c*e*f+c*d*g-b*e*g)*(d+e*x)^(13/2)/(c*e^2*(2*c*d-b*e)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+128/105*(2*c*d-b*e)^2*(7*c*e*f+13*c*d*g-10*b*e*g)*(d+e*x)^(3/2)/(c^5*e^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+32/105*(2*c*d-b*e)*(7*c*e*f+13*c*d*g-10*b*e*g)*(d+e*x)^(5/2)/(c^4*e^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+16/105*(7*c*e*f+13*c*d*g-10*b*e*g)*(d+e*x)^(7/2)/(c^3*e^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+2/21*(7*c*e*f+13*c*d*g-10*b*e*g)*(d+e*x)^(9/2)/(c^2*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-256/105*(2*c*d-b*e)^3*(7*c*e*f+13*c*d*g-10*b*e*g)*sqrt(d+e*x)/(c^6*e^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(d+e*x)^(11/2)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,5,2/3*(c*e*f+c*d*g-b*e*g)*(d+e*x)^(11/2)/(c*e^2*(2*c*d-b*e)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+16/15*(2*c*d-b*e)*(5*c*e*f+11*c*d*g-8*b*e*g)*(d+e*x)^(3/2)/(c^4*e^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+4/15*(5*c*e*f+11*c*d*g-8*b*e*g)*(d+e*x)^(5/2)/(c^3*e^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+2/15*(5*c*e*f+11*c*d*g-8*b*e*g)*(d+e*x)^(7/2)/(c^2*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-32/15*(2*c*d-b*e)^2*(5*c*e*f+11*c*d*g-8*b*e*g)*sqrt(d+e*x)/(c^5*e^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(d+e*x)^(9/2)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,4,2/3*(c*e*f+c*d*g-b*e*g)*(d+e*x)^(9/2)/(c*e^2*(2*c*d-b*e)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+8/3*(c*e*f+3*c*d*g-2*b*e*g)*(d+e*x)^(3/2)/(c^3*e^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+2/3*(c*e*f+3*c*d*g-2*b*e*g)*(d+e*x)^(5/2)/(c^2*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-16/3*(2*c*d-b*e)*(c*e*f+3*c*d*g-2*b*e*g)*sqrt(d+e*x)/(c^4*e^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(d+e*x)^(7/2)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,3,2/3*(c*e*f+c*d*g-b*e*g)*(d+e*x)^(7/2)/(c*e^2*(2*c*d-b*e)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+2/3*(c*e*f+7*c*d*g-4*b*e*g)*(d+e*x)^(3/2)/(c^2*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-4/3*(c*e*f+7*c*d*g-4*b*e*g)*sqrt(d+e*x)/(c^3*e^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(d+e*x)^(5/2)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,2,2/3*(c*e*f+c*d*g-b*e*g)*(d+e*x)^(5/2)/(c*e^2*(2*c*d-b*e)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+2/3*(c*e*f-5*c*d*g+2*b*e*g)*sqrt(d+e*x)/(c^2*e^2*(2*c*d-b*e)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(d+e*x)^(3/2)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,4,2/3*(c*e*f+c*d*g-b*e*g)*(d+e*x)^(3/2)/(c*e^2*(2*c*d-b*e)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))-2*(e*f-d*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(5/2))+2*(e*f-d*g)*sqrt(d+e*x)/(e^2*(2*c*d-b*e)^2*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(d+e*x)^(1/2)*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,5,-(5*c*e*f-c*d*g-2*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(7/2))+2/3*(c*e*f+c*d*g-b*e*g)*sqrt(d+e*x)/(c*e^2*(2*c*d-b*e)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))+1/3*(-5*c*e*f+c*d*g+2*b*e*g)/(c*e^2*(2*c*d-b*e)^2*sqrt(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+(5*c*e*f-c*d*g-2*b*e*g)*sqrt(d+e*x)/(e^2*(2*c*d-b*e)^3*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(f+g*x)/((d+e*x)^(1/2)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)),x,6,-5/4*c*(7*c*e*f+c*d*g-4*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(9/2))+1/2*(-e*f+d*g)/(e^2*(2*c*d-b*e)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)*sqrt(d+e*x))+1/6*(7*c*e*f+c*d*g-4*b*e*g)*sqrt(d+e*x)/(e^2*(2*c*d-b*e)^2*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))-5/12*(7*c*e*f+c*d*g-4*b*e*g)/(e^2*(2*c*d-b*e)^3*sqrt(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+5/4*c*(7*c*e*f+c*d*g-4*b*e*g)*sqrt(d+e*x)/(e^2*(2*c*d-b*e)^4*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(f+g*x)/((d+e*x)^(3/2)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2)),x,7,1/3*(-e*f+d*g)/(e^2*(2*c*d-b*e)*(d+e*x)^(3/2)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))-35/8*c^2*(3*c*e*f+c*d*g-2*b*e*g)*arctanh(sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(sqrt(2*c*d-b*e)*sqrt(d+e*x)))/(e^2*(2*c*d-b*e)^(11/2))+1/4*(-3*c*e*f-c*d*g+2*b*e*g)/(e^2*(2*c*d-b*e)^2*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)*sqrt(d+e*x))+7/12*c*(3*c*e*f+c*d*g-2*b*e*g)*sqrt(d+e*x)/(e^2*(2*c*d-b*e)^3*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))-35/24*c*(3*c*e*f+c*d*g-2*b*e*g)/(e^2*(2*c*d-b*e)^4*sqrt(d+e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))+35/8*c^2*(3*c*e*f+c*d*g-2*b*e*g)*sqrt(d+e*x)/(e^2*(2*c*d-b*e)^5*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],

# Integrands of the form (d+e x)^m (A+B x) (c d^2-b d e-b e^2 x-c e^2 x^2)^(p/2) when m symbolic
[(d+e*x)^m*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,5,-g*(d+e*x)^m*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(7/2)/(c*e^2*(7+m))+1/7*(2*c*d-b*e)^2*(b*e*g*(7+2*m)-2*c*(d*g*m+e*f*(7+m)))*(d+e*x)^m*(c*(d+e*x)/(2*c*d-b*e))^(-1/2-m)*(c*d-b*e-c*e*x)^3*hypergeom([7/2,-5/2-m],[9/2],(c*d-b*e-c*e*x)/(2*c*d-b*e))*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^4*e^2*(7+m))],
[(d+e*x)^m*(f+g*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,5,-g*(d+e*x)^m*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(5/2)/(c*e^2*(5+m))+1/5*(2*c*d-b*e)*(b*e*g*(5+2*m)-2*c*(d*g*m+e*f*(5+m)))*(d+e*x)^m*(c*(d+e*x)/(2*c*d-b*e))^(-1/2-m)*(c*d-b*e-c*e*x)^2*hypergeom([5/2,-3/2-m],[7/2],(c*d-b*e-c*e*x)/(2*c*d-b*e))*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^3*e^2*(5+m))],
[(d+e*x)^m*(f+g*x)*sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,5,-g*(d+e*x)^m*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2)/(c*e^2*(3+m))+1/3*(b*e*g*(3+2*m)-2*c*(d*g*m+e*f*(3+m)))*(d+e*x)^m*(c*(d+e*x)/(2*c*d-b*e))^(-1/2-m)*(c*d-b*e-c*e*x)*hypergeom([3/2,-1/2-m],[5/2],(c*d-b*e-c*e*x)/(2*c*d-b*e))*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c^2*e^2*(3+m))],
[(d+e*x)^m*(f+g*x)/sqrt(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2),x,5,(b*e*g*(1+2*m)-2*c*(d*g*m+e*f*(1+m)))*(d+e*x)^m*(c*(d+e*x)/(2*c*d-b*e))^(1/2-m)*(c*d-b*e-c*e*x)*hypergeom([1/2,1/2-m],[3/2],(c*d-b*e-c*e*x)/(2*c*d-b*e))/(c^2*e^2*(1+m)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-g*(d+e*x)^m*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)/(c*e^2*(1+m))],
[(d+e*x)^m*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(3/2),x,5,g*(d+e*x)^m/(c*e^2*(1-m)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))-(b*e*g*(1-2*m)-2*c*(e*f*(1-m)-d*g*m))*(d+e*x)^m*(c*(d+e*x)/(2*c*d-b*e))^(1/2-m)*hypergeom([-1/2,3/2-m],[1/2],(c*d-b*e-c*e*x)/(2*c*d-b*e))/(c*e^2*(2*c*d-b*e)*(1-m)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],
[(d+e*x)^m*(f+g*x)/(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^(5/2),x,5,g*(d+e*x)^m/(c*e^2*(3-m)*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(3/2))-1/3*(b*e*g*(3-2*m)-2*c*(e*f*(3-m)-d*g*m))*(d+e*x)^m*(c*(d+e*x)/(2*c*d-b*e))^(1/2-m)*hypergeom([-3/2,5/2-m],[-1/2],(c*d-b*e-c*e*x)/(2*c*d-b*e))/(e^2*(2*c*d-b*e)^2*(3-m)*(c*d-b*e-c*e*x)*sqrt(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2))],

# Integrands of the form (d+e x)^m (A+B x) (c d^2-b d e-b e^2 x-c e^2 x^2)^p when p symbolic
[(d+e*x)^m*(c*d*m-b*e*(1+m+p)-c*e*(2+m+2*p)*x)*(c*d^2-b*d*e-b*e^2*x-c*e^2*x^2)^p,x,1,(d+e*x)^m*(d*(c*d-b*e)-b*e^2*x-c*e^2*x^2)^(1+p)/e],
[(d+e*x)^(-3-2*p)*(f+g*x)*(d*(e*f+d*g+d*g*p)+e*(e*f+3*d*g+2*d*g*p)*x+e^2*g*(2+p)*x^2)^p,x,1,-(d+e*x)^(-3-2*p)*(d*(e*f+d*g*(1+p))+e*(e*f+d*g*(3+2*p))*x+e^2*g*(2+p)*x^2)^(1+p)/(e^2*(2+p))],

# Integrands of the form (d+e x)^m (f+g x) (a+b x+c x^2)^p when c f^2-b f g+a g^2=0
[(d+e*x)^2*(f+g*x)/(c*f^2-b*f*g-b*g^2*x-c*g^2*x^2)^2,x,3,(c*e*f+c*d*g-b*e*g)^2/(c^2*g^3*(2*c*f-b*g)*(c*f-b*g-c*g*x))+(e*f-d*g)^2*log(f+g*x)/(g^3*(2*c*f-b*g)^2)+(3*c*e*f-c*d*g-b*e*g)*(c*e*f+c*d*g-b*e*g)*log(c*f-b*g-c*g*x)/(c^2*g^3*(2*c*f-b*g)^2)],

# Integrands of the form (d+e x)^m (f+g x) (a+b x+c x^2)^p when m=p, b d+a e=0 and c d+b e=0

# Integrands of the form (d+e x)^p (A+B x) (a+b x+c x^2)^p when b d+a e=0 and c d+b e=0
[(1+x)^4*(a+b*x)*(1-x+x^2)^4,x,2,a*x+1/2*b*x^2+a*x^4+4/5*b*x^5+6/7*a*x^7+3/4*b*x^8+2/5*a*x^10+4/11*b*x^11+1/13*a*x^13+1/14*b*x^14],
[(1+x)^3*(a+b*x)*(1-x+x^2)^3,x,2,a*x+1/2*b*x^2+3/4*a*x^4+3/5*b*x^5+3/7*a*x^7+3/8*b*x^8+1/10*a*x^10+1/11*b*x^11],
[(1+x)^2*(a+b*x)*(1-x+x^2)^2,x,2,a*x+1/2*b*x^2+1/2*a*x^4+2/5*b*x^5+1/7*a*x^7+1/8*b*x^8],
[(1+x)*(a+b*x)*(1-x+x^2),x,2,a*x+1/2*b*x^2+1/4*a*x^4+1/5*b*x^5],
[(a+b*x)/((1+x)*(1-x+x^2)),x,6,1/3*(a-b)*log(1+x)-1/6*(a-b)*log(1-x+x^2)-(a+b)*arctan((1-2*x)/sqrt(3))/sqrt(3)],
[(a+b*x)/((1+x)^2*(1-x+x^2)^2),x,8,1/3*x*(a+b*x)/(1+x^3)+1/9*(2*a-b)*log(1+x)-1/18*(2*a-b)*log(1-x+x^2)-1/3*(2*a+b)*arctan((1-2*x)/sqrt(3))/sqrt(3)],
[(a+b*x)/((1+x)^3*(1-x+x^2)^3),x,9,1/6*x*(a+b*x)/(1+x^3)^2+1/18*x*(5*a+4*b*x)/(1+x^3)+1/27*(5*a-2*b)*log(1+x)-1/54*(5*a-2*b)*log(1-x+x^2)-1/9*(5*a+2*b)*arctan((1-2*x)/sqrt(3))/sqrt(3)],

# Integrands of the form (d+e x)^(p/2) (A+B x) (a+b x+c x^2)^(p/2) when b d+a e=0 and c d+b e=0
[(1+x)^(3/2)*(a+b*x)*(1-x+x^2)^(3/2),x,6,18/5005*(91*a*x+55*b*x^2)*sqrt(1+x)*sqrt(1-x+x^2)+2/143*(13*a*x+11*b*x^2)*(1+x^3)*sqrt(1+x)*sqrt(1-x+x^2)+54/91*b*sqrt(1+x)*sqrt(1-x+x^2)/(1+x+sqrt(3))-27/91*3^(1/4)*b*(1+x)^(3/2)*EllipticE((1+x-sqrt(3))/(1+x+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt(1-x+x^2)*sqrt(2-sqrt(3))*sqrt((1-x+x^2)/(1+x+sqrt(3))^2)/((1+x^3)*sqrt((1+x)/(1+x+sqrt(3))^2))+18/5005*3^(3/4)*(1+x)^(3/2)*EllipticF((1+x-sqrt(3))/(1+x+sqrt(3)),sqrt(-7-4*sqrt(3)))*(91*a-55*b*(1-sqrt(3)))*sqrt(1-x+x^2)*sqrt(2+sqrt(3))*sqrt((1-x+x^2)/(1+x+sqrt(3))^2)/((1+x^3)*sqrt((1+x)/(1+x+sqrt(3))^2))],
[(1+x)^(1/2)*(a+b*x)*(1-x+x^2)^(1/2),x,5,2/35*(7*a*x+5*b*x^2)*sqrt(1+x)*sqrt(1-x+x^2)+6/7*b*sqrt(1+x)*sqrt(1-x+x^2)/(1+x+sqrt(3))-3/7*3^(1/4)*b*(1+x)^(3/2)*EllipticE((1+x-sqrt(3))/(1+x+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt(1-x+x^2)*sqrt(2-sqrt(3))*sqrt((1-x+x^2)/(1+x+sqrt(3))^2)/((1+x^3)*sqrt((1+x)/(1+x+sqrt(3))^2))+2/35*3^(3/4)*(1+x)^(3/2)*EllipticF((1+x-sqrt(3))/(1+x+sqrt(3)),sqrt(-7-4*sqrt(3)))*(7*a-5*b*(1-sqrt(3)))*sqrt(1-x+x^2)*sqrt(2+sqrt(3))*sqrt((1-x+x^2)/(1+x+sqrt(3))^2)/((1+x^3)*sqrt((1+x)/(1+x+sqrt(3))^2))],
[(a+b*x)/((1+x)^(1/2)*(1-x+x^2)^(1/2)),x,4,2*b*(1+x^3)/((1+x+sqrt(3))*sqrt(1+x)*sqrt(1-x+x^2))-3^(1/4)*b*EllipticE((1+x-sqrt(3))/(1+x+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt(1+x)*sqrt(2-sqrt(3))*sqrt((1-x+x^2)/(1+x+sqrt(3))^2)/(sqrt(1-x+x^2)*sqrt((1+x)/(1+x+sqrt(3))^2))+2*EllipticF((1+x-sqrt(3))/(1+x+sqrt(3)),sqrt(-7-4*sqrt(3)))*(a-b*(1-sqrt(3)))*sqrt(1+x)*sqrt(2+sqrt(3))*sqrt((1-x+x^2)/(1+x+sqrt(3))^2)/(3^(1/4)*sqrt(1-x+x^2)*sqrt((1+x)/(1+x+sqrt(3))^2))],
[(a+b*x)/((1+x)^(3/2)*(1-x+x^2)^(3/2)),x,5,2/3*x*(a+b*x)/(sqrt(1+x)*sqrt(1-x+x^2))-2/3*b*(1+x^3)/((1+x+sqrt(3))*sqrt(1+x)*sqrt(1-x+x^2))+b*EllipticE((1+x-sqrt(3))/(1+x+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt(1+x)*sqrt(2-sqrt(3))*sqrt((1-x+x^2)/(1+x+sqrt(3))^2)/(3^(3/4)*sqrt(1-x+x^2)*sqrt((1+x)/(1+x+sqrt(3))^2))+2/3*EllipticF((1+x-sqrt(3))/(1+x+sqrt(3)),sqrt(-7-4*sqrt(3)))*(a+b-b*sqrt(3))*sqrt(1+x)*sqrt(2+sqrt(3))*sqrt((1-x+x^2)/(1+x+sqrt(3))^2)/(3^(1/4)*sqrt(1-x+x^2)*sqrt((1+x)/(1+x+sqrt(3))^2))],
[(a+b*x)/((1+x)^(5/2)*(1-x+x^2)^(5/2)),x,6,2/27*x*(7*a+5*b*x)/(sqrt(1+x)*sqrt(1-x+x^2))+2/9*x*(a+b*x)/((1+x^3)*sqrt(1+x)*sqrt(1-x+x^2))-10/27*b*(1+x^3)/((1+x+sqrt(3))*sqrt(1+x)*sqrt(1-x+x^2))+5/9*b*EllipticE((1+x-sqrt(3))/(1+x+sqrt(3)),sqrt(-7-4*sqrt(3)))*sqrt(1+x)*sqrt(2-sqrt(3))*sqrt((1-x+x^2)/(1+x+sqrt(3))^2)/(3^(3/4)*sqrt(1-x+x^2)*sqrt((1+x)/(1+x+sqrt(3))^2))+2/27*EllipticF((1+x-sqrt(3))/(1+x+sqrt(3)),sqrt(-7-4*sqrt(3)))*(7*a+5*b*(1-sqrt(3)))*sqrt(1+x)*sqrt(2+sqrt(3))*sqrt((1-x+x^2)/(1+x+sqrt(3))^2)/(3^(1/4)*sqrt(1-x+x^2)*sqrt((1+x)/(1+x+sqrt(3))^2))],

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

# Integrands of the form (d+e x)^m (A+B x) (a+b x+c x^2)^p

# p>0
[(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2),x,2,-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4-1/6*(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^6/e^4-1/7*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^7/e^4+1/8*B*c*(d+e*x)^8/e^4],
[(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2),x,2,-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^4/e^4-1/5*(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^5/e^4-1/6*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^6/e^4+1/7*B*c*(d+e*x)^7/e^4],
[(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2),x,2,-1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^3/e^4-1/4*(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^4/e^4-1/5*(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^5/e^4+1/6*B*c*(d+e*x)^6/e^4],
[(A+B*x)*(d+e*x)*(a+b*x+c*x^2),x,2,a*A*d*x+1/2*(A*b*d+a*B*d+a*A*e)*x^2+1/3*(b*B*d+A*c*d+A*b*e+a*B*e)*x^3+1/4*(B*c*d+b*B*e+A*c*e)*x^4+1/5*B*c*e*x^5],
[(A+B*x)*(a+b*x+c*x^2),x,2,a*A*x+1/2*(A*b+a*B)*x^2+1/3*(b*B+A*c)*x^3+1/4*B*c*x^4],
[(A+B*x)*(a+b*x+c*x^2)/(d+e*x),x,2,-(A*e*(c*d-b*e)-B*(c*d^2-e*(b*d-a*e)))*x/e^3-1/2*(B*c*d-b*B*e-A*c*e)*x^2/e^2+1/3*B*c*x^3/e-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4],
[(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^2,x,2,-(2*B*c*d-b*B*e-A*c*e)*x/e^3+1/2*B*c*x^2/e^2+(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x))-(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))*log(d+e*x)/e^4],
[(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^3,x,2,B*c*x/e^3+1/2*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x))-(3*B*c*d-b*B*e-A*c*e)*log(d+e*x)/e^4],
[(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^4,x,2,1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+1/2*(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^2)+(3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x))+B*c*log(d+e*x)/e^4],
[(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^5,x,2,1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+1/3*(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^3)+1/2*(3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x)^2)-B*c/(e^4*(d+e*x))],
[(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^6,x,2,1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^5)+1/4*(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^4)+1/3*(3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x)^3)-1/2*B*c/(e^4*(d+e*x)^2)],
[(A+B*x)*(a+b*x+c*x^2)/(d+e*x)^7,x,2,1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^6)+1/5*(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))/(e^4*(d+e*x)^5)+1/4*(3*B*c*d-b*B*e-A*c*e)/(e^4*(d+e*x)^4)-1/3*B*c/(e^4*(d+e*x)^3)],
[(A+B*x)*(d+e*x)^5*(a+b*x+c*x^2)^2,x,2,-1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^6/e^6-1/7*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*(d+e*x)^7/e^6-1/8*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^8/e^6-1/9*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*(d+e*x)^9/e^6-1/10*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^10/e^6+1/11*B*c^2*(d+e*x)^11/e^6],
[(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2)^2,x,2,-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^5/e^6-1/6*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*(d+e*x)^6/e^6-1/7*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^7/e^6-1/8*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*(d+e*x)^8/e^6-1/9*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^9/e^6+1/10*B*c^2*(d+e*x)^10/e^6],
[(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2)^2,x,2,-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^4/e^6-1/5*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*(d+e*x)^5/e^6-1/6*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^6/e^6-1/7*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*(d+e*x)^7/e^6-1/8*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^8/e^6+1/9*B*c^2*(d+e*x)^9/e^6],
[(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2)^2,x,2,-1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^3/e^6-1/4*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*(d+e*x)^4/e^6-1/5*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^5/e^6-1/6*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*(d+e*x)^6/e^6-1/7*c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^7/e^6+1/8*B*c^2*(d+e*x)^8/e^6],
[(A+B*x)*(d+e*x)*(a+b*x+c*x^2)^2,x,2,a^2*A*d*x+1/2*a*(2*A*b*d+a*B*d+a*A*e)*x^2+1/3*(a*B*(2*b*d+a*e)+A*(b^2*d+2*a*c*d+2*a*b*e))*x^3+1/4*(b^2*(B*d+A*e)+2*a*c*(B*d+A*e)+2*b*(A*c*d+a*B*e))*x^4+1/5*(b^2*B*e+2*b*c*(B*d+A*e)+c*(A*c*d+2*a*B*e))*x^5+1/6*c*(B*c*d+2*b*B*e+A*c*e)*x^6+1/7*B*c^2*e*x^7],
[(A+B*x)*(a+b*x+c*x^2)^2,x,2,a^2*A*x+1/2*a*(2*A*b+a*B)*x^2+1/3*(2*a*b*B+A*(b^2+2*a*c))*x^3+1/4*(b^2*B+2*A*b*c+2*a*B*c)*x^4+1/5*c*(2*b*B+A*c)*x^5+1/6*B*c^2*x^6],
[(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x),x,2,-(A*e*(c*d-b*e)*(c*d^2-e*(b*d-2*a*e))-B*(c*d^2-e*(b*d-a*e))^2)*x/e^5-1/2*(B*(c*d-b*e)*(c*d^2-e*(b*d-2*a*e))-A*e*(c^2*d^2+b^2*e^2-2*c*e*(b*d-a*e)))*x^2/e^4-1/3*(A*c*e*(c*d-2*b*e)-B*(c^2*d^2+b^2*e^2-2*c*e*(b*d-a*e)))*x^3/e^3-1/4*c*(B*c*d-2*b*B*e-A*c*e)*x^4/e^2+1/5*B*c^2*x^5/e-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*log(d+e*x)/e^6],
[(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^2,x,2,-(2*B*(2*c*d-b*e)*(c*d^2-e*(b*d-a*e))-A*e*(3*c^2*d^2+b^2*e^2-2*c*e*(2*b*d-a*e)))*x/e^5-1/2*(2*A*c*e*(c*d-b*e)-B*(3*c^2*d^2+b^2*e^2-2*c*e*(2*b*d-a*e)))*x^2/e^4-1/3*c*(2*B*c*d-2*b*B*e-A*c*e)*x^3/e^3+1/4*B*c^2*x^4/e^2+(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x))-(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*log(d+e*x)/e^6],
[(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^3,x,2,-(A*c*e*(3*c*d-2*b*e)-B*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*x/e^5-1/2*c*(3*B*c*d-2*b*B*e-A*c*e)*x^2/e^4+1/3*B*c^2*x^3/e^3+1/2*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^2)+(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x))-(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*log(d+e*x)/e^6],
[(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^4,x,2,-c*(4*B*c*d-2*b*B*e-A*c*e)*x/e^5+1/2*B*c^2*x^2/e^4+1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^3)+1/2*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^2)+(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x))-(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*log(d+e*x)/e^6],
[(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^5,x,2,B*c^2*x/e^5+1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^4)+1/3*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^3)+1/2*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^2)+(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/(e^6*(d+e*x))-c*(5*B*c*d-2*b*B*e-A*c*e)*log(d+e*x)/e^6],
[(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^6,x,2,1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^5)+1/4*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^4)+1/3*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^3)+1/2*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/(e^6*(d+e*x)^2)+c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x))+B*c^2*log(d+e*x)/e^6],
[(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^7,x,2,1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^6)+1/5*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^5)+1/4*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^4)+1/3*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/(e^6*(d+e*x)^3)+1/2*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^2)-B*c^2/(e^6*(d+e*x))],
[(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^8,x,2,1/7*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^7)+1/6*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^6)+1/5*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^5)+1/4*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/(e^6*(d+e*x)^4)+1/3*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^3)-1/2*B*c^2/(e^6*(d+e*x)^2)],
[(A+B*x)*(a+b*x+c*x^2)^2/(d+e*x)^9,x,2,1/8*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2/(e^6*(d+e*x)^8)+1/7*(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))/(e^6*(d+e*x)^7)+1/6*(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))/(e^6*(d+e*x)^6)+1/5*(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))/(e^6*(d+e*x)^5)+1/4*c*(5*B*c*d-2*b*B*e-A*c*e)/(e^6*(d+e*x)^4)-1/3*B*c^2/(e^6*(d+e*x)^3)],
[(A+B*x)*(d+e*x)^5*(a+b*x+c*x^2)^3,x,2,-1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^6/e^8-1/7*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*(d+e*x)^7/e^8-3/8*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^8/e^8-1/9*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^9/e^8-1/10*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^10/e^8-3/11*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^11/e^8-1/12*c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^12/e^8+1/13*B*c^3*(d+e*x)^13/e^8],
[(A+B*x)*(d+e*x)^4*(a+b*x+c*x^2)^3,x,2,-1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^5/e^8-1/6*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*(d+e*x)^6/e^8-3/7*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^7/e^8-1/8*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^8/e^8-1/9*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^9/e^8-3/10*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^10/e^8-1/11*c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^11/e^8+1/12*B*c^3*(d+e*x)^12/e^8],
[(A+B*x)*(d+e*x)^3*(a+b*x+c*x^2)^3,x,2,-1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^4/e^8-1/5*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*(d+e*x)^5/e^8-1/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^6/e^8-1/7*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^7/e^8-1/8*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^8/e^8-1/3*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^9/e^8-1/10*c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^10/e^8+1/11*B*c^3*(d+e*x)^11/e^8],
[(A+B*x)*(d+e*x)^2*(a+b*x+c*x^2)^3,x,2,-1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^3/e^8-1/4*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*(d+e*x)^4/e^8-3/5*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^5/e^8-1/6*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^6/e^8-1/7*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^7/e^8-3/8*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^8/e^8-1/9*c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^9/e^8+1/10*B*c^3*(d+e*x)^10/e^8],
[(A+B*x)*(d+e*x)*(a+b*x+c*x^2)^3,x,2,a^3*A*d*x+1/2*a^2*(3*A*b*d+a*B*d+a*A*e)*x^2+1/3*a*(a*B*(3*b*d+a*e)+3*A*(b^2*d+a*c*d+a*b*e))*x^3+1/4*(3*a*B*(b^2*d+a*c*d+a*b*e)+A*(b^3*d+6*a*b*c*d+3*a*b^2*e+3*a^2*c*e))*x^4+1/5*(b^3*(B*d+A*e)+6*a*b*c*(B*d+A*e)+3*b^2*(A*c*d+a*B*e)+3*a*c*(A*c*d+a*B*e))*x^5+1/6*(b^3*B*e+3*b^2*c*(B*d+A*e)+3*a*c^2*(B*d+A*e)+3*b*c*(A*c*d+2*a*B*e))*x^6+1/7*c*(3*b^2*B*e+3*b*c*(B*d+A*e)+c*(A*c*d+3*a*B*e))*x^7+1/8*c^2*(B*c*d+3*b*B*e+A*c*e)*x^8+1/9*B*c^3*e*x^9],
[(A+B*x)*(a+b*x+c*x^2)^3,x,2,a^3*A*x+1/2*a^2*(3*A*b+a*B)*x^2+a*(a*b*B+A*(b^2+a*c))*x^3+1/4*(3*a*B*(b^2+a*c)+A*(b^3+6*a*b*c))*x^4+1/5*(b^3*B+3*A*b^2*c+6*a*b*B*c+3*a*A*c^2)*x^5+1/2*c*(b^2*B+A*b*c+a*B*c)*x^6+1/7*c^2*(3*b*B+A*c)*x^7+1/8*B*c^3*x^8],
[(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x),x,2,-(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*x/e^7-3/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^2/e^8-1/3*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^3/e^8-1/4*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^4/e^8-3/5*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^5/e^8-1/6*c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^6/e^8+1/7*B*c^3*(d+e*x)^7/e^8-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*log(d+e*x)/e^8],
[(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^2,x,2,-(3*B*(2*c*d-b*e)*(c*d^2-e*(b*d-a*e))^2-A*e*(5*c^3*d^4-b^2*e^3*(2*b*d-3*a*e)-3*c^2*d^2*e*(4*b*d-3*a*e)+3*c*e^2*(3*b^2*d^2-4*a*b*d*e+a^2*e^2)))*x/e^7-1/2*(A*e*(c*d-b*e)*(4*c^2*d^2+b^2*e^2-c*e*(5*b*d-6*a*e))-B*(5*c^3*d^4-b^2*e^3*(2*b*d-3*a*e)-3*c^2*d^2*e*(4*b*d-3*a*e)+3*c*e^2*(3*b^2*d^2-4*a*b*d*e+a^2*e^2)))*x^2/e^6-1/3*(B*(c*d-b*e)*(4*c^2*d^2+b^2*e^2-c*e*(5*b*d-6*a*e))-3*A*c*e*(c^2*d^2+b^2*e^2-c*e*(2*b*d-a*e)))*x^3/e^5-1/4*c*(A*c*e*(2*c*d-3*b*e)-3*B*(c^2*d^2+b^2*e^2-c*e*(2*b*d-a*e)))*x^4/e^4-1/5*c^2*(2*B*c*d-3*b*B*e-A*c*e)*x^5/e^3+1/6*B*c^3*x^6/e^2+(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x))-(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*log(d+e*x)/e^8],
[(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^3,x,2,-(A*e*(10*c^3*d^3-b^3*e^3+3*b*c*e^2*(3*b*d-2*a*e)-9*c^2*d*e*(2*b*d-a*e))-3*B*(5*c^3*d^4-2*c^2*d^2*e*(5*b*d-3*a*e)-b^2*e^3*(b*d-a*e)+c*e^2*(6*b^2*d^2-6*a*b*d*e+a^2*e^2)))*x/e^7-1/2*(B*(10*c^3*d^3-b^3*e^3+3*b*c*e^2*(3*b*d-2*a*e)-9*c^2*d*e*(2*b*d-a*e))-3*A*c*e*(2*c^2*d^2+b^2*e^2-c*e*(3*b*d-a*e)))*x^2/e^6-c*(A*c*e*(c*d-b*e)-B*(2*c^2*d^2+b^2*e^2-c*e*(3*b*d-a*e)))*x^3/e^5-1/4*c^2*(3*B*c*d-3*b*B*e-A*c*e)*x^4/e^4+1/5*B*c^3*x^5/e^3+1/2*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^2)+(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x))-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*log(d+e*x)/e^8],
[(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^4,x,2,-(B*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-A*c*e*(10*c^2*d^2+3*b^2*e^2-3*c*e*(4*b*d-a*e)))*x/e^7-1/2*c*(A*c*e*(4*c*d-3*b*e)-B*(10*c^2*d^2+3*b^2*e^2-3*c*e*(4*b*d-a*e)))*x^2/e^6-1/3*c^2*(4*B*c*d-3*b*B*e-A*c*e)*x^3/e^5+1/4*B*c^3*x^4/e^4+1/3*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^3)+1/2*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^2)+3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x))-(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*log(d+e*x)/e^8],
[(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^5,x,2,-c*(A*c*e*(5*c*d-3*b*e)-3*B*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*x/e^7-1/2*c^2*(5*B*c*d-3*b*B*e-A*c*e)*x^2/e^6+1/3*B*c^3*x^3/e^5+1/4*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^4)+1/3*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^3)+3/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^2)+(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x))-(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*log(d+e*x)/e^8],
[(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^6,x,2,-c^2*(6*B*c*d-3*b*B*e-A*c*e)*x/e^7+1/2*B*c^3*x^2/e^6+1/5*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^5)+1/4*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^4)+(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^3)+1/2*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^2)+(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x))-3*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*log(d+e*x)/e^8],
[(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^7,x,2,B*c^3*x/e^7+1/6*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^6)+1/5*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^5)+3/4*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^4)+1/3*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^3)+1/2*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^2)+3*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))/(e^8*(d+e*x))-c^2*(7*B*c*d-3*b*B*e-A*c*e)*log(d+e*x)/e^8],
[(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^8,x,2,1/7*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^7)+1/6*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^6)+3/5*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^5)+1/4*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^4)+1/3*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^3)+3/2*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))/(e^8*(d+e*x)^2)+c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*(d+e*x))+B*c^3*log(d+e*x)/e^8],
[(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^9,x,2,1/8*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^8)+1/7*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^7)+1/2*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^6)+1/5*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^5)+1/4*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^4)+c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))/(e^8*(d+e*x)^3)+1/2*c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*(d+e*x)^2)-B*c^3/(e^8*(d+e*x))],
[(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^10,x,2,1/9*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^9)+1/8*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^8)+3/7*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^7)+1/6*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^6)+1/5*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^5)+3/4*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))/(e^8*(d+e*x)^4)+1/3*c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*(d+e*x)^3)-1/2*B*c^3/(e^8*(d+e*x)^2)],
[(A+B*x)*(a+b*x+c*x^2)^3/(d+e*x)^11,x,2,1/10*(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3/(e^8*(d+e*x)^10)+1/9*(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))/(e^8*(d+e*x)^9)+3/8*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^8)+1/7*(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))/(e^8*(d+e*x)^7)+1/6*(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))/(e^8*(d+e*x)^6)+3/5*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))/(e^8*(d+e*x)^5)+1/4*c^2*(7*B*c*d-3*b*B*e-A*c*e)/(e^8*(d+e*x)^4)-1/3*B*c^3/(e^8*(d+e*x)^3)],
[x*(d+e*x)^m*(a+b*x+c*x^2),x,2,-d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))+(3*c*d^2-e*(2*b*d-a*e))*(d+e*x)^(2+m)/(e^4*(2+m))-(3*c*d-b*e)*(d+e*x)^(3+m)/(e^4*(3+m))+c*(d+e*x)^(4+m)/(e^4*(4+m))],
[x*(d+e*x)^5*(a+b*x+c*x^2),x,2,-1/6*d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^6/e^4+1/7*(3*c*d^2-e*(2*b*d-a*e))*(d+e*x)^7/e^4-1/8*(3*c*d-b*e)*(d+e*x)^8/e^4+1/9*c*(d+e*x)^9/e^4],
[x*(d+e*x)^4*(a+b*x+c*x^2),x,2,-1/5*d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^5/e^4+1/6*(3*c*d^2-e*(2*b*d-a*e))*(d+e*x)^6/e^4-1/7*(3*c*d-b*e)*(d+e*x)^7/e^4+1/8*c*(d+e*x)^8/e^4],
[x*(d+e*x)^3*(a+b*x+c*x^2),x,2,-1/4*d*(c*d^2-b*d*e+a*e^2)*(d+e*x)^4/e^4+1/5*(3*c*d^2-e*(2*b*d-a*e))*(d+e*x)^5/e^4-1/6*(3*c*d-b*e)*(d+e*x)^6/e^4+1/7*c*(d+e*x)^7/e^4],
[x*(d+e*x)^2*(a+b*x+c*x^2),x,2,1/2*a*d^2*x^2+1/3*d*(b*d+2*a*e)*x^3+1/4*(c*d^2+e*(2*b*d+a*e))*x^4+1/5*e*(2*c*d+b*e)*x^5+1/6*c*e^2*x^6],
[x*(d+e*x)*(a+b*x+c*x^2),x,2,1/2*a*d*x^2+1/3*(b*d+a*e)*x^3+1/4*(c*d+b*e)*x^4+1/5*c*e*x^5],
[x*(a+b*x+c*x^2),x,2,1/2*a*x^2+1/3*b*x^3+1/4*c*x^4],
[x*(a+b*x+c*x^2)/(d+e*x),x,2,(c*d^2-b*d*e+a*e^2)*x/e^3-1/2*(c*d-b*e)*x^2/e^2+1/3*c*x^3/e-d*(c*d^2-b*d*e+a*e^2)*log(d+e*x)/e^4],
[x*(a+b*x+c*x^2)/(d+e*x)^2,x,2,-(2*c*d-b*e)*x/e^3+1/2*c*x^2/e^2+d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x))+(3*c*d^2-e*(2*b*d-a*e))*log(d+e*x)/e^4],
[x*(a+b*x+c*x^2)/(d+e*x)^3,x,2,c*x/e^3+1/2*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^2)+(-3*c*d^2+e*(2*b*d-a*e))/(e^4*(d+e*x))-(3*c*d-b*e)*log(d+e*x)/e^4],
[x*(a+b*x+c*x^2)/(d+e*x)^4,x,2,1/3*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^3)+1/2*(-3*c*d^2+e*(2*b*d-a*e))/(e^4*(d+e*x)^2)+(3*c*d-b*e)/(e^4*(d+e*x))+c*log(d+e*x)/e^4],
[x*(a+b*x+c*x^2)/(d+e*x)^5,x,2,1/4*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^4)+1/3*(-3*c*d^2+e*(2*b*d-a*e))/(e^4*(d+e*x)^3)+1/2*(3*c*d-b*e)/(e^4*(d+e*x)^2)-c/(e^4*(d+e*x))],
[x*(a+b*x+c*x^2)/(d+e*x)^6,x,2,1/5*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^5)+1/4*(-3*c*d^2+e*(2*b*d-a*e))/(e^4*(d+e*x)^4)+1/3*(3*c*d-b*e)/(e^4*(d+e*x)^3)-1/2*c/(e^4*(d+e*x)^2)],
[x*(a+b*x+c*x^2)/(d+e*x)^7,x,2,1/6*d*(c*d^2-b*d*e+a*e^2)/(e^4*(d+e*x)^6)+1/5*(-3*c*d^2+e*(2*b*d-a*e))/(e^4*(d+e*x)^5)+1/4*(3*c*d-b*e)/(e^4*(d+e*x)^4)-1/3*c/(e^4*(d+e*x)^3)],

# p<0
[(A+B*x)*(d+e*x)^3/(a+b*x+c*x^2),x,6,e*(A*c*e*(3*c*d-b*e)+B*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e)))*x/c^3+1/2*e^2*(3*B*c*d-b*B*e+A*c*e)*x^2/c^2+1/3*B*e^3*x^3/c+1/2*(A*c*e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e))+B*(c^3*d^3-b^3*e^3-3*c^2*d*e*(b*d+a*e)+b*c*e^2*(3*b*d+2*a*e)))*log(a+b*x+c*x^2)/c^4-(b^4*B*e^3-b^3*c*e^2*(3*B*d+A*e)+b^2*c*e*(3*B*c*d^2+3*A*c*d*e-4*a*B*e^2)-b*c^2*(B*c*d^3+3*A*c*d^2*e-9*a*B*d*e^2-3*a*A*e^3)+2*c^2*(A*c*d*(c*d^2-3*a*e^2)-a*B*e*(3*c*d^2-a*e^2)))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^4*sqrt(b^2-4*a*c))],
[(A+B*x)*(d+e*x)^2/(a+b*x+c*x^2),x,6,e*(2*B*c*d-b*B*e+A*c*e)*x/c^2+1/2*B*e^2*x^2/c+1/2*(A*c*e*(2*c*d-b*e)+B*(c^2*d^2+b^2*e^2-c*e*(2*b*d+a*e)))*log(a+b*x+c*x^2)/c^3+(b^3*B*e^2-b^2*c*e*(2*B*d+A*e)-2*c^2*(A*c*d^2-2*a*B*d*e-a*A*e^2)+b*c*(B*c*d^2+2*A*c*d*e-3*a*B*e^2))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*sqrt(b^2-4*a*c))],
[(A+B*x)*(d+e*x)/(a+b*x+c*x^2),x,5,B*e*x/c+1/2*(B*c*d-b*B*e+A*c*e)*log(a+b*x+c*x^2)/c^2-(b^2*B*e-b*c*(B*d+A*e)+2*c*(A*c*d-a*B*e))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^2*sqrt(b^2-4*a*c))],
[(A+B*x)/(a+b*x+c*x^2),x,4,1/2*B*log(a+b*x+c*x^2)/c+(b*B-2*A*c)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c*sqrt(b^2-4*a*c))],
[(A+B*x)/((d+e*x)*(a+b*x+c*x^2)),x,6,-(B*d-A*e)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)+1/2*(B*d-A*e)*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)+(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)*sqrt(b^2-4*a*c))],
[(A+B*x)/((d+e*x)^2*(a+b*x+c*x^2)),x,6,(B*d-A*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x))+(A*e*(2*c*d-b*e)-B*(c*d^2-a*e^2))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^2-1/2*(A*e*(2*c*d-b*e)-B*(c*d^2-a*e^2))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^2-(A*b^2*e^2+2*c*(A*c*d^2+2*a*B*d*e-a*A*e^2)-b*(B*c*d^2+2*A*c*d*e+a*B*e^2))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c))],
[(A+B*x)/((d+e*x)^3*(a+b*x+c*x^2)),x,6,1/2*(B*d-A*e)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)+(-A*e*(2*c*d-b*e)+B*(c*d^2-a*e^2))/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))-(B*(c^2*d^3-3*a*c*d*e^2+a*b*e^3)-A*e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e)))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3+1/2*(B*(c^2*d^3-3*a*c*d*e^2+a*b*e^3)-A*e*(3*c^2*d^2+b^2*e^2-c*e*(3*b*d+a*e)))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^3+(A*b^3*e^3-b^2*e^2*(3*A*c*d+a*B*e)+b*c*(B*c*d^3+3*A*c*d^2*e+3*a*B*d*e^2-3*a*A*e^3)-2*c*(A*c*d*(c*d^2-3*a*e^2)+a*B*e*(3*c*d^2-a*e^2)))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^3*sqrt(b^2-4*a*c))],
[(d+e*x)^4*(f+g*x)/(a+b*x+c*x^2)^3,x,6,1/2*(d+e*x)^3*(2*a*c*(e*f+d*g)-b*(c*d*f+a*e*g)-(2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^2)+1/2*(d+e*x)*(b^3*e*(c*d^2-2*a*e^2)*g-b^2*c*d*(a*e^2*g+3*c*d*(2*e*f+d*g))+2*b*c*(3*c^2*d^3*f+7*a^2*e^3*g+a*c*d*e*(9*e*f+7*d*g))-4*a*c^2*e*(3*c*d^2*f+a*e*(3*e*f+8*d*g))+(12*c^4*d^3*f-2*b^4*e^3*g+b^2*c*e^2*(b*d+15*a*e)*g-2*c^3*d*(3*b*d*(3*e*f+d*g)-2*a*e*(3*e*f+4*d*g))-c^2*e*(16*a^2*e^2*g-b^2*d*(6*e*f+5*d*g)+2*a*b*e*(3*e*f+11*d*g)))*x)/(c^2*(b^2-4*a*c)^2*(a+b*x+c*x^2))-(12*c^5*d^4*f-b^5*e^4*g+10*a*b^3*c*e^4*g-30*a^2*b*c^2*e^4*g-2*c^4*d^2*(3*b*d*(4*e*f+d*g)-4*a*e*(3*e*f+2*d*g))+4*c^3*e*(b^2*d^2*(3*e*f+2*d*g)-3*a*b*d*e*(2*e*f+3*d*g)+3*a^2*e^2*(e*f+4*d*g)))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(c^3*(b^2-4*a*c)^(5/2))+1/2*e^4*g*log(a+b*x+c*x^2)/c^3],
[(d+e*x)^3*(f+g*x)/(a+b*x+c*x^2)^3,x,4,-1/2*(d+e*x)^3*(b*f-2*a*g+(2*c*f-b*g)*x)/((b^2-4*a*c)*(a+b*x+c*x^2)^2)+3/2*(2*c*d*f-b*e*f-b*d*g+2*a*e*g)*(d+e*x)*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)^2*(a+b*x+c*x^2))-6*(c*d^2-b*d*e+a*e^2)*(2*c*d*f-b*e*f-b*d*g+2*a*e*g)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(b^2-4*a*c)^(5/2)],
[(d+e*x)^2*(f+g*x)/(a+b*x+c*x^2)^3,x,4,-1/2*(d+e*x)^2*(b*f-2*a*g+(2*c*f-b*g)*x)/((b^2-4*a*c)*(a+b*x+c*x^2)^2)+1/2*(-8*a*c*e*(2*c*d*f+a*e*g)+6*b*c*(c*d^2*f+a*e*(e*f+2*d*g))-b^2*(a*e^2*g+c*d*(2*e*f+3*d*g))+(12*c^3*d^2*f-b^3*e^2*g-2*b*c*e*(a*e*g-2*b*(e*f+d*g))-2*c^2*(2*a*e*(e*f-2*d*g)+3*b*d*(2*e*f+d*g)))*x)/(c*(b^2-4*a*c)^2*(a+b*x+c*x^2))-2*(6*c^2*d^2*f+b*e*(b*e*f+2*b*d*g-3*a*e*g)-c*(3*b*d*(2*e*f+d*g)-2*a*e*(e*f+2*d*g)))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(b^2-4*a*c)^(5/2)],
[(d+e*x)*(f+g*x)/(a+b*x+c*x^2)^3,x,4,1/2*(2*a*c*(e*f+d*g)-b*(c*d*f+a*e*g)-(2*c^2*d*f+b^2*e*g-c*(b*e*f+b*d*g+2*a*e*g))*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^2)+1/2*(6*c^2*d*f+b^2*e*g+c*(2*a*e*g-3*b*(e*f+d*g)))*(b+2*c*x)/(c*(b^2-4*a*c)^2*(a+b*x+c*x^2))-2*(6*c^2*d*f+b^2*e*g+c*(2*a*e*g-3*b*(e*f+d*g)))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(b^2-4*a*c)^(5/2)],
[(f+g*x)/(a+b*x+c*x^2)^3,x,4,1/2*(-b*f+2*a*g-(2*c*f-b*g)*x)/((b^2-4*a*c)*(a+b*x+c*x^2)^2)+3/2*(2*c*f-b*g)*(b+2*c*x)/((b^2-4*a*c)^2*(a+b*x+c*x^2))-6*c*(2*c*f-b*g)*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/(b^2-4*a*c)^(5/2)],
[(f+g*x)/((d+e*x)*(a+b*x+c*x^2)^3),x,8,1/2*(-b*c*d*f+b^2*e*f-2*a*c*e*f+2*a*c*d*g-a*b*e*g-c*(2*c*d*f+2*a*e*g-b*(e*f+d*g))*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^2)+1/2*(-3*a*c*e*(2*c*d-b*e)*(2*c*d*f+2*a*e*g-b*(e*f+d*g))+(b*c*d-b^2*e+2*a*c*e)*(6*c^2*d^2*f-2*b^2*e*(e*f-d*g)+c*(2*a*e*(4*e*f-d*g)-3*b*d*(e*f+d*g)))-c*(3*c*e*(b*d-2*a*e)*(2*c*d*f+2*a*e*g-b*(e*f+d*g))-(2*c*d-b*e)*(6*c^2*d^2*f-2*b^2*e*(e*f-d*g)+c*(2*a*e*(4*e*f-d*g)-3*b*d*(e*f+d*g))))*x)/((b^2-4*a*c)^2*(c*d^2-b*d*e+a*e^2)^2*(a+b*x+c*x^2))-(12*c^5*d^5*f-b^5*e^4*(e*f-d*g)+10*a*b^3*c*e^4*(e*f-d*g)+2*c^4*d^3*(2*a*e*(10*e*f-d*g)-3*b*d*(5*e*f+d*g))-6*c^2*e^2*(2*b^3*d^3*g-6*a*b^2*d^2*e*g-2*a^3*e^3*g+a^2*b*e^2*(5*e*f+d*g))+4*c^3*d*e*(3*a^2*e^2*(5*e*f-2*d*g)-3*a*b*d*e*(5*e*f+d*g)+b^2*d^2*(5*e*f+4*d*g)))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/((b^2-4*a*c)^(5/2)*(c*d^2-b*d*e+a*e^2)^3)+e^4*(e*f-d*g)*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^3-1/2*e^4*(e*f-d*g)*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^3],
[(f+g*x)/((d+e*x)^2*(a+b*x+c*x^2)^3),x,8,e*(6*c^4*d^4*f-b^3*e^3*(3*b*e*f-2*b*d*g-a*e*g)-b*c*e^2*(7*a^2*e^2*g-a*b*e*(21*e*f-13*d*g)-3*b^2*d*(e*f-d*g))+c^3*d^2*(4*a*e*(6*e*f-d*g)-3*b*d*(4*e*f+d*g))-c^2*e*(2*a^2*e^2*(15*e*f-22*d*g)+6*a*b*d*e*(4*e*f+d*g)-b^2*d^2*(3*e*f+7*d*g)))/((b^2-4*a*c)^2*(c*d^2-b*d*e+a*e^2)^3*(d+e*x))+1/2*(-b*c*d*f+b^2*e*f-2*a*c*e*f+2*a*c*d*g-a*b*e*g-c*(2*c*d*f+2*a*e*g-b*(e*f+d*g))*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*(a+b*x+c*x^2)^2)+1/2*(-4*a*c*e*(2*c*d-b*e)*(2*c*d*f+2*a*e*g-b*(e*f+d*g))+(b*c*d-b^2*e+2*a*c*e)*(6*c^2*d^2*f-b*e*(3*b*e*f-2*b*d*g-a*e*g)+c*(2*a*e*(5*e*f-2*d*g)-b*d*(2*e*f+3*d*g)))+c*(12*c^3*d^3*f+b^2*e^2*(3*b*e*f-2*b*d*g-a*e*g)+2*c^2*d*(2*a*e*(9*e*f-2*d*g)-3*b*d*(3*e*f+d*g))+c*e*(11*b^2*d^2*g+16*a^2*e^2*g-2*a*b*e*(9*e*f+5*d*g)))*x)/((b^2-4*a*c)^2*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)*(a+b*x+c*x^2))-(12*c^6*d^6*f+b^5*e^5*(3*b*e*f-2*b*d*g-a*e*g)+b^3*c*e^4*(10*a^2*e^2*g-b^2*d*(6*e*f-5*d*g)-10*a*b*e*(3*e*f-2*d*g))-10*a*b*c^2*e^4*(3*a^2*e^2*g-b^2*d*(6*e*f-5*d*g)-3*a*b*e*(3*e*f-2*d*g))-10*c^3*e^2*(2*b^3*d^4*g-8*a*b^2*d^3*e*g+6*a^3*e^3*(e*f-2*d*g)+3*a^2*b*d*e^2*(6*e*f-d*g))+2*c^5*d^4*(2*a*e*(15*e*f-2*d*g)-3*b*d*(6*e*f+d*g))+10*c^4*d^2*e*(2*a^2*e^2*(9*e*f-4*d*g)-a*b*d*e*(12*e*f+d*g)+b^2*d^2*(3*e*f+2*d*g)))*arctanh((b+2*c*x)/sqrt(b^2-4*a*c))/((b^2-4*a*c)^(5/2)*(c*d^2-b*d*e+a*e^2)^4)+e^4*(c*d*(6*e*f-5*d*g)-e*(3*b*e*f-2*b*d*g-a*e*g))*log(d+e*x)/(c*d^2-b*d*e+a*e^2)^4-1/2*e^4*(c*d*(6*e*f-5*d*g)-e*(3*b*e*f-2*b*d*g-a*e*g))*log(a+b*x+c*x^2)/(c*d^2-b*d*e+a*e^2)^4],
[(5-x)*(3+2*x)^4/(2+5*x+3*x^2),x,5,11576/81*x+1156/27*x^2+32/27*x^3-4/3*x^4-6*log(1+x)+10625/243*log(2+3*x)],
[(5-x)*(3+2*x)^3/(2+5*x+3*x^2),x,5,922/27*x+26/9*x^2-8/9*x^3-6*log(1+x)+2125/81*log(2+3*x)],
[(5-x)*(3+2*x)^2/(2+5*x+3*x^2),x,5,44/9*x-2/3*x^2-6*log(1+x)+425/27*log(2+3*x)],
[(5-x)*(3+2*x)/(2+5*x+3*x^2),x,4,-2/3*x-6*log(1+x)+85/9*log(2+3*x)],
[(5-x)/(2+5*x+3*x^2),x,3,-6*log(1+x)+17/3*log(2+3*x)],
[(5-x)/((3+2*x)*(2+5*x+3*x^2)),x,2,-6*log(1+x)+13/5*log(3+2*x)+17/5*log(2+3*x)],
[(5-x)/((3+2*x)^2*(2+5*x+3*x^2)),x,2,(-13/5)/(3+2*x)-6*log(1+x)+99/25*log(3+2*x)+51/25*log(2+3*x)],
[(5-x)/((3+2*x)^3*(2+5*x+3*x^2)),x,2,(-13/10)/(3+2*x)^2+(-99/25)/(3+2*x)-6*log(1+x)+597/125*log(3+2*x)+153/125*log(2+3*x)],
[(5-x)/((3+2*x)^4*(2+5*x+3*x^2)),x,2,(-13/15)/(3+2*x)^3+(-99/50)/(3+2*x)^2+(-597/125)/(3+2*x)-6*log(1+x)+3291/625*log(3+2*x)+459/625*log(2+3*x)],
[(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^2,x,7,112/27*x-8/9*x^2+1/81*(-11597-12083*x)/(2+5*x+3*x^2)+83*log(1+x)-1625/27*log(2+3*x)],
[(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^2,x,7,-8/9*x+1/27*(-2449-2611*x)/(2+5*x+3*x^2)+71*log(1+x)-1825/27*log(2+3*x)],
[(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^2,x,5,1/9*(-533-587*x)/(2+5*x+3*x^2)+59*log(1+x)-535/9*log(2+3*x)],
[(5-x)*(3+2*x)/(2+5*x+3*x^2)^2,x,4,1/3*(-121-139*x)/(2+5*x+3*x^2)+47*log(1+x)-47*log(2+3*x)],
[(5-x)/(2+5*x+3*x^2)^2,x,4,(-29-35*x)/(2+5*x+3*x^2)+35*log(1+x)-35*log(2+3*x)],
[(5-x)/((3+2*x)*(2+5*x+3*x^2)^2),x,3,-3/5*(37+47*x)/(2+5*x+3*x^2)+23*log(1+x)+52/25*log(3+2*x)-627/25*log(2+3*x)],
[(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^2),x,3,(-454/25)/(3+2*x)-3/5*(37+47*x)/((3+2*x)*(2+5*x+3*x^2))+11*log(1+x)+812/125*log(3+2*x)-2187/125*log(2+3*x)],
[(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^2),x,3,(-428/25)/(3+2*x)^2+(-2618/125)/(3+2*x)-3/5*(37+47*x)/((3+2*x)^2*(2+5*x+3*x^2))-log(1+x)+8104/625*log(3+2*x)-7479/625*log(2+3*x)],
[(5-x)/((3+2*x)^4*(2+5*x+3*x^2)^2),x,3,(-1258/75)/(3+2*x)^3+(-2212/125)/(3+2*x)^2+(-16522/625)/(3+2*x)-3/5*(37+47*x)/((3+2*x)^3*(2+5*x+3*x^2))-13*log(1+x)+65816/3125*log(3+2*x)-25191/3125*log(2+3*x)],
[(5-x)*(3+2*x)^5/(2+5*x+3*x^2)^3,x,8,-32/27*x+1/486*(-56041-57499*x)/(2+5*x+3*x^2)^2+1/486*(398585+502254*x)/(2+5*x+3*x^2)-1085*log(1+x)+29375/27*log(2+3*x)],
[(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^3,x,6,1/162*(-11597-12083*x)/(2+5*x+3*x^2)^2+7/162*(16651+20298*x)/(2+5*x+3*x^2)-883*log(1+x)+23825/27*log(2+3*x)],
[(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^3,x,5,-1/2*(3+2*x)^3*(29+35*x)/(2+5*x+3*x^2)^2+141/2*(3+2*x)*(7+8*x)/(2+5*x+3*x^2)-705*log(1+x)+705*log(2+3*x)],
[(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^3,x,6,1/18*(-533-587*x)/(2+5*x+3*x^2)^2+1/18*(8269+9918*x)/(2+5*x+3*x^2)-551*log(1+x)+551*log(2+3*x)],
[(5-x)*(3+2*x)/(2+5*x+3*x^2)^3,x,5,1/6*(-121-139*x)/(2+5*x+3*x^2)^2+421/6*(5+6*x)/(2+5*x+3*x^2)-421*log(1+x)+421*log(2+3*x)],
[(5-x)/(2+5*x+3*x^2)^3,x,5,1/2*(-29-35*x)/(2+5*x+3*x^2)^2+105/2*(5+6*x)/(2+5*x+3*x^2)-315*log(1+x)+315*log(2+3*x)],
[(5-x)/((3+2*x)*(2+5*x+3*x^2)^3),x,4,-3/10*(37+47*x)/(2+5*x+3*x^2)^2+1/50*(9587+11442*x)/(2+5*x+3*x^2)-233*log(1+x)+208/125*log(3+2*x)+28917/125*log(2+3*x)],
[(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^3),x,4,12946/125/(3+2*x)-3/10*(37+47*x)/((3+2*x)*(2+5*x+3*x^2)^2)+1/50*(9293+10848*x)/((3+2*x)*(2+5*x+3*x^2))-175*log(1+x)+4912/625*log(3+2*x)+104463/625*log(2+3*x)],
[(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^3),x,4,11856/125/(3+2*x)^2+35886/625/(3+2*x)-3/10*(37+47*x)/((3+2*x)^2*(2+5*x+3*x^2)^2)+1/50*(8999+10254*x)/((3+2*x)^2*(2+5*x+3*x^2))-141*log(1+x)+68592/3125*log(3+2*x)+372033/3125*log(2+3*x)],
[x*(1+x)^2/(1+x+x^2)^3,x,2,-1/6*(1+x)*(1+2*x)/(1+x+x^2)^2+(-1/6)/(1+x+x^2)],

# Integrands of the form (d+e x)^m (A+B x) (a+b x+c x^2)^(p/2)

# p>0
#  {(f + g*x)*(a + b*x + c*x^2)^(7/2)*(d + e*x)^3, x, 9, -((7*(b^2 - 4*a*c)^3*(640*c^4*d^3*f + 65*b^4*e^3*g - 104*b^2*c*e^2*(b*e*f + 3*b*d*g + a*e*g) - 64*c^3*d*(3*a*e*(e*f + d*g) + 5*b*d*(3*e*f + d*g)) + 16*c^2*e*(a^2*e^2*g + 33*b^2*d*(e*f + d*g) + 6*a*b*e*(e*f + 3*d*g)))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(2097152*c^8)) + (7*(b^2 - 4*a*c)^2*(640*c^4*d^3*f + 65*b^4*e^3*g - 104*b^2*c*e^2*(b*e*f + 3*b*d*g + a*e*g) - 64*c^3*d*(3*a*e*(e*f + d*g) + 5*b*d*(3*e*f + d*g)) + 16*c^2*e*(a^2*e^2*g + 33*b^2*d*(e*f + d*g) + 6*a*b*e*(e*f + 3*d*g)))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(786432*c^7) - (7*(b^2 - 4*a*c)*(640*c^4*d^3*f + 65*b^4*e^3*g - 104*b^2*c*e^2*(b*e*f + 3*b*d*g + a*e*g) - 64*c^3*d*(3*a*e*(e*f + d*g) + 5*b*d*(3*e*f + d*g)) + 16*c^2*e*(a^2*e^2*g + 33*b^2*d*(e*f + d*g) + 6*a*b*e*(e*f + 3*d*g)))*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(245760*c^6) + ((640*c^4*d^3*f + 65*b^4*e^3*g - 104*b^2*c*e^2*(b*e*f + 3*b*d*g + a*e*g) - 64*c^3*d*(3*a*e*(e*f + d*g) + 5*b*d*(3*e*f + d*g)) + 16*c^2*e*(a^2*e^2*g + 33*b^2*d*(e*f + d*g) + 6*a*b*e*(e*f + 3*d*g)))*(b + 2*c*x)*(a + b*x + c*x^2)^(7/2))/(10240*c^5) + ((8*c*e*f + 2*c*d*g - 5*b*e*g)*(d + e*x)^2*(a + b*x + c*x^2)^(9/2))/(88*c^2) + (g*(d + e*x)^3*(a + b*x + c*x^2)^(9/2))/(12*c) - ((715*b^3*e^3*g - 160*c^3*d^2*(48*e*f + d*g) - 52*b*c*e^2*(17*a*e*g + 22*b*(e*f + 3*d*g)) + 8*c^2*e*(80*a*e*(e*f + 3*d*g) + 3*b*d*(242*e*f + 167*d*g)) - 18*c*e*(65*b^2*e^2*g + 8*c^2*d*(26*e*f + d*g) - 4*c*e*(26*b*e*f + 28*b*d*g + 11*a*e*g))*x)*(a + b*x + c*x^2)^(9/2))/(31680*c^4) + (7*(b^2 - 4*a*c)^4*(640*c^4*d^3*f + 65*b^4*e^3*g - 104*b^2*c*e^2*(b*e*f + 3*b*d*g + a*e*g) - 64*c^3*d*(3*a*e*(e*f + d*g) + 5*b*d*(3*e*f + d*g)) + 16*c^2*e*(a^2*e^2*g + 33*b^2*d*(e*f + d*g) + 6*a*b*e*(e*f + 3*d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(4194304*c^(17/2))}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)*(d + e*x)^2, x, 8, -((7*(b^2 - 4*a*c)^3*(80*c^3*d^2*f - 13*b^3*e^2*g + 2*b*c*e*(6*a*e*g + 11*b*(e*f + 2*d*g)) - 8*c^2*(5*b*d*(2*e*f + d*g) + a*e*(e*f + 2*d*g)))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(262144*c^7)) + (7*(b^2 - 4*a*c)^2*(80*c^3*d^2*f - 13*b^3*e^2*g + 2*b*c*e*(6*a*e*g + 11*b*(e*f + 2*d*g)) - 8*c^2*(5*b*d*(2*e*f + d*g) + a*e*(e*f + 2*d*g)))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(98304*c^6) - (7*(b^2 - 4*a*c)*(80*c^3*d^2*f - 13*b^3*e^2*g + 2*b*c*e*(6*a*e*g + 11*b*(e*f + 2*d*g)) - 8*c^2*(5*b*d*(2*e*f + d*g) + a*e*(e*f + 2*d*g)))*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(30720*c^5) + ((80*c^3*d^2*f - 13*b^3*e^2*g + 2*b*c*e*(6*a*e*g + 11*b*(e*f + 2*d*g)) - 8*c^2*(5*b*d*(2*e*f + d*g) + a*e*(e*f + 2*d*g)))*(b + 2*c*x)*(a + b*x + c*x^2)^(7/2))/(1280*c^4) + (g*(d + e*x)^2*(a + b*x + c*x^2)^(9/2))/(11*c) + ((143*b^2*e^2*g + 80*c^2*d*(11*e*f + d*g) - 2*c*e*(40*a*e*g + 121*b*(e*f + 2*d*g)) + 18*c*e*(22*c*e*f + 4*c*d*g - 13*b*e*g)*x)*(a + b*x + c*x^2)^(9/2))/(3960*c^3) + (7*(b^2 - 4*a*c)^4*(80*c^3*d^2*f - 13*b^3*e^2*g + 2*b*c*e*(6*a*e*g + 11*b*(e*f + 2*d*g)) - 8*c^2*(5*b*d*(2*e*f + d*g) + a*e*(e*f + 2*d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(524288*c^(15/2))}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)*(d + e*x)^1, x, 7, -((7*(b^2 - 4*a*c)^3*(40*c^2*d*f + 11*b^2*e*g - 4*c*(a*e*g + 5*b*(e*f + d*g)))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(131072*c^6)) + (7*(b^2 - 4*a*c)^2*(40*c^2*d*f + 11*b^2*e*g - 4*c*(a*e*g + 5*b*(e*f + d*g)))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(49152*c^5) - (7*(b^2 - 4*a*c)*(40*c^2*d*f + 11*b^2*e*g - 4*c*(a*e*g + 5*b*(e*f + d*g)))*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(15360*c^4) + ((40*c^2*d*f + 11*b^2*e*g - 4*c*(a*e*g + 5*b*(e*f + d*g)))*(b + 2*c*x)*(a + b*x + c*x^2)^(7/2))/(640*c^3) - ((11*b*e*g - 20*c*(e*f + d*g) - 18*c*e*g*x)*(a + b*x + c*x^2)^(9/2))/(180*c^2) + (7*(b^2 - 4*a*c)^4*(40*c^2*d*f + 11*b^2*e*g - 4*c*(a*e*g + 5*b*(e*f + d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(262144*c^(13/2))}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)*(d + e*x)^0, x, 7, -((35*(b^2 - 4*a*c)^3*(2*c*f - b*g)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(32768*c^5)) + (35*(b^2 - 4*a*c)^2*(2*c*f - b*g)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(12288*c^4) - (7*(b^2 - 4*a*c)*(2*c*f - b*g)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(768*c^3) + ((2*c*f - b*g)*(b + 2*c*x)*(a + b*x + c*x^2)^(7/2))/(32*c^2) + (g*(a + b*x + c*x^2)^(9/2))/(9*c) + (35*(b^2 - 4*a*c)^4*(2*c*f - b*g)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(65536*c^(11/2))}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)/(d + e*x)^1, x, 9, -((35*(b^2 - 4*a*c)^3*g*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(16384*c^4*e)) - (5*(b^2 - 4*a*c)^2*(2*c*d - b*e)*(e*f - d*g)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(1024*c^3*e^3) + (3*(b^2 - 4*a*c)*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(128*c^2*e^5) + ((c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)*(8*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 4*a*e) - 2*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(8*c*e^8) + ((c*d^2 - b*d*e + a*e^2)^2*(e*f - d*g)*(a + b*x + c*x^2)^(3/2))/(3*e^6) + (35*(b^2 - 4*a*c)^2*g*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(6144*c^3*e) + (5*(b^2 - 4*a*c)*(2*c*d - b*e)*(e*f - d*g)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(384*c^2*e^3) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(16*c*e^5) + ((c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*(a + b*x + c*x^2)^(5/2))/(5*e^4) - (7*(b^2 - 4*a*c)*g*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(384*c^2*e) - ((2*c*d - b*e)*(e*f - d*g)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(24*c*e^3) + ((e*f - d*g)*(a + b*x + c*x^2)^(7/2))/(7*e^2) + (g*(b + 2*c*x)*(a + b*x + c*x^2)^(7/2))/(16*c*e) + (35*(b^2 - 4*a*c)^4*g*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(32768*c^(9/2)*e) + (5*(b^2 - 4*a*c)^3*(2*c*d - b*e)*(e*f - d*g)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2048*c^(7/2)*e^3) - (3*(b^2 - 4*a*c)^2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(e*f - d*g)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(5/2)*e^5) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*(e*f - d*g)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(3/2)*e^9) + ((c*d^2 - b*d*e + a*e^2)^(7/2)*(e*f - d*g)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/e^9, -((1/(16384*c^4*e^8))*((35*b^7*e^7*g - 16384*c^7*d^6*(e*f - d*g) + 4096*c^6*d^4*e*(13*b*d - 12*a*e)*(e*f - d*g) - 1024*c^5*d^2*e^2*(58*b^2*d^2 - 107*a*b*d*e + 48*a^2*e^2)*(e*f - d*g) + 256*c^4*e^3*(93*b^3*d^3 - 258*a*b^2*d^2*e + 230*a^2*b*d*e^2 - 64*a^3*e^3)*(e*f - d*g) - 20*b^5*c*e^6*(4*b*e*f - 4*b*d*g + 21*a*e*g) + 16*b^3*c^2*e^5*(105*a^2*e^2*g - 14*b^2*d*(e*f - d*g) + 64*a*b*e*(e*f - d*g)) - 64*b*c^3*e^4*(35*a^3*e^3*g + 14*b^3*d^2*(e*f - d*g) - 56*a*b^2*d*e*(e*f - d*g) + 76*a^2*b*e^2*(e*f - d*g)) + 2*c*e*(35*b^6*e^6*g + 4096*c^6*d^5*(e*f - d*g) - 1024*c^5*d^3*e*(10*b*d - 11*a*e)*(e*f - d*g) + 256*c^4*d*e^2*(29*b^2*d^2 - 66*a*b*d*e + 38*a^2*e^2)*(e*f - d*g) - 20*b^4*c*e^5*(4*b*e*f - 4*b*d*g + 21*a*e*g) + 16*b^2*c^2*e^4*(105*a^2*e^2*g - 14*b^2*d*(e*f - d*g) + 64*a*b*e*(e*f - d*g)) - 64*c^3*e^3*(35*a^3*e^3*g + 14*b^3*d^2*(e*f - d*g) - 56*a*b^2*d*e*(e*f - d*g) + 76*a^2*b*e^2*(e*f - d*g)))*x)*Sqrt[a + b*x + c*x^2])) + (1/(6144*c^3*e^6))*((35*b^5*e^5*g + 2048*c^5*d^4*(e*f - d*g) - 256*c^4*d^2*e*(19*b*d - 16*a*e)*(e*f - d*g) + 128*c^3*e^2*(25*b^2*d^2 - 43*a*b*d*e + 16*a^2*e^2)*(e*f - d*g) - 40*b^3*c*e^4*(2*b*e*f - 2*b*d*g + 7*a*e*g) + 16*b*c^2*e^3*(35*a^2*e^2*g - 14*b^2*d*(e*f - d*g) + 44*a*b*e*(e*f - d*g)) + 2*c*e*(35*b^4*e^4*g - 768*c^4*d^3*(e*f - d*g) + 128*c^3*d*e*(9*b*d - 11*a*e)*(e*f - d*g) - 40*b^2*c*e^3*(2*b*e*f - 2*b*d*g + 7*a*e*g) + 16*c^2*e^2*(35*a^2*e^2*g - 14*b^2*d*(e*f - d*g) + 44*a*b*e*(e*f - d*g)))*x)*(a + b*x + c*x^2)^(3/2)) - ((35*b^3*e^3*g - 384*c^3*d^2*(e*f - d*g) + 32*c^2*e*(17*b*d - 12*a*e)*(e*f - d*g) - 20*b*c*e^2*(4*b*e*f - 4*b*d*g + 7*a*e*g) + 10*c*e*(7*b^2*e^2*g + 32*c^2*d*(e*f - d*g) - 4*c*e*(4*b*e*f - 4*b*d*g + 7*a*e*g))*x)*(a + b*x + c*x^2)^(5/2))/(1920*c^2*e^4) + ((16*c*e*f - 16*c*d*g + 7*b*e*g + 14*c*e*g*x)*(a + b*x + c*x^2)^(7/2))/(112*c*e^2) + (1/(32768*c^(9/2)*e^9))*((35*b^8*e^8*g - 32768*c^8*d^7*(e*f - d*g) + 114688*c^7*d^5*e*(b*d - a*e)*(e*f - d*g) - 143360*c^6*d^3*e^2*(b*d - a*e)^2*(e*f - d*g) + 71680*c^5*d*e^3*(b*d - a*e)^3*(e*f - d*g) - 80*b^6*c*e^7*(b*e*f - b*d*g + 7*a*e*g) + 224*b^4*c^2*e^6*(15*a^2*e^2*g - b^2*d*(e*f - d*g) + 6*a*b*e*(e*f - d*g)) - 896*b^2*c^3*e^5*(10*a^3*e^3*g + b^3*d^2*(e*f - d*g) - 5*a*b^2*d*e*(e*f - d*g) + 10*a^2*b*e^2*(e*f - d*g)) + 8960*c^4*e^4*(a^4*e^4*g - b^4*d^3*(e*f - d*g) + 4*a*b^3*d^2*e*(e*f - d*g) - 6*a^2*b^2*d*e^2*(e*f - d*g) + 4*a^3*b*e^3*(e*f - d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])]) + ((c*d^2 - b*d*e + a*e^2)^(7/2)*(e*f - d*g)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/e^9}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)/(d + e*x)^2, x, 9, (5*(b^2 - 4*a*c)^2*(b*e*g + 2*c*(7*e*f - 8*d*g))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(1024*c^3*e^3) - (3*(b^2 - 4*a*c)*(2*c*d - b*e)*(2*c*d*(7*e*f - 8*d*g) - e*(7*b*e*f - 9*b*d*g + 2*a*e*g))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(256*c^2*e^5) - ((c*d^2 - b*d*e + a*e^2)*(2*c*d*(7*e*f - 8*d*g) - e*(7*b*e*f - 9*b*d*g + 2*a*e*g))*(8*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 4*a*e) - 2*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(16*c*e^8) - ((c*d^2 - b*d*e + a*e^2)*(2*c*d*(7*e*f - 8*d*g) - e*(7*b*e*f - 9*b*d*g + 2*a*e*g))*(a + b*x + c*x^2)^(3/2))/(6*e^6) - (5*(b^2 - 4*a*c)*(b*e*g + 2*c*(7*e*f - 8*d*g))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(384*c^2*e^3) + ((2*c*d - b*e)*(2*c*d*(7*e*f - 8*d*g) - e*(7*b*e*f - 9*b*d*g + 2*a*e*g))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(32*c*e^5) - ((2*c*d*(7*e*f - 8*d*g) - e*(7*b*e*f - 9*b*d*g + 2*a*e*g))*(a + b*x + c*x^2)^(5/2))/(10*e^4) + ((14*c*e*f - 16*c*d*g + b*e*g)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(24*c*e^3) - ((7*e*f - 8*d*g - e*g*x)*(a + b*x + c*x^2)^(7/2))/(7*e^2*(d + e*x)) - (5*(b^2 - 4*a*c)^3*(b*e*g + 2*c*(7*e*f - 8*d*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2048*c^(7/2)*e^3) + (3*(b^2 - 4*a*c)^2*(2*c*d - b*e)*(2*c*d*(7*e*f - 8*d*g) - e*(7*b*e*f - 9*b*d*g + 2*a*e*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(512*c^(5/2)*e^5) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*(2*c*d*(7*e*f - 8*d*g) - e*(7*b*e*f - 9*b*d*g + 2*a*e*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(32*c^(3/2)*e^9) - ((c*d^2 - b*d*e + a*e^2)^(5/2)*(2*c*d*(7*e*f - 8*d*g) - e*(7*b*e*f - 9*b*d*g + 2*a*e*g))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2*e^9), ((3*(5*b^6*e^6*g - 1024*c^6*d^5*(7*e*f - 8*d*g) + 16*c^3*e^3*(64*a^3*e^3*g - 2*a*b^2*d*e*(322*e*f - 451*d*g) + b^3*d^2*(343*e*f - 436*d*g) + 2*a^2*b*e^2*(147*e*f - 262*d*g)) + 256*c^5*d^3*e*(b*d*(77*e*f - 90*d*g) - 4*a*e*(14*e*f - 17*d*g)) + 64*c^4*d*e^2*(a*b*d*e*(385*e*f - 492*d*g) - 2*b^2*d^2*(140*e*f - 169*d*g) - 16*a^2*e^2*(7*e*f - 10*d*g)) - 2*b^4*c*e^5*(32*a*e*g + 7*b*(e*f - 2*d*g)) + 8*b^2*c^2*e^4*(38*a^2*e^2*g - 7*b^2*d*(2*e*f - 3*d*g) + 28*a*b*e*(e*f - 2*d*g))) - 2*c*e*(-8*c*e*(2*c*d - b*e)*(12*c*e*(b*d - 2*a*e)*(7*b*e*f - 8*b*d*g + 2*a*e*g) - d*(12*b*c*d - 5*b^2*e - 4*a*c*e)*(14*c*e*f - 16*c*d*g + b*e*g)) + 2*(8*c^2*d^2 - 4*b*c*d*e - (3*b^2*e^2)/2 + 6*a*c*e^2)*(12*c*e*(2*c*d - b*e)*(7*b*e*f - 8*b*d*g + 2*a*e*g) - (24*c^2*d^2 - 5*b^2*e^2 - 4*c*e*(3*b*d - 5*a*e))*(b*e*g + 2*c*(7*e*f - 8*d*g))))*x)*Sqrt[a + b*x + c*x^2])/(3072*c^3*e^8) - ((5*b^4*e^4*g + 128*c^4*d^3*(7*e*f - 8*d*g) - 8*c^2*e^2*(16*a^2*e^2*g + a*b*e*(91*e*f - 134*d*g) - b^2*d*(98*e*f - 123*d*g)) - 16*c^3*d*e*(b*d*(105*e*f - 124*d*g) - 8*a*e*(7*e*f - 9*d*g)) - 2*b^2*c*e^3*(22*a*e*g + 7*b*(e*f - 2*d*g)) + 2*c*e*(12*c*e*(2*c*d - b*e)*(7*b*e*f - 8*b*d*g + 2*a*e*g) - (24*c^2*d^2 - 5*b^2*e^2 - 4*c*e*(3*b*d - 5*a*e))*(b*e*g + 2*c*(7*e*f - 8*d*g)))*x)*(a + b*x + c*x^2)^(3/2))/(384*c^2*e^6) + ((5*b^2*e^2*g - 24*c^2*d*(7*e*f - 8*d*g) + 2*c*e*(77*b*e*f - 94*b*d*g + 12*a*e*g) + 10*c*e*(14*c*e*f - 16*c*d*g + b*e*g)*x)*(a + b*x + c*x^2)^(5/2))/(120*c*e^4) - ((7*e*f - 8*d*g - e*g*x)*(a + b*x + c*x^2)^(7/2))/(7*e^2*(d + e*x)) - ((5*b^7*e^7*g - 2048*c^7*d^6*(7*e*f - 8*d*g) - 14*b^5*c*e^6*(b*e*f - 2*b*d*g + 6*a*e*g) + 7168*c^6*d^4*e*(b*d*(6*e*f - 7*d*g) - a*e*(5*e*f - 6*d*g)) - 8960*c^5*d^2*e^2*(b*d - a*e)*(b*d*(5*e*f - 6*d*g) - a*e*(3*e*f - 4*d*g)) + 4480*c^4*e^3*(b*d - a*e)^2*(b*d*(4*e*f - 5*d*g) - a*e*(e*f - 2*d*g)) + 56*b^3*c^2*e^5*(10*a^2*e^2*g - b^2*d*(2*e*f - 3*d*g) + 5*a*b*e*(e*f - 2*d*g)) - 560*b*c^3*e^4*(4*a^3*e^3*g + b^3*d^2*(3*e*f - 4*d*g) - 4*a*b^2*d*e*(2*e*f - 3*d*g) + 6*a^2*b*e^2*(e*f - 2*d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2048*c^(7/2)*e^9) - ((c*d^2 - b*d*e + a*e^2)^(5/2)*(2*c*d*(7*e*f - 8*d*g) - e*(7*b*e*f - 9*b*d*g + 2*a*e*g))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2*e^9)}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)/(d + e*x)^3, x, 9, -((7*(b^2 - 4*a*c)*(b^2*e^2*g - 24*c^2*d*(3*e*f - 4*d*g) + 4*c*e*(9*b*e*f - 15*b*d*g + 5*a*e*g))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(512*c^2*e^5)) + (7*(8*c^2*d^2*(3*e*f - 4*d*g) + b*e^2*(5*b*e*f - 9*b*d*g + 4*a*e*g) + 4*c*e*(a*e*(e*f - 3*d*g) - 3*b*d*(2*e*f - 3*d*g)))*(8*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 4*a*e) - 2*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(64*c*e^8) + (7*(8*c^2*d^2*(3*e*f - 4*d*g) + b*e^2*(5*b*e*f - 9*b*d*g + 4*a*e*g) + 4*c*e*(a*e*(e*f - 3*d*g) - 3*b*d*(2*e*f - 3*d*g)))*(a + b*x + c*x^2)^(3/2))/(24*e^6) + (7*(b^2*e^2*g - 24*c^2*d*(3*e*f - 4*d*g) + 4*c*e*(9*b*e*f - 15*b*d*g + 5*a*e*g))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(192*c*e^5) + (7*(12*c*d*(3*e*f - 4*d*g) - e*(15*b*e*f - 26*b*d*g + 10*a*e*g) + e*(6*c*e*f - 8*c*d*g + b*e*g)*x)*(a + b*x + c*x^2)^(5/2))/(60*e^4*(d + e*x)) - ((3*e*f - 4*d*g - e*g*x)*(a + b*x + c*x^2)^(7/2))/(6*e^2*(d + e*x)^2) + (7*(b^2 - 4*a*c)^2*(b^2*e^2*g - 24*c^2*d*(3*e*f - 4*d*g) + 4*c*e*(9*b*e*f - 15*b*d*g + 5*a*e*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(5/2)*e^5) - (7*(2*c*d - b*e)*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*(8*c^2*d^2*(3*e*f - 4*d*g) + b*e^2*(5*b*e*f - 9*b*d*g + 4*a*e*g) + 4*c*e*(a*e*(e*f - 3*d*g) - 3*b*d*(2*e*f - 3*d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(3/2)*e^9) + (7*(c*d^2 - b*d*e + a*e^2)^(3/2)*(8*c^2*d^2*(3*e*f - 4*d*g) + b*e^2*(5*b*e*f - 9*b*d*g + 4*a*e*g) + 4*c*e*(a*e*(e*f - 3*d*g) - 3*b*d*(2*e*f - 3*d*g)))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(8*e^9), -((7*(3*(b^5*e^5*g - 512*c^5*d^4*(3*e*f - 4*d*g) - 4*b^3*c*e^4*(b*e*f - 3*b*d*g + 4*a*e*g) - 8*b*c^2*e^3*(42*a^2*e^2*g - b^2*d*(65*e*f - 114*d*g) + 2*a*b*e*(31*e*f - 77*d*g)) + 128*c^4*d^2*e*(b*d*(27*e*f - 38*d*g) - 2*a*e*(7*e*f - 11*d*g)) + 32*c^3*e^2*(a*b*d*e*(67*e*f - 122*d*g) - 4*b^2*d^2*(19*e*f - 29*d*g) - 8*a^2*e^2*(e*f - 3*d*g))) - 2*c*e*(2*(8*c^2*d^2 - 4*b*c*d*e - (3*b^2*e^2)/2 + 6*a*c*e^2)*(b^2*e^2*g - 24*c^2*d*(3*e*f - 4*d*g) + 4*c*e*(9*b*e*f - 15*b*d*g + 5*a*e*g)) - 8*c*e*(2*c*d - b*e)*(5*b*e*(3*b*e*f - 4*b*d*g + 2*a*e*g) - 2*(3*b*d - a*e)*(6*c*e*f - 8*c*d*g + b*e*g)))*x)*Sqrt[a + b*x + c*x^2])/(1536*c^2*e^8)) + (7*(b^3*e^3*g + 64*c^3*d^2*(3*e*f - 4*d*g) + 4*b*c*e^2*(19*b*e*f - 33*b*d*g + 13*a*e*g) - 8*c^2*e*(3*b*d*(11*e*f - 16*d*g) - 4*a*e*(e*f - 3*d*g)) + 2*c*e*(b^2*e^2*g - 24*c^2*d*(3*e*f - 4*d*g) + 4*c*e*(9*b*e*f - 15*b*d*g + 5*a*e*g))*x)*(a + b*x + c*x^2)^(3/2))/(192*c*e^6) + (7*(12*c*d*(3*e*f - 4*d*g) - e*(15*b*e*f - 26*b*d*g + 10*a*e*g) + e*(6*c*e*f - 8*c*d*g + b*e*g)*x)*(a + b*x + c*x^2)^(5/2))/(60*e^4*(d + e*x)) - ((3*e*f - 4*d*g - e*g*x)*(a + b*x + c*x^2)^(7/2))/(6*e^2*(d + e*x)^2) + (7*(b^6*e^6*g - 1024*c^6*d^5*(3*e*f - 4*d*g) - 4*b^4*c*e^5*(b*e*f - 3*b*d*g + 5*a*e*g) - 320*c^3*e^3*(b*d - a*e)*(a^2*e^2*g + a*b*e*(3*e*f - 8*d*g) - 2*b^2*d*(3*e*f - 5*d*g)) + 512*c^5*d^3*e*(3*b*d*(5*e*f - 7*d*g) - 5*a*e*(2*e*f - 3*d*g)) + 40*b^2*c^2*e^4*(6*a^2*e^2*g + 4*a*b*e*(e*f - 3*d*g) - 3*b^2*d*(e*f - 2*d*g)) + 640*c^4*d*e^2*(4*a*b*d*e*(3*e*f - 5*d*g) - 5*b^2*d^2*(2*e*f - 3*d*g) - 3*a^2*e^2*(e*f - 2*d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(5/2)*e^9) + (7*(c*d^2 - b*d*e + a*e^2)^(3/2)*(8*c^2*d^2*(3*e*f - 4*d*g) + b*e^2*(5*b*e*f - 9*b*d*g + 4*a*e*g) + 4*c*e*(a*e*(e*f - 3*d*g) - 3*b*d*(2*e*f - 3*d*g)))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(8*e^9)}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)/(d + e*x)^4, x, 9, (1/(128*c*e^8))*(7*(b^4*e^4*g - 128*c^4*d^3*(5*e*f - 8*d*g) + 8*c^2*e^2*(8*a^2*e^2*g + a*b*e*(25*e*f - 92*d*g) - 2*b^2*d*(35*e*f - 73*d*g)) + 2*b^2*c*e^3*(62*a*e*g + 5*b*(7*e*f - 20*d*g)) + 32*c^3*d*e*(b*d*(35*e*f - 62*d*g) - 2*a*e*(5*e*f - 12*d*g)) + 2*c*e*(b^3*e^3*g + 32*c^3*d^2*(5*e*f - 8*d*g) - 8*c^2*e*(2*b*d*(10*e*f - 19*d*g) - a*e*(5*e*f - 16*d*g)) + 2*b*c*e^2*(22*a*e*g + 5*b*(3*e*f - 8*d*g)))*x)*Sqrt[a + b*x + c*x^2]) - (7*(16*c^2*d^2*(5*e*f - 8*d*g) + b*e^2*(10*b*e*f - 29*b*d*g + 18*a*e*g) - 2*c*e*(b*d*(35*e*f - 68*d*g) - 2*a*e*(5*e*f - 16*d*g)) - e*(b^2*e^2*g - 4*c^2*d*(5*e*f - 8*d*g) + 2*c*e*(5*b*e*f - 11*b*d*g + 4*a*e*g))*x)*(a + b*x + c*x^2)^(3/2))/(48*e^6*(d + e*x)) + (7*(6*c*d*(5*e*f - 8*d*g) - e*(10*b*e*f - 25*b*d*g + 12*a*e*g) + e*(10*c*e*f - 16*c*d*g + 3*b*e*g)*x)*(a + b*x + c*x^2)^(5/2))/(120*e^4*(d + e*x)^2) - ((5*e*f - 8*d*g - 3*e*g*x)*(a + b*x + c*x^2)^(7/2))/(15*e^2*(d + e*x)^3) - (1/(256*c^(3/2)*e^9))*(7*(b^5*e^5*g - 256*c^5*d^4*(5*e*f - 8*d*g) - 10*b^3*c*e^4*(b*e*f - 4*b*d*g + 4*a*e*g) - 80*b*c^2*e^3*(3*a^2*e^2*g - 2*b^2*d*(2*e*f - 5*d*g) + 3*a*b*e*(e*f - 4*d*g)) + 160*c^3*e^2*(4*a*b*d*e*(2*e*f - 5*d*g) - a^2*e^2*(e*f - 4*d*g) - 10*b^2*d^2*(e*f - 2*d*g)) + 640*c^4*d^2*e*(b*d*(4*e*f - 7*d*g) - 2*a*e*(e*f - 2*d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])]) - (7*Sqrt[c*d^2 - b*d*e + a*e^2]*(16*c^3*d^3*(5*e*f - 8*d*g) - 5*b^2*e^3*(b*e*f - 3*b*d*g + 2*a*e*g) - 2*c*e^2*(4*a^2*e^2*g - b^2*d*(25*e*f - 54*d*g) + 2*a*b*e*(5*e*f - 19*d*g)) + 8*c^2*d*e*(a*e*(5*e*f - 12*d*g) - 3*b*d*(5*e*f - 9*d*g)))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(16*e^9)}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)/(d + e*x)^5, x, 9, (1/(64*e^8*(d + e*x)))*(35*(64*c^3*d^3*(e*f - 2*d*g) - b^2*e^3*(b*e*f - 8*b*d*g + 6*a*e*g) - 4*c*e^2*(2*a^2*e^2*g + a*b*e*(3*e*f - 16*d*g) - 2*b^2*d*(3*e*f - 10*d*g)) - 16*c^2*d*e*(b*d*(5*e*f - 12*d*g) - 2*a*e*(e*f - 3*d*g)) + e*(b^3*e^3*g + 32*c^3*d^2*(e*f - 2*d*g) + 6*b*c*e^2*(b*e*f - 4*b*d*g + 2*a*e*g) - 8*c^2*e*(2*b*d*(2*e*f - 5*d*g) - a*e*(e*f - 4*d*g)))*x)*Sqrt[a + b*x + c*x^2]) - (35*(16*c^2*d^2*(e*f - 2*d*g) + b*e^2*(b*e*f - 6*b*d*g + 4*a*e*g) - 4*c*e*(b*d*(3*e*f - 8*d*g) - a*e*(e*f - 4*d*g)) - e*(b^2*e^2*g - 8*c^2*d*(e*f - 2*d*g) + 4*c*e*(b*e*f - 3*b*d*g + a*e*g))*x)*(a + b*x + c*x^2)^(3/2))/(96*e^6*(d + e*x)^2) + (7*(4*c*d*(e*f - 2*d*g) - e*(b*e*f - 4*b*d*g + 2*a*e*g) + e*(2*c*e*f - 4*c*d*g + b*e*g)*x)*(a + b*x + c*x^2)^(5/2))/(24*e^4*(d + e*x)^3) - ((e*f - 2*d*g - e*g*x)*(a + b*x + c*x^2)^(7/2))/(4*e^2*(d + e*x)^4) + (35*(b^4*e^4*g - 128*c^4*d^3*(e*f - 2*d*g) + 8*b^2*c*e^3*(b*e*f - 5*b*d*g + 3*a*e*g) + 16*c^2*e^2*(a^2*e^2*g + 2*a*b*e*(e*f - 5*d*g) - 5*b^2*d*(e*f - 3*d*g)) + 64*c^3*d*e*(b*d*(3*e*f - 7*d*g) - a*e*(e*f - 3*d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*Sqrt[c]*e^9) + (1/(128*e^9*Sqrt[c*d^2 - b*d*e + a*e^2]))*(35*(128*c^4*d^4*(e*f - 2*d*g) + b^3*e^4*(b*e*f - 9*b*d*g + 8*a*e*g) + 8*b*c*e^3*(4*a^2*e^2*g + a*b*e*(3*e*f - 17*d*g) - b^2*d*(4*e*f - 15*d*g)) + 16*c^2*e^2*(b^2*d^2*(10*e*f - 27*d*g) - 2*a*b*d*e*(4*e*f - 13*d*g) + a^2*e^2*(e*f - 5*d*g)) - 64*c^3*d^2*e*(b*d*(4*e*f - 9*d*g) - a*e*(2*e*f - 5*d*g)))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)/(d + e*x)^6, x, 13, -((7*(5*b^3*e^3*g + 16*c^3*d^2*(3*e*f - 8*d*g) + 10*b*c*e^2*(b*e*f - 6*b*d*g + 2*a*e*g) - 8*c^2*e*(3*b*d*(2*e*f - 7*d*g) - a*e*(e*f - 6*d*g)))*Sqrt[a + b*x + c*x^2])/(16*e^8*(d + e*x))) - (1/(128*e^7*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2))*(7*(32*c^3*d^3*(3*e*f - 8*d*g) - b^2*e^3*(b*e*f - 31*b*d*g + 30*a*e*g) + 8*c^2*d*e*(a*e*(11*e*f - 36*d*g) - 2*b*d*(9*e*f - 29*d*g)) - 2*c*e^2*(20*a^2*e^2*g + 2*a*b*e*(11*e*f - 61*d*g) - 5*b^2*d*(5*e*f - 24*d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2]) - (7*(16*c^2*d^2*(3*e*f - 8*d*g) + b*e^2*(b*e*f - 21*b*d*g + 10*a*e*g) + 2*c*e*(4*a*e*(e*f - 6*d*g) - 15*b*d*(e*f - 4*d*g)) - 2*e*(5*b^2*e^2*g - 6*c^2*d*(3*e*f - 8*d*g) + c*e*(9*b*e*f - 39*b*d*g + 10*a*e*g))*x)*(a + b*x + c*x^2)^(3/2))/(48*e^6*(d + e*x)^3) + (7*(6*c*d*(3*e*f - 8*d*g) - e*(3*b*e*f - 23*b*d*g + 10*a*e*g) + 2*e*(6*c*e*f - 16*c*d*g + 5*b*e*g)*x)*(a + b*x + c*x^2)^(5/2))/(120*e^4*(d + e*x)^4) - ((3*e*f - 8*d*g - 5*e*g*x)*(a + b*x + c*x^2)^(7/2))/(15*e^2*(d + e*x)^5) + (7*Sqrt[c]*(5*b^3*e^3*g + 16*c^3*d^2*(3*e*f - 8*d*g) + 10*b*c*e^2*(b*e*f - 6*b*d*g + 2*a*e*g) - 8*c^2*e*(3*b*d*(2*e*f - 7*d*g) - a*e*(e*f - 6*d*g)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*e^9) + (1/(256*e^7*(c*d^2 - b*d*e + a*e^2)^(3/2)))*(7*(b^2 - 4*a*c)*(32*c^3*d^3*(3*e*f - 8*d*g) - b^2*e^3*(b*e*f - 31*b*d*g + 30*a*e*g) + 8*c^2*d*e*(a*e*(11*e*f - 36*d*g) - 2*b*d*(9*e*f - 29*d*g)) - 2*c*e^2*(20*a^2*e^2*g + 2*a*b*e*(11*e*f - 61*d*g) - 5*b^2*d*(5*e*f - 24*d*g)))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])]) - (7*(2*c*d - b*e)*(5*b^3*e^3*g + 16*c^3*d^2*(3*e*f - 8*d*g) + 10*b*c*e^2*(b*e*f - 6*b*d*g + 2*a*e*g) - 8*c^2*e*(3*b*d*(2*e*f - 7*d*g) - a*e*(e*f - 6*d*g)))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(32*e^9*Sqrt[c*d^2 - b*d*e + a*e^2])}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)/(d + e*x)^7, x, 18, -((7*c*(5*b^2*e^2*g - 8*c^2*d*(e*f - 4*d*g) + 4*c*e*(b*e*f - 7*b*d*g + a*e*g))*Sqrt[a + b*x + c*x^2])/(8*e^8*(d + e*x))) - (7*(2*c*d - b*e)*(5*b^2*e^2*g - 8*c^2*d*(e*f - 4*d*g) + 4*c*e*(b*e*f - 7*b*d*g + a*e*g))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(64*e^7*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) - (7*(b^2 - 4*a*c)*(24*c^2*d^2*(e*f - 4*d*g) + b*e^2*(b*e*f - 37*b*d*g + 36*a*e*g) + 4*c*e*(a*e*(5*e*f - 23*d*g) - 3*b*d*(2*e*f - 11*d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(512*e^5*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) - (7*(5*b^2*e^2*g - 8*c^2*d*(e*f - 4*d*g) + 4*c*e*(b*e*f - 7*b*d*g + a*e*g))*(a + b*x + c*x^2)^(3/2))/(24*e^6*(d + e*x)^3) + (7*(24*c^2*d^2*(e*f - 4*d*g) + b*e^2*(b*e*f - 37*b*d*g + 36*a*e*g) + 4*c*e*(a*e*(5*e*f - 23*d*g) - 3*b*d*(2*e*f - 11*d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(192*e^5*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^4) + (7*(12*c*d*(e*f - 4*d*g) - e*(b*e*f - 22*b*d*g + 6*a*e*g) + 5*e*(2*c*e*f - 8*c*d*g + 3*b*e*g)*x)*(a + b*x + c*x^2)^(5/2))/(60*e^4*(d + e*x)^5) - ((e*f - 4*d*g - 3*e*g*x)*(a + b*x + c*x^2)^(7/2))/(6*e^2*(d + e*x)^6) + (7*c^(3/2)*(5*b^2*e^2*g - 8*c^2*d*(e*f - 4*d*g) + 4*c*e*(b*e*f - 7*b*d*g + a*e*g))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*e^9) + (7*(b^2 - 4*a*c)*(2*c*d - b*e)*(5*b^2*e^2*g - 8*c^2*d*(e*f - 4*d*g) + 4*c*e*(b*e*f - 7*b*d*g + a*e*g))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(128*e^7*(c*d^2 - b*d*e + a*e^2)^(3/2)) - (7*c*(2*c*d - b*e)*(5*b^2*e^2*g - 8*c^2*d*(e*f - 4*d*g) + 4*c*e*(b*e*f - 7*b*d*g + a*e*g))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(16*e^9*Sqrt[c*d^2 - b*d*e + a*e^2]) + (7*(b^2 - 4*a*c)^2*(24*c^2*d^2*(e*f - 4*d*g) + b*e^2*(b*e*f - 37*b*d*g + 36*a*e*g) + 4*c*e*(a*e*(5*e*f - 23*d*g) - 3*b*d*(2*e*f - 11*d*g)))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(1024*e^5*(c*d^2 - b*d*e + a*e^2)^(5/2))}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)/(d + e*x)^8, x, 24, -((c^2*(2*c*e*f - 16*c*d*g + 7*b*e*g)*Sqrt[a + b*x + c*x^2])/(2*e^8*(d + e*x))) - (c*(2*c*d - b*e)*(2*c*e*f - 16*c*d*g + 7*b*e*g)*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(16*e^7*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) + (3*(b^2 - 4*a*c)*(2*c*d - b*e)*(7*b*e*g + 2*c*(e*f - 8*d*g))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(256*e^5*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) - (5*(b^2 - 4*a*c)^2*(2*c*d*(e*f - 8*d*g) - e*(b*e*f - 15*b*d*g + 14*a*e*g))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(1024*e^3*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^2) - (c*(2*c*e*f - 16*c*d*g + 7*b*e*g)*(a + b*x + c*x^2)^(3/2))/(6*e^6*(d + e*x)^3) - ((2*c*d - b*e)*(2*c*e*f - 16*c*d*g + 7*b*e*g)*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(32*e^5*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^4) + (5*(b^2 - 4*a*c)*(2*c*d*(e*f - 8*d*g) - e*(b*e*f - 15*b*d*g + 14*a*e*g))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(384*e^3*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^4) - ((2*c*e*f - 16*c*d*g + 7*b*e*g)*(a + b*x + c*x^2)^(5/2))/(10*e^4*(d + e*x)^5) - ((2*c*d*(e*f - 8*d*g) - e*(b*e*f - 15*b*d*g + 14*a*e*g))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(5/2))/(24*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^6) - ((e*f - 8*d*g - 7*e*g*x)*(a + b*x + c*x^2)^(7/2))/(7*e^2*(d + e*x)^7) + (c^(5/2)*(2*c*e*f - 16*c*d*g + 7*b*e*g)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*e^9) - (3*(b^2 - 4*a*c)^2*(2*c*d - b*e)*(2*c*e*f - 16*c*d*g + 7*b*e*g)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(512*e^5*(c*d^2 - b*d*e + a*e^2)^(5/2)) + (c*(b^2 - 4*a*c)*(2*c*d - b*e)*(7*b*e*g + 2*c*(e*f - 8*d*g))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(32*e^7*(c*d^2 - b*d*e + a*e^2)^(3/2)) - (c^2*(2*c*d - b*e)*(7*b*e*g + 2*c*(e*f - 8*d*g))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(4*e^9*Sqrt[c*d^2 - b*d*e + a*e^2]) + (5*(b^2 - 4*a*c)^3*(2*c*d*(e*f - 8*d*g) - e*(b*e*f - 15*b*d*g + 14*a*e*g))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2048*e^3*(c*d^2 - b*d*e + a*e^2)^(7/2))}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)/(d + e*x)^9, x, 31, -((c^3*g*Sqrt[a + b*x + c*x^2])/(e^8*(d + e*x))) - (5*(b^2 - 4*a*c)^2*(2*c*d - b*e)*g*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(1024*e^3*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^2) + (3*c*(b^2 - 4*a*c)*(2*c*d - b*e)*g*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(128*e^5*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) - (c^2*(2*c*d - b*e)*g*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(8*e^7*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) - (35*(b^2 - 4*a*c)^3*(e*f - d*g)*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(16384*e*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^2) - (c^2*g*(a + b*x + c*x^2)^(3/2))/(3*e^6*(d + e*x)^3) + (5*(b^2 - 4*a*c)*(2*c*d - b*e)*g*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(384*e^3*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^4) - (c*(2*c*d - b*e)*g*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(16*e^5*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^4) + (35*(b^2 - 4*a*c)^2*(e*f - d*g)*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(6144*e*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^4) - (c*g*(a + b*x + c*x^2)^(5/2))/(5*e^4*(d + e*x)^5) - ((2*c*d - b*e)*g*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(5/2))/(24*e^3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^6) - (7*(b^2 - 4*a*c)*(e*f - d*g)*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(5/2))/(384*e*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^6) - (g*(a + b*x + c*x^2)^(7/2))/(7*e^2*(d + e*x)^7) + ((e*f - d*g)*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(7/2))/(16*e*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^8) + (c^(7/2)*g*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/e^9 + (5*(b^2 - 4*a*c)^3*(2*c*d - b*e)*g*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2048*e^3*(c*d^2 - b*d*e + a*e^2)^(7/2)) - (3*c*(b^2 - 4*a*c)^2*(2*c*d - b*e)*g*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(256*e^5*(c*d^2 - b*d*e + a*e^2)^(5/2)) + (c^2*(b^2 - 4*a*c)*(2*c*d - b*e)*g*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(16*e^7*(c*d^2 - b*d*e + a*e^2)^(3/2)) - (c^3*(2*c*d - b*e)*g*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2*e^9*Sqrt[c*d^2 - b*d*e + a*e^2]) + (35*(b^2 - 4*a*c)^4*(e*f - d*g)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(32768*e*(c*d^2 - b*d*e + a*e^2)^(9/2))}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)/(d + e*x)^10, x, 7, -((35*(b^2 - 4*a*c)^3*(2*c*d*f - b*e*f - b*d*g + 2*a*e*g)*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(32768*(c*d^2 - b*d*e + a*e^2)^5*(d + e*x)^2)) + (35*(b^2 - 4*a*c)^2*(2*c*d*f - b*e*f - b*d*g + 2*a*e*g)*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(12288*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^4) - (7*(b^2 - 4*a*c)*(2*c*d*f - b*e*f - b*d*g + 2*a*e*g)*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(5/2))/(768*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^6) + ((2*c*d*f - b*e*f - b*d*g + 2*a*e*g)*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(7/2))/(32*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^8) - ((e*f - d*g)*(a + b*x + c*x^2)^(9/2))/(9*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^9) + (35*(b^2 - 4*a*c)^4*(2*c*d*f - b*e*f - b*d*g + 2*a*e*g)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(65536*(c*d^2 - b*d*e + a*e^2)^(11/2))}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)/(d + e*x)^11, x, 8, -((7*(b^2 - 4*a*c)^3*(40*c^2*d^2*f + b*e*(11*b*e*f + 9*b*d*g - 20*a*e*g) - 4*c*(a*e*(e*f - 11*d*g) + 5*b*d*(2*e*f + d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(131072*(c*d^2 - b*d*e + a*e^2)^6*(d + e*x)^2)) + (7*(b^2 - 4*a*c)^2*(40*c^2*d^2*f + b*e*(11*b*e*f + 9*b*d*g - 20*a*e*g) - 4*c*(a*e*(e*f - 11*d*g) + 5*b*d*(2*e*f + d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(49152*(c*d^2 - b*d*e + a*e^2)^5*(d + e*x)^4) - (7*(b^2 - 4*a*c)*(40*c^2*d^2*f + b*e*(11*b*e*f + 9*b*d*g - 20*a*e*g) - 4*c*(a*e*(e*f - 11*d*g) + 5*b*d*(2*e*f + d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(5/2))/(15360*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^6) + ((40*c^2*d^2*f + b*e*(11*b*e*f + 9*b*d*g - 20*a*e*g) - 4*c*(a*e*(e*f - 11*d*g) + 5*b*d*(2*e*f + d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(7/2))/(640*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^8) - ((e*f - d*g)*(a + b*x + c*x^2)^(9/2))/(10*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^10) - ((2*c*d*(11*e*f - d*g) - e*(11*b*e*f + 9*b*d*g - 20*a*e*g))*(a + b*x + c*x^2)^(9/2))/(180*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^9) + (7*(b^2 - 4*a*c)^4*(40*c^2*d^2*f + b*e*(11*b*e*f + 9*b*d*g - 20*a*e*g) - 4*c*(a*e*(e*f - 11*d*g) + 5*b*d*(2*e*f + d*g)))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(262144*(c*d^2 - b*d*e + a*e^2)^(13/2))}
# {(f + g*x)*(a + b*x + c*x^2)^(7/2)/(d + e*x)^12, x, 9, -((7*(b^2 - 4*a*c)^3*(80*c^3*d^3*f - b^2*e^2*(13*b*e*f + 9*b*d*g - 22*a*e*g) - 8*c^2*d*(3*a*e*(e*f - 4*d*g) + 5*b*d*(3*e*f + d*g)) - 2*c*e*(4*a^2*e^2*g - 6*a*b*e*(e*f - 7*d*g) - 3*b^2*d*(11*e*f + 6*d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(262144*(c*d^2 - b*d*e + a*e^2)^7*(d + e*x)^2)) + (7*(b^2 - 4*a*c)^2*(80*c^3*d^3*f - b^2*e^2*(13*b*e*f + 9*b*d*g - 22*a*e*g) - 8*c^2*d*(3*a*e*(e*f - 4*d*g) + 5*b*d*(3*e*f + d*g)) - 2*c*e*(4*a^2*e^2*g - 6*a*b*e*(e*f - 7*d*g) - 3*b^2*d*(11*e*f + 6*d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(98304*(c*d^2 - b*d*e + a*e^2)^6*(d + e*x)^4) - (7*(b^2 - 4*a*c)*(80*c^3*d^3*f - b^2*e^2*(13*b*e*f + 9*b*d*g - 22*a*e*g) - 8*c^2*d*(3*a*e*(e*f - 4*d*g) + 5*b*d*(3*e*f + d*g)) - 2*c*e*(4*a^2*e^2*g - 6*a*b*e*(e*f - 7*d*g) - 3*b^2*d*(11*e*f + 6*d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(5/2))/(30720*(c*d^2 - b*d*e + a*e^2)^5*(d + e*x)^6) + ((80*c^3*d^3*f - b^2*e^2*(13*b*e*f + 9*b*d*g - 22*a*e*g) - 8*c^2*d*(3*a*e*(e*f - 4*d*g) + 5*b*d*(3*e*f + d*g)) - 2*c*e*(4*a^2*e^2*g - 6*a*b*e*(e*f - 7*d*g) - 3*b^2*d*(11*e*f + 6*d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(7/2))/(1280*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^8) - ((e*f - d*g)*(a + b*x + c*x^2)^(9/2))/(11*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^11) - ((c*(26*d*e*f - 4*d^2*g) - e*(13*b*e*f + 9*b*d*g - 22*a*e*g))*(a + b*x + c*x^2)^(9/2))/(220*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^10) - ((4*c^2*d^2*(123*e*f - 2*d*g) + 11*b*e^2*(13*b*e*f + 9*b*d*g - 22*a*e*g) - 2*c*e*(2*a*e*(20*e*f - 141*d*g) + 3*b*d*(82*e*f + 39*d*g)))*(a + b*x + c*x^2)^(9/2))/(3960*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^9) + (7*(b^2 - 4*a*c)^4*(80*c^3*d^3*f - b^2*e^2*(13*b*e*f + 9*b*d*g - 22*a*e*g) - 8*c^2*d*(3*a*e*(e*f - 4*d*g) + 5*b*d*(3*e*f + d*g)) - 2*c*e*(4*a^2*e^2*g - 6*a*b*e*(e*f - 7*d*g) - 3*b^2*d*(11*e*f + 6*d*g)))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(524288*(c*d^2 - b*d*e + a*e^2)^(15/2))}

# {(f + g*x)*(a + b*x + c*x^2)^(7/2)/(d + e*x)^13, x, 10, -((1/(2097152*(c*d^2 - b*d*e + a*e^2)^8*(d + e*x)^2))*(7*(b^2 - 4*a*c)^3*(640*c^4*d^4*f + 13*b^3*e^3*(5*b*e*f + 3*b*d*g - 8*a*e*g) - 64*c^3*d^2*(a*e*(6*e*f - 13*d*g) + 5*b*d*(4*e*f + d*g)) + 16*c^2*e*(a^2*e^2*(e*f - 13*d*g) + 6*a*b*d*e*(4*e*f - 11*d*g) + 3*b^2*d^2*(22*e*f + 9*d*g)) + 8*b*c*e^2*(12*a^2*e^2*g - a*b*e*(13*e*f - 67*d*g) - b^2*d*(52*e*f + 27*d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])) + (1/(786432*(c*d^2 - b*d*e + a*e^2)^7*(d + e*x)^4))*(7*(b^2 - 4*a*c)^2*(640*c^4*d^4*f + 13*b^3*e^3*(5*b*e*f + 3*b*d*g - 8*a*e*g) - 64*c^3*d^2*(a*e*(6*e*f - 13*d*g) + 5*b*d*(4*e*f + d*g)) + 16*c^2*e*(a^2*e^2*(e*f - 13*d*g) + 6*a*b*d*e*(4*e*f - 11*d*g) + 3*b^2*d^2*(22*e*f + 9*d*g)) + 8*b*c*e^2*(12*a^2*e^2*g - a*b*e*(13*e*f - 67*d*g) - b^2*d*(52*e*f + 27*d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2)) - (1/(245760*(c*d^2 - b*d*e + a*e^2)^6*(d + e*x)^6))*(7*(b^2 - 4*a*c)*(640*c^4*d^4*f + 13*b^3*e^3*(5*b*e*f + 3*b*d*g - 8*a*e*g) - 64*c^3*d^2*(a*e*(6*e*f - 13*d*g) + 5*b*d*(4*e*f + d*g)) + 16*c^2*e*(a^2*e^2*(e*f - 13*d*g) + 6*a*b*d*e*(4*e*f - 11*d*g) + 3*b^2*d^2*(22*e*f + 9*d*g)) + 8*b*c*e^2*(12*a^2*e^2*g - a*b*e*(13*e*f - 67*d*g) - b^2*d*(52*e*f + 27*d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(5/2)) + (1/(10240*(c*d^2 - b*d*e + a*e^2)^5*(d + e*x)^8))*((640*c^4*d^4*f + 13*b^3*e^3*(5*b*e*f + 3*b*d*g - 8*a*e*g) - 64*c^3*d^2*(a*e*(6*e*f - 13*d*g) + 5*b*d*(4*e*f + d*g)) + 16*c^2*e*(a^2*e^2*(e*f - 13*d*g) + 6*a*b*d*e*(4*e*f - 11*d*g) + 3*b^2*d^2*(22*e*f + 9*d*g)) + 8*b*c*e^2*(12*a^2*e^2*g - a*b*e*(13*e*f - 67*d*g) - b^2*d*(52*e*f + 27*d*g)))*(b*d - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(7/2)) - ((e*f - d*g)*(a + b*x + c*x^2)^(9/2))/(12*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^12) - ((2*c*d*(5*e*f - d*g) - e*(5*b*e*f + 3*b*d*g - 8*a*e*g))*(a + b*x + c*x^2)^(9/2))/(88*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^11) - ((8*c^2*d^2*(27*e*f - d*g) + 13*b*e^2*(5*b*e*f + 3*b*d*g - 8*a*e*g) - 4*c*e*(a*e*(11*e*f - 63*d*g) + 6*b*d*(9*e*f + 4*d*g)))*(a + b*x + c*x^2)^(9/2))/(1760*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^10) - ((16*c^3*d^3*(247*e*f - d*g) - 143*b^2*e^3*(5*b*e*f + 3*b*d*g - 8*a*e*g) - 8*c^2*d*e*(a*e*(221*e*f - 633*d*g) + 3*b*d*(247*e*f + 81*d*g)) - 2*c*e^2*(320*a^2*e^2*g - 2*a*b*e*(221*e*f - 1045*d*g) - b^2*d*(1703*e*f + 837*d*g)))*(a + b*x + c*x^2)^(9/2))/(31680*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^9) + (1/(4194304*(c*d^2 - b*d*e + a*e^2)^(17/2)))*(7*(b^2 - 4*a*c)^4*(640*c^4*d^4*f + 13*b^3*e^3*(5*b*e*f + 3*b*d*g - 8*a*e*g) - 64*c^3*d^2*(a*e*(6*e*f - 13*d*g) + 5*b*d*(4*e*f + d*g)) + 16*c^2*e*(a^2*e^2*(e*f - 13*d*g) + 6*a*b*d*e*(4*e*f - 11*d*g) + 3*b^2*d^2*(22*e*f + 9*d*g)) + 8*b*c*e^2*(12*a^2*e^2*g - a*b*e*(13*e*f - 67*d*g) - b^2*d*(52*e*f + 27*d*g)))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])} 
[(5-x)*(3+2*x)^4*sqrt(2+5*x+3*x^2),x,7,478/315*(3+2*x)^2*(2+5*x+3*x^2)^(3/2)+229/378*(3+2*x)^3*(2+5*x+3*x^2)^(3/2)-1/21*(3+2*x)^4*(2+5*x+3*x^2)^(3/2)+1/68040*(874301+378774*x)*(2+5*x+3*x^2)^(3/2)-25969/31104*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+25969/15552*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^3*sqrt(2+5*x+3*x^2),x,6,11/15*(3+2*x)^2*(2+5*x+3*x^2)^(3/2)-1/18*(3+2*x)^3*(2+5*x+3*x^2)^(3/2)+1/3240*(27487+11538*x)*(2+5*x+3*x^2)^(3/2)-6221/10368*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+6221/5184*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^2*sqrt(2+5*x+3*x^2),x,5,-1/15*(3+2*x)^2*(2+5*x+3*x^2)^(3/2)+1/1620*(7969+3006*x)*(2+5*x+3*x^2)^(3/2)-2267/5184*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+2267/2592*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)*sqrt(2+5*x+3*x^2),x,4,1/108*(109-18*x)*(2+5*x+3*x^2)^(3/2)-559/1728*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+559/864*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*sqrt(2+5*x+3*x^2),x,4,-1/9*(2+5*x+3*x^2)^(3/2)-35/144*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+35/72*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x),x,6,-311/48*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+13/8*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+1/24*(73-6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2,x,6,43/8*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-57/8*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-1/2*(8+x)*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^3,x,6,-1/8*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+27/80*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+1/40*(121+124*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^4,x,4,-13/15*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3-47/400*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+47/200*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^5,x,5,-13/20*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4-4/5*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3-153/1600*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+153/800*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^6,x,6,-13/25*(2+5*x+3*x^2)^(3/2)/(3+2*x)^5-339/500*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4-87/125*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3-3159/40000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+3159/20000*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^7,x,7,-13/30*(2+5*x+3*x^2)^(3/2)/(3+2*x)^6-73/125*(2+5*x+3*x^2)^(3/2)/(3+2*x)^5-3113/5000*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4-2237/3750*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3-26453/400000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+26453/200000*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(3+2*x)^4*(2+5*x+3*x^2)^(3/2),x,8,454969/559872*(5+6*x)*(2+5*x+3*x^2)^(3/2)+487/486*(3+2*x)^2*(2+5*x+3*x^2)^(5/2)+299/648*(3+2*x)^3*(2+5*x+3*x^2)^(5/2)-1/27*(3+2*x)^4*(2+5*x+3*x^2)^(5/2)+1/58320*(420721+188910*x)*(2+5*x+3*x^2)^(5/2)+454969/8957952*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-454969/4478976*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^3*(2+5*x+3*x^2)^(3/2),x,7,12277/20736*(5+6*x)*(2+5*x+3*x^2)^(3/2)+67/126*(3+2*x)^2*(2+5*x+3*x^2)^(5/2)-1/24*(3+2*x)^3*(2+5*x+3*x^2)^(5/2)+1/15120*(75451+33210*x)*(2+5*x+3*x^2)^(5/2)+12277/331776*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-12277/165888*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^2*(2+5*x+3*x^2)^(3/2),x,6,1129/2592*(5+6*x)*(2+5*x+3*x^2)^(3/2)-1/21*(3+2*x)^2*(2+5*x+3*x^2)^(5/2)+1/1890*(5827+2370*x)*(2+5*x+3*x^2)^(5/2)+1129/41472*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-1129/20736*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)*(2+5*x+3*x^2)^(3/2),x,5,839/2592*(5+6*x)*(2+5*x+3*x^2)^(3/2)+1/270*(161-30*x)*(2+5*x+3*x^2)^(5/2)+839/41472*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-839/20736*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(3/2),x,5,35/144*(5+6*x)*(2+5*x+3*x^2)^(3/2)-1/15*(2+5*x+3*x^2)^(5/2)+35/2304*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-35/1152*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x),x,7,1/48*(47-6*x)*(2+5*x+3*x^2)^(3/2)-2011/256*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+65/32*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+1/128*(175-414*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2,x,7,-1/6*(21+x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)+3743/192*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-161/32*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)-1/96*(361-726*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3,x,7,-1/4*(8+x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-343/64*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+1329/64*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+3/16*(93+43*x)*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4,x,7,1/120*(383+342*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3+51/32*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)-1973/320*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-1/160*(845+402*x)*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^5,x,7,1/240*(333+352*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4-3/32*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+2359/6400*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+1/3200*(2087+1528*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^6,x,5,47/400*(7+8*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4-13/25*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5+141/32000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-141/16000*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^7,x,6,1141/12000*(7+8*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4-13/30*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6-167/375*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5+1141/320000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-1141/160000*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^8,x,7,4663/60000*(7+8*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4-13/35*(2+5*x+3*x^2)^(5/2)/(3+2*x)^7-433/1050*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6-4892/13125*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5+4663/1600000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-4663/800000*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^9,x,8,51309/800000*(7+8*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4-13/40*(2+5*x+3*x^2)^(5/2)/(3+2*x)^8-19/50*(2+5*x+3*x^2)^(5/2)/(3+2*x)^7-717/2000*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6-3879/12500*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5+153927/64000000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-153927/32000000*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(3+2*x)^4*(2+5*x+3*x^2)^(5/2),x,9,-249299/4478976*(5+6*x)*(2+5*x+3*x^2)^(3/2)+249299/466560*(5+6*x)*(2+5*x+3*x^2)^(5/2)+3298/4455*(3+2*x)^2*(2+5*x+3*x^2)^(7/2)+41/110*(3+2*x)^3*(2+5*x+3*x^2)^(7/2)-1/33*(3+2*x)^4*(2+5*x+3*x^2)^(7/2)+1/1496880*(7405817+3365726*x)*(2+5*x+3*x^2)^(7/2)-249299/71663616*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+249299/35831808*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^3*(2+5*x+3*x^2)^(5/2),x,8,-182917/4478976*(5+6*x)*(2+5*x+3*x^2)^(3/2)+182917/466560*(5+6*x)*(2+5*x+3*x^2)^(5/2)+169/405*(3+2*x)^2*(2+5*x+3*x^2)^(7/2)-1/30*(3+2*x)^3*(2+5*x+3*x^2)^(7/2)+1/136080*(477101+213878*x)*(2+5*x+3*x^2)^(7/2)-182917/71663616*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+182917/35831808*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^2*(2+5*x+3*x^2)^(5/2),x,7,-22535/746496*(5+6*x)*(2+5*x+3*x^2)^(3/2)+4507/15552*(5+6*x)*(2+5*x+3*x^2)^(5/2)-1/27*(3+2*x)^2*(2+5*x+3*x^2)^(7/2)+1/4536*(10211+4298*x)*(2+5*x+3*x^2)^(7/2)-22535/11943936*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+22535/5971968*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)*(2+5*x+3*x^2)^(5/2),x,6,-1865/82944*(5+6*x)*(2+5*x+3*x^2)^(3/2)+373/1728*(5+6*x)*(2+5*x+3*x^2)^(5/2)+1/168*(71-14*x)*(2+5*x+3*x^2)^(7/2)-1865/1327104*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+1865/663552*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(5/2),x,6,-175/10368*(5+6*x)*(2+5*x+3*x^2)^(3/2)+35/216*(5+6*x)*(2+5*x+3*x^2)^(5/2)-1/21*(2+5*x+3*x^2)^(7/2)-175/165888*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+175/82944*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x),x,8,1/3456*(25-5586*x)*(2+5*x+3*x^2)^(3/2)+1/360*(209-30*x)*(2+5*x+3*x^2)^(5/2)-543811/55296*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+325/128*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+1/27648*(51455-106734*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^2,x,8,-1/192*(65-1194*x)*(2+5*x+3*x^2)^(3/2)-1/10*(34+x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)+41053/1024*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-1325/128*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)-1/512*(3865-8082*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^3,x,8,5/192*(573+164*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)-1/16*(29+2*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^2-199615/3072*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+4295/256*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+5/1536*(3763-7854*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^4,x,8,5/48*(93+43*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2-1/6*(8+x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^3+13505/256*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-3487/256*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)-5/64*(736+343*x)*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5,x,8,-1/384*(3727+2898*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3-1/16*(19+4*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^4-1875/256*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+29047/1024*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+1/512*(12265+5718*x)*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6,x,8,1/9600*(17051+13074*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3+1/80*(119+114*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5+177/128*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)-137111/25600*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-1/12800*(57845+26934*x)*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^7,x,8,1/1920*(437+328*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4+1/120*(109+116*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6-9/128*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+13931/51200*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+1/25600*(14083+10952*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^8,x,6,-47/9600*(7+8*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4+47/600*(7+8*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6-13/35*(2+5*x+3*x^2)^(7/2)/(3+2*x)^7-47/256000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+47/128000*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^9,x,7,-1517/384000*(7+8*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4+1517/24000*(7+8*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6-13/40*(2+5*x+3*x^2)^(7/2)/(3+2*x)^8-107/350*(2+5*x+3*x^2)^(7/2)/(3+2*x)^7-1517/10240000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+1517/5120000*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^10,x,8,-6167/1920000*(7+8*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4+6167/120000*(7+8*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6-13/45*(2+5*x+3*x^2)^(7/2)/(3+2*x)^9-527/1800*(2+5*x+3*x^2)^(7/2)/(3+2*x)^8-1321/5250*(2+5*x+3*x^2)^(7/2)/(3+2*x)^7-6167/51200000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+6167/25600000*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(3+2*x)^4*(2+5*x+3*x^2)^(7/2),x,10,2595845/644972544*(5+6*x)*(2+5*x+3*x^2)^(3/2)-519169/13436928*(5+6*x)*(2+5*x+3*x^2)^(5/2)+74167/186624*(5+6*x)*(2+5*x+3*x^2)^(7/2)+205/351*(3+2*x)^2*(2+5*x+3*x^2)^(9/2)+439/1404*(3+2*x)^3*(2+5*x+3*x^2)^(9/2)-1/39*(3+2*x)^4*(2+5*x+3*x^2)^(9/2)+1/227448*(852175+389394*x)*(2+5*x+3*x^2)^(9/2)+2595845/10319560704*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-2595845/5159780352*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^3*(2+5*x+3*x^2)^(7/2),x,9,637609/214990848*(5+6*x)*(2+5*x+3*x^2)^(3/2)-637609/22394880*(5+6*x)*(2+5*x+3*x^2)^(5/2)+91087/311040*(5+6*x)*(2+5*x+3*x^2)^(7/2)+34/99*(3+2*x)^2*(2+5*x+3*x^2)^(9/2)-1/36*(3+2*x)^3*(2+5*x+3*x^2)^(9/2)+1/320760*(863825+390798*x)*(2+5*x+3*x^2)^(9/2)+637609/3439853568*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-637609/1719926784*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^2*(2+5*x+3*x^2)^(7/2),x,8,39389/17915904*(5+6*x)*(2+5*x+3*x^2)^(3/2)-39389/1866240*(5+6*x)*(2+5*x+3*x^2)^(5/2)+5627/25920*(5+6*x)*(2+5*x+3*x^2)^(7/2)-1/33*(3+2*x)^2*(2+5*x+3*x^2)^(9/2)+1/26730*(47425+20358*x)*(2+5*x+3*x^2)^(9/2)+39389/286654464*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-39389/143327232*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)*(2+5*x+3*x^2)^(7/2),x,7,9793/5971968*(5+6*x)*(2+5*x+3*x^2)^(3/2)-9793/622080*(5+6*x)*(2+5*x+3*x^2)^(5/2)+1399/8640*(5+6*x)*(2+5*x+3*x^2)^(7/2)+1/810*(265-54*x)*(2+5*x+3*x^2)^(9/2)+9793/95551488*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-9793/47775744*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(7/2),x,7,1225/995328*(5+6*x)*(2+5*x+3*x^2)^(3/2)-245/20736*(5+6*x)*(2+5*x+3*x^2)^(5/2)+35/288*(5+6*x)*(2+5*x+3*x^2)^(7/2)-1/27*(2+5*x+3*x^2)^(9/2)+1225/15925248*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-1225/7962624*(5+6*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(7/2)/(3+2*x),x,9,5/331776*(6205-127338*x)*(2+5*x+3*x^2)^(3/2)-1/6912*(589+7446*x)*(2+5*x+3*x^2)^(5/2)+1/672*(277-42*x)*(2+5*x+3*x^2)^(7/2)-65251715/5308416*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+1625/512*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+5/2654208*(1229315-2568342*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^2,x,9,-1/13824*(6925-151098*x)*(2+5*x+3*x^2)^(3/2)+1/1440*(283+8310*x)*(2+5*x+3*x^2)^(5/2)-1/14*(47+x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)+15434623/221184*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-9225/512*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)-1/110592*(1454315-3037062*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^3,x,9,7/4608*(805-17394*x)*(2+5*x+3*x^2)^(3/2)+7/240*(584+121*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)-1/12*(21+x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^2-12443893/73728*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+44625/1024*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+7/36864*(167495-349806*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^4,x,9,-7/768*(5713+1652*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)+7/960*(1171+414*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^2-1/30*(37+3*x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^3+2776697/12288*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-59745/1024*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)-7/6144*(37375-78054*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^5,x,9,-35/768*(736+343*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^2+7/96*(93+43*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^3-1/8*(8+x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^4-744275/4096*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+192171/4096*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))*sqrt(5)+35/1024*(5795+2701*x)*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^6,x,9,7/7680*(42733+33142*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3+7/960*(1003+548*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^4-1/30*(27+5*x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^5+30275/1024*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)-2345091/20480*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-21/10240*(47145+21974*x)*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^7,x,9,-7/25600*(40201+31174*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3-7/1920*(1301+1046*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5-1/12*(11+3*x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^6-8547/1024*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+6620481/204800*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+63/102400*(44365+20678*x)*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^8,x,9,1/25600*(39767+30858*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^3+3/640*(135+106*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^5+1/280*(269+266*x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^7+603/512*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)-934161/204800*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-3/102400*(131465+61278*x)*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^9,x,9,1/102400*(20959+17096*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4+1/6400*(881+664*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6+1/1120*(757+808*x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^8-27/512*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)+1673211/8192000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+3/4096000*(559841+434104*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^10,x,7,329/1536000*(7+8*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4-329/96000*(7+8*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6+47/800*(7+8*x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^8-13/45*(2+5*x+3*x^2)^(9/2)/(3+2*x)^9+329/40960000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-329/20480000*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^11,x,8,4417/25600000*(7+8*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4-4417/1600000*(7+8*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6+1893/40000*(7+8*x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^8-13/50*(2+5*x+3*x^2)^(9/2)/(3+2*x)^10-29/125*(2+5*x+3*x^2)^(9/2)/(3+2*x)^9+13251/2048000000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-13251/1024000000*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^12,x,9,17899/128000000*(7+8*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4-17899/8000000*(7+8*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6+7671/200000*(7+8*x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^8-13/55*(2+5*x+3*x^2)^(9/2)/(3+2*x)^11-621/2750*(2+5*x+3*x^2)^(9/2)/(3+2*x)^10-3904/20625*(2+5*x+3*x^2)^(9/2)/(3+2*x)^9+53697/10240000000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-53697/5120000000*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],
[(5-x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^13,x,10,58373/512000000*(7+8*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^4-58373/32000000*(7+8*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^6+25017/800000*(7+8*x)*(2+5*x+3*x^2)^(7/2)/(3+2*x)^8-13/60*(2+5*x+3*x^2)^(9/2)/(3+2*x)^12-12/55*(2+5*x+3*x^2)^(9/2)/(3+2*x)^11-2067/11000*(2+5*x+3*x^2)^(9/2)/(3+2*x)^10-6379/41250*(2+5*x+3*x^2)^(9/2)/(3+2*x)^9+175119/40960000000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-175119/20480000000*(7+8*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^2],

# p<0
[(A+B*x)*(d+e*x)^3/sqrt(a+b*x+c*x^2),x,5,1/128*(35*b^4*B*e^3-40*b^3*c*e^2*(3*B*d+A*e)+24*b^2*c*e*(6*B*c*d^2+6*A*c*d*e-5*a*B*e^2)-32*b*c^2*(2*B*c*d^3+6*A*c*d^2*e-9*a*B*d*e^2-3*a*A*e^3)+16*c^2*(4*A*c*d*(2*c*d^2-3*a*e^2)-3*a*B*e*(4*c*d^2-a*e^2)))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)+1/24*(6*B*c*d-7*b*B*e+8*A*c*e)*(d+e*x)^2*sqrt(a+b*x+c*x^2)/c^2+1/4*B*(d+e*x)^3*sqrt(a+b*x+c*x^2)/c+1/192*(8*A*c*e*(64*c^2*d^2+15*b^2*e^2-2*c*e*(27*b*d+8*a*e))+B*(96*c^3*d^3-105*b^3*e^3+20*b*c*e^2*(18*b*d+11*a*e)-8*c^2*d*e*(47*b*d+48*a*e))+2*c*e*(40*A*c*e*(2*c*d-b*e)+B*(24*c^2*d^2+35*b^2*e^2-4*c*e*(16*b*d+9*a*e)))*x)*sqrt(a+b*x+c*x^2)/c^4],
[(A+B*x)*(d+e*x)^2/sqrt(a+b*x+c*x^2),x,4,-1/16*(5*b^3*B*e^2-6*b^2*c*e*(2*B*d+A*e)-8*c^2*(2*A*c*d^2-2*a*B*d*e-a*A*e^2)+4*b*c*(2*B*c*d^2+4*A*c*d*e-3*a*B*e^2))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+1/3*B*(d+e*x)^2*sqrt(a+b*x+c*x^2)/c+1/24*(6*A*c*e*(8*c*d-3*b*e)+B*(16*c^2*d^2+15*b^2*e^2-4*c*e*(9*b*d+4*a*e))+2*c*e*(4*B*c*d-5*b*B*e+6*A*c*e)*x)*sqrt(a+b*x+c*x^2)/c^3],
[(A+B*x)*(d+e*x)/sqrt(a+b*x+c*x^2),x,3,1/8*(3*b^2*B*e-4*b*c*(B*d+A*e)+4*c*(2*A*c*d-a*B*e))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-1/4*(3*b*B*e-4*c*(B*d+A*e)-2*B*c*e*x)*sqrt(a+b*x+c*x^2)/c^2],
[(A+B*x)/sqrt(a+b*x+c*x^2),x,3,-1/2*(b*B-2*A*c)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)+B*sqrt(a+b*x+c*x^2)/c],
[(A+B*x)/((d+e*x)*sqrt(a+b*x+c*x^2)),x,5,B*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/(e*sqrt(c))-(B*d-A*e)*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(e*sqrt(c*d^2-b*d*e+a*e^2))],
[(A+B*x)/((d+e*x)^2*sqrt(a+b*x+c*x^2)),x,3,-1/2*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(3/2)+(B*d-A*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x))],
[(A+B*x)/((d+e*x)^3*sqrt(a+b*x+c*x^2)),x,4,1/8*(b^2*e*(B*d+3*A*e)+4*c*(2*A*c*d^2+3*a*B*d*e-a*A*e^2)-4*b*(B*c*d^2+2*A*c*d*e+a*B*e^2))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)+1/2*(B*d-A*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^2)-1/4*(3*A*e*(2*c*d-b*e)-B*(2*c*d^2+e*(b*d-4*a*e)))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x))],
[(A+B*x)/((d+e*x)^4*sqrt(a+b*x+c*x^2)),x,5,-1/16*(b^3*e^2*(B*d+5*A*e)-2*b^2*e*(2*B*c*d^2+9*A*c*d*e+3*a*B*e^2)+4*b*c*(2*B*c*d^3+6*A*c*d^2*e+5*a*B*d*e^2-3*a*A*e^3)-8*c*(A*c*d*(2*c*d^2-3*a*e^2)+a*B*e*(4*c*d^2-a*e^2)))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)+1/3*(B*d-A*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^3)-1/12*(5*A*e*(2*c*d-b*e)-B*(4*c*d^2+e*(b*d-6*a*e)))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*(d+e*x)^2)+1/24*(B*(8*c^2*d^3+2*c*d*e*(5*b*d-26*a*e)-3*b*e^2*(b*d-6*a*e))-A*e*(44*c^2*d^2+15*b^2*e^2-4*c*e*(11*b*d+4*a*e)))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^3*(d+e*x))],
[(A+B*x)*(d+e*x)^3/(a+b*x+c*x^2)^(3/2),x,4,3/8*e*(4*A*c*e*(2*c*d-b*e)+B*(8*c^2*d^2+5*b^2*e^2-4*c*e*(3*b*d+a*e)))*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+2*(d+e*x)^2*(2*a*c*(B*d+A*e)-b*(A*c*d+a*B*e)-(b^2*B*e-b*c*(B*d+A*e)+2*c*(A*c*d-a*B*e))*x)/(c*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))-1/4*e*(15*b^3*B*e^2-12*b^2*c*e*(3*B*d+A*e)-32*c^2*(A*c*d^2-3*a*B*d*e-a*A*e^2)+4*b*c*(4*B*c*d^2+6*A*c*d*e-13*a*B*e^2)-2*c*e*(8*A*c^2*d+5*b^2*B*e-4*c*(b*B*d+A*b*e+3*a*B*e))*x)*sqrt(a+b*x+c*x^2)/(c^3*(b^2-4*a*c))],
[(A+B*x)*(d+e*x)^2/(a+b*x+c*x^2)^(3/2),x,4,1/2*e*(4*B*c*d-3*b*B*e+2*A*c*e)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)+2*(d+e*x)*(2*a*c*(B*d+A*e)-b*(A*c*d+a*B*e)-(b^2*B*e-b*c*(B*d+A*e)+2*c*(A*c*d-a*B*e))*x)/(c*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))+e*(4*A*c^2*d+3*b^2*B*e-2*c*(b*B*d+A*b*e+4*a*B*e))*sqrt(a+b*x+c*x^2)/(c^2*(b^2-4*a*c))],
[(A+B*x)*(d+e*x)/(a+b*x+c*x^2)^(3/2),x,3,B*e*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(3/2)+2*(2*a*c*(B*d+A*e)-b*(A*c*d+a*B*e)-(b^2*B*e-b*c*(B*d+A*e)+2*c*(A*c*d-a*B*e))*x)/(c*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))],
[(A+B*x)/(a+b*x+c*x^2)^(3/2),x,1,-2*(A*b-2*a*B-(b*B-2*A*c)*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))],
[(A+B*x)/((d+e*x)*(a+b*x+c*x^2)^(3/2)),x,4,-e*(B*d-A*e)*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(3/2)+2*(a*B*(2*c*d-b*e)-A*(b*c*d-b^2*e+2*a*c*e)+c*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2))],
[(A+B*x)/((d+e*x)^2*(a+b*x+c*x^2)^(3/2)),x,4,1/2*e*(3*A*e*(2*c*d-b*e)-B*(4*c*d^2-e*(b*d+2*a*e)))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)+2*(a*B*(2*c*d-b*e)-A*(b*c*d-b^2*e+2*a*c*e)+c*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*sqrt(a+b*x+c*x^2))+e*(b^2*e*(B*d-3*A*e)-4*c*(A*c*d^2+3*a*B*d*e-2*a*A*e^2)+2*b*(B*c*d^2+2*A*c*d*e+a*B*e^2))*sqrt(a+b*x+c*x^2)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x))],
[(A+B*x)/((d+e*x)^3*(a+b*x+c*x^2)^(3/2)),x,5,3/8*e*(A*e*(16*c^2*d^2+5*b^2*e^2-4*c*e*(4*b*d+a*e))-B*(8*c^2*d^3-4*c*d*e*(b*d+3*a*e)+b*e^2*(b*d+4*a*e)))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)+2*(a*B*(2*c*d-b*e)-A*(b*c*d-b^2*e+2*a*c*e)+c*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^2*sqrt(a+b*x+c*x^2))+1/2*e*(b^2*e*(B*d-5*A*e)-4*c*(2*A*c*d^2+5*a*B*d*e-3*a*A*e^2)+4*b*(B*c*d^2+2*A*c*d*e+a*B*e^2))*sqrt(a+b*x+c*x^2)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^2)-1/4*e*(3*b^3*e^2*(B*d-5*A*e)-2*b^2*e*(5*B*c*d^2-19*A*c*d*e-6*a*B*e^2)-4*b*c*(2*B*c*d^3+6*A*c*d^2*e+9*a*B*d*e^2-13*a*A*e^3)+8*c*(A*c*d*(2*c*d^2-13*a*e^2)+a*B*e*(11*c*d^2-4*a*e^2)))*sqrt(a+b*x+c*x^2)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x))],
[(A+B*x)*(d+e*x)^4/(a+b*x+c*x^2)^(5/2),x,5,2/3*(d+e*x)^3*(2*a*c*(B*d+A*e)-b*(A*c*d+a*B*e)-(b^2*B*e-b*c*(B*d+A*e)+2*c*(A*c*d-a*B*e))*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^(3/2))+1/2*e^3*(8*B*c*d-5*b*B*e+2*A*c*e)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+2/3*(d+e*x)*(b^3*B*e*(c*d^2-5*a*e^2)-8*a*c^2*e*(A*c*d^2+8*a*B*d*e+3*a*A*e^2)-2*b^2*c*(2*B*c*d^3+5*A*c*d^2*e-2*a*B*d*e^2-a*A*e^3)+4*b*c*(2*A*c*d*(c*d^2+3*a*e^2)+a*B*e*(5*c*d^2+7*a*e^2))-(5*b^4*B*e^3-2*b^3*c*e^2*(3*B*d+A*e)-4*b^2*c*e*(B*c*d^2+A*c*d*e+8*a*B*e^2)+8*b*c^2*(B*c*d^3+3*A*c*d^2*e+6*a*B*d*e^2+2*a*A*e^3)-16*c^2*(2*a*B*e*(c*d^2-a*e^2)+A*c*d*(c*d^2+2*a*e^2)))*x)/(c^2*(b^2-4*a*c)^2*sqrt(a+b*x+c*x^2))+1/3*e*(15*b^4*B*e^3-2*b^3*c*e^2*(7*B*d+3*A*e)-4*b^2*c*e*(2*B*c*d^2+A*c*d*e+25*a*B*e^2)+8*b*c^2*(2*B*c*d^3+6*A*c*d^2*e+13*a*B*d*e^2+5*a*A*e^3)-16*c^2*(4*a*B*e*(c*d^2-2*a*e^2)+A*c*d*(2*c*d^2+5*a*e^2)))*sqrt(a+b*x+c*x^2)/(c^3*(b^2-4*a*c)^2)],
[(A+B*x)*(d+e*x)^3/(a+b*x+c*x^2)^(5/2),x,4,2/3*(d+e*x)^2*(2*a*c*(B*d+A*e)-b*(A*c*d+a*B*e)-(b^2*B*e-b*c*(B*d+A*e)+2*c*(A*c*d-a*B*e))*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^(3/2))+B*e^3*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(5/2)-2/3*(4*b^2*c^2*d^2*(B*d+2*A*e)+16*a*c^2*e*(A*c*d^2+3*a*B*d*e+a*A*e^2)-b^3*B*(c*d^2*e-3*a*e^3)-4*b*c*(5*a*B*e*(c*d^2+a*e^2)+2*A*c*d*(c*d^2+3*a*e^2))-(2*b^3*B*c*d*e^2-3*b^4*B*e^3+2*b^2*c*e*(3*B*c*d^2+4*A*c*d*e+11*a*B*e^2)-8*b*c^2*(B*c*d^3+3*A*c*d^2*e+4*a*B*d*e^2+a*A*e^3)+8*c^2*(3*a*B*e*(c*d^2-a*e^2)+2*A*c*d*(c*d^2+a*e^2)))*x)/(c^2*(b^2-4*a*c)^2*sqrt(a+b*x+c*x^2))],
[(A+B*x)*(d+e*x)^2/(a+b*x+c*x^2)^(5/2),x,2,-2/3*(A*b-2*a*B-(b*B-2*A*c)*x)*(d+e*x)^2/((b^2-4*a*c)*(a+b*x+c*x^2)^(3/2))-8/3*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)^2*sqrt(a+b*x+c*x^2))],
[(A+B*x)*(d+e*x)/(a+b*x+c*x^2)^(5/2),x,2,2/3*(2*a*c*(B*d+A*e)-b*(A*c*d+a*B*e)-(b^2*B*e-b*c*(B*d+A*e)+2*c*(A*c*d-a*B*e))*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^(3/2))+2/3*(b^2*B*e-4*b*c*(B*d+A*e)+4*c*(2*A*c*d+a*B*e))*(b+2*c*x)/(c*(b^2-4*a*c)^2*sqrt(a+b*x+c*x^2))],
[(A+B*x)/(a+b*x+c*x^2)^(5/2),x,2,-2/3*(A*b-2*a*B-(b*B-2*A*c)*x)/((b^2-4*a*c)*(a+b*x+c*x^2)^(3/2))-8/3*(b*B-2*A*c)*(b+2*c*x)/((b^2-4*a*c)^2*sqrt(a+b*x+c*x^2))],
[(A+B*x)/((d+e*x)*(a+b*x+c*x^2)^(5/2)),x,5,2/3*(a*B*(2*c*d-b*e)-A*(b*c*d-b^2*e+2*a*c*e)+c*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(3/2))-e^3*(B*d-A*e)*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(5/2)+2/3*(4*a*c*e*(2*c*d-b*e)*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)+(b*c*d-b^2*e+2*a*c*e)*(3*b^2*e*(B*d-A*e)-4*b*c*d*(B*d+A*e)+4*c*(2*A*c*d^2-a*B*d*e+3*a*A*e^2))+c*(4*c*e*(b*d-2*a*e)*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)+(2*c*d-b*e)*(3*b^2*e*(B*d-A*e)-4*b*c*d*(B*d+A*e)+4*c*(2*A*c*d^2-a*B*d*e+3*a*A*e^2)))*x)/((b^2-4*a*c)^2*(c*d^2-b*d*e+a*e^2)^2*sqrt(a+b*x+c*x^2))],
[(A+B*x)/((d+e*x)^2*(a+b*x+c*x^2)^(5/2)),x,5,2/3*(a*B*(2*c*d-b*e)-A*(b*c*d-b^2*e+2*a*c*e)+c*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(d+e*x)*(a+b*x+c*x^2)^(3/2))+1/2*e^3*(5*A*e*(2*c*d-b*e)-B*(8*c*d^2-e*(3*b*d+2*a*e)))*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)+2/3*(6*a*c*e*(2*c*d-b*e)*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)+(b*c*d-b^2*e+2*a*c*e)*(b^2*e*(3*B*d-5*A*e)+8*c*(A*c*d^2-a*B*d*e+2*a*A*e^2)-2*b*(2*B*c*d^2+A*c*d*e-a*B*e^2))+c*(6*c*e*(b*d-2*a*e)*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)+(2*c*d-b*e)*(b^2*e*(3*B*d-5*A*e)+8*c*(A*c*d^2-a*B*d*e+2*a*A*e^2)-2*b*(2*B*c*d^2+A*c*d*e-a*B*e^2)))*x)/((b^2-4*a*c)^2*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)*sqrt(a+b*x+c*x^2))+1/3*e*(3*b^4*e^3*(3*B*d-5*A*e)-2*b^3*e^2*(9*B*c*d^2-10*A*c*d*e-3*a*B*e^2)+4*b^2*c*e*(10*B*c*d^3+3*A*c*d^2*e-14*a*B*d*e^2+25*a*A*e^3)-16*c^2*(a*B*d*e*(2*c*d^2-13*a*e^2)-A*(2*c^2*d^4+9*a*c*d^2*e^2-8*a^2*e^4))-8*b*c*(2*A*c*d*e*(4*c*d^2+9*a*e^2)+B*(2*c^2*d^4+3*a*c*d^2*e^2+5*a^2*e^4)))*sqrt(a+b*x+c*x^2)/((b^2-4*a*c)^2*(c*d^2-b*d*e+a*e^2)^3*(d+e*x))],

#  {(A + B*x)*(d + e*x)^7/(a + b*x + c*x^2)^(7/2), x, 6, (2*(d + e*x)^6*(2*a*c*(B*d + A*e) - b*(A*c*d + a*B*e) - (b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*x))/(5*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(5/2)) + (1/(15*c^2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(3/2)))*(2*(d + e*x)^4*(3*b^3*B*e*(c*d^2 - 3*a*e^2) - 16*a*c^2*e*(A*c*d^2 + 7*a*B*d*e + 3*a*A*e^2) - 4*b^2*c*(2*B*c*d^3 + 5*A*c*d^2*e - a*B*d*e^2 - a*A*e^3) + 4*b*c*(4*A*c*d*(c*d^2 + 3*a*e^2) + a*B*e*(9*c*d^2 + 13*a*e^2)) - (9*b^4*B*e^3 - 2*b^3*c*e^2*(5*B*d + 2*A*e) - 2*b^2*c*e*(5*B*c*d^2 + 4*A*c*d*e + 29*a*B*e^2) + 8*b*c^2*(2*B*c*d^3 + 6*A*c*d^2*e + 11*a*B*d*e^2 + 4*a*A*e^3) - 8*c^2*(7*a*B*e*(c*d^2 - a*e^2) + 4*A*c*d*(c*d^2 + 2*a*e^2)))*x)) + (1/(15*c^3*(b^2 - 4*a*c)^3*Sqrt[a + b*x + c*x^2]))*(2*(d + e*x)^2*(9*b^5*B*e^3*(c*d^2 - 7*a*e^2) - 64*a^2*c^3*e^3*(2*A*c*d^2 - 49*a*B*d*e - 12*a*A*e^2) - 4*b^4*c*e^2*(B*c*d^3 + A*c*d^2*e - 22*a*B*d*e^2 - 7*a*A*e^3) - 8*b^3*c*e*(A*c*d*e*(27*c*d^2 + a*e^2) + B*(13*c^2*d^4 + 8*a*c*d^2*e^2 - 71*a^2*e^4)) - 16*b*c^2*(2*A*c*d*(4*c^2*d^4 + 13*a*c*d^2*e^2 + 19*a^2*e^4) + a*B*e*(14*c^2*d^4 + 73*a*c*d^2*e^2 + 87*a^2*e^4)) + 16*b^2*c^2*(A*e*(20*c^2*d^4 + 43*a*c*d^2*e^2 - 15*a^2*e^4) + B*(4*c^2*d^5 + 41*a*c*d^3*e^2 - 51*a^2*d*e^4)) - (63*b^6*B*e^5 - 2*b^5*c*e^4*(53*B*d + 14*A*e) - 2*b^4*c*e^3*(5*B*c*d^2 - 8*A*c*d*e + 311*a*B*e^2) + 8*b^3*c^2*e^2*(B*c*d^3 - A*c*d^2*e + 133*a*B*d*e^2 + 33*a*A*e^3) + 32*c^3*(7*a*B*e*(2*c^2*d^4 + 11*a*c*d^2*e^2 - 5*a^2*e^4) + 2*A*c*d*(4*c^2*d^4 + 13*a*c*d^2*e^2 + 23*a^2*e^4)) + 16*b^2*c^2*e*(A*c*d*e*(27*c*d^2 - 7*a*e^2) + B*(13*c^2*d^4 + 4*a*c*d^2*e^2 + 114*a^2*e^4)) - 32*b*c^3*(A*e*(20*c^2*d^4 + 39*a*c*d^2*e^2 + 23*a^2*e^4) + B*(4*c^2*d^5 + 41*a*c*d^3*e^2 + 100*a^2*d*e^4)))*x)) - (1/(60*c^5*(b^2 - 4*a*c)^3))*(e*(945*b^7*B*e^6 - 420*b^6*c*e^5*(7*B*d + A*e) + 84*b^5*c*e^4*(24*B*c*d^2 + 10*A*c*d*e - 125*a*B*e^2) + 32*b^4*c^2*e^3*(22*B*c*d^3 + 7*A*c*d^2*e + 980*a*B*d*e^2 + 140*a*A*e^3) - 16*b^3*c^2*e^2*(4*A*c*d*e*(c*d^2 + 140*a*e^2) - B*(12*c^2*d^4 - 1396*a*c*d^2*e^2 + 2359*a^2*e^4)) - 192*b^2*c^3*e*(A*e*(44*c^2*d^4 + 10*a*c*d^2*e^2 + 77*a^2*e^4) + B*(20*c^2*d^5 + 34*a*c*d^3*e^2 + 539*a^2*d*e^4)) + 64*b*c^3*(22*A*c*d*e*(8*c^2*d^4 + 22*a*c*d^2*e^2 + 21*a^2*e^4) + B*(32*c^3*d^6 + 388*a*c^2*d^4*e^2 + 1212*a^2*c*d^2*e^4 - 663*a^3*e^6)) - 512*c^4*(7*a*B*d*e*(2*c^2*d^4 + 13*a*c*d^2*e^2 - 24*a^2*e^4) + A*(8*c^3*d^6 + 34*a*c^2*d^4*e^2 + 72*a^2*c*d^2*e^4 - 24*a^3*e^6)) - 2*c*e*(315*b^6*B*e^5 - 28*b^5*c*e^4*(17*B*d + 5*A*e) - 4*b^4*c*e^3*(20*B*c*d^2 - 14*A*c*d*e + 791*a*B*e^2) + 32*b^3*c^2*e^2*(3*B*c*d^3 + 5*A*c*d^2*e + 152*a*B*d*e^2 + 42*a*A*e^3) + 64*c^3*(7*a*B*e*(4*c^2*d^4 + 24*a*c*d^2*e^2 - 15*a^2*e^4) + 2*A*c*d*(8*c^2*d^4 + 30*a*c*d^2*e^2 + 57*a^2*e^4)) + 16*b^2*c^2*e*(4*A*c*d*e*(25*c*d^2 - 12*a*e^2) + B*(52*c^2*d^4 + 12*a*c*d^2*e^2 + 597*a^2*e^4)) - 64*b*c^3*(A*e*(40*c^2*d^4 + 90*a*c*d^2*e^2 + 57*a^2*e^4) + B*(8*c^2*d^5 + 86*a*c*d^3*e^2 + 225*a^2*d*e^4)))*x)*Sqrt[a + b*x + c*x^2]) + (7*e^5*(4*A*c*e*(2*c*d - b*e) + B*(24*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(7*b*d + a*e)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(11/2))} 
[(A+B*x)*(d+e*x)^6/(a+b*x+c*x^2)^(7/2),x,6,2/5*(d+e*x)^5*(2*a*c*(B*d+A*e)-b*(A*c*d+a*B*e)-(b^2*B*e-b*c*(B*d+A*e)+2*c*(A*c*d-a*B*e))*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^(5/2))+2/15*(d+e*x)^3*(b^3*B*e*(3*c*d^2-7*a*e^2)-8*a*c^2*e*(3*A*c*d^2+12*a*B*d*e+5*a*A*e^2)-2*b^2*c*(4*B*c*d^3+9*A*c*d^2*e-a*A*e^3)+4*b*c*(4*A*c*d*(c*d^2+3*a*e^2)+a*B*e*(9*c*d^2+11*a*e^2))-(7*b^4*B*e^3-2*b^3*c*e^2*(3*B*d+A*e)-12*b^2*c*e*(B*c*d^2+A*c*d*e+4*a*B*e^2)+8*b*c^2*(2*B*c*d^3+6*A*c*d^2*e+9*a*B*d*e^2+3*a*A*e^3)-16*c^2*(3*a*B*e*(c*d^2-a*e^2)+A*c*d*(2*c*d^2+3*a*e^2)))*x)/(c^2*(b^2-4*a*c)^2*(a+b*x+c*x^2)^(3/2))+1/2*e^5*(12*B*c*d-7*b*B*e+2*A*c*e)*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(9/2)+2/15*(d+e*x)*(7*b^5*B*e^3*(c*d^2-5*a*e^2)-2*b^4*c*e^3*(A*c*d^2-16*a*B*d*e-5*a*A*e^2)-8*b^3*c*e*(A*c*d*e*(21*c*d^2-a*e^2)+6*B*(2*c^2*d^4+a*c*d^2*e^2-7*a^2*e^4))+32*a*c^3*e*(6*a*B*d*e*(c*d^2+11*a*e^2)+A*(4*c^2*d^4+9*a*c*d^2*e^2+15*a^2*e^4))-16*b*c^2*(2*A*c*d*(4*c^2*d^4+19*a*c*d^2*e^2+21*a^2*e^4)+a*B*e*(16*c^2*d^4+75*a*c*d^2*e^2+57*a^2*e^4))+16*b^2*c^2*(6*A*e*(3*c^2*d^4+6*a*c*d^2*e^2-a^2*e^4)+B*(4*c^2*d^5+37*a*c*d^3*e^2-21*a^2*d*e^4))-(35*b^6*B*e^5-2*b^5*c*e^4*(23*B*d+5*A*e)-4*b^4*c*e^3*(5*B*c*d^2+A*c*d*e+91*a*B*e^2)-8*b^3*c^2*e^2*(5*B*c*d^3+7*A*c*d^2*e-63*a*B*d*e^2-13*a*A*e^3)+64*c^3*(6*a*B*e*(c^2*d^4+4*a*c*d^2*e^2-2*a^2*e^4)+A*c*d*(4*c^2*d^4+11*a*c*d^2*e^2+12*a^2*e^4))+16*b^2*c^2*e*(A*c*d*e*(29*c*d^2+9*a*e^2)+B*(14*c^2*d^4+21*a*c*d^2*e^2+72*a^2*e^4))-32*b*c^3*(A*e*(20*c^2*d^4+33*a*c*d^2*e^2+12*a^2*e^4)+B*(4*c^2*d^5+35*a*c*d^3*e^2+60*a^2*d*e^4)))*x)/(c^3*(b^2-4*a*c)^3*sqrt(a+b*x+c*x^2))+1/15*e*(105*b^6*B*e^5-10*b^5*c*e^4*(11*B*d+3*A*e)-16*b^3*c^2*e^2*(3*B*c*d^3+A*c*d^2*e-78*a*B*d*e^2-20*a*A*e^3)-4*b^4*c*e^3*(5*A*c*d*e+8*B*(2*c*d^2+35*a*e^2))+16*b^2*c^2*e*(6*A*c*d*e*(9*c*d^2+2*a*e^2)+7*B*(4*c^2*d^4+6*a*c*d^2*e^2+33*a^2*e^4))+64*c^3*(6*a*B*e*(2*c^2*d^4+9*a*c*d^2*e^2-8*a^2*e^4)+A*c*d*(8*c^2*d^4+26*a*c*d^2*e^2+33*a^2*e^4))-32*b*c^3*(A*e*(40*c^2*d^4+78*a*c*d^2*e^2+33*a^2*e^4)+B*(8*c^2*d^5+74*a*c*d^3*e^2+141*a^2*d*e^4)))*sqrt(a+b*x+c*x^2)/(c^4*(b^2-4*a*c)^3)],
[(A+B*x)*(d+e*x)^5/(a+b*x+c*x^2)^(7/2),x,5,2/5*(d+e*x)^4*(2*a*c*(B*d+A*e)-b*(A*c*d+a*B*e)-(b^2*B*e-b*c*(B*d+A*e)+2*c*(A*c*d-a*B*e))*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^(5/2))+2/15*(d+e*x)^2*(b^3*B*e*(3*c*d^2-5*a*e^2)-4*b^2*c*d*(2*B*c*d^2+4*A*c*d*e+a*B*e^2)-16*a*c^2*e*(5*a*B*d*e+2*A*(c*d^2+a*e^2))+4*b*c*(9*a*B*e*(c*d^2+a*e^2)+4*A*c*d*(c*d^2+3*a*e^2))+(2*b^3*B*c*d*e^2-5*b^4*B*e^3+2*b^2*c*e*(7*B*c*d^2+8*A*c*d*e+19*a*B*e^2)-8*b*c^2*(2*B*c*d^3+6*A*c*d^2*e+7*a*B*d*e^2+2*a*A*e^3)+8*c^2*(5*a*B*e*(c*d^2-a*e^2)+4*A*c*d*(c*d^2+a*e^2)))*x)/(c^2*(b^2-4*a*c)^2*(a+b*x+c*x^2)^(3/2))+B*e^5*arctanh(1/2*(b+2*c*x)/(sqrt(c)*sqrt(a+b*x+c*x^2)))/c^(7/2)+2/15*(4*b^4*B*c^2*d^3*e^2+5*b^5*B*e^3*(c*d^2-3*a*e^2)+32*b^2*c^3*d^2*(2*B*c*d^3+8*A*c*d^2*e+17*a*B*d*e^2+16*a*A*e^3)+64*a*c^3*e*(4*A*(c*d^2+a*e^2)^2+5*a*B*d*e*(c*d^2+4*a*e^2))-8*b^3*c*e*(16*A*c^2*d^3*e+B*(11*c^2*d^4+7*a*c*d^2*e^2-20*a^2*e^4))-16*b*c^2*(8*A*c*d*(c^2*d^4+6*a*c*d^2*e^2+5*a^2*e^4)+a*B*e*(18*c^2*d^4+71*a*c*d^2*e^2+33*a^2*e^4))+(10*b^5*B*c*d*e^4-15*b^6*B*e^5+2*b^4*B*c*e^3*(3*c*d^2+85*a*e^2)+16*b^3*c^2*d*e^2*(6*B*c*d^2+8*A*c*d*e-7*a*B*e^2)-32*c^3*(8*A*c*d*(c*d^2+a*e^2)^2+5*a*B*e*(2*c^2*d^4+5*a*c*d^2*e^2-3*a^2*e^4))-16*b^2*c^2*e*(16*A*c*d*e*(2*c*d^2+a*e^2)+B*(15*c^2*d^4+29*a*c*d^2*e^2+39*a^2*e^4))+32*b*c^3*(4*A*e*(5*c^2*d^4+6*a*c*d^2*e^2+a^2*e^4)+B*(4*c^2*d^5+28*a*c*d^3*e^2+29*a^2*d*e^4)))*x)/(c^3*(b^2-4*a*c)^3*sqrt(a+b*x+c*x^2))],
[(A+B*x)*(d+e*x)^4/(a+b*x+c*x^2)^(7/2),x,3,-2/5*(A*b-2*a*B-(b*B-2*A*c)*x)*(d+e*x)^4/((b^2-4*a*c)*(a+b*x+c*x^2)^(5/2))-16/15*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*(d+e*x)^2*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)^2*(a+b*x+c*x^2)^(3/2))+128/15*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*(c*d^2-b*d*e+a*e^2)*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)^3*sqrt(a+b*x+c*x^2))],
[(A+B*x)*(d+e*x)^3/(a+b*x+c*x^2)^(7/2),x,3,-2/5*(A*b-2*a*B-(b*B-2*A*c)*x)*(d+e*x)^3/((b^2-4*a*c)*(a+b*x+c*x^2)^(5/2))-4/15*(d+e*x)^2*(4*a*A*c*e+b^2*(4*B*d+3*A*e)-8*b*(A*c*d+a*B*e)-(b^2*B*e-8*b*c*(B*d+A*e)+4*c*(4*A*c*d+3*a*B*e))*x)/((b^2-4*a*c)^2*(a+b*x+c*x^2)^(3/2))-16/15*(b^2*e*(5*B*d+3*A*e)+4*c*(4*A*c*d^2+3*a*B*d*e+a*A*e^2)-8*b*(B*c*d^2+2*A*c*d*e+a*B*e^2))*(b*d-2*a*e+(2*c*d-b*e)*x)/((b^2-4*a*c)^3*sqrt(a+b*x+c*x^2))],
[(A+B*x)*(d+e*x)^2/(a+b*x+c*x^2)^(7/2),x,3,-2/5*(A*b-2*a*B-(b*B-2*A*c)*x)*(d+e*x)^2/((b^2-4*a*c)*(a+b*x+c*x^2)^(5/2))-8/15*(4*a*c*e*(3*A*c*d+a*B*e)-4*b*c*(A*c*d^2+2*a*B*d*e+a*A*e^2)+b^2*(2*B*c*d^2+A*c*d*e+a*B*e^2)+(b^3*B*e^2-3*b^2*c*e*(B*d+A*e)+4*b*c^2*d*(B*d+2*A*e)-4*c^2*(2*A*c*d^2+a*B*d*e-a*A*e^2))*x)/(c*(b^2-4*a*c)^2*(a+b*x+c*x^2)^(3/2))+8/15*(b^3*B*e^2-6*b^2*c*e*(2*B*d+A*e)-8*c^2*(4*A*c*d^2+2*a*B*d*e+a*A*e^2)+4*b*c*(4*B*c*d^2+8*A*c*d*e+3*a*B*e^2))*(b+2*c*x)/(c*(b^2-4*a*c)^3*sqrt(a+b*x+c*x^2))],
[(A+B*x)*(d+e*x)/(a+b*x+c*x^2)^(7/2),x,3,2/5*(2*a*c*(B*d+A*e)-b*(A*c*d+a*B*e)-(b^2*B*e-b*c*(B*d+A*e)+2*c*(A*c*d-a*B*e))*x)/(c*(b^2-4*a*c)*(a+b*x+c*x^2)^(5/2))+2/15*(3*b^2*B*e-8*b*c*(B*d+A*e)+4*c*(4*A*c*d+a*B*e))*(b+2*c*x)/(c*(b^2-4*a*c)^2*(a+b*x+c*x^2)^(3/2))-16/15*(3*b^2*B*e-8*b*c*(B*d+A*e)+4*c*(4*A*c*d+a*B*e))*(b+2*c*x)/((b^2-4*a*c)^3*sqrt(a+b*x+c*x^2))],
[(A+B*x)/(a+b*x+c*x^2)^(7/2),x,3,-2/5*(A*b-2*a*B-(b*B-2*A*c)*x)/((b^2-4*a*c)*(a+b*x+c*x^2)^(5/2))-16/15*(b*B-2*A*c)*(b+2*c*x)/((b^2-4*a*c)^2*(a+b*x+c*x^2)^(3/2))+128/15*c*(b*B-2*A*c)*(b+2*c*x)/((b^2-4*a*c)^3*sqrt(a+b*x+c*x^2))],
[(A+B*x)/((d+e*x)*(a+b*x+c*x^2)^(7/2)),x,6,2/5*(a*B*(2*c*d-b*e)-A*(b*c*d-b^2*e+2*a*c*e)+c*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2)^(5/2))+2/15*(8*a*c*e*(2*c*d-b*e)*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)+(b*c*d-b^2*e+2*a*c*e)*(5*b^2*e*(B*d-A*e)-8*b*c*d*(B*d+A*e)+4*c*(4*A*c*d^2-a*B*d*e+5*a*A*e^2))+c*(8*c*e*(b*d-2*a*e)*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)+(2*c*d-b*e)*(5*b^2*e*(B*d-A*e)-8*b*c*d*(B*d+A*e)+4*c*(4*A*c*d^2-a*B*d*e+5*a*A*e^2)))*x)/((b^2-4*a*c)^2*(c*d^2-b*d*e+a*e^2)^2*(a+b*x+c*x^2)^(3/2))-e^5*(B*d-A*e)*arctanh(1/2*(b*d-2*a*e+(2*c*d-b*e)*x)/(sqrt(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)))/(c*d^2-b*d*e+a*e^2)^(7/2)+2/15*(4*a*c*e*(2*c*d-b*e)*(8*c*e*(b*d-2*a*e)*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)+(2*c*d-b*e)*(5*b^2*e*(B*d-A*e)-8*b*c*d*(B*d+A*e)+4*c*(4*A*c*d^2-a*B*d*e+5*a*A*e^2)))-(b*c*d-b^2*e+2*a*c*e)*(8*c*d*e*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*(4*b*c*d-3*b^2*e+4*a*c*e)+(8*c^2*d^2-3*b^2*e^2-4*c*e*(b*d-3*a*e))*(5*b^2*e*(B*d-A*e)-8*b*c*d*(B*d+A*e)+4*c*(4*A*c*d^2-a*B*d*e+5*a*A*e^2)))+c*(4*c*e*(b*d-2*a*e)*(8*c*e*(b*d-2*a*e)*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)+(2*c*d-b*e)*(5*b^2*e*(B*d-A*e)-8*b*c*d*(B*d+A*e)+4*c*(4*A*c*d^2-a*B*d*e+5*a*A*e^2)))-(2*c*d-b*e)*(8*c*d*e*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*(4*b*c*d-3*b^2*e+4*a*c*e)+(8*c^2*d^2-3*b^2*e^2-4*c*e*(b*d-3*a*e))*(5*b^2*e*(B*d-A*e)-8*b*c*d*(B*d+A*e)+4*c*(4*A*c*d^2-a*B*d*e+5*a*A*e^2))))*x)/((b^2-4*a*c)^3*(c*d^2-b*d*e+a*e^2)^3*sqrt(a+b*x+c*x^2))],

#  {(A + B*x)/((d + e*x)^2*(a + b*x + c*x^2)^(7/2)), x, 6, (2*(a*B*(2*c*d - b*e) - A*(b*c*d - b^2*e + 2*a*c*e) + c*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*x))/(5*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a + b*x + c*x^2)^(5/2)) + (1/(15*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)*(a + b*x + c*x^2)^(3/2)))*(2*(10*a*c*e*(2*c*d - b*e)*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e) + (b*c*d - b^2*e + 2*a*c*e)*(b^2*e*(5*B*d - 7*A*e) + 8*c*(2*A*c*d^2 - a*B*d*e + 3*a*A*e^2) - b*(8*B*c*d^2 + 6*A*c*d*e - 2*a*B*e^2)) + c*(10*c*e*(b*d - 2*a*e)*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e) + (2*c*d - b*e)*(b^2*e*(5*B*d - 7*A*e) + 8*c*(2*A*c*d^2 - a*B*d*e + 3*a*A*e^2) - b*(8*B*c*d^2 + 6*A*c*d*e - 2*a*B*e^2)))*x)) + (1/(15*(b^2 - 4*a*c)^3*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)*Sqrt[a + b*x + c*x^2]))*(2*(6*a*c*e*(2*c*d - b*e)*(10*c*e*(b*d - 2*a*e)*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e) + (2*c*d - b*e)*(b^2*e*(5*B*d - 7*A*e) + 8*c*(2*A*c*d^2 - a*B*d*e + 3*a*A*e^2) - b*(8*B*c*d^2 + 6*A*c*d*e - 2*a*B*e^2))) - (b*c*d - b^2*e + 2*a*c*e)*(20*c*e*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*((1/2)*b*d*(4*c*d - 3*b*e) + a*e*(4*c*d - b*e)) + (8*c^2*d^2 - 5*b^2*e^2 - 2*c*e*(b*d - 8*a*e))*(b^2*e*(5*B*d - 7*A*e) + 8*c*(2*A*c*d^2 - a*B*d*e + 3*a*A*e^2) - b*(8*B*c*d^2 + 6*A*c*d*e - 2*a*B*e^2))) + c*(6*c*e*(b*d - 2*a*e)*(10*c*e*(b*d - 2*a*e)*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e) + (2*c*d - b*e)*(b^2*e*(5*B*d - 7*A*e) + 8*c*(2*A*c*d^2 - a*B*d*e + 3*a*A*e^2) - b*(8*B*c*d^2 + 6*A*c*d*e - 2*a*B*e^2))) - (2*c*d - b*e)*(20*c*e*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*((1/2)*b*d*(4*c*d - 3*b*e) + a*e*(4*c*d - b*e)) + (8*c^2*d^2 - 5*b^2*e^2 - 2*c*e*(b*d - 8*a*e))*(b^2*e*(5*B*d - 7*A*e) + 8*c*(2*A*c*d^2 - a*B*d*e + 3*a*A*e^2) - b*(8*B*c*d^2 + 6*A*c*d*e - 2*a*B*e^2))))*x)) + (1/(15*(b^2 - 4*a*c)^3*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)))*(e*(15*b^6*e^5*(5*B*d - 7*A*e) - 10*b^5*e^4*(13*B*c*d^2 - 14*A*c*d*e - 3*a*B*e^2) + 4*b^4*c*e^3*(7*A*e*(3*c*d^2 + 40*a*e^2) - 5*B*(4*c*d^3 + 39*a*d*e^2)) + 16*b^3*c*e^2*(2*A*c*d*e*(2*c*d^2 - 49*a*e^2) + B*(51*c^2*d^4 + 91*a*c*d^2*e^2 - 20*a^2*e^4)) - 16*b^2*c^2*e*(A*e*(82*c^2*d^4 + 54*a*c*d^2*e^2 + 231*a^2*e^4) + B*(52*c^2*d^5 + 168*a*c*d^3*e^2 - 153*a^2*d*e^4)) + 64*c^3*(a*B*d*e*(4*c^2*d^4 + 28*a*c*d^2*e^2 - 81*a^2*e^4) - A*(8*c^3*d^6 + 38*a*c^2*d^4*e^2 + 87*a^2*c*d^2*e^4 - 48*a^3*e^6)) + 32*b*c^2*(2*A*c*d*e*(24*c^2*d^4 + 76*a*c*d^2*e^2 + 87*a^2*e^4) + B*(8*c^3*d^6 + 18*a*c^2*d^4*e^2 + 3*a^2*c*d^2*e^4 + 33*a^3*e^6)))*Sqrt[a + b*x + c*x^2]) + (e^5*(7*A*e*(2*c*d - b*e) - B*(12*c*d^2 - e*(5*b*d + 2*a*e)))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2*(c*d^2 - b*d*e + a*e^2)^(9/2))} 
[(5-x)*(3+2*x)^4/sqrt(2+5*x+3*x^2),x,6,28051/1296*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+391/135*(3+2*x)^2*sqrt(2+5*x+3*x^2)+53/60*(3+2*x)^3*sqrt(2+5*x+3*x^2)-1/15*(3+2*x)^4*sqrt(2+5*x+3*x^2)+1/648*(27519+9650*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^3/sqrt(2+5*x+3*x^2),x,5,19405/1296*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+32/27*(3+2*x)^2*sqrt(2+5*x+3*x^2)-1/12*(3+2*x)^3*sqrt(2+5*x+3*x^2)+5/648*(3261+1078*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^2/sqrt(2+5*x+3*x^2),x,4,1147/108*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-1/9*(3+2*x)^2*sqrt(2+5*x+3*x^2)+1/54*(699+194*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)/sqrt(2+5*x+3*x^2),x,3,31/4*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+1/6*(19-2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)/sqrt(2+5*x+3*x^2),x,3,35/6*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-1/3*sqrt(2+5*x+3*x^2)],
[(5-x)/((3+2*x)*sqrt(2+5*x+3*x^2)),x,5,-1/2*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+13/2*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)],
[(5-x)/((3+2*x)^2*sqrt(2+5*x+3*x^2)),x,3,47/10*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-13/5*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^3*sqrt(2+5*x+3*x^2)),x,4,389/100*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-13/10*sqrt(2+5*x+3*x^2)/(3+2*x)^2-73/25*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^4*sqrt(2+5*x+3*x^2)),x,5,331/100*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-13/15*sqrt(2+5*x+3*x^2)/(3+2*x)^3-49/30*sqrt(2+5*x+3*x^2)/(3+2*x)^2-72/25*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^5*sqrt(2+5*x+3*x^2)),x,6,5771/2000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-13/20*sqrt(2+5*x+3*x^2)/(3+2*x)^4-86/75*sqrt(2+5*x+3*x^2)/(3+2*x)^3-41/24*sqrt(2+5*x+3*x^2)/(3+2*x)^2-681/250*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^6*sqrt(2+5*x+3*x^2)),x,7,128381/50000*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-13/25*sqrt(2+5*x+3*x^2)/(3+2*x)^5-443/500*sqrt(2+5*x+3*x^2)/(3+2*x)^4-2321/1875*sqrt(2+5*x+3*x^2)/(3+2*x)^3-1007/600*sqrt(2+5*x+3*x^2)/(3+2*x)^2-15891/6250*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^(3/2),x,5,6265/81*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-2/3*(3+2*x)^3*(121+139*x)/sqrt(2+5*x+3*x^2)+1664/27*(3+2*x)^2*sqrt(2+5*x+3*x^2)+10/81*(3369+1438*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^(3/2),x,4,247/9*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-2/3*(3+2*x)^2*(121+139*x)/sqrt(2+5*x+3*x^2)+2/9*(1239+554*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^(3/2),x,4,2*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))*sqrt(3)-2/3*(3+2*x)*(121+139*x)/sqrt(2+5*x+3*x^2)+184/3*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)/(2+5*x+3*x^2)^(3/2),x,3,-2/3*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)-2/3*(121+139*x)/sqrt(2+5*x+3*x^2)],
[(5-x)/(2+5*x+3*x^2)^(3/2),x,1,-2*(29+35*x)/sqrt(2+5*x+3*x^2)],
[(5-x)/((3+2*x)*(2+5*x+3*x^2)^(3/2)),x,4,26/5*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-6/5*(37+47*x)/sqrt(2+5*x+3*x^2)],
[(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^(3/2)),x,4,302/25*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-6/5*(37+47*x)/((3+2*x)*sqrt(2+5*x+3*x^2))-856/25*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^(3/2)),x,5,483/25*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-6/5*(37+47*x)/((3+2*x)^2*sqrt(2+5*x+3*x^2))-166/5*sqrt(2+5*x+3*x^2)/(3+2*x)^2-864/25*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^4*(2+5*x+3*x^2)^(3/2)),x,6,3289/125*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-6/5*(37+47*x)/((3+2*x)^3*sqrt(2+5*x+3*x^2))-2464/75*sqrt(2+5*x+3*x^2)/(3+2*x)^3-478/15*sqrt(2+5*x+3*x^2)/(3+2*x)^2-4632/125*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^5*(2+5*x+3*x^2)^(3/2)),x,7,82039/2500*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)-6/5*(37+47*x)/((3+2*x)^4*sqrt(2+5*x+3*x^2))-817/25*sqrt(2+5*x+3*x^2)/(3+2*x)^4-11596/375*sqrt(2+5*x+3*x^2)/(3+2*x)^3-973/30*sqrt(2+5*x+3*x^2)/(3+2*x)^2-25458/625*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)*(3+2*x)^4/(2+5*x+3*x^2)^(5/2),x,5,-2/9*(3+2*x)^3*(121+139*x)/(2+5*x+3*x^2)^(3/2)+152/27*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+4/27*(3+2*x)*(6809+7976*x)/sqrt(2+5*x+3*x^2)-6848/9*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^3/(2+5*x+3*x^2)^(5/2),x,4,-2/9*(3+2*x)^2*(121+139*x)/(2+5*x+3*x^2)^(3/2)-8/9*arctanh(1/2*(5+6*x)/(sqrt(3)*sqrt(2+5*x+3*x^2)))/sqrt(3)+4/9*(2481+2834*x)/sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^2/(2+5*x+3*x^2)^(5/2),x,2,-2/3*(3+2*x)^2*(29+35*x)/(2+5*x+3*x^2)^(3/2)+376/3*(7+8*x)/sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)/(2+5*x+3*x^2)^(5/2),x,2,-2/9*(121+139*x)/(2+5*x+3*x^2)^(3/2)+1124/9*(5+6*x)/sqrt(2+5*x+3*x^2)],
[(5-x)/(2+5*x+3*x^2)^(5/2),x,2,-2/3*(29+35*x)/(2+5*x+3*x^2)^(3/2)+280/3*(5+6*x)/sqrt(2+5*x+3*x^2)],
[(5-x)/((3+2*x)*(2+5*x+3*x^2)^(5/2)),x,5,-2/5*(37+47*x)/(2+5*x+3*x^2)^(3/2)+104/25*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+12/25*(701+836*x)/sqrt(2+5*x+3*x^2)],
[(5-x)/((3+2*x)^2*(2+5*x+3*x^2)^(5/2)),x,5,-2/5*(37+47*x)/((3+2*x)*(2+5*x+3*x^2)^(3/2))+408/25*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+4/5*(401+462*x)/((3+2*x)*sqrt(2+5*x+3*x^2))+4416/25*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^3*(2+5*x+3*x^2)^(5/2)),x,6,-2/5*(37+47*x)/((3+2*x)^2*(2+5*x+3*x^2)^(3/2))+4884/125*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+4/25*(1907+2112*x)/((3+2*x)^2*sqrt(2+5*x+3*x^2))+152*sqrt(2+5*x+3*x^2)/(3+2*x)^2+11808/125*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(5-x)/((3+2*x)^4*(2+5*x+3*x^2)^(5/2)),x,7,-2/5*(37+47*x)/((3+2*x)^3*(2+5*x+3*x^2)^(3/2))+46108/625*arctanh(1/2*(7+8*x)/(sqrt(5)*sqrt(2+5*x+3*x^2)))/sqrt(5)+12/25*(603+638*x)/((3+2*x)^3*sqrt(2+5*x+3*x^2))+47552/375*sqrt(2+5*x+3*x^2)/(3+2*x)^3+1048/15*sqrt(2+5*x+3*x^2)/(3+2*x)^2+9696/625*sqrt(2+5*x+3*x^2)/(3+2*x)],
[(-1+x)/((1+x)*sqrt(1+x+x^2)),x,5,arcsinh((1+2*x)/sqrt(3))+2*arctanh(1/2*(1-x)/sqrt(1+x+x^2))],

# Integrands of the form (d+e x)^(m/2) (A+B x) (a+b x+c x^2)^p

# p>0
[(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2),x,2,65/72*(3+2*x)^(9/2)-109/88*(3+2*x)^(11/2)+47/104*(3+2*x)^(13/2)-1/40*(3+2*x)^(15/2)],
[(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2),x,2,65/56*(3+2*x)^(7/2)-109/72*(3+2*x)^(9/2)+47/88*(3+2*x)^(11/2)-3/104*(3+2*x)^(13/2)],
[(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2),x,2,13/8*(3+2*x)^(5/2)-109/56*(3+2*x)^(7/2)+47/72*(3+2*x)^(9/2)-3/88*(3+2*x)^(11/2)],
[(5-x)*(2+5*x+3*x^2)*sqrt(3+2*x),x,2,65/24*(3+2*x)^(3/2)-109/40*(3+2*x)^(5/2)+47/56*(3+2*x)^(7/2)-1/24*(3+2*x)^(9/2)],
[(5-x)*(2+5*x+3*x^2)/sqrt(3+2*x),x,2,-109/24*(3+2*x)^(3/2)+47/40*(3+2*x)^(5/2)-3/56*(3+2*x)^(7/2)+65/8*sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)/(3+2*x)^(3/2),x,2,47/24*(3+2*x)^(3/2)-3/40*(3+2*x)^(5/2)+(-65/8)/sqrt(3+2*x)-109/8*sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)/(3+2*x)^(5/2),x,2,(-65/24)/(3+2*x)^(3/2)-1/8*(3+2*x)^(3/2)+109/8/sqrt(3+2*x)+47/8*sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)/(3+2*x)^(7/2),x,2,(-13/8)/(3+2*x)^(5/2)+109/24/(3+2*x)^(3/2)+(-47/8)/sqrt(3+2*x)-3/8*sqrt(3+2*x)],
[(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^2,x,2,325/288*(3+2*x)^(9/2)-1065/352*(3+2*x)^(11/2)+651/208*(3+2*x)^(13/2)-359/240*(3+2*x)^(15/2)+165/544*(3+2*x)^(17/2)-9/608*(3+2*x)^(19/2)],
[(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^2,x,2,325/224*(3+2*x)^(7/2)-355/96*(3+2*x)^(9/2)+651/176*(3+2*x)^(11/2)-359/208*(3+2*x)^(13/2)+11/32*(3+2*x)^(15/2)-9/544*(3+2*x)^(17/2)],
[(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^2,x,2,65/32*(3+2*x)^(5/2)-1065/224*(3+2*x)^(7/2)+217/48*(3+2*x)^(9/2)-359/176*(3+2*x)^(11/2)+165/416*(3+2*x)^(13/2)-3/160*(3+2*x)^(15/2)],
[(5-x)*(2+5*x+3*x^2)^2*sqrt(3+2*x),x,2,325/96*(3+2*x)^(3/2)-213/32*(3+2*x)^(5/2)+93/16*(3+2*x)^(7/2)-359/144*(3+2*x)^(9/2)+15/32*(3+2*x)^(11/2)-9/416*(3+2*x)^(13/2)],
[(5-x)*(2+5*x+3*x^2)^2/sqrt(3+2*x),x,2,-355/32*(3+2*x)^(3/2)+651/80*(3+2*x)^(5/2)-359/112*(3+2*x)^(7/2)+55/96*(3+2*x)^(9/2)-9/352*(3+2*x)^(11/2)+325/32*sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(3/2),x,2,217/16*(3+2*x)^(3/2)-359/80*(3+2*x)^(5/2)+165/224*(3+2*x)^(7/2)-1/32*(3+2*x)^(9/2)+(-325/32)/sqrt(3+2*x)-1065/32*sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(5/2),x,2,(-325/96)/(3+2*x)^(3/2)-359/48*(3+2*x)^(3/2)+33/32*(3+2*x)^(5/2)-9/224*(3+2*x)^(7/2)+1065/32/sqrt(3+2*x)+651/16*sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^2/(3+2*x)^(7/2),x,2,(-65/32)/(3+2*x)^(5/2)+355/32/(3+2*x)^(3/2)+55/32*(3+2*x)^(3/2)-9/160*(3+2*x)^(5/2)+(-651/16)/sqrt(3+2*x)-359/16*sqrt(3+2*x)],
[(5-x)*(3+2*x)^(7/2)*(2+5*x+3*x^2)^3,x,2,1625/1152*(3+2*x)^(9/2)-7925/1408*(3+2*x)^(11/2)+16005/1664*(3+2*x)^(13/2)-17201/1920*(3+2*x)^(15/2)+10475/2176*(3+2*x)^(17/2)-3519/2432*(3+2*x)^(19/2)+27/128*(3+2*x)^(21/2)-27/2944*(3+2*x)^(23/2)],
[(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^3,x,2,1625/896*(3+2*x)^(7/2)-7925/1152*(3+2*x)^(9/2)+1455/128*(3+2*x)^(11/2)-17201/1664*(3+2*x)^(13/2)+2095/384*(3+2*x)^(15/2)-207/128*(3+2*x)^(17/2)+567/2432*(3+2*x)^(19/2)-9/896*(3+2*x)^(21/2)],
[(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^3,x,2,325/128*(3+2*x)^(5/2)-7925/896*(3+2*x)^(7/2)+5335/384*(3+2*x)^(9/2)-17201/1408*(3+2*x)^(11/2)+10475/1664*(3+2*x)^(13/2)-1173/640*(3+2*x)^(15/2)+567/2176*(3+2*x)^(17/2)-27/2432*(3+2*x)^(19/2)],
[(5-x)*(2+5*x+3*x^2)^3*sqrt(3+2*x),x,2,1625/384*(3+2*x)^(3/2)-1585/128*(3+2*x)^(5/2)+16005/896*(3+2*x)^(7/2)-17201/1152*(3+2*x)^(9/2)+10475/1408*(3+2*x)^(11/2)-3519/1664*(3+2*x)^(13/2)+189/640*(3+2*x)^(15/2)-27/2176*(3+2*x)^(17/2)],
[(5-x)*(2+5*x+3*x^2)^3/sqrt(3+2*x),x,2,-7925/384*(3+2*x)^(3/2)+3201/128*(3+2*x)^(5/2)-17201/896*(3+2*x)^(7/2)+10475/1152*(3+2*x)^(9/2)-3519/1408*(3+2*x)^(11/2)+567/1664*(3+2*x)^(13/2)-9/640*(3+2*x)^(15/2)+1625/128*sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(3/2),x,2,5335/128*(3+2*x)^(3/2)-17201/640*(3+2*x)^(5/2)+10475/896*(3+2*x)^(7/2)-391/128*(3+2*x)^(9/2)+567/1408*(3+2*x)^(11/2)-27/1664*(3+2*x)^(13/2)+(-1625/128)/sqrt(3+2*x)-7925/128*sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(5/2),x,2,(-1625/384)/(3+2*x)^(3/2)-17201/384*(3+2*x)^(3/2)+2095/128*(3+2*x)^(5/2)-3519/896*(3+2*x)^(7/2)+63/128*(3+2*x)^(9/2)-27/1408*(3+2*x)^(11/2)+7925/128/sqrt(3+2*x)+16005/128*sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^3/(3+2*x)^(7/2),x,2,(-325/128)/(3+2*x)^(5/2)+7925/384/(3+2*x)^(3/2)+10475/384*(3+2*x)^(3/2)-3519/640*(3+2*x)^(5/2)+81/128*(3+2*x)^(7/2)-3/128*(3+2*x)^(9/2)+(-16005/128)/sqrt(3+2*x)-17201/128*sqrt(3+2*x)],

# p<0
[(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2),x,8,526/81*(3+2*x)^(3/2)+62/45*(3+2*x)^(5/2)-2/21*(3+2*x)^(7/2)+12*arctanh(sqrt(3+2*x))-4250/81*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+3278/81*sqrt(3+2*x)],
[(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2),x,7,62/27*(3+2*x)^(3/2)-2/15*(3+2*x)^(5/2)+12*arctanh(sqrt(3+2*x))-850/27*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+526/27*sqrt(3+2*x)],
[(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2),x,6,-2/9*(3+2*x)^(3/2)+12*arctanh(sqrt(3+2*x))-170/9*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+62/9*sqrt(3+2*x)],
[(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2),x,5,12*arctanh(sqrt(3+2*x))-34/3*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-2/3*sqrt(3+2*x)],
[(5-x)/((2+5*x+3*x^2)*sqrt(3+2*x)),x,4,12*arctanh(sqrt(3+2*x))-34*arctanh(sqrt(3/5)*sqrt(3+2*x))/sqrt(15)],
[(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)),x,5,12*arctanh(sqrt(3+2*x))-34/5*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-26/5)/sqrt(3+2*x)],
[(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)),x,6,(-26/15)/(3+2*x)^(3/2)+12*arctanh(sqrt(3+2*x))-102/25*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-198/25)/sqrt(3+2*x)],
[(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)),x,7,(-26/25)/(3+2*x)^(5/2)+(-66/25)/(3+2*x)^(3/2)+12*arctanh(sqrt(3+2*x))-306/125*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-1194/125)/sqrt(3+2*x)],
[(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^2,x,7,826/27*(3+2*x)^(3/2)-1/3*(3+2*x)^(5/2)*(121+139*x)/(2+5*x+3*x^2)-154*arctanh(sqrt(3+2*x))+2800/27*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+1358/27*sqrt(3+2*x)],
[(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^2,x,6,-1/3*(3+2*x)^(3/2)*(121+139*x)/(2+5*x+3*x^2)-130*arctanh(sqrt(3+2*x))+100*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+30*sqrt(3+2*x)],
[(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^2,x,5,-106*arctanh(sqrt(3+2*x))+248/3*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-1/3*(121+139*x)*sqrt(3+2*x)/(2+5*x+3*x^2)],
[(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2,x,5,-82*arctanh(sqrt(3+2*x))+316*arctanh(sqrt(3/5)*sqrt(3+2*x))/sqrt(15)-(29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2)],
[(5-x)/((2+5*x+3*x^2)^2*sqrt(3+2*x)),x,5,-58*arctanh(sqrt(3+2*x))+384/5*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-3/5*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2)],
[(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^2),x,6,-34*arctanh(sqrt(3+2*x))+1356/25*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-506/25)/sqrt(3+2*x)-3/5*(37+47*x)/((2+5*x+3*x^2)*sqrt(3+2*x))],
[(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^2),x,7,(-262/15)/(3+2*x)^(3/2)-3/5*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2))-10*arctanh(sqrt(3+2*x))+936/25*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-686/25)/sqrt(3+2*x)],
[(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^2),x,8,(-2114/125)/(3+2*x)^(5/2)+(-7042/375)/(3+2*x)^(3/2)-3/5*(37+47*x)/((3+2*x)^(5/2)*(2+5*x+3*x^2))+14*arctanh(sqrt(3+2*x))+15876/625*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-24626/625)/sqrt(3+2*x)],
[(5-x)*(3+2*x)^(9/2)/(2+5*x+3*x^2)^3,x,7,-1/6*(3+2*x)^(7/2)*(121+139*x)/(2+5*x+3*x^2)^2+1/18*(3+2*x)^(3/2)*(10832+12473*x)/(2+5*x+3*x^2)+1962*arctanh(sqrt(3+2*x))-13675/9*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)-3983/9*sqrt(3+2*x)],
[(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^3,x,6,-1/6*(3+2*x)^(5/2)*(121+139*x)/(2+5*x+3*x^2)^2+1582*arctanh(sqrt(3+2*x))-1225*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+7/6*(546+619*x)*sqrt(3+2*x)/(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^3,x,6,-1/6*(3+2*x)^(3/2)*(121+139*x)/(2+5*x+3*x^2)^2+1250*arctanh(sqrt(3+2*x))-2905/3*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(5/3)+25/6*(112+131*x)*sqrt(3+2*x)/(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^3,x,6,966*arctanh(sqrt(3+2*x))-1247*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-1/6*(121+139*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2+1/6*(2090+2529*x)*sqrt(3+2*x)/(2+5*x+3*x^2)],
[(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2)^3,x,6,730*arctanh(sqrt(3+2*x))-4713/5*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-1/2*(29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2+3/10*(878+1063*x)*sqrt(3+2*x)/(2+5*x+3*x^2)],
[(5-x)/((2+5*x+3*x^2)^3*sqrt(3+2*x)),x,6,542*arctanh(sqrt(3+2*x))-17463/25*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)-3/10*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^2+1/50*(9734+11739*x)*sqrt(3+2*x)/(2+5*x+3*x^2)],
[(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^3),x,7,402*arctanh(sqrt(3+2*x))-12717/25*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+2667/25/sqrt(3+2*x)-3/10*(37+47*x)/((2+5*x+3*x^2)^2*sqrt(3+2*x))+1/10*(1888+2229*x)/((2+5*x+3*x^2)*sqrt(3+2*x))],
[(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^3),x,8,7451/75/(3+2*x)^(3/2)-3/10*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^2)+1/50*(9146+10551*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2))+310*arctanh(sqrt(3+2*x))-45603/125*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+6853/125/sqrt(3+2*x)],
[(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^3),x,9,56399/625/(3+2*x)^(5/2)+102697/1875/(3+2*x)^(3/2)-3/10*(37+47*x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^2)+1/50*(8852+9957*x)/((3+2*x)^(5/2)*(2+5*x+3*x^2))+266*arctanh(sqrt(3+2*x))-806841/3125*arctanh(sqrt(3/5)*sqrt(3+2*x))*sqrt(3/5)+(-24409/3125)/sqrt(3+2*x)],
[(5+10*x+sqrt(35))/((2+3*x+5*x^2)*sqrt(1+2*x)),x,6,-2*arctan((-sqrt(10+20*x)+sqrt(2+sqrt(35)))/sqrt(-2+sqrt(35)))*sqrt(10/(-2+sqrt(35)))+2*arctan((sqrt(10+20*x)+sqrt(2+sqrt(35)))/sqrt(-2+sqrt(35)))*sqrt(10/(-2+sqrt(35))),-2*arctan((-10*sqrt(1+2*x)+sqrt(10*(2+sqrt(35))))/sqrt(10*(-2+sqrt(35))))*sqrt(10/(-2+sqrt(35)))+2*arctan((10*sqrt(1+2*x)+sqrt(10*(2+sqrt(35))))/sqrt(10*(-2+sqrt(35))))*sqrt(10/(-2+sqrt(35)))],

# Integrands of the form (d+e x)^(m/2) (A+B x) (a+b x+c x^2)^(p/2)

# p>0
[(5-x)*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2),x,9,730/891*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)-2/33*(3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2)+12130/6237*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)-32567/16038*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+168145/112266*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+1/56133*(250447+280359*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2),x,8,-2/27*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)+202/189*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)-4729/2430*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+5773/3402*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+1/8505*(27914+30033*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2),x,7,-2/21*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)-697/270*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+1039/378*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+1/945*(2327+2169*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*sqrt(2+5*x+3*x^2)/sqrt(3+2*x),x,6,-761/90*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+191/18*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+1/45*(88-9*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2),x,6,121/6*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-161/6*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-1/3*(21+x)*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2),x,6,-67/10*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+17/2*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+1/15*(146+119*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)],
[(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(7/2),x,7,-49/250*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)+9/50*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)+1/25*(32+43*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)+49/125*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(9/2),x,8,-159/1250*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)+183/1750*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)+183/875*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+1/175*(46+139*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(7/2)+159/625*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2),x,10,202/351*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)-2/45*(3+2*x)^(5/2)*(2+5*x+3*x^2)^(5/2)+1/243243*(534271+629153*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+13318/11583*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)-207851/6254820*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+1015187/8756748*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-1/21891870*(6006884+7817373*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2),x,9,-2/39*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)+1/27027*(43822+50771*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+886/1287*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)-152657/694980*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+332459/972972*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-1/2432430*(486863+783711*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x),x,8,1/99*(119+127*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)-2/33*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)-15283/17820*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+4153/3564*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-1/8910*(1246+3987*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(3/2)/sqrt(3+2*x),x,7,1/63*(52-7*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)-11123/1620*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+20501/2268*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-1/5670*(107+12429*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2),x,7,-1/7*(47+x)*(2+5*x+3*x^2)^(3/2)/sqrt(3+2*x)+2411/60*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-4427/84*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-1/210*(136-2493*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(5/2),x,7,-1/15*(37+3*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2)+289/4*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-367/20*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)+1/10*(241+69*x)*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(7/2),x,7,1/75*(408+337*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(5/2)+2779/100*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-243/20*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)-1/50*(614+181*x)*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(9/2),x,7,1/175*(358+347*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(7/2)-721/500*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)+1327/700*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)+1/1750*(8561+6179*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(11/2),x,8,1/45*(44+51*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(9/2)+23/7500*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+7/1500*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-1/2250*(189+211*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)-23/11250*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(13/2),x,9,1/495*(258+367*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(11/2)-5861/412500*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+14807/577500*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+14807/866250*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-1/57750*(15647+14773*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(7/2)+5861/618750*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)*(3+2*x)^(5/2)*(2+5*x+3*x^2)^(5/2),x,11,430/969*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)-2/57*(3+2*x)^(5/2)*(2+5*x+3*x^2)^(7/2)-125/52378326*(64006+79583*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+25/1247103*(72737+86493*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+2350/2907*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)-16503475/269374248*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+142149125/1885619736*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+25/942809868*(749099+216603*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2),x,10,-2/51*(3+2*x)^(3/2)*(2+5*x+3*x^2)^(7/2)-1/8270262*(949997+1332121*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+1/984555*(1063774+1253571*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)+1166/2295*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)-34355693/212663880*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+62005241/297729432*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+1/744323580*(12174838-22593339*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x),x,9,-1/162162*(15076+34643*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+1/19305*(15467+17193*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)-2/45*(2+5*x+3*x^2)^(7/2)*sqrt(3+2*x)-2742319/4169880*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+5021353/5837832*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+1/14594580*(287729-2667537*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/sqrt(3+2*x),x,8,-5/18018*(563+4669*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+1/429*(224-33*x)*(2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)-651617/92664*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+5983645/648648*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+1/324324*(34372-676791*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(3/2),x,8,-1/11*(73+x)*(2+5*x+3*x^2)^(5/2)/sqrt(3+2*x)+5/1386*(218+3031*x)*(2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)+451331/7128*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-4145485/49896*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-1/24948*(21871-471213*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(5/2),x,8,-1/9*(21+x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(3/2)+5/126*(745+121*x)*(2+5*x+3*x^2)^(3/2)/sqrt(3+2*x)-33335/216*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+306175/1512*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+5/756*(326-6957*x)*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(7/2),x,8,1/210*(2291+879*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(3/2)-1/35*(53+5*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(5/2)-12857/56*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+2333/40*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)-1/140*(10763+3117*x)*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(9/2),x,8,-1/210*(3354+2531*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(5/2)-1/35*(43+7*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(7/2)-4091/40*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+2505/56*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)+1/140*(6292+1823*x)*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(11/2),x,8,1/3150*(14311+10729*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(5/2)+1/63*(124+113*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(9/2)+17699/600*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-32513/840*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-1/2100*(27213+7877*x)*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(13/2),x,8,1/34650*(24161+18699*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(7/2)+1/99*(114+115*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(11/2)-107857/33000*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+198109/46200*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+1/346500*(1301762+948443*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(15/2),x,9,1/6930*(73-33*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(9/2)+1/11*(8+9*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(13/2)+5083/165000*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-9421/231000*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+1/346500*(21492+17833*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)-5083/247500*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(17/2),x,10,-1/64350*(8901+8399*x)*(2+5*x+3*x^2)^(3/2)/(3+2*x)^(11/2)+1/195*(94+119*x)*(2+5*x+3*x^2)^(5/2)/(3+2*x)^(15/2)-335723/53625000*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+594851/75075000*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+594851/112612500*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-1/7507500*(386846+328339*x)*sqrt(2+5*x+3*x^2)/(3+2*x)^(7/2)+335723/80437500*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],

# p<0
[(5-x)*(3+2*x)^(5/2)/sqrt(2+5*x+3*x^2),x,8,865/27*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-2525/189*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+10/7*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2)-2/21*(3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)+1010/189*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^(3/2)/sqrt(2+5*x+3*x^2),x,7,2743/135*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-163/27*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-2/15*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2)+326/135*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2),x,6,101/9*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+5/9*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-2/9*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)/(sqrt(3+2*x)*sqrt(2+5*x+3*x^2)),x,5,-EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+13*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))],
[(5-x)/((3+2*x)^(3/2)*sqrt(2+5*x+3*x^2)),x,6,-EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+13/5*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)-26/5*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)/((3+2*x)^(5/2)*sqrt(2+5*x+3*x^2)),x,7,193/25*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-13/5*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-26/15*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-386/75*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)/((3+2*x)^(7/2)*sqrt(2+5*x+3*x^2)),x,8,4501/625*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-391/125*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-26/25*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)-782/375*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-9002/1875*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^(3/2),x,8,-2/3*(3+2*x)^(5/2)*(121+139*x)/sqrt(2+5*x+3*x^2)+34174/135*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-6034/27*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+308/5*(3+2*x)^(3/2)*sqrt(2+5*x+3*x^2)+12068/135*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(3/2),x,7,-2/3*(3+2*x)^(3/2)*(121+139*x)/sqrt(2+5*x+3*x^2)+3830/27*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-4150/27*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+1660/27*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(3/2),x,6,-2/3*(121+139*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2)+274/3*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-350/3*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))],
[(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2)^(3/2),x,6,-2*(29+35*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2)+70*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-94*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))],
[(5-x)/((2+5*x+3*x^2)^(3/2)*sqrt(3+2*x)),x,6,-6/5*(37+47*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2)-70*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+94/5*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)],
[(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2)),x,7,-6/5*(37+47*x)/(sqrt(3+2*x)*sqrt(2+5*x+3*x^2))+454/25*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)-94/5*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)-908/25*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2)),x,8,-6/5*(37+47*x)/((3+2*x)^(3/2)*sqrt(2+5*x+3*x^2))+7438/125*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-1258/25*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-2516/75*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-14876/375*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(3/2)),x,9,-6/5*(37+47*x)/((3+2*x)^(5/2)*sqrt(2+5*x+3*x^2))+213374/3125*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-30734/625*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-4124/125*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)-61468/1875*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)-426748/9375*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)*(3+2*x)^(9/2)/(2+5*x+3*x^2)^(5/2),x,8,-2/9*(3+2*x)^(7/2)*(121+139*x)/(2+5*x+3*x^2)^(3/2)+4/9*(3+2*x)^(3/2)*(2164+2571*x)/sqrt(2+5*x+3*x^2)-110516/81*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+148780/81*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))-59512/81*sqrt(3+2*x)*sqrt(2+5*x+3*x^2)],
[(5-x)*(3+2*x)^(7/2)/(2+5*x+3*x^2)^(5/2),x,7,-2/9*(3+2*x)^(5/2)*(121+139*x)/(2+5*x+3*x^2)^(3/2)+28/27*(1018+1177*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2)-31892/27*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+41860/27*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))],
[(5-x)*(3+2*x)^(5/2)/(2+5*x+3*x^2)^(5/2),x,7,-2/9*(3+2*x)^(3/2)*(121+139*x)/(2+5*x+3*x^2)^(3/2)+20/9*(364+431*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2)-8620/9*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+11300/9*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))],
[(5-x)*(3+2*x)^(3/2)/(2+5*x+3*x^2)^(5/2),x,7,-2/9*(121+139*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^(3/2)+4/9*(1390+1689*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2)-2252/3*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+2956/3*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))],
[(5-x)*sqrt(3+2*x)/(2+5*x+3*x^2)^(5/2),x,7,-2/3*(29+35*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^(3/2)+4/15*(1759+2139*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2)-2852/5*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+748*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))],
[(5-x)/((2+5*x+3*x^2)^(5/2)*sqrt(3+2*x)),x,7,-2/5*(37+47*x)*sqrt(3+2*x)/(2+5*x+3*x^2)^(3/2)+4/25*(2152+2607*x)*sqrt(3+2*x)/sqrt(2+5*x+3*x^2)-3476/25*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)+916/5*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)],
[(5-x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(5/2)),x,8,-2/5*(37+47*x)/((2+5*x+3*x^2)^(3/2)*sqrt(3+2*x))+4/25*(2054+2409*x)/(sqrt(3+2*x)*sqrt(2+5*x+3*x^2))-11732/125*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)+3212/25*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)+23464/125*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(5/2)),x,9,-2/5*(37+47*x)/((3+2*x)^(3/2)*(2+5*x+3*x^2)^(3/2))+12/25*(652+737*x)/((3+2*x)^(3/2)*sqrt(2+5*x+3*x^2))-95396/625*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+30836/125*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(-2-5*x-3*x^2)/(sqrt(3)*sqrt(2+5*x+3*x^2))+61672/375*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+190792/1875*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(5-x)/((3+2*x)^(7/2)*(2+5*x+3*x^2)^(5/2)),x,10,-2/5*(37+47*x)/((3+2*x)^(5/2)*(2+5*x+3*x^2)^(3/2))+4/25*(1858+2013*x)/((3+2*x)^(5/2)*sqrt(2+5*x+3*x^2))-107548/15625*EllipticE(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)+129268/3125*EllipticF(sqrt(3)*sqrt(1+x),sqrt(-2/3))*sqrt(3)*sqrt(-2-5*x-3*x^2)/sqrt(2+5*x+3*x^2)+87144/625*sqrt(2+5*x+3*x^2)/(3+2*x)^(5/2)+258536/3125*sqrt(2+5*x+3*x^2)/(3+2*x)^(3/2)+215096/15625*sqrt(2+5*x+3*x^2)/sqrt(3+2*x)],
[(A+B*x)*(d+e*x)^(3/2)/sqrt(a+b*x+c*x^2),x,7,2/5*B*(d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)/c+2/15*(3*B*c*d-4*b*B*e+5*A*c*e)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c^2+1/15*(10*A*c*e*(2*c*d-b*e)+B*(3*c^2*d^2+8*b^2*e^2-c*e*(13*b*d+9*a*e)))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c^3*e*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-2/15*(3*B*c*d-4*b*B*e+5*A*c*e)*(c*d^2-b*d*e+a*e^2)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^3*e*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(A+B*x)*(d+e*x)^(1/2)/sqrt(a+b*x+c*x^2),x,6,2/3*B*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/c+1/3*(B*c*d-2*b*B*e+3*A*c*e)*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c^2*e*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-2/3*B*(c*d^2-b*d*e+a*e^2)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^2*e*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(A+B*x)/((d+e*x)^(1/2)*sqrt(a+b*x+c*x^2)),x,5,B*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c*e*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-2*(B*d-A*e)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c*e*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(A+B*x)/((d+e*x)^(3/2)*sqrt(a+b*x+c*x^2)),x,6,2*(B*d-A*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*sqrt(d+e*x))-(B*d-A*e)*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(e*(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+2*B*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c*e*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(A+B*x)/((d+e*x)^(5/2)*sqrt(a+b*x+c*x^2)),x,7,2/3*(B*d-A*e)*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)*(d+e*x)^(3/2))-2/3*(2*A*e*(2*c*d-b*e)-B*(c*d^2+e*(b*d-3*a*e)))*sqrt(a+b*x+c*x^2)/((c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))+1/3*(2*A*e*(2*c*d-b*e)-B*(c*d^2+e*(b*d-3*a*e)))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(e*(c*d^2-b*d*e+a*e^2)^2*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+2/3*(B*d-A*e)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(b^2-4*a*c)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(e*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(A+B*x)*(d+e*x)^(5/2)/(a+b*x+c*x^2)^(3/2),x,7,2*(d+e*x)^(3/2)*(2*a*c*(B*d+A*e)-b*(A*c*d+a*B*e)-(b^2*B*e-b*c*(B*d+A*e)+2*c*(A*c*d-a*B*e))*x)/(c*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))+2/3*e*(4*b^2*B*e-3*b*c*(B*d+A*e)+2*c*(3*A*c*d-5*a*B*e))*sqrt(d+e*x)*sqrt(a+b*x+c*x^2)/(c^2*(b^2-4*a*c))-1/3*(8*b^3*B*e^2-b^2*c*e*(13*B*d+6*A*e)-2*c^2*(3*A*c*d^2-20*a*B*d*e-9*a*A*e^2)+b*c*(3*B*c*d^2+6*A*c*d*e-29*a*B*e^2))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c^3*sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))-2/3*(c*d^2-b*d*e+a*e^2)*(4*b^2*B*e-3*b*c*(B*d+A*e)+2*c*(3*A*c*d-5*a*B*e))*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^3*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(A+B*x)*(d+e*x)^(3/2)/(a+b*x+c*x^2)^(3/2),x,6,2*(2*a*c*(B*d+A*e)-b*(A*c*d+a*B*e)-(b^2*B*e-b*c*(B*d+A*e)+2*c*(A*c*d-a*B*e))*x)*sqrt(d+e*x)/(c*(b^2-4*a*c)*sqrt(a+b*x+c*x^2))+(2*A*c^2*d+2*b^2*B*e-c*(b*B*d+A*b*e+6*a*B*e))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c^2*sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+2*(b*B-2*A*c)*(c*d^2-b*d*e+a*e^2)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c^2*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(A+B*x)*(d+e*x)^(1/2)/(a+b*x+c*x^2)^(3/2),x,6,-2*(A*b-2*a*B-(b*B-2*A*c)*x)*sqrt(d+e*x)/((b^2-4*a*c)*sqrt(a+b*x+c*x^2))-(b*B-2*A*c)*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/(c*sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+2*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(A+B*x)/((d+e*x)^(1/2)*(a+b*x+c*x^2)^(3/2)),x,6,2*(a*B*(2*c*d-b*e)-A*(b*c*d-b^2*e+2*a*c*e)+c*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*x)*sqrt(d+e*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*sqrt(a+b*x+c*x^2))-(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)*sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+2*(b*B-2*A*c)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/(c*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],
[(A+B*x)/((d+e*x)^(3/2)*(a+b*x+c*x^2)^(3/2)),x,7,2*(a*B*(2*c*d-b*e)-A*(b*c*d-b^2*e+2*a*c*e)+c*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))+2*e*(b^2*e*(B*d-2*A*e)-2*c*(A*c*d^2+4*a*B*d*e-3*a*A*e^2)+b*(B*c*d^2+2*A*c*d*e+a*B*e^2))*sqrt(a+b*x+c*x^2)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)^2*sqrt(d+e*x))-(b^2*e*(B*d-2*A*e)-2*c*(A*c*d^2+4*a*B*d*e-3*a*A*e^2)+b*(B*c*d^2+2*A*c*d*e+a*B*e^2))*EllipticE(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(d+e*x)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)^2*sqrt(b^2-4*a*c)*sqrt(a+b*x+c*x^2)*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))+2*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*EllipticF(sqrt((b+2*c*x+sqrt(b^2-4*a*c))/sqrt(b^2-4*a*c))/sqrt(2),sqrt(-2*e*sqrt(b^2-4*a*c)/(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*sqrt(2)*sqrt(-c*(a+b*x+c*x^2)/(b^2-4*a*c))*sqrt(c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))/((c*d^2-b*d*e+a*e^2)*sqrt(b^2-4*a*c)*sqrt(d+e*x)*sqrt(a+b*x+c*x^2))],

# Integrands of the form (d+e x)^m (A+B x) (a+b x+c x^2)^p when m symbolic
[(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2)^3,x,2,-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^3*(d+e*x)^(1+m)/(e^8*(1+m))-(c*d^2-b*d*e+a*e^2)^2*(3*A*e*(2*c*d-b*e)-B*(7*c*d^2-e*(4*b*d-a*e)))*(d+e*x)^(2+m)/(e^8*(2+m))-3*(c*d^2-b*d*e+a*e^2)*(B*(7*c^2*d^3-c*d*e*(8*b*d-3*a*e)+b*e^2*(2*b*d-a*e))-A*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^(3+m)/(e^8*(3+m))-(A*e*(2*c*d-b*e)*(10*c^2*d^2+b^2*e^2-2*c*e*(5*b*d-3*a*e))-B*(35*c^3*d^4-b^2*e^3*(4*b*d-3*a*e)-30*c^2*d^2*e*(2*b*d-a*e)+3*c*e^2*(10*b^2*d^2-8*a*b*d*e+a^2*e^2)))*(d+e*x)^(4+m)/(e^8*(4+m))-(B*(35*c^3*d^3-b^3*e^3+3*b*c*e^2*(5*b*d-2*a*e)-15*c^2*d*e*(3*b*d-a*e))-3*A*c*e*(5*c^2*d^2+b^2*e^2-c*e*(5*b*d-a*e)))*(d+e*x)^(5+m)/(e^8*(5+m))-3*c*(A*c*e*(2*c*d-b*e)-B*(7*c^2*d^2+b^2*e^2-c*e*(6*b*d-a*e)))*(d+e*x)^(6+m)/(e^8*(6+m))-c^2*(7*B*c*d-3*b*B*e-A*c*e)*(d+e*x)^(7+m)/(e^8*(7+m))+B*c^3*(d+e*x)^(8+m)/(e^8*(8+m))],
[(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2)^2,x,2,-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)^2*(d+e*x)^(1+m)/(e^6*(1+m))-(c*d^2-b*d*e+a*e^2)*(2*A*e*(2*c*d-b*e)-B*(5*c*d^2-e*(3*b*d-a*e)))*(d+e*x)^(2+m)/(e^6*(2+m))-(B*(10*c^2*d^3+b*e^2*(3*b*d-2*a*e)-6*c*d*e*(2*b*d-a*e))-A*e*(6*c^2*d^2+b^2*e^2-2*c*e*(3*b*d-a*e)))*(d+e*x)^(3+m)/(e^6*(3+m))-(2*A*c*e*(2*c*d-b*e)-B*(10*c^2*d^2+b^2*e^2-2*c*e*(4*b*d-a*e)))*(d+e*x)^(4+m)/(e^6*(4+m))-c*(5*B*c*d-2*b*B*e-A*c*e)*(d+e*x)^(5+m)/(e^6*(5+m))+B*c^2*(d+e*x)^(6+m)/(e^6*(6+m))],
[(A+B*x)*(d+e*x)^m*(a+b*x+c*x^2),x,2,-(B*d-A*e)*(c*d^2-b*d*e+a*e^2)*(d+e*x)^(1+m)/(e^4*(1+m))-(A*e*(2*c*d-b*e)-B*(3*c*d^2-e*(2*b*d-a*e)))*(d+e*x)^(2+m)/(e^4*(2+m))-(3*B*c*d-b*B*e-A*c*e)*(d+e*x)^(3+m)/(e^4*(3+m))+B*c*(d+e*x)^(4+m)/(e^4*(4+m))],
[(A+B*x)*(d+e*x)^m/(a+b*x+c*x^2),x,4,-(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],2*c*(d+e*x)/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(B+(-b*B+2*A*c)/sqrt(b^2-4*a*c))/((1+m)*(2*c*d-e*(b-sqrt(b^2-4*a*c))))-(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],2*c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(B+(b*B-2*A*c)/sqrt(b^2-4*a*c))/((1+m)*(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(A+B*x)*(d+e*x)^m/(a+b*x+c*x^2)^2,x,5,(d+e*x)^(1+m)*(a*B*(2*c*d-b*e)-A*(b*c*d-b^2*e+2*a*c*e)+c*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*x)/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(a+b*x+c*x^2))+c*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],2*c*(d+e*x)/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(e*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*m+(-2*b*(B*c*d^2+2*A*c*d*e+a*B*e^2)+b^2*e*(B*d*(2-m)+A*e*m)+4*c*(A*(c*d^2+a*e^2*(1-m))+a*B*d*e*m))/sqrt(b^2-4*a*c))/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(1+m)*(2*c*d-e*(b-sqrt(b^2-4*a*c))))+c*(d+e*x)^(1+m)*hypergeom([1,1+m],[2+m],2*c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(e*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*m+(2*b*(B*c*d^2+2*A*c*d*e+a*B*e^2)-b^2*e*(B*d*(2-m)+A*e*m)-4*c*(A*(c*d^2+a*e^2*(1-m))+a*B*d*e*m))/sqrt(b^2-4*a*c))/((b^2-4*a*c)*(c*d^2-b*d*e+a*e^2)*(1+m)*(2*c*d-e*(b+sqrt(b^2-4*a*c))))],
[(A+B*x)*(d+e*x)^(1+m)/(a+b*x+c*x^2),x,4,-(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],2*c*(d+e*x)/(2*c*d-e*(b-sqrt(b^2-4*a*c))))*(B+(-b*B+2*A*c)/sqrt(b^2-4*a*c))/((2+m)*(2*c*d-e*(b-sqrt(b^2-4*a*c))))-(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],2*c*(d+e*x)/(2*c*d-e*(b+sqrt(b^2-4*a*c))))*(B+(b*B-2*A*c)/sqrt(b^2-4*a*c))/((2+m)*(2*c*d-e*(b+sqrt(b^2-4*a*c))))],

# Integrands of the form (d+e x)^m (A+B x) (a+b x+c x^2)^p when p symbolic
[(A+B*x)*(d+e*x)^(-3-2*p)*(a+b*x+c*x^2)^p,x,2,1/2*(B*d-A*e)*(a+b*x+c*x^2)^(1+p)/((c*d^2-b*d*e+a*e^2)*(1+p)*(d+e*x)^(2*(1+p)))-1/2*(b*B*d-2*A*c*d+A*b*e-2*a*B*e)*(d+e*x)^(-1-2*p)*(a+b*x+c*x^2)^p*hypergeom([-1-2*p,-p],[-2*p],-4*c*(d+e*x)*sqrt(b^2-4*a*c)/((b+2*c*x-sqrt(b^2-4*a*c))*(2*c*d-e*(b+sqrt(b^2-4*a*c)))))*(b+2*c*x-sqrt(b^2-4*a*c))/((c*d^2-b*d*e+a*e^2)*(1+2*p)*(2*c*d-e*(b-sqrt(b^2-4*a*c)))*((2*c*d-e*(b-sqrt(b^2-4*a*c)))*(b+2*c*x+sqrt(b^2-4*a*c))/((b+2*c*x-sqrt(b^2-4*a*c))*(2*c*d-e*(b+sqrt(b^2-4*a*c)))))^p)]]:
