# Maple integration test file: "3 Logarithms\3.4 u (a+b log(c (d+e x^m)^n))^p.txt"

lst:=[

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

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

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

# n>0
[x^4*log(c*(a+b*x^2)^p),x,4,-2/5*a^2*p*x/b^2+2/15*a*p*x^3/b-2/25*p*x^5+2/5*a^(5/2)*p*arctan(x*sqrt(b)/sqrt(a))/b^(5/2)+1/5*x^5*log(c*(a+b*x^2)^p)],
[x^3*log(c*(a+b*x^2)^p),x,4,1/4*a*p*x^2/b-1/8*p*x^4-1/4*a^2*p*log(a+b*x^2)/b^2+1/4*x^4*log(c*(a+b*x^2)^p)],
[x^2*log(c*(a+b*x^2)^p),x,4,2/3*a*p*x/b-2/9*p*x^3-2/3*a^(3/2)*p*arctan(x*sqrt(b)/sqrt(a))/b^(3/2)+1/3*x^3*log(c*(a+b*x^2)^p)],
[x*log(c*(a+b*x^2)^p),x,3,-1/2*p*x^2+1/2*(a+b*x^2)*log(c*(a+b*x^2)^p)/b],
[log(c*(a+b*x^2)^p),x,3,-2*p*x+x*log(c*(a+b*x^2)^p)+2*p*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/sqrt(b)],
[log(c*(a+b*x^2)^p)/x,x,3,1/2*log(-b*x^2/a)*log(c*(a+b*x^2)^p)+1/2*p*polylog(2,1+b*x^2/a)],
[log(c*(a+b*x^2)^p)/x^2,x,2,-log(c*(a+b*x^2)^p)/x+2*p*arctan(x*sqrt(b)/sqrt(a))*sqrt(b)/sqrt(a)],
[log(c*(a+b*x^2)^p)/x^3,x,5,b*p*log(x)/a-1/2*(a+b*x^2)*log(c*(a+b*x^2)^p)/(a*x^2),b*p*log(x)/a-1/2*b*p*log(a+b*x^2)/a-1/2*log(c*(a+b*x^2)^p)/x^2],
[log(c*(a+b*x^2)^p)/x^4,x,3,-2/3*b*p/(a*x)-2/3*b^(3/2)*p*arctan(x*sqrt(b)/sqrt(a))/a^(3/2)-1/3*log(c*(a+b*x^2)^p)/x^3],
[log(c*(a+b*x^2)^p)/x^5,x,4,-1/4*b*p/(a*x^2)-1/2*b^2*p*log(x)/a^2+1/4*b^2*p*log(a+b*x^2)/a^2-1/4*log(c*(a+b*x^2)^p)/x^4],
[log(c*(a+b*x^2)^p)/x^6,x,4,-2/15*b*p/(a*x^3)+2/5*b^2*p/(a^2*x)+2/5*b^(5/2)*p*arctan(x*sqrt(b)/sqrt(a))/a^(5/2)-1/5*log(c*(a+b*x^2)^p)/x^5],
[log(c*(a+b*x^2)^p)/x^7,x,4,-1/12*b*p/(a*x^4)+1/6*b^2*p/(a^2*x^2)+1/3*b^3*p*log(x)/a^3-1/6*b^3*p*log(a+b*x^2)/a^3-1/6*log(c*(a+b*x^2)^p)/x^6],
[x^5*log(c*(a+b*x^3)^p),x,4,1/6*a*p*x^3/b-1/12*p*x^6-1/6*a^2*p*log(a+b*x^3)/b^2+1/6*x^6*log(c*(a+b*x^3)^p)],
[x^4*log(c*(a+b*x^3)^p),x,9,3/10*a*p*x^2/b-3/25*p*x^5+1/5*a^(5/3)*p*log(a^(1/3)+b^(1/3)*x)/b^(5/3)-1/10*a^(5/3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(5/3)+1/5*x^5*log(c*(a+b*x^3)^p)+1/5*a^(5/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(5/3)],
[x^3*log(c*(a+b*x^3)^p),x,9,3/4*a*p*x/b-3/16*p*x^4-1/4*a^(4/3)*p*log(a^(1/3)+b^(1/3)*x)/b^(4/3)+1/8*a^(4/3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(4/3)+1/4*x^4*log(c*(a+b*x^3)^p)+1/4*a^(4/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(4/3)],
[x^2*log(c*(a+b*x^3)^p),x,3,-1/3*p*x^3+1/3*(a+b*x^3)*log(c*(a+b*x^3)^p)/b],
[x*log(c*(a+b*x^3)^p),x,8,-3/4*p*x^2-1/2*a^(2/3)*p*log(a^(1/3)+b^(1/3)*x)/b^(2/3)+1/4*a^(2/3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(2/3)+1/2*x^2*log(c*(a+b*x^3)^p)-1/2*a^(2/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(2/3)],
[log(c*(a+b*x^3)^p),x,8,-3*p*x+a^(1/3)*p*log(a^(1/3)+b^(1/3)*x)/b^(1/3)-1/2*a^(1/3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(1/3)+x*log(c*(a+b*x^3)^p)-a^(1/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(1/3)],
[log(c*(a+b*x^3)^p)/x,x,3,1/3*log(-b*x^3/a)*log(c*(a+b*x^3)^p)+1/3*p*polylog(2,1+b*x^3/a)],
[log(c*(a+b*x^3)^p)/x^2,x,7,-b^(1/3)*p*log(a^(1/3)+b^(1/3)*x)/a^(1/3)+1/2*b^(1/3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(1/3)-log(c*(a+b*x^3)^p)/x-b^(1/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(1/3)],
[log(c*(a+b*x^3)^p)/x^3,x,7,1/2*b^(2/3)*p*log(a^(1/3)+b^(1/3)*x)/a^(2/3)-1/4*b^(2/3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(2/3)-1/2*log(c*(a+b*x^3)^p)/x^2-1/2*b^(2/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(2/3)],
[log(c*(a+b*x^3)^p)/x^4,x,5,b*p*log(x)/a-1/3*b*p*log(a+b*x^3)/a-1/3*log(c*(a+b*x^3)^p)/x^3],
[log(c*(a+b*x^3)^p)/x^5,x,8,-3/4*b*p/(a*x)+1/4*b^(4/3)*p*log(a^(1/3)+b^(1/3)*x)/a^(4/3)-1/8*b^(4/3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(4/3)-1/4*log(c*(a+b*x^3)^p)/x^4+1/4*b^(4/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(4/3)],
[log(c*(a+b*x^3)^p)/x^6,x,8,-3/10*b*p/(a*x^2)-1/5*b^(5/3)*p*log(a^(1/3)+b^(1/3)*x)/a^(5/3)+1/10*b^(5/3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(5/3)-1/5*log(c*(a+b*x^3)^p)/x^5+1/5*b^(5/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(5/3)],
[log(c*(a+b*x^3)^p)/x^7,x,4,-1/6*b*p/(a*x^3)-1/2*b^2*p*log(x)/a^2+1/6*b^2*p*log(a+b*x^3)/a^2-1/6*log(c*(a+b*x^3)^p)/x^6],

# n<0
[x^4*log(c*(a+b/x)^p),x,4,-1/5*b^4*p*x/a^4+1/10*b^3*p*x^2/a^3-1/15*b^2*p*x^3/a^2+1/20*b*p*x^4/a+1/5*x^5*log(c*(a+b/x)^p)+1/5*b^5*p*log(b+a*x)/a^5],
[x^3*log(c*(a+b/x)^p),x,4,1/4*b^3*p*x/a^3-1/8*b^2*p*x^2/a^2+1/12*b*p*x^3/a+1/4*x^4*log(c*(a+b/x)^p)-1/4*b^4*p*log(b+a*x)/a^4],
[x^2*log(c*(a+b/x)^p),x,4,-1/3*b^2*p*x/a^2+1/6*b*p*x^2/a+1/3*x^3*log(c*(a+b/x)^p)+1/3*b^3*p*log(b+a*x)/a^3],
[x*log(c*(a+b/x)^p),x,4,1/2*b*p*x/a+1/2*x^2*log(c*(a+b/x)^p)-1/2*b^2*p*log(b+a*x)/a^2],
[log(c*(a+b/x)^p),x,3,x*log(c*(a+b/x)^p)+b*p*log(b+a*x)/a],
[log(c*(a+b/x)^p)/x,x,3,-log(c*(a+b/x)^p)*log(-b/(a*x))-p*polylog(2,1+b/(a*x))],
[log(c*(a+b/x)^p)/x^2,x,3,p/x-(a+b/x)*log(c*(a+b/x)^p)/b],
[log(c*(a+b/x)^p)/x^3,x,4,1/4*p/x^2-1/2*a*p/(b*x)+1/2*a^2*p*log(a+b/x)/b^2-1/2*log(c*(a+b/x)^p)/x^2],
[log(c*(a+b/x)^p)/x^4,x,4,1/9*p/x^3-1/6*a*p/(b*x^2)+1/3*a^2*p/(b^2*x)-1/3*a^3*p*log(a+b/x)/b^3-1/3*log(c*(a+b/x)^p)/x^3],
[log(c*(a+b/x)^p)/x^5,x,4,1/16*p/x^4-1/12*a*p/(b*x^3)+1/8*a^2*p/(b^2*x^2)-1/4*a^3*p/(b^3*x)+1/4*a^4*p*log(a+b/x)/b^4-1/4*log(c*(a+b/x)^p)/x^4],
[x^4*log(c*(a+b/x^2)^p),x,5,-2/5*b^2*p*x/a^2+2/15*b*p*x^3/a+2/5*b^(5/2)*p*arctan(x*sqrt(a)/sqrt(b))/a^(5/2)+1/5*x^5*log(c*(a+b/x^2)^p)],
[x^3*log(c*(a+b/x^2)^p),x,5,1/4*b*p*x^2/a+1/4*x^4*log(c*(a+b/x^2)^p)-1/4*b^2*p*log(b+a*x^2)/a^2],
[x^2*log(c*(a+b/x^2)^p),x,4,2/3*b*p*x/a-2/3*b^(3/2)*p*arctan(x*sqrt(a)/sqrt(b))/a^(3/2)+1/3*x^3*log(c*(a+b/x^2)^p)],
[x*log(c*(a+b/x^2)^p),x,3,1/2*x^2*log(c*(a+b/x^2)^p)+1/2*b*p*log(b+a*x^2)/a],
[log(c*(a+b/x^2)^p),x,3,x*log(c*(a+b/x^2)^p)+2*p*arctan(x*sqrt(a)/sqrt(b))*sqrt(b)/sqrt(a)],
[log(c*(a+b/x^2)^p)/x,x,3,-1/2*log(c*(a+b/x^2)^p)*log(-b/(a*x^2))-1/2*p*polylog(2,1+b/(a*x^2))],
[log(c*(a+b/x^2)^p)/x^2,x,4,2*p/x-log(c*(a+b/x^2)^p)/x+2*p*arctan(x*sqrt(a)/sqrt(b))*sqrt(a)/sqrt(b)],
[log(c*(a+b/x^2)^p)/x^3,x,3,1/2*p/x^2-1/2*(a+b/x^2)*log(c*(a+b/x^2)^p)/b],
[log(c*(a+b/x^2)^p)/x^4,x,5,2/9*p/x^3-2/3*a*p/(b*x)-2/3*a^(3/2)*p*arctan(x*sqrt(a)/sqrt(b))/b^(3/2)-1/3*log(c*(a+b/x^2)^p)/x^3],
[log(1+b/x)/x,x,1,polylog(2,-b/x)],

# Integrands of the form x^q Log[c (d+e x^(m/2))^n]

# n>0
[x^3*log(c*(a+b*sqrt(x))^p),x,4,-1/8*a^6*p*x/b^6+1/12*a^5*p*x^(3/2)/b^5-1/16*a^4*p*x^2/b^4+1/20*a^3*p*x^(5/2)/b^3-1/24*a^2*p*x^3/b^2+1/28*a*p*x^(7/2)/b-1/32*p*x^4-1/4*a^8*p*log(a+b*sqrt(x))/b^8+1/4*x^4*log(c*(a+b*sqrt(x))^p)+1/4*a^7*p*sqrt(x)/b^7],
[x^2*log(c*(a+b*sqrt(x))^p),x,4,-1/6*a^4*p*x/b^4+1/9*a^3*p*x^(3/2)/b^3-1/12*a^2*p*x^2/b^2+1/15*a*p*x^(5/2)/b-1/18*p*x^3-1/3*a^6*p*log(a+b*sqrt(x))/b^6+1/3*x^3*log(c*(a+b*sqrt(x))^p)+1/3*a^5*p*sqrt(x)/b^5],
[x*log(c*(a+b*sqrt(x))^p),x,4,-1/4*a^2*p*x/b^2+1/6*a*p*x^(3/2)/b-1/8*p*x^2-1/2*a^4*p*log(a+b*sqrt(x))/b^4+1/2*x^2*log(c*(a+b*sqrt(x))^p)+1/2*a^3*p*sqrt(x)/b^3],
[log(c*(a+b*sqrt(x))^p),x,4,-1/2*p*x-a^2*p*log(a+b*sqrt(x))/b^2+x*log(c*(a+b*sqrt(x))^p)+a*p*sqrt(x)/b],
[log(c*(a+b*sqrt(x))^p)/x,x,3,2*log(-b*sqrt(x)/a)*log(c*(a+b*sqrt(x))^p)+2*p*polylog(2,1+b*sqrt(x)/a)],
[log(c*(a+b*sqrt(x))^p)/x^2,x,4,-1/2*b^2*p*log(x)/a^2+b^2*p*log(a+b*sqrt(x))/a^2-log(c*(a+b*sqrt(x))^p)/x-b*p/(a*sqrt(x))],
[log(c*(a+b*sqrt(x))^p)/x^3,x,4,-1/6*b*p/(a*x^(3/2))+1/4*b^2*p/(a^2*x)-1/4*b^4*p*log(x)/a^4+1/2*b^4*p*log(a+b*sqrt(x))/a^4-1/2*log(c*(a+b*sqrt(x))^p)/x^2-1/2*b^3*p/(a^3*sqrt(x))],
[log(c*(a+b*sqrt(x))^p)/x^4,x,4,-1/15*b*p/(a*x^(5/2))+1/12*b^2*p/(a^2*x^2)-1/9*b^3*p/(a^3*x^(3/2))+1/6*b^4*p/(a^4*x)-1/6*b^6*p*log(x)/a^6+1/3*b^6*p*log(a+b*sqrt(x))/a^6-1/3*log(c*(a+b*sqrt(x))^p)/x^3-1/3*b^5*p/(a^5*sqrt(x))],

# n<0

# Integrands of the form (f x)^(q/2) Log[c (d+e x^(m/2))^n]

# n>0
[log(a+b*sqrt(x))/sqrt(x),x,3,-2*sqrt(x)+2*log(a+b*sqrt(x))*(a+b*sqrt(x))/b],

# n<0

# Integrands of the form (f x)^q Log[c (d+e x^m)^n] when q symbolic
[(f*x)^m*log(c*(d+e*x^3)^p),x,3,-3*e*p*(f*x)^(4+m)*hypergeom([1,1/3*(4+m)],[1/3*(7+m)],-e*x^3/d)/(d*f^4*(1+m)*(4+m))+(f*x)^(1+m)*log(c*(d+e*x^3)^p)/(f*(1+m))],
[(f*x)^m*log(c*(d+e*x^2)^p),x,3,-2*e*p*(f*x)^(3+m)*hypergeom([1,1/2*(3+m)],[1/2*(5+m)],-e*x^2/d)/(d*f^3*(1+m)*(3+m))+(f*x)^(1+m)*log(c*(d+e*x^2)^p)/(f*(1+m))],
[(f*x)^m*log(c*(d+e*x)^p),x,2,-e*p*(f*x)^(2+m)*hypergeom([1,2+m],[3+m],-e*x/d)/(d*f^2*(1+m)*(2+m))+(f*x)^(1+m)*log(c*(d+e*x)^p)/(f*(1+m))],
[(f*x)^m*log(c*(d+e/x)^p),x,4,e*p*(f*x)^m*hypergeom([1,-m],[1-m],-e/(d*x))/(d*m*(1+m))+(f*x)^(1+m)*log(c*(d+e/x)^p)/(f*(1+m))],
[(f*x)^m*log(c*(d+e/x^2)^p),x,4,-2*e*f*p*(f*x)^(-1+m)*hypergeom([1,1/2*(1-m)],[1/2*(3-m)],-e/(d*x^2))/(d*(1-m^2))+(f*x)^(1+m)*log(c*(d+e/x^2)^p)/(f*(1+m))],
[(f*x)^m*log(c*(d+e/x^3)^p),x,4,-3*e*f^2*p*(f*x)^(-2+m)*hypergeom([1,1/3*(2-m)],[1/3*(5-m)],-e/(d*x^3))/(d*(2+m-m^2))+(f*x)^(1+m)*log(c*(d+e/x^3)^p)/(f*(1+m))],
[(f*x)^m*log(c*(d+e*sqrt(x))^p),x,4,-e*p*x^(3/2)*(f*x)^m*hypergeom([1,3+2*m],[2*(2+m)],-e*sqrt(x)/d)/(d*(1+m)*(3+2*m))+(f*x)^(1+m)*log(c*(d+e*sqrt(x))^p)/(f*(1+m))],
[(f*x)^m*log(c*(d+e/sqrt(x))^p),x,5,1/2*p*x*(f*x)^m*hypergeom([1,2*(1+m)],[3+2*m],-d*sqrt(x)/e)/(1+m)^2+(f*x)^(1+m)*log(c*(d+e/sqrt(x))^p)/(f*(1+m))],

# Integrands of the form (f x)^q Log[c (d+e x^m)^n] when m symbolic
[(f*x)^m*log(c*(d+e*x^n)^p),x,3,-e*n*p*x^(1+n)*(f*x)^m*hypergeom([1,(1+m+n)/n],[(1+m+2*n)/n],-e*x^n/d)/(d*(1+m)*(1+m+n))+(f*x)^(1+m)*log(c*(d+e*x^n)^p)/(f*(1+m))],
[(f*x)^(-1+3*n)*log(c*(d+e*x^n)^p),x,5,-1/9*p*(f*x)^(3*n)/(f*n)-1/3*d^2*p*(f*x)^(3*n)/(e^2*f*n*x^(2*n))+1/6*d*p*(f*x)^(3*n)/(e*f*n*x^n)+1/3*d^3*p*(f*x)^(3*n)*log(d+e*x^n)/(e^3*f*n*x^(3*n))+1/3*(f*x)^(3*n)*log(c*(d+e*x^n)^p)/(f*n)],
[(f*x)^(-1+2*n)*log(c*(d+e*x^n)^p),x,5,-1/4*p*(f*x)^(2*n)/(f*n)+1/2*d*p*(f*x)^(2*n)/(e*f*n*x^n)-1/2*d^2*p*(f*x)^(2*n)*log(d+e*x^n)/(e^2*f*n*x^(2*n))+1/2*(f*x)^(2*n)*log(c*(d+e*x^n)^p)/(f*n)],
[(f*x)^(-1+n)*log(c*(d+e*x^n)^p),x,5,-p*(f*x)^n/(f*n)+d*p*(f*x)^n*log(d+e*x^n)/(e*f*n*x^n)+(f*x)^n*log(c*(d+e*x^n)^p)/(f*n)],
[log(c*(d+e*x^n)^p)/(f*x),x,4,log(-e*x^n/d)*log(c*(d+e*x^n)^p)/(f*n)+p*polylog(2,1+e*x^n/d)/(f*n)],
[(f*x)^(-1-n)*log(c*(d+e*x^n)^p),x,6,e*p*x^n*log(x)/(d*f*(f*x)^n)-e*p*x^n*log(d+e*x^n)/(d*f*n*(f*x)^n)-log(c*(d+e*x^n)^p)/(f*n*(f*x)^n)],
[(f*x)^(-1-2*n)*log(c*(d+e*x^n)^p),x,5,-1/2*e*p*x^n/(d*f*n*(f*x)^(2*n))-1/2*e^2*p*x^(2*n)*log(x)/(d^2*f*(f*x)^(2*n))+1/2*e^2*p*x^(2*n)*log(d+e*x^n)/(d^2*f*n*(f*x)^(2*n))-1/2*log(c*(d+e*x^n)^p)/(f*n*(f*x)^(2*n))],
[x^2*log(c*(d+e*x^n)^p),x,2,-1/3*e*n*p*x^(3+n)*hypergeom([1,(3+n)/n],[2+3/n],-e*x^n/d)/(d*(3+n))+1/3*x^3*log(c*(d+e*x^n)^p)],
[x*log(c*(d+e*x^n)^p),x,2,-1/2*e*n*p*x^(2+n)*hypergeom([1,(2+n)/n],[2*(1+1/n)],-e*x^n/d)/(d*(2+n))+1/2*x^2*log(c*(d+e*x^n)^p)],
[log(c*(d+e*x^n)^p),x,2,-e*n*p*x^(1+n)*hypergeom([1,1+1/n],[2+1/n],-e*x^n/d)/(d*(1+n))+x*log(c*(d+e*x^n)^p)],
[log(c*(d+e*x^n)^p)/x,x,3,log(-e*x^n/d)*log(c*(d+e*x^n)^p)/n+p*polylog(2,1+e*x^n/d)/n],
[log(c*(d+e*x^n)^p)/x^2,x,2,-e*n*p*x^(-1+n)*hypergeom([1,(-1+n)/n],[2+(-1)/n],-e*x^n/d)/(d*(1-n))-log(c*(d+e*x^n)^p)/x],
[log(c*(d+e*x^n)^p)/x^3,x,2,-1/2*e*n*p*x^(-2+n)*hypergeom([1,(-2+n)/n],[2*(1+(-1)/n)],-e*x^n/d)/(d*(2-n))-1/2*log(c*(d+e*x^n)^p)/x^2],
[log(c*(d+e*x^n)^p)/x^4,x,2,-1/3*e*n*p*x^(-3+n)*hypergeom([1,(-3+n)/n],[2+(-3)/n],-e*x^n/d)/(d*(3-n))-1/3*log(c*(d+e*x^n)^p)/x^3],

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

# Integrands of the form x^q Log[c (d+e x^2)^n]^p 

# p>0
[x^5*log(c*(a+b*x^2)^p)^2,x,8,a^2*p^2*x^2/b^2-1/4*a*p^2*(a+b*x^2)^2/b^3+1/27*p^2*(a+b*x^2)^3/b^3-1/6*a^3*p^2*log(a+b*x^2)^2/b^3-a^2*p*(a+b*x^2)*log(c*(a+b*x^2)^p)/b^3+1/2*a*p*(a+b*x^2)^2*log(c*(a+b*x^2)^p)/b^3-1/9*p*(a+b*x^2)^3*log(c*(a+b*x^2)^p)/b^3+1/3*a^3*p*log(a+b*x^2)*log(c*(a+b*x^2)^p)/b^3+1/6*x^6*log(c*(a+b*x^2)^p)^2],
[x^3*log(c*(a+b*x^2)^p)^2,x,9,-a*p^2*x^2/b+1/8*p^2*(a+b*x^2)^2/b^2+a*p*(a+b*x^2)*log(c*(a+b*x^2)^p)/b^2-1/4*p*(a+b*x^2)^2*log(c*(a+b*x^2)^p)/b^2-1/2*a*(a+b*x^2)*log(c*(a+b*x^2)^p)^2/b^2+1/4*(a+b*x^2)^2*log(c*(a+b*x^2)^p)^2/b^2],
[x*log(c*(a+b*x^2)^p)^2,x,4,p^2*x^2-p*(a+b*x^2)*log(c*(a+b*x^2)^p)/b+1/2*(a+b*x^2)*log(c*(a+b*x^2)^p)^2/b],
[log(c*(a+b*x^2)^p)^2/x,x,5,1/2*log(-b*x^2/a)*log(c*(a+b*x^2)^p)^2+p*log(c*(a+b*x^2)^p)*polylog(2,1+b*x^2/a)-p^2*polylog(3,1+b*x^2/a)],
[log(c*(a+b*x^2)^p)^2/x^3,x,4,b*p*log(-b*x^2/a)*log(c*(a+b*x^2)^p)/a-1/2*(a+b*x^2)*log(c*(a+b*x^2)^p)^2/(a*x^2)+b*p^2*polylog(2,1+b*x^2/a)/a],
[log(c*(a+b*x^2)^p)^2/x^5,x,8,b^2*p^2*log(x)/a^2-1/2*b*p*(a+b*x^2)*log(c*(a+b*x^2)^p)/(a^2*x^2)-1/4*log(c*(a+b*x^2)^p)^2/x^4-1/2*b^2*p*log(c*(a+b*x^2)^p)*log(1-a/(a+b*x^2))/a^2+1/2*b^2*p^2*polylog(2,a/(a+b*x^2))/a^2],
[log(c*(a+b*x^2)^p)^2/x^7,x,12,-1/6*b^2*p^2/(a^2*x^2)-b^3*p^2*log(x)/a^3+1/6*b^3*p^2*log(a+b*x^2)/a^3-1/6*b*p*log(c*(a+b*x^2)^p)/(a*x^4)+1/3*b^2*p*(a+b*x^2)*log(c*(a+b*x^2)^p)/(a^3*x^2)-1/6*log(c*(a+b*x^2)^p)^2/x^6+1/3*b^3*p*log(c*(a+b*x^2)^p)*log(1-a/(a+b*x^2))/a^3-1/3*b^3*p^2*polylog(2,a/(a+b*x^2))/a^3],
[x^4*log(c*(a+b*x^2)^p)^2,x,20,184/75*a^2*p^2*x/b^2-64/225*a*p^2*x^3/b+8/125*p^2*x^5-184/75*a^(5/2)*p^2*arctan(x*sqrt(b)/sqrt(a))/b^(5/2)+4/5*I*a^(5/2)*p^2*arctan(x*sqrt(b)/sqrt(a))^2/b^(5/2)-4/5*a^2*p*x*log(c*(a+b*x^2)^p)/b^2+4/15*a*p*x^3*log(c*(a+b*x^2)^p)/b-4/25*p*x^5*log(c*(a+b*x^2)^p)+4/5*a^(5/2)*p*arctan(x*sqrt(b)/sqrt(a))*log(c*(a+b*x^2)^p)/b^(5/2)+1/5*x^5*log(c*(a+b*x^2)^p)^2+8/5*a^(5/2)*p^2*arctan(x*sqrt(b)/sqrt(a))*log(2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/b^(5/2)+4/5*I*a^(5/2)*p^2*polylog(2,1-2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/b^(5/2)],
[x^2*log(c*(a+b*x^2)^p)^2,x,16,-32/9*a*p^2*x/b+8/27*p^2*x^3+32/9*a^(3/2)*p^2*arctan(x*sqrt(b)/sqrt(a))/b^(3/2)-4/3*I*a^(3/2)*p^2*arctan(x*sqrt(b)/sqrt(a))^2/b^(3/2)+4/3*a*p*x*log(c*(a+b*x^2)^p)/b-4/9*p*x^3*log(c*(a+b*x^2)^p)-4/3*a^(3/2)*p*arctan(x*sqrt(b)/sqrt(a))*log(c*(a+b*x^2)^p)/b^(3/2)+1/3*x^3*log(c*(a+b*x^2)^p)^2-8/3*a^(3/2)*p^2*arctan(x*sqrt(b)/sqrt(a))*log(2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/b^(3/2)-4/3*I*a^(3/2)*p^2*polylog(2,1-2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/b^(3/2)],
[log(c*(a+b*x^2)^p)^2,x,12,8*p^2*x-4*p*x*log(c*(a+b*x^2)^p)+x*log(c*(a+b*x^2)^p)^2-8*p^2*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/sqrt(b)+4*I*p^2*arctan(x*sqrt(b)/sqrt(a))^2*sqrt(a)/sqrt(b)+4*p*arctan(x*sqrt(b)/sqrt(a))*log(c*(a+b*x^2)^p)*sqrt(a)/sqrt(b)+8*p^2*arctan(x*sqrt(b)/sqrt(a))*log(2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))*sqrt(a)/sqrt(b)+4*I*p^2*polylog(2,1-2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))*sqrt(a)/sqrt(b)],
[log(c*(a+b*x^2)^p)^2/x^2,x,7,-log(c*(a+b*x^2)^p)^2/x+4*I*p^2*arctan(x*sqrt(b)/sqrt(a))^2*sqrt(b)/sqrt(a)+4*p*arctan(x*sqrt(b)/sqrt(a))*log(c*(a+b*x^2)^p)*sqrt(b)/sqrt(a)+8*p^2*arctan(x*sqrt(b)/sqrt(a))*log(2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))*sqrt(b)/sqrt(a)+4*I*p^2*polylog(2,1-2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))*sqrt(b)/sqrt(a)],
[log(c*(a+b*x^2)^p)^2/x^4,x,11,8/3*b^(3/2)*p^2*arctan(x*sqrt(b)/sqrt(a))/a^(3/2)-4/3*I*b^(3/2)*p^2*arctan(x*sqrt(b)/sqrt(a))^2/a^(3/2)-4/3*b*p*log(c*(a+b*x^2)^p)/(a*x)-4/3*b^(3/2)*p*arctan(x*sqrt(b)/sqrt(a))*log(c*(a+b*x^2)^p)/a^(3/2)-1/3*log(c*(a+b*x^2)^p)^2/x^3-8/3*b^(3/2)*p^2*arctan(x*sqrt(b)/sqrt(a))*log(2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/a^(3/2)-4/3*I*b^(3/2)*p^2*polylog(2,1-2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/a^(3/2)],
[log(c*(a+b*x^2)^p)^2/x^6,x,14,-8/15*b^2*p^2/(a^2*x)-32/15*b^(5/2)*p^2*arctan(x*sqrt(b)/sqrt(a))/a^(5/2)+4/5*I*b^(5/2)*p^2*arctan(x*sqrt(b)/sqrt(a))^2/a^(5/2)-4/15*b*p*log(c*(a+b*x^2)^p)/(a*x^3)+4/5*b^2*p*log(c*(a+b*x^2)^p)/(a^2*x)+4/5*b^(5/2)*p*arctan(x*sqrt(b)/sqrt(a))*log(c*(a+b*x^2)^p)/a^(5/2)-1/5*log(c*(a+b*x^2)^p)^2/x^5+8/5*b^(5/2)*p^2*arctan(x*sqrt(b)/sqrt(a))*log(2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/a^(5/2)+4/5*I*b^(5/2)*p^2*polylog(2,1-2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/a^(5/2)],
[log(c*(a+b*x^2)^p)^2/x^8,x,18,-8/105*b^2*p^2/(a^2*x^3)+64/105*b^3*p^2/(a^3*x)+184/105*b^(7/2)*p^2*arctan(x*sqrt(b)/sqrt(a))/a^(7/2)-4/7*I*b^(7/2)*p^2*arctan(x*sqrt(b)/sqrt(a))^2/a^(7/2)-4/35*b*p*log(c*(a+b*x^2)^p)/(a*x^5)+4/21*b^2*p*log(c*(a+b*x^2)^p)/(a^2*x^3)-4/7*b^3*p*log(c*(a+b*x^2)^p)/(a^3*x)-4/7*b^(7/2)*p*arctan(x*sqrt(b)/sqrt(a))*log(c*(a+b*x^2)^p)/a^(7/2)-1/7*log(c*(a+b*x^2)^p)^2/x^7-8/7*b^(7/2)*p^2*arctan(x*sqrt(b)/sqrt(a))*log(2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/a^(7/2)-4/7*I*b^(7/2)*p^2*polylog(2,1-2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/a^(7/2)],
[x^5*log(c*(a+b*x^2)^p)^3,x,15,-3*a^2*p^3*x^2/b^2+3/8*a*p^3*(a+b*x^2)^2/b^3-1/27*p^3*(a+b*x^2)^3/b^3+3*a^2*p^2*(a+b*x^2)*log(c*(a+b*x^2)^p)/b^3-3/4*a*p^2*(a+b*x^2)^2*log(c*(a+b*x^2)^p)/b^3+1/9*p^2*(a+b*x^2)^3*log(c*(a+b*x^2)^p)/b^3-3/2*a^2*p*(a+b*x^2)*log(c*(a+b*x^2)^p)^2/b^3+3/4*a*p*(a+b*x^2)^2*log(c*(a+b*x^2)^p)^2/b^3-1/6*p*(a+b*x^2)^3*log(c*(a+b*x^2)^p)^2/b^3+1/2*a^2*(a+b*x^2)*log(c*(a+b*x^2)^p)^3/b^3-1/2*a*(a+b*x^2)^2*log(c*(a+b*x^2)^p)^3/b^3+1/6*(a+b*x^2)^3*log(c*(a+b*x^2)^p)^3/b^3],
[x^3*log(c*(a+b*x^2)^p)^3,x,11,3*a*p^3*x^2/b-3/16*p^3*(a+b*x^2)^2/b^2-3*a*p^2*(a+b*x^2)*log(c*(a+b*x^2)^p)/b^2+3/8*p^2*(a+b*x^2)^2*log(c*(a+b*x^2)^p)/b^2+3/2*a*p*(a+b*x^2)*log(c*(a+b*x^2)^p)^2/b^2-3/8*p*(a+b*x^2)^2*log(c*(a+b*x^2)^p)^2/b^2-1/2*a*(a+b*x^2)*log(c*(a+b*x^2)^p)^3/b^2+1/4*(a+b*x^2)^2*log(c*(a+b*x^2)^p)^3/b^2],
[x*log(c*(a+b*x^2)^p)^3,x,5,-3*p^3*x^2+3*p^2*(a+b*x^2)*log(c*(a+b*x^2)^p)/b-3/2*p*(a+b*x^2)*log(c*(a+b*x^2)^p)^2/b+1/2*(a+b*x^2)*log(c*(a+b*x^2)^p)^3/b],
[log(c*(a+b*x^2)^p)^3/x,x,6,1/2*log(-b*x^2/a)*log(c*(a+b*x^2)^p)^3+3/2*p*log(c*(a+b*x^2)^p)^2*polylog(2,1+b*x^2/a)-3*p^2*log(c*(a+b*x^2)^p)*polylog(3,1+b*x^2/a)+3*p^3*polylog(4,1+b*x^2/a)],
[log(c*(a+b*x^2)^p)^3/x^3,x,6,3/2*b*p*log(-b*x^2/a)*log(c*(a+b*x^2)^p)^2/a-1/2*(a+b*x^2)*log(c*(a+b*x^2)^p)^3/(a*x^2)+3*b*p^2*log(c*(a+b*x^2)^p)*polylog(2,1+b*x^2/a)/a-3*b*p^3*polylog(3,1+b*x^2/a)/a],
[log(c*(a+b*x^2)^p)^3/x^5,x,10,3/2*b^2*p^2*log(-b*x^2/a)*log(c*(a+b*x^2)^p)/a^2-3/4*b*p*(a+b*x^2)*log(c*(a+b*x^2)^p)^2/(a^2*x^2)-1/4*log(c*(a+b*x^2)^p)^3/x^4-3/4*b^2*p*log(c*(a+b*x^2)^p)^2*log(1-a/(a+b*x^2))/a^2+3/2*b^2*p^2*log(c*(a+b*x^2)^p)*polylog(2,a/(a+b*x^2))/a^2+3/2*b^2*p^3*polylog(2,1+b*x^2/a)/a^2+3/2*b^2*p^3*polylog(3,a/(a+b*x^2))/a^2],
[log(c*(a+b*x^2)^p)^3/x^7,x,17,b^3*p^3*log(x)/a^3-1/2*b^2*p^2*(a+b*x^2)*log(c*(a+b*x^2)^p)/(a^3*x^2)-b^3*p^2*log(-b*x^2/a)*log(c*(a+b*x^2)^p)/a^3-1/4*b*p*log(c*(a+b*x^2)^p)^2/(a*x^4)+1/2*b^2*p*(a+b*x^2)*log(c*(a+b*x^2)^p)^2/(a^3*x^2)-1/6*log(c*(a+b*x^2)^p)^3/x^6-1/2*b^3*p^2*log(c*(a+b*x^2)^p)*log(1-a/(a+b*x^2))/a^3+1/2*b^3*p*log(c*(a+b*x^2)^p)^2*log(1-a/(a+b*x^2))/a^3+1/2*b^3*p^3*polylog(2,a/(a+b*x^2))/a^3-b^3*p^2*log(c*(a+b*x^2)^p)*polylog(2,a/(a+b*x^2))/a^3-b^3*p^3*polylog(2,1+b*x^2/a)/a^3-b^3*p^3*polylog(3,a/(a+b*x^2))/a^3],
[x^2*log(c*(a+b*x^2)^p)^3,x,31,208/9*a*p^3*x/b-16/27*p^3*x^3-208/9*a^(3/2)*p^3*arctan(x*sqrt(b)/sqrt(a))/b^(3/2)+32/3*I*a^(3/2)*p^3*arctan(x*sqrt(b)/sqrt(a))^2/b^(3/2)-32/3*a*p^2*x*log(c*(a+b*x^2)^p)/b+8/9*p^2*x^3*log(c*(a+b*x^2)^p)+32/3*a^(3/2)*p^2*arctan(x*sqrt(b)/sqrt(a))*log(c*(a+b*x^2)^p)/b^(3/2)+2*a*p*x*log(c*(a+b*x^2)^p)^2/b-2/3*p*x^3*log(c*(a+b*x^2)^p)^2+1/3*x^3*log(c*(a+b*x^2)^p)^3+64/3*a^(3/2)*p^3*arctan(x*sqrt(b)/sqrt(a))*log(2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/b^(3/2)+32/3*I*a^(3/2)*p^3*polylog(2,1-2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/b^(3/2)-2*a^2*p*Unintegrable(log(c*(a+b*x^2)^p)^2/(a+b*x^2),x)/b],
[log(c*(a+b*x^2)^p)^3,x,15,-48*p^3*x+24*p^2*x*log(c*(a+b*x^2)^p)-6*p*x*log(c*(a+b*x^2)^p)^2+x*log(c*(a+b*x^2)^p)^3+48*p^3*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/sqrt(b)-24*I*p^3*arctan(x*sqrt(b)/sqrt(a))^2*sqrt(a)/sqrt(b)-24*p^2*arctan(x*sqrt(b)/sqrt(a))*log(c*(a+b*x^2)^p)*sqrt(a)/sqrt(b)-48*p^3*arctan(x*sqrt(b)/sqrt(a))*log(2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))*sqrt(a)/sqrt(b)-24*I*p^3*polylog(2,1-2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))*sqrt(a)/sqrt(b)+6*a*p*Unintegrable(log(c*(a+b*x^2)^p)^2/(a+b*x^2),x)],
[log(c*(a+b*x^2)^p)^3/x^2,x,1,-log(c*(a+b*x^2)^p)^3/x+6*b*p*Unintegrable(log(c*(a+b*x^2)^p)^2/(a+b*x^2),x)],
[log(c*(a+b*x^2)^p)^3/x^4,x,10,8*I*b^(3/2)*p^3*arctan(x*sqrt(b)/sqrt(a))^2/a^(3/2)+8*b^(3/2)*p^2*arctan(x*sqrt(b)/sqrt(a))*log(c*(a+b*x^2)^p)/a^(3/2)-2*b*p*log(c*(a+b*x^2)^p)^2/(a*x)-1/3*log(c*(a+b*x^2)^p)^3/x^3+16*b^(3/2)*p^3*arctan(x*sqrt(b)/sqrt(a))*log(2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/a^(3/2)+8*I*b^(3/2)*p^3*polylog(2,1-2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/a^(3/2)-2*b^2*p*Unintegrable(log(c*(a+b*x^2)^p)^2/(a+b*x^2),x)/a],

# p<0
[x^3/log(c*(a+b*x^2)^p),x,9,-1/2*a*(a+b*x^2)*Ei(log(c*(a+b*x^2)^p)/p)/(b^2*p*(c*(a+b*x^2)^p)^(1/p))+1/2*(a+b*x^2)^2*Ei(2*log(c*(a+b*x^2)^p)/p)/(b^2*p*(c*(a+b*x^2)^p)^(2/p))],
[x/log(c*(a+b*x^2)^p),x,4,1/2*(a+b*x^2)*Ei(log(c*(a+b*x^2)^p)/p)/(b*p*(c*(a+b*x^2)^p)^(1/p))],
[1/(x*log(c*(a+b*x^2)^p)),x,0,Unintegrable(1/(x*log(c*(a+b*x^2)^p)),x)],
[1/(x^3*log(c*(a+b*x^2)^p)),x,0,Unintegrable(1/(x^3*log(c*(a+b*x^2)^p)),x)],
[x^2/log(c*(a+b*x^2)^p),x,0,Unintegrable(x^2/log(c*(a+b*x^2)^p),x)],
[1/log(c*(a+b*x^2)^p),x,0,Unintegrable(1/log(c*(a+b*x^2)^p),x)],
[1/(x^2*log(c*(a+b*x^2)^p)),x,0,Unintegrable(1/(x^2*log(c*(a+b*x^2)^p)),x)],
[x^3/log(c*(a+b*x^2)^p)^2,x,13,-1/2*a*(a+b*x^2)*Ei(log(c*(a+b*x^2)^p)/p)/(b^2*p^2*(c*(a+b*x^2)^p)^(1/p))+(a+b*x^2)^2*Ei(2*log(c*(a+b*x^2)^p)/p)/(b^2*p^2*(c*(a+b*x^2)^p)^(2/p))-1/2*x^2*(a+b*x^2)/(b*p*log(c*(a+b*x^2)^p))],
[x/log(c*(a+b*x^2)^p)^2,x,5,1/2*(a+b*x^2)*Ei(log(c*(a+b*x^2)^p)/p)/(b*p^2*(c*(a+b*x^2)^p)^(1/p))+1/2*(-a-b*x^2)/(b*p*log(c*(a+b*x^2)^p))],
[1/(x*log(c*(a+b*x^2)^p)^2),x,0,Unintegrable(1/(x*log(c*(a+b*x^2)^p)^2),x)],
[1/(x^3*log(c*(a+b*x^2)^p)^2),x,0,Unintegrable(1/(x^3*log(c*(a+b*x^2)^p)^2),x)],
[x^2/log(c*(a+b*x^2)^p)^2,x,0,Unintegrable(x^2/log(c*(a+b*x^2)^p)^2,x)],
[1/log(c*(a+b*x^2)^p)^2,x,0,Unintegrable(1/log(c*(a+b*x^2)^p)^2,x)],
[1/(x^2*log(c*(a+b*x^2)^p)^2),x,0,Unintegrable(1/(x^2*log(c*(a+b*x^2)^p)^2),x)],
[x^3/log(c*(a+b*x^2)^p)^3,x,18,-1/4*a*(a+b*x^2)*Ei(log(c*(a+b*x^2)^p)/p)/(b^2*p^3*(c*(a+b*x^2)^p)^(1/p))+(a+b*x^2)^2*Ei(2*log(c*(a+b*x^2)^p)/p)/(b^2*p^3*(c*(a+b*x^2)^p)^(2/p))-1/4*x^2*(a+b*x^2)/(b*p*log(c*(a+b*x^2)^p)^2)-1/4*a*(a+b*x^2)/(b^2*p^2*log(c*(a+b*x^2)^p))-1/2*x^2*(a+b*x^2)/(b*p^2*log(c*(a+b*x^2)^p))],
[x/log(c*(a+b*x^2)^p)^3,x,6,1/4*(a+b*x^2)*Ei(log(c*(a+b*x^2)^p)/p)/(b*p^3*(c*(a+b*x^2)^p)^(1/p))+1/4*(-a-b*x^2)/(b*p*log(c*(a+b*x^2)^p)^2)+1/4*(-a-b*x^2)/(b*p^2*log(c*(a+b*x^2)^p))],
[1/(x*log(c*(a+b*x^2)^p)^3),x,0,Unintegrable(1/(x*log(c*(a+b*x^2)^p)^3),x)],
[1/(x^3*log(c*(a+b*x^2)^p)^3),x,0,Unintegrable(1/(x^3*log(c*(a+b*x^2)^p)^3),x)],
[x^2/log(c*(a+b*x^2)^p)^3,x,0,Unintegrable(x^2/log(c*(a+b*x^2)^p)^3,x)],
[1/log(c*(a+b*x^2)^p)^3,x,0,Unintegrable(1/log(c*(a+b*x^2)^p)^3,x)],
[1/(x^2*log(c*(a+b*x^2)^p)^3),x,0,Unintegrable(1/(x^2*log(c*(a+b*x^2)^p)^3),x)],
[x^3/log(c*(a+b*x^2)),x,8,1/2*Ei(2*log(c*(a+b*x^2)))/(b^2*c^2)-1/2*a*Li(c*(a+b*x^2))/(b^2*c)],
[x/log(c*(a+b*x^2)),x,3,1/2*Li(c*(a+b*x^2))/(b*c)],
[x^3/log(c*(a+b*x^2))^2,x,11,Ei(2*log(c*(a+b*x^2)))/(b^2*c^2)-1/2*a*Li(c*(a+b*x^2))/(b^2*c)-1/2*x^2*(a+b*x^2)/(b*log(c*(a+b*x^2)))],
[x/log(c*(a+b*x^2))^2,x,4,1/2*Li(c*(a+b*x^2))/(b*c)+1/2*(-a-b*x^2)/(b*log(c*(a+b*x^2)))],
[x^3/log(c*(a+b*x^2))^3,x,15,Ei(2*log(c*(a+b*x^2)))/(b^2*c^2)-1/4*a*Li(c*(a+b*x^2))/(b^2*c)-1/4*x^2*(a+b*x^2)/(b*log(c*(a+b*x^2))^2)-1/4*a*(a+b*x^2)/(b^2*log(c*(a+b*x^2)))-1/2*x^2*(a+b*x^2)/(b*log(c*(a+b*x^2)))],
[x/log(c*(a+b*x^2))^3,x,5,1/4*Li(c*(a+b*x^2))/(b*c)+1/4*(-a-b*x^2)/(b*log(c*(a+b*x^2))^2)+1/4*(-a-b*x^2)/(b*log(c*(a+b*x^2)))],

# Integrands of the form x^q Log[c (d+e x^3)^n]^p 

# p>0
[x^5*log(c*(d+e*x^3)^p)^2,x,9,-2/3*d*p^2*x^3/e+1/12*p^2*(d+e*x^3)^2/e^2+2/3*d*p*(d+e*x^3)*log(c*(d+e*x^3)^p)/e^2-1/6*p*(d+e*x^3)^2*log(c*(d+e*x^3)^p)/e^2-1/3*d*(d+e*x^3)*log(c*(d+e*x^3)^p)^2/e^2+1/6*(d+e*x^3)^2*log(c*(d+e*x^3)^p)^2/e^2],
[x^2*log(c*(d+e*x^3)^p)^2,x,4,2/3*p^2*x^3-2/3*p*(d+e*x^3)*log(c*(d+e*x^3)^p)/e+1/3*(d+e*x^3)*log(c*(d+e*x^3)^p)^2/e],
[log(c*(d+e*x^3)^p)^2/x,x,5,1/3*log(-e*x^3/d)*log(c*(d+e*x^3)^p)^2+2/3*p*log(c*(d+e*x^3)^p)*polylog(2,1+e*x^3/d)-2/3*p^2*polylog(3,1+e*x^3/d)],
[log(c*(d+e*x^3)^p)^2/x^4,x,4,2/3*e*p*log(-e*x^3/d)*log(c*(d+e*x^3)^p)/d-1/3*(d+e*x^3)*log(c*(d+e*x^3)^p)^2/(d*x^3)+2/3*e*p^2*polylog(2,1+e*x^3/d)/d],
[x*log(c*(d+e*x^3)^p)^2,x,51,9/4*p^2*x^2+3/2*d^(2/3)*p^2*log(d^(1/3)+e^(1/3)*x)/e^(2/3)+1/2*d^(2/3)*p^2*log(d^(1/3)+e^(1/3)*x)^2/e^(2/3)+d^(2/3)*p^2*log(d^(1/3)+e^(1/3)*x)*log((-(-1)^(2/3)*d^(1/3)-e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/e^(2/3)-(-1)^(1/3)*d^(2/3)*p^2*log((-1)^(1/3)*(d^(1/3)+e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/e^(2/3)-1/2*(-1)^(1/3)*d^(2/3)*p^2*log(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)^2/e^(2/3)+(-1)^(2/3)*d^(2/3)*p^2*log(-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/e^(2/3)+(-1)^(2/3)*d^(2/3)*p^2*log((-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/e^(2/3)+1/2*(-1)^(2/3)*d^(2/3)*p^2*log(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)^2/e^(2/3)-(-1)^(2/3)*d^(2/3)*p^2*log((-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log((d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/e^(2/3)+d^(2/3)*p^2*log(d^(1/3)+e^(1/3)*x)*log((-1)^(1/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/e^(2/3)-(-1)^(2/3)*d^(2/3)*p^2*log(-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log((d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/e^(2/3)+(-1)^(1/3)*d^(2/3)*p^2*log(-(-1)^(1/3)*((-1)^(2/3)*d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log(-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/e^(2/3)-(-1)^(1/3)*d^(2/3)*p^2*log(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)*log(-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/e^(2/3)-3/4*d^(2/3)*p^2*log(d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/e^(2/3)-3/2*p*x^2*log(c*(d+e*x^3)^p)-d^(2/3)*p*log(d^(1/3)+e^(1/3)*x)*log(c*(d+e*x^3)^p)/e^(2/3)+(-1)^(1/3)*d^(2/3)*p*log(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)*log(c*(d+e*x^3)^p)/e^(2/3)-(-1)^(2/3)*d^(2/3)*p*log(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)*log(c*(d+e*x^3)^p)/e^(2/3)+1/2*x^2*log(c*(d+e*x^3)^p)^2+d^(2/3)*p^2*polylog(2,(d^(1/3)+e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/e^(2/3)-(-1)^(2/3)*d^(2/3)*p^2*polylog(2,-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/e^(2/3)-(-1)^(1/3)*d^(2/3)*p^2*polylog(2,(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/e^(2/3)-(-1)^(2/3)*d^(2/3)*p^2*polylog(2,(-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/e^(2/3)+(-1)^(1/3)*d^(2/3)*p^2*polylog(2,-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/e^(2/3)+d^(2/3)*p^2*polylog(2,2*(d^(1/3)+e^(1/3)*x)/(d^(1/3)*(3-I*sqrt(3))))/e^(2/3)+3/2*d^(2/3)*p^2*arctan((d^(1/3)-2*e^(1/3)*x)/(d^(1/3)*sqrt(3)))*sqrt(3)/e^(2/3)],
[log(c*(d+e*x^3)^p)^2,x,51,18*p^2*x-d^(1/3)*p^2*log(-d^(1/3)-e^(1/3)*x)^2/e^(1/3)-6*d^(1/3)*p^2*log(d^(1/3)+e^(1/3)*x)/e^(1/3)-2*d^(1/3)*p^2*log(-d^(1/3)-e^(1/3)*x)*log((-(-1)^(2/3)*d^(1/3)-e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/e^(1/3)-2*(-1)^(2/3)*d^(1/3)*p^2*log((-1)^(1/3)*(d^(1/3)+e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log(-d^(1/3)+(-1)^(1/3)*e^(1/3)*x)/e^(1/3)-(-1)^(2/3)*d^(1/3)*p^2*log(-d^(1/3)+(-1)^(1/3)*e^(1/3)*x)^2/e^(1/3)+2*(-1)^(1/3)*d^(1/3)*p^2*log(-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log(-d^(1/3)-(-1)^(2/3)*e^(1/3)*x)/e^(1/3)+2*(-1)^(1/3)*d^(1/3)*p^2*log((-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log(-d^(1/3)-(-1)^(2/3)*e^(1/3)*x)/e^(1/3)+(-1)^(1/3)*d^(1/3)*p^2*log(-d^(1/3)-(-1)^(2/3)*e^(1/3)*x)^2/e^(1/3)-2*(-1)^(1/3)*d^(1/3)*p^2*log((-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log((d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/e^(1/3)-2*d^(1/3)*p^2*log(-d^(1/3)-e^(1/3)*x)*log((-1)^(1/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/e^(1/3)-2*(-1)^(1/3)*d^(1/3)*p^2*log(-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log((d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/e^(1/3)+2*(-1)^(2/3)*d^(1/3)*p^2*log(-(-1)^(1/3)*((-1)^(2/3)*d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log(-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/e^(1/3)-2*(-1)^(2/3)*d^(1/3)*p^2*log(-d^(1/3)+(-1)^(1/3)*e^(1/3)*x)*log(-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/e^(1/3)+3*d^(1/3)*p^2*log(d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/e^(1/3)-6*p*x*log(c*(d+e*x^3)^p)+2*d^(1/3)*p*log(-d^(1/3)-e^(1/3)*x)*log(c*(d+e*x^3)^p)/e^(1/3)+2*(-1)^(2/3)*d^(1/3)*p*log(-d^(1/3)+(-1)^(1/3)*e^(1/3)*x)*log(c*(d+e*x^3)^p)/e^(1/3)-2*(-1)^(1/3)*d^(1/3)*p*log(-d^(1/3)-(-1)^(2/3)*e^(1/3)*x)*log(c*(d+e*x^3)^p)/e^(1/3)+x*log(c*(d+e*x^3)^p)^2-2*d^(1/3)*p^2*polylog(2,(d^(1/3)+e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/e^(1/3)-2*(-1)^(1/3)*d^(1/3)*p^2*polylog(2,-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/e^(1/3)-2*(-1)^(2/3)*d^(1/3)*p^2*polylog(2,(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/e^(1/3)-2*(-1)^(1/3)*d^(1/3)*p^2*polylog(2,(-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/e^(1/3)+2*(-1)^(2/3)*d^(1/3)*p^2*polylog(2,-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/e^(1/3)-2*d^(1/3)*p^2*polylog(2,2*(d^(1/3)+e^(1/3)*x)/(d^(1/3)*(3-I*sqrt(3))))/e^(1/3)+6*d^(1/3)*p^2*arctan((d^(1/3)-2*e^(1/3)*x)/(d^(1/3)*sqrt(3)))*sqrt(3)/e^(1/3)],
[log(c*(d+e*x^3)^p)^2/x^2,x,41,e^(1/3)*p^2*log(d^(1/3)+e^(1/3)*x)^2/d^(1/3)+2*e^(1/3)*p^2*log(d^(1/3)+e^(1/3)*x)*log((-(-1)^(2/3)*d^(1/3)-e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(1/3)-2*(-1)^(1/3)*e^(1/3)*p^2*log((-1)^(1/3)*(d^(1/3)+e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/d^(1/3)-(-1)^(1/3)*e^(1/3)*p^2*log(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)^2/d^(1/3)+2*(-1)^(2/3)*e^(1/3)*p^2*log(-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/d^(1/3)+2*(-1)^(2/3)*e^(1/3)*p^2*log((-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/d^(1/3)+(-1)^(2/3)*e^(1/3)*p^2*log(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)^2/d^(1/3)-2*(-1)^(2/3)*e^(1/3)*p^2*log((-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log((d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(1/3)+2*e^(1/3)*p^2*log(d^(1/3)+e^(1/3)*x)*log((-1)^(1/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(1/3)-2*(-1)^(2/3)*e^(1/3)*p^2*log(-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log((d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(1/3)+2*(-1)^(1/3)*e^(1/3)*p^2*log(-(-1)^(1/3)*((-1)^(2/3)*d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log(-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(1/3)-2*(-1)^(1/3)*e^(1/3)*p^2*log(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)*log(-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(1/3)-2*e^(1/3)*p*log(d^(1/3)+e^(1/3)*x)*log(c*(d+e*x^3)^p)/d^(1/3)+2*(-1)^(1/3)*e^(1/3)*p*log(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)*log(c*(d+e*x^3)^p)/d^(1/3)-2*(-1)^(2/3)*e^(1/3)*p*log(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)*log(c*(d+e*x^3)^p)/d^(1/3)-log(c*(d+e*x^3)^p)^2/x+2*e^(1/3)*p^2*polylog(2,(d^(1/3)+e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(1/3)-2*(-1)^(2/3)*e^(1/3)*p^2*polylog(2,-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(1/3)-2*(-1)^(1/3)*e^(1/3)*p^2*polylog(2,(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(1/3)-2*(-1)^(2/3)*e^(1/3)*p^2*polylog(2,(-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(1/3)+2*(-1)^(1/3)*e^(1/3)*p^2*polylog(2,-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(1/3)+2*e^(1/3)*p^2*polylog(2,2*(d^(1/3)+e^(1/3)*x)/(d^(1/3)*(3-I*sqrt(3))))/d^(1/3)],
[log(c*(d+e*x^3)^p)^2/x^3,x,41,-1/2*e^(2/3)*p^2*log(-d^(1/3)-e^(1/3)*x)^2/d^(2/3)-e^(2/3)*p^2*log(-d^(1/3)-e^(1/3)*x)*log((-(-1)^(2/3)*d^(1/3)-e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(2/3)-(-1)^(2/3)*e^(2/3)*p^2*log((-1)^(1/3)*(d^(1/3)+e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log(-d^(1/3)+(-1)^(1/3)*e^(1/3)*x)/d^(2/3)-1/2*(-1)^(2/3)*e^(2/3)*p^2*log(-d^(1/3)+(-1)^(1/3)*e^(1/3)*x)^2/d^(2/3)+(-1)^(1/3)*e^(2/3)*p^2*log(-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log(-d^(1/3)-(-1)^(2/3)*e^(1/3)*x)/d^(2/3)+(-1)^(1/3)*e^(2/3)*p^2*log((-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log(-d^(1/3)-(-1)^(2/3)*e^(1/3)*x)/d^(2/3)+1/2*(-1)^(1/3)*e^(2/3)*p^2*log(-d^(1/3)-(-1)^(2/3)*e^(1/3)*x)^2/d^(2/3)-(-1)^(1/3)*e^(2/3)*p^2*log((-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log((d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(2/3)-e^(2/3)*p^2*log(-d^(1/3)-e^(1/3)*x)*log((-1)^(1/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(2/3)-(-1)^(1/3)*e^(2/3)*p^2*log(-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log((d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(2/3)+(-1)^(2/3)*e^(2/3)*p^2*log(-(-1)^(1/3)*((-1)^(2/3)*d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log(-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(2/3)-(-1)^(2/3)*e^(2/3)*p^2*log(-d^(1/3)+(-1)^(1/3)*e^(1/3)*x)*log(-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(2/3)+e^(2/3)*p*log(-d^(1/3)-e^(1/3)*x)*log(c*(d+e*x^3)^p)/d^(2/3)+(-1)^(2/3)*e^(2/3)*p*log(-d^(1/3)+(-1)^(1/3)*e^(1/3)*x)*log(c*(d+e*x^3)^p)/d^(2/3)-(-1)^(1/3)*e^(2/3)*p*log(-d^(1/3)-(-1)^(2/3)*e^(1/3)*x)*log(c*(d+e*x^3)^p)/d^(2/3)-1/2*log(c*(d+e*x^3)^p)^2/x^2-e^(2/3)*p^2*polylog(2,(d^(1/3)+e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(2/3)-(-1)^(1/3)*e^(2/3)*p^2*polylog(2,-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(2/3)-(-1)^(2/3)*e^(2/3)*p^2*polylog(2,(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(2/3)-(-1)^(1/3)*e^(2/3)*p^2*polylog(2,(-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(2/3)+(-1)^(2/3)*e^(2/3)*p^2*polylog(2,-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(2/3)-e^(2/3)*p^2*polylog(2,2*(d^(1/3)+e^(1/3)*x)/(d^(1/3)*(3-I*sqrt(3))))/d^(2/3)],
[log(c*(d+e*x^3)^p)^2/x^5,x,50,-3/2*e^(4/3)*p^2*log(d^(1/3)+e^(1/3)*x)/d^(4/3)-1/4*e^(4/3)*p^2*log(d^(1/3)+e^(1/3)*x)^2/d^(4/3)-1/2*e^(4/3)*p^2*log(d^(1/3)+e^(1/3)*x)*log((-(-1)^(2/3)*d^(1/3)-e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(4/3)+1/2*(-1)^(1/3)*e^(4/3)*p^2*log((-1)^(1/3)*(d^(1/3)+e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/d^(4/3)+1/4*(-1)^(1/3)*e^(4/3)*p^2*log(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)^2/d^(4/3)-1/2*(-1)^(2/3)*e^(4/3)*p^2*log(-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/d^(4/3)-1/2*(-1)^(2/3)*e^(4/3)*p^2*log((-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/d^(4/3)-1/4*(-1)^(2/3)*e^(4/3)*p^2*log(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)^2/d^(4/3)+1/2*(-1)^(2/3)*e^(4/3)*p^2*log((-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))*log((d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(4/3)-1/2*e^(4/3)*p^2*log(d^(1/3)+e^(1/3)*x)*log((-1)^(1/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(4/3)+1/2*(-1)^(2/3)*e^(4/3)*p^2*log(-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log((d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(4/3)-1/2*(-1)^(1/3)*e^(4/3)*p^2*log(-(-1)^(1/3)*((-1)^(2/3)*d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))*log(-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(4/3)+1/2*(-1)^(1/3)*e^(4/3)*p^2*log(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)*log(-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(4/3)+3/4*e^(4/3)*p^2*log(d^(2/3)-d^(1/3)*e^(1/3)*x+e^(2/3)*x^2)/d^(4/3)-3/2*e*p*log(c*(d+e*x^3)^p)/(d*x)+1/2*e^(4/3)*p*log(d^(1/3)+e^(1/3)*x)*log(c*(d+e*x^3)^p)/d^(4/3)-1/2*(-1)^(1/3)*e^(4/3)*p*log(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)*log(c*(d+e*x^3)^p)/d^(4/3)+1/2*(-1)^(2/3)*e^(4/3)*p*log(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)*log(c*(d+e*x^3)^p)/d^(4/3)-1/4*log(c*(d+e*x^3)^p)^2/x^4-1/2*e^(4/3)*p^2*polylog(2,(d^(1/3)+e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(4/3)+1/2*(-1)^(2/3)*e^(4/3)*p^2*polylog(2,-(-1)^(2/3)*(d^(1/3)+e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(4/3)+1/2*(-1)^(1/3)*e^(4/3)*p^2*polylog(2,(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(4/3)+1/2*(-1)^(2/3)*e^(4/3)*p^2*polylog(2,(-1)^(1/3)*(d^(1/3)-(-1)^(1/3)*e^(1/3)*x)/((1+(-1)^(1/3))*d^(1/3)))/d^(4/3)-1/2*(-1)^(1/3)*e^(4/3)*p^2*polylog(2,-(-1)^(2/3)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)/((1-(-1)^(2/3))*d^(1/3)))/d^(4/3)-1/2*e^(4/3)*p^2*polylog(2,2*(d^(1/3)+e^(1/3)*x)/(d^(1/3)*(3-I*sqrt(3))))/d^(4/3)-3/2*e^(4/3)*p^2*arctan((d^(1/3)-2*e^(1/3)*x)/(d^(1/3)*sqrt(3)))*sqrt(3)/d^(4/3)],

# p<0
[x^8/log(c*(d+e*x^3)^p),x,12,1/3*d^2*(d+e*x^3)*Ei(log(c*(d+e*x^3)^p)/p)/(e^3*p*(c*(d+e*x^3)^p)^(1/p))-2/3*d*(d+e*x^3)^2*Ei(2*log(c*(d+e*x^3)^p)/p)/(e^3*p*(c*(d+e*x^3)^p)^(2/p))+1/3*(d+e*x^3)^3*Ei(3*log(c*(d+e*x^3)^p)/p)/(e^3*p*(c*(d+e*x^3)^p)^(3/p))],
[x^5/log(c*(d+e*x^3)^p),x,9,-1/3*d*(d+e*x^3)*Ei(log(c*(d+e*x^3)^p)/p)/(e^2*p*(c*(d+e*x^3)^p)^(1/p))+1/3*(d+e*x^3)^2*Ei(2*log(c*(d+e*x^3)^p)/p)/(e^2*p*(c*(d+e*x^3)^p)^(2/p))],
[x^2/log(c*(d+e*x^3)^p),x,4,1/3*(d+e*x^3)*Ei(log(c*(d+e*x^3)^p)/p)/(e*p*(c*(d+e*x^3)^p)^(1/p))],
[1/(x*log(c*(d+e*x^3)^p)),x,0,Unintegrable(1/(x*log(c*(d+e*x^3)^p)),x)],
[1/(x^4*log(c*(d+e*x^3)^p)),x,0,Unintegrable(1/(x^4*log(c*(d+e*x^3)^p)),x)],
[x^3/log(c*(d+e*x^3)^p),x,0,Unintegrable(x^3/log(c*(d+e*x^3)^p),x)],
[x/log(c*(d+e*x^3)^p),x,0,Unintegrable(x/log(c*(d+e*x^3)^p),x)],
[1/log(c*(d+e*x^3)^p),x,0,Unintegrable(1/log(c*(d+e*x^3)^p),x)],
[1/(x^2*log(c*(d+e*x^3)^p)),x,0,Unintegrable(1/(x^2*log(c*(d+e*x^3)^p)),x)],
[1/(x^3*log(c*(d+e*x^3)^p)),x,0,Unintegrable(1/(x^3*log(c*(d+e*x^3)^p)),x)],
[x^8/log(c*(d+e*x^3)^p)^2,x,21,1/3*d^2*(d+e*x^3)*Ei(log(c*(d+e*x^3)^p)/p)/(e^3*p^2*(c*(d+e*x^3)^p)^(1/p))-4/3*d*(d+e*x^3)^2*Ei(2*log(c*(d+e*x^3)^p)/p)/(e^3*p^2*(c*(d+e*x^3)^p)^(2/p))+(d+e*x^3)^3*Ei(3*log(c*(d+e*x^3)^p)/p)/(e^3*p^2*(c*(d+e*x^3)^p)^(3/p))-1/3*x^6*(d+e*x^3)/(e*p*log(c*(d+e*x^3)^p))],
[x^5/log(c*(d+e*x^3)^p)^2,x,13,-1/3*d*(d+e*x^3)*Ei(log(c*(d+e*x^3)^p)/p)/(e^2*p^2*(c*(d+e*x^3)^p)^(1/p))+2/3*(d+e*x^3)^2*Ei(2*log(c*(d+e*x^3)^p)/p)/(e^2*p^2*(c*(d+e*x^3)^p)^(2/p))-1/3*x^3*(d+e*x^3)/(e*p*log(c*(d+e*x^3)^p))],
[x^2/log(c*(d+e*x^3)^p)^2,x,5,1/3*(d+e*x^3)*Ei(log(c*(d+e*x^3)^p)/p)/(e*p^2*(c*(d+e*x^3)^p)^(1/p))+1/3*(-d-e*x^3)/(e*p*log(c*(d+e*x^3)^p))],
[1/(x*log(c*(d+e*x^3)^p)^2),x,0,Unintegrable(1/(x*log(c*(d+e*x^3)^p)^2),x)],
[1/(x^4*log(c*(d+e*x^3)^p)^2),x,0,Unintegrable(1/(x^4*log(c*(d+e*x^3)^p)^2),x)],
[x^3/log(c*(d+e*x^3)^p)^2,x,0,Unintegrable(x^3/log(c*(d+e*x^3)^p)^2,x)],
[x/log(c*(d+e*x^3)^p)^2,x,0,Unintegrable(x/log(c*(d+e*x^3)^p)^2,x)],
[1/log(c*(d+e*x^3)^p)^2,x,0,Unintegrable(1/log(c*(d+e*x^3)^p)^2,x)],
[1/(x^2*log(c*(d+e*x^3)^p)^2),x,0,Unintegrable(1/(x^2*log(c*(d+e*x^3)^p)^2),x)],
[1/(x^3*log(c*(d+e*x^3)^p)^2),x,0,Unintegrable(1/(x^3*log(c*(d+e*x^3)^p)^2),x)],

# Integrands of the form (f x)^q Log[c (d+e x^2)^n]^p when q symbolic
[(f*x)^m*log(c*(d+e*x^2)^p)^3,x,1,(f*x)^(1+m)*log(c*(d+e*x^2)^p)^3/(f*(1+m))-6*e*p*Unintegrable((f*x)^(2+m)*log(c*(d+e*x^2)^p)^2/(d+e*x^2),x)/(f^2*(1+m))],
[(f*x)^m*log(c*(d+e*x^2)^p)^2,x,1,(f*x)^(1+m)*log(c*(d+e*x^2)^p)^2/(f*(1+m))-4*e*p*Unintegrable((f*x)^(2+m)*log(c*(d+e*x^2)^p)/(d+e*x^2),x)/(f^2*(1+m))],
[(f*x)^m*log(c*(d+e*x^2)^p),x,3,-2*e*p*(f*x)^(3+m)*hypergeom([1,1/2*(3+m)],[1/2*(5+m)],-e*x^2/d)/(d*f^3*(1+m)*(3+m))+(f*x)^(1+m)*log(c*(d+e*x^2)^p)/(f*(1+m))],
[(f*x)^m/log(c*(d+e*x^2)^p),x,0,Unintegrable((f*x)^m/log(c*(d+e*x^2)^p),x)],
[(f*x)^m/log(c*(d+e*x^2)^p)^2,x,0,Unintegrable((f*x)^m/log(c*(d+e*x^2)^p)^2,x)],
[(f*x)^(-1+3*n)*log(c*(d+e*x^n)^p)^2,x,9,2*d^2*p^2*x^(1-2*n)*(f*x)^(-1+3*n)/(e^2*n)-1/2*d*p^2*x^(1-3*n)*(f*x)^(-1+3*n)*(d+e*x^n)^2/(e^3*n)+2/27*p^2*x^(1-3*n)*(f*x)^(-1+3*n)*(d+e*x^n)^3/(e^3*n)-1/3*d^3*p^2*x^(1-3*n)*(f*x)^(-1+3*n)*log(d+e*x^n)^2/(e^3*n)-2*d^2*p*x^(1-3*n)*(f*x)^(-1+3*n)*(d+e*x^n)*log(c*(d+e*x^n)^p)/(e^3*n)+d*p*x^(1-3*n)*(f*x)^(-1+3*n)*(d+e*x^n)^2*log(c*(d+e*x^n)^p)/(e^3*n)-2/9*p*x^(1-3*n)*(f*x)^(-1+3*n)*(d+e*x^n)^3*log(c*(d+e*x^n)^p)/(e^3*n)+2/3*d^3*p*x^(1-3*n)*(f*x)^(-1+3*n)*log(d+e*x^n)*log(c*(d+e*x^n)^p)/(e^3*n)+1/3*x*(f*x)^(-1+3*n)*log(c*(d+e*x^n)^p)^2/n],
[(f*x)^(-1+2*n)*log(c*(d+e*x^n)^p)^2,x,10,-2*d*p^2*x^(1-n)*(f*x)^(-1+2*n)/(e*n)+1/4*p^2*x^(1-2*n)*(f*x)^(-1+2*n)*(d+e*x^n)^2/(e^2*n)+2*d*p*x^(1-2*n)*(f*x)^(-1+2*n)*(d+e*x^n)*log(c*(d+e*x^n)^p)/(e^2*n)-1/2*p*x^(1-2*n)*(f*x)^(-1+2*n)*(d+e*x^n)^2*log(c*(d+e*x^n)^p)/(e^2*n)-d*x^(1-2*n)*(f*x)^(-1+2*n)*(d+e*x^n)*log(c*(d+e*x^n)^p)^2/(e^2*n)+1/2*x^(1-2*n)*(f*x)^(-1+2*n)*(d+e*x^n)^2*log(c*(d+e*x^n)^p)^2/(e^2*n)],
[(f*x)^(-1+n)*log(c*(d+e*x^n)^p)^2,x,5,2*p^2*x*(f*x)^(-1+n)/n-2*p*x^(1-n)*(f*x)^(-1+n)*(d+e*x^n)*log(c*(d+e*x^n)^p)/(e*n)+x^(1-n)*(f*x)^(-1+n)*(d+e*x^n)*log(c*(d+e*x^n)^p)^2/(e*n)],
[log(c*(d+e*x^n)^p)^2/(f*x),x,6,log(-e*x^n/d)*log(c*(d+e*x^n)^p)^2/(f*n)+2*p*log(c*(d+e*x^n)^p)*polylog(2,1+e*x^n/d)/(f*n)-2*p^2*polylog(3,1+e*x^n/d)/(f*n)],
[(f*x)^(-1-n)*log(c*(d+e*x^n)^p)^2,x,5,2*e*p*x^(1+n)*(f*x)^(-1-n)*log(-e*x^n/d)*log(c*(d+e*x^n)^p)/(d*n)-x*(f*x)^(-1-n)*(d+e*x^n)*log(c*(d+e*x^n)^p)^2/(d*n)+2*e*p^2*x^(1+n)*(f*x)^(-1-n)*polylog(2,1+e*x^n/d)/(d*n)],
[(f*x)^(-1-2*n)*log(c*(d+e*x^n)^p)^2,x,9,e^2*p^2*x^(1+2*n)*(f*x)^(-1-2*n)*log(x)/d^2-e*p*x^(1+n)*(f*x)^(-1-2*n)*(d+e*x^n)*log(c*(d+e*x^n)^p)/(d^2*n)-1/2*x*(f*x)^(-1-2*n)*log(c*(d+e*x^n)^p)^2/n-e^2*p*x^(1+2*n)*(f*x)^(-1-2*n)*log(c*(d+e*x^n)^p)*log(1-d/(d+e*x^n))/(d^2*n)+e^2*p^2*x^(1+2*n)*(f*x)^(-1-2*n)*polylog(2,d/(d+e*x^n))/(d^2*n)],

# Integrands of the form (f x)^q Log[c (d+e x^m)^n]^p when m symbolic
[log(1+e*x^n)/x,x,1,-polylog(2,-e*x^n)/n],
[log(2+e*x^n)/x,x,3,log(2)*log(x)-polylog(2,-1/2*e*x^n)/n],
[log(2*(3+e*x^n))/x,x,3,log(6)*log(x)-polylog(2,-1/3*e*x^n)/n],
[log(c*(d+e*x^n))/x,x,3,log(-e*x^n/d)*log(c*(d+e*x^n))/n+polylog(2,1+e*x^n/d)/n],
[log(c*(d+e*x^n)^p)/x,x,3,log(-e*x^n/d)*log(c*(d+e*x^n)^p)/n+p*polylog(2,1+e*x^n/d)/n],
[log(c*(d+e*x^n)^p)^2/x,x,5,log(-e*x^n/d)*log(c*(d+e*x^n)^p)^2/n+2*p*log(c*(d+e*x^n)^p)*polylog(2,1+e*x^n/d)/n-2*p^2*polylog(3,1+e*x^n/d)/n],
[log(c*(d+e*x^n)^p)^3/x,x,6,log(-e*x^n/d)*log(c*(d+e*x^n)^p)^3/n+3*p*log(c*(d+e*x^n)^p)^2*polylog(2,1+e*x^n/d)/n-6*p^2*log(c*(d+e*x^n)^p)*polylog(3,1+e*x^n/d)/n+6*p^3*polylog(4,1+e*x^n/d)/n],

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

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

# n>0
[(d+e*x)^3*log(c*(a+b*x)^p),x,3,-1/4*(b*d-a*e)^3*p*x/b^3-1/8*(b*d-a*e)^2*p*(d+e*x)^2/(b^2*e)-1/12*(b*d-a*e)*p*(d+e*x)^3/(b*e)-1/16*p*(d+e*x)^4/e-1/4*(b*d-a*e)^4*p*log(a+b*x)/(b^4*e)+1/4*(d+e*x)^4*log(c*(a+b*x)^p)/e],
[(d+e*x)^2*log(c*(a+b*x)^p),x,3,-1/3*(b*d-a*e)^2*p*x/b^2-1/6*(b*d-a*e)*p*(d+e*x)^2/(b*e)-1/9*p*(d+e*x)^3/e-1/3*(b*d-a*e)^3*p*log(a+b*x)/(b^3*e)+1/3*(d+e*x)^3*log(c*(a+b*x)^p)/e],
[(d+e*x)*log(c*(a+b*x)^p),x,3,-1/2*(b*d-a*e)*p*x/b-1/4*p*(d+e*x)^2/e-1/2*(b*d-a*e)^2*p*log(a+b*x)/(b^2*e)+1/2*(d+e*x)^2*log(c*(a+b*x)^p)/e],
[log(c*(a+b*x)^p),x,2,-p*x+(a+b*x)*log(c*(a+b*x)^p)/b],
[log(c*(a+b*x)^p)/(d+e*x),x,3,log(c*(a+b*x)^p)*log(b*(d+e*x)/(b*d-a*e))/e+p*polylog(2,-e*(a+b*x)/(b*d-a*e))/e],
[log(c*(a+b*x)^p)/(d+e*x)^2,x,4,b*p*log(a+b*x)/(e*(b*d-a*e))-log(c*(a+b*x)^p)/(e*(d+e*x))-b*p*log(d+e*x)/(e*(b*d-a*e))],
[log(c*(a+b*x)^p)/(d+e*x)^3,x,3,1/2*b*p/(e*(b*d-a*e)*(d+e*x))+1/2*b^2*p*log(a+b*x)/(e*(b*d-a*e)^2)-1/2*log(c*(a+b*x)^p)/(e*(d+e*x)^2)-1/2*b^2*p*log(d+e*x)/(e*(b*d-a*e)^2)],
[log(c*(a+b*x)^p)/(d+e*x)^4,x,3,1/6*b*p/(e*(b*d-a*e)*(d+e*x)^2)+1/3*b^2*p/(e*(b*d-a*e)^2*(d+e*x))+1/3*b^3*p*log(a+b*x)/(e*(b*d-a*e)^3)-1/3*log(c*(a+b*x)^p)/(e*(d+e*x)^3)-1/3*b^3*p*log(d+e*x)/(e*(b*d-a*e)^3)],
[(d+e*x)^3*log(c*(a+b*x^2)^p),x,6,-2*d*(b*d^2-a*e^2)*p*x/b-1/4*e*(6*b*d^2-a*e^2)*p*x^2/b-2/3*d*e^2*p*x^3-1/8*e^3*p*x^4-1/4*(b^2*d^4-6*a*b*d^2*e^2+a^2*e^4)*p*log(a+b*x^2)/(b^2*e)+1/4*(d+e*x)^4*log(c*(a+b*x^2)^p)/e+2*d*(b*d^2-a*e^2)*p*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2)],
[(d+e*x)^2*log(c*(a+b*x^2)^p),x,6,-2/3*(3*b*d^2-a*e^2)*p*x/b-d*e*p*x^2-2/9*e^2*p*x^3-1/3*d*(b*d^2-3*a*e^2)*p*log(a+b*x^2)/(b*e)+1/3*(d+e*x)^3*log(c*(a+b*x^2)^p)/e+2/3*(3*b*d^2-a*e^2)*p*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2)],
[(d+e*x)*log(c*(a+b*x^2)^p),x,6,-2*d*p*x-1/2*e*p*x^2-1/2*(b*d^2-a*e^2)*p*log(a+b*x^2)/(b*e)+1/2*(d+e*x)^2*log(c*(a+b*x^2)^p)/e+2*d*p*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/sqrt(b)],
[log(c*(a+b*x^2)^p),x,3,-2*p*x+x*log(c*(a+b*x^2)^p)+2*p*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/sqrt(b)],
[log(c*(a+b*x^2)^p)/(d+e*x),x,9,log(d+e*x)*log(c*(a+b*x^2)^p)/e-p*log(d+e*x)*log(e*(sqrt(-a)-x*sqrt(b))/(e*sqrt(-a)+d*sqrt(b)))/e-p*log(d+e*x)*log(-e*(sqrt(-a)+x*sqrt(b))/(-e*sqrt(-a)+d*sqrt(b)))/e-p*polylog(2,(d+e*x)*sqrt(b)/(-e*sqrt(-a)+d*sqrt(b)))/e-p*polylog(2,(d+e*x)*sqrt(b)/(e*sqrt(-a)+d*sqrt(b)))/e],
[log(c*(a+b*x^2)^p)/(d+e*x)^2,x,6,-2*b*d*p*log(d+e*x)/(e*(b*d^2+a*e^2))+b*d*p*log(a+b*x^2)/(e*(b*d^2+a*e^2))-log(c*(a+b*x^2)^p)/(e*(d+e*x))+2*p*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)*sqrt(b)/(b*d^2+a*e^2)],
[log(c*(a+b*x^2)^p)/(d+e*x)^3,x,6,b*d*p/(e*(b*d^2+a*e^2)*(d+e*x))-b*(b*d^2-a*e^2)*p*log(d+e*x)/(e*(b*d^2+a*e^2)^2)+1/2*b*(b*d^2-a*e^2)*p*log(a+b*x^2)/(e*(b*d^2+a*e^2)^2)-1/2*log(c*(a+b*x^2)^p)/(e*(d+e*x)^2)+2*b^(3/2)*d*p*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/(b*d^2+a*e^2)^2],
[(d+e*x)^3*log(c*(a+b*x^3)^p),x,13,-3/4*(4*b*d^3-a*e^3)*p*x/b-9/4*d^2*e*p*x^2-d*e^2*p*x^3-3/16*e^3*p*x^4+1/4*a^(1/3)*(4*b*d^3-6*a^(1/3)*b^(2/3)*d^2*e-a*e^3)*p*log(a^(1/3)+b^(1/3)*x)/b^(4/3)-1/8*a^(1/3)*(4*b*d^3-6*a^(1/3)*b^(2/3)*d^2*e-a*e^3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(4/3)-1/4*d*(b*d^3-4*a*e^3)*p*log(a+b*x^3)/(b*e)+1/4*(d+e*x)^4*log(c*(a+b*x^3)^p)/e-1/4*a^(1/3)*(4*b*d^3+6*a^(1/3)*b^(2/3)*d^2*e-a*e^3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(4/3)],
[(d+e*x)^2*log(c*(a+b*x^3)^p),x,12,-3*d^2*p*x-3/2*d*e*p*x^2-1/3*e^2*p*x^3+a^(1/3)*d*(b^(1/3)*d-a^(1/3)*e)*p*log(a^(1/3)+b^(1/3)*x)/b^(2/3)-1/2*a^(1/3)*d*(b^(1/3)*d-a^(1/3)*e)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(2/3)-1/3*(b*d^3-a*e^3)*p*log(a+b*x^3)/(b*e)+1/3*(d+e*x)^3*log(c*(a+b*x^3)^p)/e-a^(1/3)*d*(b^(1/3)*d+a^(1/3)*e)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(2/3)],
[(d+e*x)*log(c*(a+b*x^3)^p),x,11,-3*d*p*x-3/4*e*p*x^2+1/2*a^(1/3)*(2*b^(1/3)*d-a^(1/3)*e)*p*log(a^(1/3)+b^(1/3)*x)/b^(2/3)-1/4*a^(1/3)*(2*b^(1/3)*d-a^(1/3)*e)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(2/3)-1/2*d^2*p*log(a+b*x^3)/e+1/2*(d+e*x)^2*log(c*(a+b*x^3)^p)/e-1/2*a^(1/3)*(2*b^(1/3)*d+a^(1/3)*e)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(2/3)],
[log(c*(a+b*x^3)^p),x,8,-3*p*x+a^(1/3)*p*log(a^(1/3)+b^(1/3)*x)/b^(1/3)-1/2*a^(1/3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(1/3)+x*log(c*(a+b*x^3)^p)-a^(1/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/b^(1/3)],
[log(c*(a+b*x^3)^p)/(d+e*x),x,12,-p*log(-e*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-a^(1/3)*e))*log(d+e*x)/e-p*log(-e*((-1)^(2/3)*a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))*log(d+e*x)/e-p*log((-1)^(1/3)*e*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))*log(d+e*x)/e+log(d+e*x)*log(c*(a+b*x^3)^p)/e-p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-a^(1/3)*e))/e-p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))/e-p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))/e],
[log(c*(a+b*x^3)^p)/(d+e*x)^2,x,11,a^(1/3)*b^(1/3)*(b^(1/3)*d+a^(1/3)*e)*p*log(a^(1/3)+b^(1/3)*x)/(b*d^3-a*e^3)-3*b*d^2*p*log(d+e*x)/(e*(b*d^3-a*e^3))-1/2*a^(1/3)*b^(1/3)*(b^(1/3)*d+a^(1/3)*e)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b*d^3-a*e^3)+b*d^2*p*log(a+b*x^3)/(e*(b*d^3-a*e^3))-log(c*(a+b*x^3)^p)/(e*(d+e*x))-a^(1/3)*b^(1/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/(b^(2/3)*d^2+a^(1/3)*b^(1/3)*d*e+a^(2/3)*e^2)],
[log(c*(a+b*x^3)^p)/(d+e*x)^3,x,11,3/2*b*d^2*p/(e*(b*d^3-a*e^3)*(d+e*x))+1/2*a^(1/3)*b^(2/3)*(2*b*d^3+3*a^(1/3)*b^(2/3)*d^2*e+a*e^3)*p*log(a^(1/3)+b^(1/3)*x)/(b*d^3-a*e^3)^2-3/2*b*d*(b*d^3+2*a*e^3)*p*log(d+e*x)/(e*(b*d^3-a*e^3)^2)-1/4*a^(1/3)*b^(2/3)*(2*b*d^3+3*a^(1/3)*b^(2/3)*d^2*e+a*e^3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b*d^3-a*e^3)^2+1/2*b*d*(b*d^3+2*a*e^3)*p*log(a+b*x^3)/(e*(b*d^3-a*e^3)^2)-1/2*log(c*(a+b*x^3)^p)/(e*(d+e*x)^2)-1/2*a^(1/3)*b^(2/3)*(2*b*d^3-3*a^(1/3)*b^(2/3)*d^2*e+a*e^3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/(b*d^3-a*e^3)^2],

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

# Integrands of the form (f+g x)^q Log[c (d+e x^m)^n] when r symbolic
[(d+e*x)^m*log(c*(a+b*x^3)^p),x,6,b^(1/3)*p*(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],b^(1/3)*(d+e*x)/(b^(1/3)*d-a^(1/3)*e))/(e*(b^(1/3)*d-a^(1/3)*e)*(1+m)*(2+m))+b^(1/3)*p*(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],b^(1/3)*(d+e*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))/(e*(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e)*(1+m)*(2+m))+b^(1/3)*p*(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],b^(1/3)*(d+e*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))/(e*(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e)*(1+m)*(2+m))+(d+e*x)^(1+m)*log(c*(a+b*x^3)^p)/(e*(1+m))],
[(d+e*x)^m*log(c*(a+b*x^2)^p),x,5,(d+e*x)^(1+m)*log(c*(a+b*x^2)^p)/(e*(1+m))+p*(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],(d+e*x)*sqrt(b)/(-e*sqrt(-a)+d*sqrt(b)))*sqrt(b)/(e*(1+m)*(2+m)*(-e*sqrt(-a)+d*sqrt(b)))+p*(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],(d+e*x)*sqrt(b)/(e*sqrt(-a)+d*sqrt(b)))*sqrt(b)/(e*(1+m)*(2+m)*(e*sqrt(-a)+d*sqrt(b)))],
[(d+e*x)^m*log(c*(a+b*x)^p),x,2,b*p*(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],b*(d+e*x)/(b*d-a*e))/(e*(b*d-a*e)*(1+m)*(2+m))+(d+e*x)^(1+m)*log(c*(a+b*x)^p)/(e*(1+m))],
[(d+e*x)^m*log(c*(a+b/x)^p),x,5,a*p*(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],a*(d+e*x)/(a*d-b*e))/(e*(a*d-b*e)*(1+m)*(2+m))-p*(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],1+e*x/d)/(d*e*(2+3*m+m^2))+(d+e*x)^(1+m)*log(c*(a+b/x)^p)/(e*(1+m))],
[(d+e*x)^m*log(c*(a+b/x^2)^p),x,9,-2*p*(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],1+e*x/d)/(d*e*(2+3*m+m^2))+(d+e*x)^(1+m)*log(c*(a+b/x^2)^p)/(e*(1+m))+p*(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],(d+e*x)*sqrt(-a)/(d*sqrt(-a)-e*sqrt(b)))*sqrt(-a)/(e*(1+m)*(2+m)*(d*sqrt(-a)-e*sqrt(b)))+p*(d+e*x)^(2+m)*hypergeom([1,2+m],[3+m],(d+e*x)*sqrt(-a)/(d*sqrt(-a)+e*sqrt(b)))*sqrt(-a)/(e*(1+m)*(2+m)*(d*sqrt(-a)+e*sqrt(b)))],

# Integrands of the form (f+g x)^q Log[c (d+e x^m)^n] when n symbolic
[(f+g*x)^m*log(c*(d+e*x^n)^p),x,0,Unintegrable((f+g*x)^m*log(c*(d+e*x^n)^p),x)],
[(f+g*x)^3*log(c*(d+e*x^n)^p),x,8,-e*f^3*n*p*x^(1+n)*hypergeom([1,1+1/n],[2+1/n],-e*x^n/d)/(d*(1+n))-3/2*e*f^2*g*n*p*x^(2+n)*hypergeom([1,(2+n)/n],[2*(1+1/n)],-e*x^n/d)/(d*(2+n))-e*f*g^2*n*p*x^(3+n)*hypergeom([1,(3+n)/n],[2+3/n],-e*x^n/d)/(d*(3+n))-1/4*e*g^3*n*p*x^(4+n)*hypergeom([1,(4+n)/n],[2*(1+2/n)],-e*x^n/d)/(d*(4+n))-1/4*f^4*p*log(d+e*x^n)/g+1/4*(f+g*x)^4*log(c*(d+e*x^n)^p)/g],
[(f+g*x)^2*log(c*(d+e*x^n)^p),x,7,-e*f^2*n*p*x^(1+n)*hypergeom([1,1+1/n],[2+1/n],-e*x^n/d)/(d*(1+n))-e*f*g*n*p*x^(2+n)*hypergeom([1,(2+n)/n],[2*(1+1/n)],-e*x^n/d)/(d*(2+n))-1/3*e*g^2*n*p*x^(3+n)*hypergeom([1,(3+n)/n],[2+3/n],-e*x^n/d)/(d*(3+n))-1/3*f^3*p*log(d+e*x^n)/g+1/3*(f+g*x)^3*log(c*(d+e*x^n)^p)/g],
[(f+g*x)*log(c*(d+e*x^n)^p),x,6,-e*f*n*p*x^(1+n)*hypergeom([1,1+1/n],[2+1/n],-e*x^n/d)/(d*(1+n))-1/2*e*g*n*p*x^(2+n)*hypergeom([1,(2+n)/n],[2*(1+1/n)],-e*x^n/d)/(d*(2+n))-1/2*f^2*p*log(d+e*x^n)/g+1/2*(f+g*x)^2*log(c*(d+e*x^n)^p)/g],
[log(c*(d+e*x^n)^p),x,2,-e*n*p*x^(1+n)*hypergeom([1,1+1/n],[2+1/n],-e*x^n/d)/(d*(1+n))+x*log(c*(d+e*x^n)^p)],
[log(c*(d+e*x^n)^p)/(f+g*x),x,0,Unintegrable(log(c*(d+e*x^n)^p)/(f+g*x),x)],
[log(c*(d+e*x^n)^p)/(f+g*x)^2,x,0,Unintegrable(log(c*(d+e*x^n)^p)/(f+g*x)^2,x)],
[log(c*(d+e*x^n)^p)/(f+g*x)^3,x,0,Unintegrable(log(c*(d+e*x^n)^p)/(f+g*x)^3,x)],

# Integrands of the form (h x)^r (f+g x)^q Log[c (d+e x^m)^n]^p

# Integrands of the form x^r / (f+g x) Log[c (d+e x^m)^n]

# n>0
[x^3*log(c*(a+b*x)^p)/(d+e*x),x,13,-d^2*p*x/e^3-1/2*a*d*p*x/(b*e^2)-1/3*a^2*p*x/(b^2*e)+1/4*d*p*x^2/e^2+1/6*a*p*x^2/(b*e)-1/9*p*x^3/e+1/2*a^2*d*p*log(a+b*x)/(b^2*e^2)+1/3*a^3*p*log(a+b*x)/(b^3*e)-1/2*d*x^2*log(c*(a+b*x)^p)/e^2+1/3*x^3*log(c*(a+b*x)^p)/e+d^2*(a+b*x)*log(c*(a+b*x)^p)/(b*e^3)-d^3*log(c*(a+b*x)^p)*log(b*(d+e*x)/(b*d-a*e))/e^4-d^3*p*polylog(2,-e*(a+b*x)/(b*d-a*e))/e^4],
[x^2*log(c*(a+b*x)^p)/(d+e*x),x,10,d*p*x/e^2+1/2*a*p*x/(b*e)-1/4*p*x^2/e-1/2*a^2*p*log(a+b*x)/(b^2*e)+1/2*x^2*log(c*(a+b*x)^p)/e-d*(a+b*x)*log(c*(a+b*x)^p)/(b*e^2)+d^2*log(c*(a+b*x)^p)*log(b*(d+e*x)/(b*d-a*e))/e^3+d^2*p*polylog(2,-e*(a+b*x)/(b*d-a*e))/e^3],
[x*log(c*(a+b*x)^p)/(d+e*x),x,7,-p*x/e+(a+b*x)*log(c*(a+b*x)^p)/(b*e)-d*log(c*(a+b*x)^p)*log(b*(d+e*x)/(b*d-a*e))/e^2-d*p*polylog(2,-e*(a+b*x)/(b*d-a*e))/e^2],
[log(c*(a+b*x)^p)/(d+e*x),x,3,log(c*(a+b*x)^p)*log(b*(d+e*x)/(b*d-a*e))/e+p*polylog(2,-e*(a+b*x)/(b*d-a*e))/e],
[log(c*(a+b*x)^p)/(x*(d+e*x)),x,7,log(-b*x/a)*log(c*(a+b*x)^p)/d-log(c*(a+b*x)^p)*log(b*(d+e*x)/(b*d-a*e))/d-p*polylog(2,-e*(a+b*x)/(b*d-a*e))/d+p*polylog(2,1+b*x/a)/d],
[log(c*(a+b*x)^p)/(x^2*(d+e*x)),x,11,b*p*log(x)/(a*d)-b*p*log(a+b*x)/(a*d)-log(c*(a+b*x)^p)/(d*x)-e*log(-b*x/a)*log(c*(a+b*x)^p)/d^2+e*log(c*(a+b*x)^p)*log(b*(d+e*x)/(b*d-a*e))/d^2+e*p*polylog(2,-e*(a+b*x)/(b*d-a*e))/d^2-e*p*polylog(2,1+b*x/a)/d^2],
[log(c*(a+b*x)^p)/(x^3*(d+e*x)),x,14,-1/2*b*p/(a*d*x)-1/2*b^2*p*log(x)/(a^2*d)-b*e*p*log(x)/(a*d^2)+1/2*b^2*p*log(a+b*x)/(a^2*d)+b*e*p*log(a+b*x)/(a*d^2)-1/2*log(c*(a+b*x)^p)/(d*x^2)+e*log(c*(a+b*x)^p)/(d^2*x)+e^2*log(-b*x/a)*log(c*(a+b*x)^p)/d^3-e^2*log(c*(a+b*x)^p)*log(b*(d+e*x)/(b*d-a*e))/d^3-e^2*p*polylog(2,-e*(a+b*x)/(b*d-a*e))/d^3+e^2*p*polylog(2,1+b*x/a)/d^3],
[x^3*log(c*(a+b*x^2)^p)/(d+e*x),x,21,-2*d^2*p*x/e^3+2/3*a*p*x/(b*e)+1/2*d*p*x^2/e^2-2/9*p*x^3/e-2/3*a^(3/2)*p*arctan(x*sqrt(b)/sqrt(a))/(b^(3/2)*e)+d^2*x*log(c*(a+b*x^2)^p)/e^3+1/3*x^3*log(c*(a+b*x^2)^p)/e-1/2*d*(a+b*x^2)*log(c*(a+b*x^2)^p)/(b*e^2)-d^3*log(d+e*x)*log(c*(a+b*x^2)^p)/e^4+d^3*p*log(d+e*x)*log(e*(sqrt(-a)-x*sqrt(b))/(e*sqrt(-a)+d*sqrt(b)))/e^4+d^3*p*log(d+e*x)*log(-e*(sqrt(-a)+x*sqrt(b))/(-e*sqrt(-a)+d*sqrt(b)))/e^4+d^3*p*polylog(2,(d+e*x)*sqrt(b)/(-e*sqrt(-a)+d*sqrt(b)))/e^4+d^3*p*polylog(2,(d+e*x)*sqrt(b)/(e*sqrt(-a)+d*sqrt(b)))/e^4+2*d^2*p*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/(e^3*sqrt(b))],
[x^2*log(c*(a+b*x^2)^p)/(d+e*x),x,17,2*d*p*x/e^2-1/2*p*x^2/e-d*x*log(c*(a+b*x^2)^p)/e^2+1/2*(a+b*x^2)*log(c*(a+b*x^2)^p)/(b*e)+d^2*log(d+e*x)*log(c*(a+b*x^2)^p)/e^3-d^2*p*log(d+e*x)*log(e*(sqrt(-a)-x*sqrt(b))/(e*sqrt(-a)+d*sqrt(b)))/e^3-d^2*p*log(d+e*x)*log(-e*(sqrt(-a)+x*sqrt(b))/(-e*sqrt(-a)+d*sqrt(b)))/e^3-d^2*p*polylog(2,(d+e*x)*sqrt(b)/(-e*sqrt(-a)+d*sqrt(b)))/e^3-d^2*p*polylog(2,(d+e*x)*sqrt(b)/(e*sqrt(-a)+d*sqrt(b)))/e^3-2*d*p*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/(e^2*sqrt(b))],
[x*log(c*(a+b*x^2)^p)/(d+e*x),x,14,-2*p*x/e+x*log(c*(a+b*x^2)^p)/e-d*log(d+e*x)*log(c*(a+b*x^2)^p)/e^2+d*p*log(d+e*x)*log(e*(sqrt(-a)-x*sqrt(b))/(e*sqrt(-a)+d*sqrt(b)))/e^2+d*p*log(d+e*x)*log(-e*(sqrt(-a)+x*sqrt(b))/(-e*sqrt(-a)+d*sqrt(b)))/e^2+d*p*polylog(2,(d+e*x)*sqrt(b)/(-e*sqrt(-a)+d*sqrt(b)))/e^2+d*p*polylog(2,(d+e*x)*sqrt(b)/(e*sqrt(-a)+d*sqrt(b)))/e^2+2*p*arctan(x*sqrt(b)/sqrt(a))*sqrt(a)/(e*sqrt(b))],
[log(c*(a+b*x^2)^p)/(d+e*x),x,9,log(d+e*x)*log(c*(a+b*x^2)^p)/e-p*log(d+e*x)*log(e*(sqrt(-a)-x*sqrt(b))/(e*sqrt(-a)+d*sqrt(b)))/e-p*log(d+e*x)*log(-e*(sqrt(-a)+x*sqrt(b))/(-e*sqrt(-a)+d*sqrt(b)))/e-p*polylog(2,(d+e*x)*sqrt(b)/(-e*sqrt(-a)+d*sqrt(b)))/e-p*polylog(2,(d+e*x)*sqrt(b)/(e*sqrt(-a)+d*sqrt(b)))/e],
[log(c*(a+b*x^2)^p)/(x*(d+e*x)),x,14,1/2*log(-b*x^2/a)*log(c*(a+b*x^2)^p)/d-log(d+e*x)*log(c*(a+b*x^2)^p)/d+p*log(d+e*x)*log(e*(sqrt(-a)-x*sqrt(b))/(e*sqrt(-a)+d*sqrt(b)))/d+p*log(d+e*x)*log(-e*(sqrt(-a)+x*sqrt(b))/(-e*sqrt(-a)+d*sqrt(b)))/d+1/2*p*polylog(2,1+b*x^2/a)/d+p*polylog(2,(d+e*x)*sqrt(b)/(-e*sqrt(-a)+d*sqrt(b)))/d+p*polylog(2,(d+e*x)*sqrt(b)/(e*sqrt(-a)+d*sqrt(b)))/d],
[log(c*(a+b*x^2)^p)/(x^2*(d+e*x)),x,16,-log(c*(a+b*x^2)^p)/(d*x)-1/2*e*log(-b*x^2/a)*log(c*(a+b*x^2)^p)/d^2+e*log(d+e*x)*log(c*(a+b*x^2)^p)/d^2-e*p*log(d+e*x)*log(e*(sqrt(-a)-x*sqrt(b))/(e*sqrt(-a)+d*sqrt(b)))/d^2-e*p*log(d+e*x)*log(-e*(sqrt(-a)+x*sqrt(b))/(-e*sqrt(-a)+d*sqrt(b)))/d^2-1/2*e*p*polylog(2,1+b*x^2/a)/d^2-e*p*polylog(2,(d+e*x)*sqrt(b)/(-e*sqrt(-a)+d*sqrt(b)))/d^2-e*p*polylog(2,(d+e*x)*sqrt(b)/(e*sqrt(-a)+d*sqrt(b)))/d^2+2*p*arctan(x*sqrt(b)/sqrt(a))*sqrt(b)/(d*sqrt(a))],
[log(c*(a+b*x^2)^p)/(x^3*(d+e*x)),x,21,b*p*log(x)/(a*d)-1/2*b*p*log(a+b*x^2)/(a*d)-1/2*log(c*(a+b*x^2)^p)/(d*x^2)+e*log(c*(a+b*x^2)^p)/(d^2*x)+1/2*e^2*log(-b*x^2/a)*log(c*(a+b*x^2)^p)/d^3-e^2*log(d+e*x)*log(c*(a+b*x^2)^p)/d^3+e^2*p*log(d+e*x)*log(e*(sqrt(-a)-x*sqrt(b))/(e*sqrt(-a)+d*sqrt(b)))/d^3+e^2*p*log(d+e*x)*log(-e*(sqrt(-a)+x*sqrt(b))/(-e*sqrt(-a)+d*sqrt(b)))/d^3+1/2*e^2*p*polylog(2,1+b*x^2/a)/d^3+e^2*p*polylog(2,(d+e*x)*sqrt(b)/(-e*sqrt(-a)+d*sqrt(b)))/d^3+e^2*p*polylog(2,(d+e*x)*sqrt(b)/(e*sqrt(-a)+d*sqrt(b)))/d^3-2*e*p*arctan(x*sqrt(b)/sqrt(a))*sqrt(b)/(d^2*sqrt(a))],
[x^3*log(c*(a+b*x^3)^p)/(d+e*x),x,33,-3*d^2*p*x/e^3+3/4*d*p*x^2/e^2-1/3*p*x^3/e+a^(1/3)*d^2*p*log(a^(1/3)+b^(1/3)*x)/(b^(1/3)*e^3)+1/2*a^(2/3)*d*p*log(a^(1/3)+b^(1/3)*x)/(b^(2/3)*e^2)+d^3*p*log(-e*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-a^(1/3)*e))*log(d+e*x)/e^4+d^3*p*log(-e*((-1)^(2/3)*a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))*log(d+e*x)/e^4+d^3*p*log((-1)^(1/3)*e*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))*log(d+e*x)/e^4-1/2*a^(1/3)*d^2*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*e^3)-1/4*a^(2/3)*d*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(2/3)*e^2)+d^2*x*log(c*(a+b*x^3)^p)/e^3-1/2*d*x^2*log(c*(a+b*x^3)^p)/e^2+1/3*(a+b*x^3)*log(c*(a+b*x^3)^p)/(b*e)-d^3*log(d+e*x)*log(c*(a+b*x^3)^p)/e^4+d^3*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-a^(1/3)*e))/e^4+d^3*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))/e^4+d^3*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))/e^4-a^(1/3)*d^2*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/(b^(1/3)*e^3)+1/2*a^(2/3)*d*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/(b^(2/3)*e^2)],
[x^2*log(c*(a+b*x^3)^p)/(d+e*x),x,30,3*d*p*x/e^2-3/4*p*x^2/e-a^(1/3)*d*p*log(a^(1/3)+b^(1/3)*x)/(b^(1/3)*e^2)-1/2*a^(2/3)*p*log(a^(1/3)+b^(1/3)*x)/(b^(2/3)*e)-d^2*p*log(-e*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-a^(1/3)*e))*log(d+e*x)/e^3-d^2*p*log(-e*((-1)^(2/3)*a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))*log(d+e*x)/e^3-d^2*p*log((-1)^(1/3)*e*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))*log(d+e*x)/e^3+1/2*a^(1/3)*d*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*e^2)+1/4*a^(2/3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(2/3)*e)-d*x*log(c*(a+b*x^3)^p)/e^2+1/2*x^2*log(c*(a+b*x^3)^p)/e+d^2*log(d+e*x)*log(c*(a+b*x^3)^p)/e^3-d^2*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-a^(1/3)*e))/e^3-d^2*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))/e^3-d^2*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))/e^3+a^(1/3)*d*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/(b^(1/3)*e^2)-1/2*a^(2/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/(b^(2/3)*e)],
[x*log(c*(a+b*x^3)^p)/(d+e*x),x,22,-3*p*x/e+a^(1/3)*p*log(a^(1/3)+b^(1/3)*x)/(b^(1/3)*e)+d*p*log(-e*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-a^(1/3)*e))*log(d+e*x)/e^2+d*p*log(-e*((-1)^(2/3)*a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))*log(d+e*x)/e^2+d*p*log((-1)^(1/3)*e*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))*log(d+e*x)/e^2-1/2*a^(1/3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(b^(1/3)*e)+x*log(c*(a+b*x^3)^p)/e-d*log(d+e*x)*log(c*(a+b*x^3)^p)/e^2+d*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-a^(1/3)*e))/e^2+d*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))/e^2+d*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))/e^2-a^(1/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/(b^(1/3)*e)],
[log(c*(a+b*x^3)^p)/(d+e*x),x,12,-p*log(-e*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-a^(1/3)*e))*log(d+e*x)/e-p*log(-e*((-1)^(2/3)*a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))*log(d+e*x)/e-p*log((-1)^(1/3)*e*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))*log(d+e*x)/e+log(d+e*x)*log(c*(a+b*x^3)^p)/e-p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-a^(1/3)*e))/e-p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))/e-p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))/e],
[log(c*(a+b*x^3)^p)/(x*(d+e*x)),x,17,p*log(-e*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-a^(1/3)*e))*log(d+e*x)/d+p*log(-e*((-1)^(2/3)*a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))*log(d+e*x)/d+p*log((-1)^(1/3)*e*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))*log(d+e*x)/d+1/3*log(-b*x^3/a)*log(c*(a+b*x^3)^p)/d-log(d+e*x)*log(c*(a+b*x^3)^p)/d+p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-a^(1/3)*e))/d+p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))/d+p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))/d+1/3*p*polylog(2,1+b*x^3/a)/d],
[log(c*(a+b*x^3)^p)/(x^2*(d+e*x)),x,24,-b^(1/3)*p*log(a^(1/3)+b^(1/3)*x)/(a^(1/3)*d)-e*p*log(-e*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-a^(1/3)*e))*log(d+e*x)/d^2-e*p*log(-e*((-1)^(2/3)*a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))*log(d+e*x)/d^2-e*p*log((-1)^(1/3)*e*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))*log(d+e*x)/d^2+1/2*b^(1/3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*d)-log(c*(a+b*x^3)^p)/(d*x)-1/3*e*log(-b*x^3/a)*log(c*(a+b*x^3)^p)/d^2+e*log(d+e*x)*log(c*(a+b*x^3)^p)/d^2-e*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-a^(1/3)*e))/d^2-e*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))/d^2-e*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))/d^2-1/3*e*p*polylog(2,1+b*x^3/a)/d^2-b^(1/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/(a^(1/3)*d)],
[log(c*(a+b*x^3)^p)/(x^3*(d+e*x)),x,31,1/2*b^(2/3)*p*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*d)+b^(1/3)*e*p*log(a^(1/3)+b^(1/3)*x)/(a^(1/3)*d^2)+e^2*p*log(-e*(a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-a^(1/3)*e))*log(d+e*x)/d^3+e^2*p*log(-e*((-1)^(2/3)*a^(1/3)+b^(1/3)*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))*log(d+e*x)/d^3+e^2*p*log((-1)^(1/3)*e*(a^(1/3)+(-1)^(2/3)*b^(1/3)*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))*log(d+e*x)/d^3-1/4*b^(2/3)*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*d)-1/2*b^(1/3)*e*p*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*d^2)-1/2*log(c*(a+b*x^3)^p)/(d*x^2)+e*log(c*(a+b*x^3)^p)/(d^2*x)+1/3*e^2*log(-b*x^3/a)*log(c*(a+b*x^3)^p)/d^3-e^2*log(d+e*x)*log(c*(a+b*x^3)^p)/d^3+e^2*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-a^(1/3)*e))/d^3+e^2*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d+(-1)^(1/3)*a^(1/3)*e))/d^3+e^2*p*polylog(2,b^(1/3)*(d+e*x)/(b^(1/3)*d-(-1)^(2/3)*a^(1/3)*e))/d^3+1/3*e^2*p*polylog(2,1+b*x^3/a)/d^3-1/2*b^(2/3)*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/(a^(2/3)*d)+b^(1/3)*e*p*arctan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))*sqrt(3)/(a^(1/3)*d^2)],

# n<0
[x^3*log(c*(a+b/x)^p)/(d+e*x),x,21,-1/2*b*d*p*x/(a*e^2)-1/3*b^2*p*x/(a^2*e)+1/6*b*p*x^2/(a*e)+d^2*x*log(c*(a+b/x)^p)/e^3-1/2*d*x^2*log(c*(a+b/x)^p)/e^2+1/3*x^3*log(c*(a+b/x)^p)/e+b*d^2*p*log(b+a*x)/(a*e^3)+1/2*b^2*d*p*log(b+a*x)/(a^2*e^2)+1/3*b^3*p*log(b+a*x)/(a^3*e)-d^3*log(c*(a+b/x)^p)*log(d+e*x)/e^4-d^3*p*log(-e*x/d)*log(d+e*x)/e^4+d^3*p*log(-e*(b+a*x)/(a*d-b*e))*log(d+e*x)/e^4+d^3*p*polylog(2,a*(d+e*x)/(a*d-b*e))/e^4-d^3*p*polylog(2,1+e*x/d)/e^4],
[x^2*log(c*(a+b/x)^p)/(d+e*x),x,17,1/2*b*p*x/(a*e)-d*x*log(c*(a+b/x)^p)/e^2+1/2*x^2*log(c*(a+b/x)^p)/e-b*d*p*log(b+a*x)/(a*e^2)-1/2*b^2*p*log(b+a*x)/(a^2*e)+d^2*log(c*(a+b/x)^p)*log(d+e*x)/e^3+d^2*p*log(-e*x/d)*log(d+e*x)/e^3-d^2*p*log(-e*(b+a*x)/(a*d-b*e))*log(d+e*x)/e^3-d^2*p*polylog(2,a*(d+e*x)/(a*d-b*e))/e^3+d^2*p*polylog(2,1+e*x/d)/e^3],
[x*log(c*(a+b/x)^p)/(d+e*x),x,13,x*log(c*(a+b/x)^p)/e+b*p*log(b+a*x)/(a*e)-d*log(c*(a+b/x)^p)*log(d+e*x)/e^2-d*p*log(-e*x/d)*log(d+e*x)/e^2+d*p*log(-e*(b+a*x)/(a*d-b*e))*log(d+e*x)/e^2+d*p*polylog(2,a*(d+e*x)/(a*d-b*e))/e^2-d*p*polylog(2,1+e*x/d)/e^2],
[log(c*(a+b/x)^p)/(d+e*x),x,8,log(c*(a+b/x)^p)*log(d+e*x)/e+p*log(-e*x/d)*log(d+e*x)/e-p*log(-e*(b+a*x)/(a*d-b*e))*log(d+e*x)/e-p*polylog(2,a*(d+e*x)/(a*d-b*e))/e+p*polylog(2,1+e*x/d)/e],
[log(c*(a+b/x)^p)/(x*(d+e*x)),x,13,-log(c*(a+b/x)^p)*log(-b/(a*x))/d-log(c*(a+b/x)^p)*log(d+e*x)/d-p*log(-e*x/d)*log(d+e*x)/d+p*log(-e*(b+a*x)/(a*d-b*e))*log(d+e*x)/d-p*polylog(2,1+b/(a*x))/d+p*polylog(2,a*(d+e*x)/(a*d-b*e))/d-p*polylog(2,1+e*x/d)/d],
[log(c*(a+b/x)^p)/(x^2*(d+e*x)),x,16,p/(d*x)-(a+b/x)*log(c*(a+b/x)^p)/(b*d)+e*log(c*(a+b/x)^p)*log(-b/(a*x))/d^2+e*log(c*(a+b/x)^p)*log(d+e*x)/d^2+e*p*log(-e*x/d)*log(d+e*x)/d^2-e*p*log(-e*(b+a*x)/(a*d-b*e))*log(d+e*x)/d^2+e*p*polylog(2,1+b/(a*x))/d^2-e*p*polylog(2,a*(d+e*x)/(a*d-b*e))/d^2+e*p*polylog(2,1+e*x/d)/d^2],
[log(c*(a+b/x)^p)/(x^3*(d+e*x)),x,20,1/4*p/(d*x^2)-1/2*a*p/(b*d*x)-e*p/(d^2*x)+1/2*a^2*p*log(a+b/x)/(b^2*d)+e*(a+b/x)*log(c*(a+b/x)^p)/(b*d^2)-1/2*log(c*(a+b/x)^p)/(d*x^2)-e^2*log(c*(a+b/x)^p)*log(-b/(a*x))/d^3-e^2*log(c*(a+b/x)^p)*log(d+e*x)/d^3-e^2*p*log(-e*x/d)*log(d+e*x)/d^3+e^2*p*log(-e*(b+a*x)/(a*d-b*e))*log(d+e*x)/d^3-e^2*p*polylog(2,1+b/(a*x))/d^3+e^2*p*polylog(2,a*(d+e*x)/(a*d-b*e))/d^3-e^2*p*polylog(2,1+e*x/d)/d^3],
[x^3*log(c*(a+b/x^2)^p)/(d+e*x),x,25,2/3*b*p*x/(a*e)-2/3*b^(3/2)*p*arctan(x*sqrt(a)/sqrt(b))/(a^(3/2)*e)+d^2*x*log(c*(a+b/x^2)^p)/e^3-1/2*d*x^2*log(c*(a+b/x^2)^p)/e^2+1/3*x^3*log(c*(a+b/x^2)^p)/e-d^3*log(c*(a+b/x^2)^p)*log(d+e*x)/e^4-2*d^3*p*log(-e*x/d)*log(d+e*x)/e^4-1/2*b*d*p*log(b+a*x^2)/(a*e^2)+d^3*p*log(d+e*x)*log(-e*(x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)-e*sqrt(b)))/e^4+d^3*p*log(d+e*x)*log(e*(-x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)+e*sqrt(b)))/e^4-2*d^3*p*polylog(2,1+e*x/d)/e^4+d^3*p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)-e*sqrt(b)))/e^4+d^3*p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)+e*sqrt(b)))/e^4+2*d^2*p*arctan(x*sqrt(a)/sqrt(b))*sqrt(b)/(e^3*sqrt(a))],
[x^2*log(c*(a+b/x^2)^p)/(d+e*x),x,21,-d*x*log(c*(a+b/x^2)^p)/e^2+1/2*x^2*log(c*(a+b/x^2)^p)/e+d^2*log(c*(a+b/x^2)^p)*log(d+e*x)/e^3+2*d^2*p*log(-e*x/d)*log(d+e*x)/e^3+1/2*b*p*log(b+a*x^2)/(a*e)-d^2*p*log(d+e*x)*log(-e*(x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)-e*sqrt(b)))/e^3-d^2*p*log(d+e*x)*log(e*(-x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)+e*sqrt(b)))/e^3+2*d^2*p*polylog(2,1+e*x/d)/e^3-d^2*p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)-e*sqrt(b)))/e^3-d^2*p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)+e*sqrt(b)))/e^3-2*d*p*arctan(x*sqrt(a)/sqrt(b))*sqrt(b)/(e^2*sqrt(a))],
[x*log(c*(a+b/x^2)^p)/(d+e*x),x,18,x*log(c*(a+b/x^2)^p)/e-d*log(c*(a+b/x^2)^p)*log(d+e*x)/e^2-2*d*p*log(-e*x/d)*log(d+e*x)/e^2+d*p*log(d+e*x)*log(-e*(x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)-e*sqrt(b)))/e^2+d*p*log(d+e*x)*log(e*(-x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)+e*sqrt(b)))/e^2-2*d*p*polylog(2,1+e*x/d)/e^2+d*p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)-e*sqrt(b)))/e^2+d*p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)+e*sqrt(b)))/e^2+2*p*arctan(x*sqrt(a)/sqrt(b))*sqrt(b)/(e*sqrt(a))],
[log(c*(a+b/x^2)^p)/(d+e*x),x,13,log(c*(a+b/x^2)^p)*log(d+e*x)/e+2*p*log(-e*x/d)*log(d+e*x)/e-p*log(d+e*x)*log(-e*(x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)-e*sqrt(b)))/e-p*log(d+e*x)*log(e*(-x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)+e*sqrt(b)))/e+2*p*polylog(2,1+e*x/d)/e-p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)-e*sqrt(b)))/e-p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)+e*sqrt(b)))/e],
[log(c*(a+b/x^2)^p)/(x*(d+e*x)),x,18,-1/2*log(c*(a+b/x^2)^p)*log(-b/(a*x^2))/d-log(c*(a+b/x^2)^p)*log(d+e*x)/d-2*p*log(-e*x/d)*log(d+e*x)/d+p*log(d+e*x)*log(-e*(x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)-e*sqrt(b)))/d+p*log(d+e*x)*log(e*(-x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)+e*sqrt(b)))/d-1/2*p*polylog(2,1+b/(a*x^2))/d-2*p*polylog(2,1+e*x/d)/d+p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)-e*sqrt(b)))/d+p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)+e*sqrt(b)))/d],
[log(c*(a+b/x^2)^p)/(x^2*(d+e*x)),x,22,2*p/(d*x)-log(c*(a+b/x^2)^p)/(d*x)+1/2*e*log(c*(a+b/x^2)^p)*log(-b/(a*x^2))/d^2+e*log(c*(a+b/x^2)^p)*log(d+e*x)/d^2+2*e*p*log(-e*x/d)*log(d+e*x)/d^2-e*p*log(d+e*x)*log(-e*(x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)-e*sqrt(b)))/d^2-e*p*log(d+e*x)*log(e*(-x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)+e*sqrt(b)))/d^2+1/2*e*p*polylog(2,1+b/(a*x^2))/d^2+2*e*p*polylog(2,1+e*x/d)/d^2-e*p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)-e*sqrt(b)))/d^2-e*p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)+e*sqrt(b)))/d^2+2*p*arctan(x*sqrt(a)/sqrt(b))*sqrt(a)/(d*sqrt(b))],
[log(c*(a+b/x^2)^p)/(x^3*(d+e*x)),x,25,1/2*p/(d*x^2)-2*e*p/(d^2*x)-1/2*(a+b/x^2)*log(c*(a+b/x^2)^p)/(b*d)+e*log(c*(a+b/x^2)^p)/(d^2*x)-1/2*e^2*log(c*(a+b/x^2)^p)*log(-b/(a*x^2))/d^3-e^2*log(c*(a+b/x^2)^p)*log(d+e*x)/d^3-2*e^2*p*log(-e*x/d)*log(d+e*x)/d^3+e^2*p*log(d+e*x)*log(-e*(x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)-e*sqrt(b)))/d^3+e^2*p*log(d+e*x)*log(e*(-x*sqrt(-a)+sqrt(b))/(d*sqrt(-a)+e*sqrt(b)))/d^3-1/2*e^2*p*polylog(2,1+b/(a*x^2))/d^3-2*e^2*p*polylog(2,1+e*x/d)/d^3+e^2*p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)-e*sqrt(b)))/d^3+e^2*p*polylog(2,(d+e*x)*sqrt(-a)/(d*sqrt(-a)+e*sqrt(b)))/d^3-2*e*p*arctan(x*sqrt(a)/sqrt(b))*sqrt(a)/(d^2*sqrt(b))],
[x^3*log(c*(a+b/x^3)^p)/(d+e*x),x,37,d^2*x*log(c*(a+b/x^3)^p)/e^3-1/2*d*x^2*log(c*(a+b/x^3)^p)/e^2+1/3*x^3*log(c*(a+b/x^3)^p)/e+b^(1/3)*d^2*p*log(b^(1/3)+a^(1/3)*x)/(a^(1/3)*e^3)+1/2*b^(2/3)*d*p*log(b^(1/3)+a^(1/3)*x)/(a^(2/3)*e^2)-d^3*log(c*(a+b/x^3)^p)*log(d+e*x)/e^4-3*d^3*p*log(-e*x/d)*log(d+e*x)/e^4+d^3*p*log(-e*(b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-b^(1/3)*e))*log(d+e*x)/e^4+d^3*p*log(-e*((-1)^(2/3)*b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))*log(d+e*x)/e^4+d^3*p*log((-1)^(1/3)*e*(b^(1/3)+(-1)^(2/3)*a^(1/3)*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))*log(d+e*x)/e^4-1/2*b^(1/3)*d^2*p*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(1/3)*e^3)-1/4*b^(2/3)*d*p*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(2/3)*e^2)+1/3*b*p*log(b+a*x^3)/(a*e)+d^3*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-b^(1/3)*e))/e^4+d^3*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))/e^4+d^3*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))/e^4-3*d^3*p*polylog(2,1+e*x/d)/e^4-b^(1/3)*d^2*p*arctan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))*sqrt(3)/(a^(1/3)*e^3)+1/2*b^(2/3)*d*p*arctan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))*sqrt(3)/(a^(2/3)*e^2)],
[x^2*log(c*(a+b/x^3)^p)/(d+e*x),x,34,-d*x*log(c*(a+b/x^3)^p)/e^2+1/2*x^2*log(c*(a+b/x^3)^p)/e-b^(1/3)*d*p*log(b^(1/3)+a^(1/3)*x)/(a^(1/3)*e^2)-1/2*b^(2/3)*p*log(b^(1/3)+a^(1/3)*x)/(a^(2/3)*e)+d^2*log(c*(a+b/x^3)^p)*log(d+e*x)/e^3+3*d^2*p*log(-e*x/d)*log(d+e*x)/e^3-d^2*p*log(-e*(b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-b^(1/3)*e))*log(d+e*x)/e^3-d^2*p*log(-e*((-1)^(2/3)*b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))*log(d+e*x)/e^3-d^2*p*log((-1)^(1/3)*e*(b^(1/3)+(-1)^(2/3)*a^(1/3)*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))*log(d+e*x)/e^3+1/2*b^(1/3)*d*p*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(1/3)*e^2)+1/4*b^(2/3)*p*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(2/3)*e)-d^2*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-b^(1/3)*e))/e^3-d^2*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))/e^3-d^2*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))/e^3+3*d^2*p*polylog(2,1+e*x/d)/e^3+b^(1/3)*d*p*arctan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))*sqrt(3)/(a^(1/3)*e^2)-1/2*b^(2/3)*p*arctan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))*sqrt(3)/(a^(2/3)*e)],
[x*log(c*(a+b/x^3)^p)/(d+e*x),x,26,x*log(c*(a+b/x^3)^p)/e+b^(1/3)*p*log(b^(1/3)+a^(1/3)*x)/(a^(1/3)*e)-d*log(c*(a+b/x^3)^p)*log(d+e*x)/e^2-3*d*p*log(-e*x/d)*log(d+e*x)/e^2+d*p*log(-e*(b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-b^(1/3)*e))*log(d+e*x)/e^2+d*p*log(-e*((-1)^(2/3)*b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))*log(d+e*x)/e^2+d*p*log((-1)^(1/3)*e*(b^(1/3)+(-1)^(2/3)*a^(1/3)*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))*log(d+e*x)/e^2-1/2*b^(1/3)*p*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(1/3)*e)+d*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-b^(1/3)*e))/e^2+d*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))/e^2+d*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))/e^2-3*d*p*polylog(2,1+e*x/d)/e^2-b^(1/3)*p*arctan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))*sqrt(3)/(a^(1/3)*e)],
[log(c*(a+b/x^3)^p)/(d+e*x),x,16,log(c*(a+b/x^3)^p)*log(d+e*x)/e+3*p*log(-e*x/d)*log(d+e*x)/e-p*log(-e*(b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-b^(1/3)*e))*log(d+e*x)/e-p*log(-e*((-1)^(2/3)*b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))*log(d+e*x)/e-p*log((-1)^(1/3)*e*(b^(1/3)+(-1)^(2/3)*a^(1/3)*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))*log(d+e*x)/e-p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-b^(1/3)*e))/e-p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))/e-p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))/e+3*p*polylog(2,1+e*x/d)/e],
[log(c*(a+b/x^3)^p)/(x*(d+e*x)),x,21,-1/3*log(c*(a+b/x^3)^p)*log(-b/(a*x^3))/d-log(c*(a+b/x^3)^p)*log(d+e*x)/d-3*p*log(-e*x/d)*log(d+e*x)/d+p*log(-e*(b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-b^(1/3)*e))*log(d+e*x)/d+p*log(-e*((-1)^(2/3)*b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))*log(d+e*x)/d+p*log((-1)^(1/3)*e*(b^(1/3)+(-1)^(2/3)*a^(1/3)*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))*log(d+e*x)/d-1/3*p*polylog(2,1+b/(a*x^3))/d+p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-b^(1/3)*e))/d+p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))/d+p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))/d-3*p*polylog(2,1+e*x/d)/d],
[log(c*(a+b/x^3)^p)/(x^2*(d+e*x)),x,30,3*p/(d*x)-log(c*(a+b/x^3)^p)/(d*x)+1/3*e*log(c*(a+b/x^3)^p)*log(-b/(a*x^3))/d^2-a^(1/3)*p*log(b^(1/3)+a^(1/3)*x)/(b^(1/3)*d)+e*log(c*(a+b/x^3)^p)*log(d+e*x)/d^2+3*e*p*log(-e*x/d)*log(d+e*x)/d^2-e*p*log(-e*(b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-b^(1/3)*e))*log(d+e*x)/d^2-e*p*log(-e*((-1)^(2/3)*b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))*log(d+e*x)/d^2-e*p*log((-1)^(1/3)*e*(b^(1/3)+(-1)^(2/3)*a^(1/3)*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))*log(d+e*x)/d^2+1/2*a^(1/3)*p*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(b^(1/3)*d)+1/3*e*p*polylog(2,1+b/(a*x^3))/d^2-e*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-b^(1/3)*e))/d^2-e*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))/d^2-e*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))/d^2+3*e*p*polylog(2,1+e*x/d)/d^2-a^(1/3)*p*arctan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))*sqrt(3)/(b^(1/3)*d)],
[log(c*(a+b/x^3)^p)/(x^3*(d+e*x)),x,39,3/4*p/(d*x^2)-3*e*p/(d^2*x)-1/2*log(c*(a+b/x^3)^p)/(d*x^2)+e*log(c*(a+b/x^3)^p)/(d^2*x)-1/3*e^2*log(c*(a+b/x^3)^p)*log(-b/(a*x^3))/d^3+1/2*a^(2/3)*p*log(b^(1/3)+a^(1/3)*x)/(b^(2/3)*d)+a^(1/3)*e*p*log(b^(1/3)+a^(1/3)*x)/(b^(1/3)*d^2)-e^2*log(c*(a+b/x^3)^p)*log(d+e*x)/d^3-3*e^2*p*log(-e*x/d)*log(d+e*x)/d^3+e^2*p*log(-e*(b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-b^(1/3)*e))*log(d+e*x)/d^3+e^2*p*log(-e*((-1)^(2/3)*b^(1/3)+a^(1/3)*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))*log(d+e*x)/d^3+e^2*p*log((-1)^(1/3)*e*(b^(1/3)+(-1)^(2/3)*a^(1/3)*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))*log(d+e*x)/d^3-1/4*a^(2/3)*p*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(b^(2/3)*d)-1/2*a^(1/3)*e*p*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(b^(1/3)*d^2)-1/3*e^2*p*polylog(2,1+b/(a*x^3))/d^3+e^2*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-b^(1/3)*e))/d^3+e^2*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d+(-1)^(1/3)*b^(1/3)*e))/d^3+e^2*p*polylog(2,a^(1/3)*(d+e*x)/(a^(1/3)*d-(-1)^(2/3)*b^(1/3)*e))/d^3-3*e^2*p*polylog(2,1+e*x/d)/d^3-1/2*a^(2/3)*p*arctan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))*sqrt(3)/(b^(2/3)*d)+a^(1/3)*e*p*arctan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))*sqrt(3)/(b^(1/3)*d^2)],

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

# Integrands of the form (f+g x^2)^q Log[c (d+e x^m)^n]

# q>0

# q<0
[log(c*(d+e*x^3)^p)/(f+g*x^2),x,16,arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e*x^3)^p)/(sqrt(f)*sqrt(g))+3*p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(sqrt(f)*sqrt(g))-p*arctan(x*sqrt(g)/sqrt(f))*log(2*(d^(1/3)+e^(1/3)*x)*sqrt(f)*sqrt(g)/((I*e^(1/3)*sqrt(f)+d^(1/3)*sqrt(g))*(sqrt(f)-I*x*sqrt(g))))/(sqrt(f)*sqrt(g))-p*arctan(x*sqrt(g)/sqrt(f))*log(-2*I*((-1)^(2/3)*d^(1/3)+e^(1/3)*x)*sqrt(f)*sqrt(g)/((e^(1/3)*sqrt(f)+(-1)^(1/6)*d^(1/3)*sqrt(g))*(sqrt(f)-I*x*sqrt(g))))/(sqrt(f)*sqrt(g))-p*arctan(x*sqrt(g)/sqrt(f))*log(2*(-1)^(5/6)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)*sqrt(f)*sqrt(g)/((e^(1/3)*sqrt(f)+(-1)^(5/6)*d^(1/3)*sqrt(g))*(sqrt(f)-I*x*sqrt(g))))/(sqrt(f)*sqrt(g))-3/2*I*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(sqrt(f)*sqrt(g))+1/2*I*p*polylog(2,1-2*(d^(1/3)+e^(1/3)*x)*sqrt(f)*sqrt(g)/((I*e^(1/3)*sqrt(f)+d^(1/3)*sqrt(g))*(sqrt(f)-I*x*sqrt(g))))/(sqrt(f)*sqrt(g))+1/2*I*p*polylog(2,1+2*I*((-1)^(2/3)*d^(1/3)+e^(1/3)*x)*sqrt(f)*sqrt(g)/((e^(1/3)*sqrt(f)+(-1)^(1/6)*d^(1/3)*sqrt(g))*(sqrt(f)-I*x*sqrt(g))))/(sqrt(f)*sqrt(g))+1/2*I*p*polylog(2,1-2*(-1)^(5/6)*(d^(1/3)+(-1)^(2/3)*e^(1/3)*x)*sqrt(f)*sqrt(g)/((e^(1/3)*sqrt(f)+(-1)^(5/6)*d^(1/3)*sqrt(g))*(sqrt(f)-I*x*sqrt(g))))/(sqrt(f)*sqrt(g))],
[log(c*(d+e*x^2)^p)/(f+g*x^2),x,12,arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e*x^2)^p)/(sqrt(f)*sqrt(g))+2*p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(sqrt(f)*sqrt(g))-p*arctan(x*sqrt(g)/sqrt(f))*log(-2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/(sqrt(f)*sqrt(g))-p*arctan(x*sqrt(g)/sqrt(f))*log(2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/(sqrt(f)*sqrt(g))-I*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(sqrt(f)*sqrt(g))+1/2*I*p*polylog(2,1+2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/(sqrt(f)*sqrt(g))+1/2*I*p*polylog(2,1-2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/(sqrt(f)*sqrt(g))],
[log(c*(d+e*x)^p)/(f+g*x^2),x,8,1/2*log(c*(d+e*x)^p)*log(e*(sqrt(-f)-x*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/(sqrt(-f)*sqrt(g))-1/2*log(c*(d+e*x)^p)*log(e*(sqrt(-f)+x*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/(sqrt(-f)*sqrt(g))-1/2*p*polylog(2,-(d+e*x)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(sqrt(-f)*sqrt(g))+1/2*p*polylog(2,(d+e*x)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(sqrt(-f)*sqrt(g))],
[log(c*(d+e/x)^p)/(f+g*x^2),x,12,arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e/x)^p)/(sqrt(f)*sqrt(g))+p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(sqrt(f)*sqrt(g))-p*arctan(x*sqrt(g)/sqrt(f))*log(2*(e+d*x)*sqrt(f)*sqrt(g)/((I*d*sqrt(f)+e*sqrt(g))*(sqrt(f)-I*x*sqrt(g))))/(sqrt(f)*sqrt(g))+1/2*I*p*polylog(2,-I*x*sqrt(g)/sqrt(f))/(sqrt(f)*sqrt(g))-1/2*I*p*polylog(2,I*x*sqrt(g)/sqrt(f))/(sqrt(f)*sqrt(g))-1/2*I*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(sqrt(f)*sqrt(g))+1/2*I*p*polylog(2,1-2*(e+d*x)*sqrt(f)*sqrt(g)/((I*d*sqrt(f)+e*sqrt(g))*(sqrt(f)-I*x*sqrt(g))))/(sqrt(f)*sqrt(g))],
[log(c*(d+e/x^2)^p)/(f+g*x^2),x,18,arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e/x^2)^p)/(sqrt(f)*sqrt(g))+2*p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(sqrt(f)*sqrt(g))-p*arctan(x*sqrt(g)/sqrt(f))*log(-2*(-x*sqrt(-d)+sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(-d)*sqrt(f)-sqrt(e)*sqrt(g))))/(sqrt(f)*sqrt(g))-p*arctan(x*sqrt(g)/sqrt(f))*log(2*(x*sqrt(-d)+sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(-d)*sqrt(f)+sqrt(e)*sqrt(g))))/(sqrt(f)*sqrt(g))+I*p*polylog(2,-I*x*sqrt(g)/sqrt(f))/(sqrt(f)*sqrt(g))-I*p*polylog(2,I*x*sqrt(g)/sqrt(f))/(sqrt(f)*sqrt(g))-I*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(sqrt(f)*sqrt(g))+1/2*I*p*polylog(2,1+2*(-x*sqrt(-d)+sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(-d)*sqrt(f)-sqrt(e)*sqrt(g))))/(sqrt(f)*sqrt(g))+1/2*I*p*polylog(2,1-2*(x*sqrt(-d)+sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(-d)*sqrt(f)+sqrt(e)*sqrt(g))))/(sqrt(f)*sqrt(g))],

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

#  {Log[c*(d + e*x^(3/2))^p]/(f + g*x^2), x, 43, (p*Log[-((g^(1/4)*((-1)^(1/3)*d^(1/3) - e^(1/3)*Sqrt[x]))/(e^(1/3)*Sqrt[-Sqrt[-f]] - (-1)^(1/3)*d^(1/3)*g^(1/4)))]*Log[Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) + (p*Log[(g^(1/4)*(d^(1/3) + e^(1/3)*Sqrt[x]))/(e^(1/3)*Sqrt[-Sqrt[-f]] + d^(1/3)*g^(1/4))]*Log[Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) + (p*Log[(g^(1/4)*((-1)^(2/3)*d^(1/3) + e^(1/3)*Sqrt[x]))/(e^(1/3)*Sqrt[-Sqrt[-f]] + (-1)^(2/3)*d^(1/3)*g^(1/4))]*Log[Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (p*Log[-((g^(1/4)*((-1)^(1/3)*d^(1/3) - e^(1/3)*Sqrt[x]))/(e^(1/3)*(-f)^(1/4) - (-1)^(1/3)*d^(1/3)*g^(1/4)))]*Log[(-f)^(1/4) - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (p*Log[(g^(1/4)*(d^(1/3) + e^(1/3)*Sqrt[x]))/(e^(1/3)*(-f)^(1/4) + d^(1/3)*g^(1/4))]*Log[(-f)^(1/4) - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (p*Log[(g^(1/4)*((-1)^(2/3)*d^(1/3) + e^(1/3)*Sqrt[x]))/(e^(1/3)*(-f)^(1/4) + (-1)^(2/3)*d^(1/3)*g^(1/4))]*Log[(-f)^(1/4) - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) + (p*Log[-((g^(1/4)*(d^(1/3) + e^(1/3)*Sqrt[x]))/(e^(1/3)*Sqrt[-Sqrt[-f]] - d^(1/3)*g^(1/4)))]*Log[Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) + (p*Log[-((g^(1/4)*((-1)^(2/3)*d^(1/3) + e^(1/3)*Sqrt[x]))/(e^(1/3)*Sqrt[-Sqrt[-f]] - (-1)^(2/3)*d^(1/3)*g^(1/4)))]*Log[Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) + (p*Log[((-1)^(1/3)*g^(1/4)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*Sqrt[x]))/(e^(1/3)*Sqrt[-Sqrt[-f]] + (-1)^(1/3)*d^(1/3)*g^(1/4))]*Log[Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (p*Log[-((g^(1/4)*(d^(1/3) + e^(1/3)*Sqrt[x]))/(e^(1/3)*(-f)^(1/4) - d^(1/3)*g^(1/4)))]*Log[(-f)^(1/4) + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (p*Log[-((g^(1/4)*((-1)^(2/3)*d^(1/3) + e^(1/3)*Sqrt[x]))/(e^(1/3)*(-f)^(1/4) - (-1)^(2/3)*d^(1/3)*g^(1/4)))]*Log[(-f)^(1/4) + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (p*Log[((-1)^(1/3)*g^(1/4)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*Sqrt[x]))/(e^(1/3)*(-f)^(1/4) + (-1)^(1/3)*d^(1/3)*g^(1/4))]*Log[(-f)^(1/4) + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (Log[Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]]*Log[c*(d + e*x^(3/2))^p])/(2*Sqrt[-f]*Sqrt[g]) + (Log[(-f)^(1/4) - g^(1/4)*Sqrt[x]]*Log[c*(d + e*x^(3/2))^p])/(2*Sqrt[-f]*Sqrt[g]) - (Log[Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]]*Log[c*(d + e*x^(3/2))^p])/(2*Sqrt[-f]*Sqrt[g]) + (Log[(-f)^(1/4) + g^(1/4)*Sqrt[x]]*Log[c*(d + e*x^(3/2))^p])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (e^(1/3)*(Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]))/(e^(1/3)*Sqrt[-Sqrt[-f]] + d^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (e^(1/3)*(Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]))/(e^(1/3)*Sqrt[-Sqrt[-f]] - (-1)^(1/3)*d^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (e^(1/3)*(Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]))/(e^(1/3)*Sqrt[-Sqrt[-f]] + (-1)^(2/3)*d^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (e^(1/3)*((-f)^(1/4) - g^(1/4)*Sqrt[x]))/(e^(1/3)*(-f)^(1/4) + d^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (e^(1/3)*((-f)^(1/4) - g^(1/4)*Sqrt[x]))/(e^(1/3)*(-f)^(1/4) - (-1)^(1/3)*d^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (e^(1/3)*((-f)^(1/4) - g^(1/4)*Sqrt[x]))/(e^(1/3)*(-f)^(1/4) + (-1)^(2/3)*d^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (e^(1/3)*(Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]))/(e^(1/3)*Sqrt[-Sqrt[-f]] - d^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (e^(1/3)*(Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]))/(e^(1/3)*Sqrt[-Sqrt[-f]] + (-1)^(1/3)*d^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (e^(1/3)*(Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]))/(e^(1/3)*Sqrt[-Sqrt[-f]] - (-1)^(2/3)*d^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (e^(1/3)*((-f)^(1/4) + g^(1/4)*Sqrt[x]))/(e^(1/3)*(-f)^(1/4) - d^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (e^(1/3)*((-f)^(1/4) + g^(1/4)*Sqrt[x]))/(e^(1/3)*(-f)^(1/4) + (-1)^(1/3)*d^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (e^(1/3)*((-f)^(1/4) + g^(1/4)*Sqrt[x]))/(e^(1/3)*(-f)^(1/4) - (-1)^(2/3)*d^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g])} 
[log(c*(d+e*x^(1/2))^p)/(f+g*x^2),x,19,1/2*log(c*(d+e*sqrt(x))^p)*log(e*((-f)^(1/4)-g^(1/4)*sqrt(x))/(e*(-f)^(1/4)+d*g^(1/4)))/(sqrt(-f)*sqrt(g))+1/2*log(c*(d+e*sqrt(x))^p)*log(e*((-f)^(1/4)+g^(1/4)*sqrt(x))/(e*(-f)^(1/4)-d*g^(1/4)))/(sqrt(-f)*sqrt(g))-1/2*log(c*(d+e*sqrt(x))^p)*log(e*(g^(1/4)*sqrt(x)+sqrt(-sqrt(-f)))/(-d*g^(1/4)+e*sqrt(-sqrt(-f))))/(sqrt(-f)*sqrt(g))-1/2*log(c*(d+e*sqrt(x))^p)*log(e*(-g^(1/4)*sqrt(x)+sqrt(-sqrt(-f)))/(d*g^(1/4)+e*sqrt(-sqrt(-f))))/(sqrt(-f)*sqrt(g))+1/2*p*polylog(2,-g^(1/4)*(d+e*sqrt(x))/(e*(-f)^(1/4)-d*g^(1/4)))/(sqrt(-f)*sqrt(g))+1/2*p*polylog(2,g^(1/4)*(d+e*sqrt(x))/(e*(-f)^(1/4)+d*g^(1/4)))/(sqrt(-f)*sqrt(g))-1/2*p*polylog(2,-g^(1/4)*(d+e*sqrt(x))/(-d*g^(1/4)+e*sqrt(-sqrt(-f))))/(sqrt(-f)*sqrt(g))-1/2*p*polylog(2,g^(1/4)*(d+e*sqrt(x))/(d*g^(1/4)+e*sqrt(-sqrt(-f))))/(sqrt(-f)*sqrt(g))],
[log(c*(d+e/x^(1/2))^p)/(f+g*x^2),x,20,1/2*log(c*(d+e/sqrt(x))^p)*log(e*(g^(1/4)-(-f)^(1/4)/sqrt(x))/(d*(-f)^(1/4)+e*g^(1/4)))/(sqrt(-f)*sqrt(g))+1/2*log(c*(d+e/sqrt(x))^p)*log(-e*(g^(1/4)+(-f)^(1/4)/sqrt(x))/(d*(-f)^(1/4)-e*g^(1/4)))/(sqrt(-f)*sqrt(g))-1/2*log(c*(d+e/sqrt(x))^p)*log(e*(g^(1/4)-sqrt(-sqrt(-f))/sqrt(x))/(e*g^(1/4)+d*sqrt(-sqrt(-f))))/(sqrt(-f)*sqrt(g))-1/2*log(c*(d+e/sqrt(x))^p)*log(-e*(g^(1/4)+sqrt(-sqrt(-f))/sqrt(x))/(-e*g^(1/4)+d*sqrt(-sqrt(-f))))/(sqrt(-f)*sqrt(g))+1/2*p*polylog(2,(-f)^(1/4)*(d+e/sqrt(x))/(d*(-f)^(1/4)-e*g^(1/4)))/(sqrt(-f)*sqrt(g))+1/2*p*polylog(2,(-f)^(1/4)*(d+e/sqrt(x))/(d*(-f)^(1/4)+e*g^(1/4)))/(sqrt(-f)*sqrt(g))-1/2*p*polylog(2,(d+e/sqrt(x))*sqrt(-sqrt(-f))/(-e*g^(1/4)+d*sqrt(-sqrt(-f))))/(sqrt(-f)*sqrt(g))-1/2*p*polylog(2,(d+e/sqrt(x))*sqrt(-sqrt(-f))/(e*g^(1/4)+d*sqrt(-sqrt(-f))))/(sqrt(-f)*sqrt(g))],

#  {Log[c*(d + e/x^(3/2))^p]/(f + g*x^2), x, 0, -((Log[c*(d + e/x^(3/2))^p]*Log[Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g])) + (p*Log[-((g^(1/4)*((-1)^(1/3)*e^(1/3) - d^(1/3)*Sqrt[x]))/(d^(1/3)*Sqrt[-Sqrt[-f]] - (-1)^(1/3)*e^(1/3)*g^(1/4)))]*Log[Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) + (p*Log[(g^(1/4)*(e^(1/3) + d^(1/3)*Sqrt[x]))/(d^(1/3)*Sqrt[-Sqrt[-f]] + e^(1/3)*g^(1/4))]*Log[Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) + (p*Log[(g^(1/4)*((-1)^(2/3)*e^(1/3) + d^(1/3)*Sqrt[x]))/(d^(1/3)*Sqrt[-Sqrt[-f]] + (-1)^(2/3)*e^(1/3)*g^(1/4))]*Log[Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) + (Log[c*(d + e/x^(3/2))^p]*Log[(-f)^(1/4) - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (p*Log[-((g^(1/4)*((-1)^(1/3)*e^(1/3) - d^(1/3)*Sqrt[x]))/(d^(1/3)*(-f)^(1/4) - (-1)^(1/3)*e^(1/3)*g^(1/4)))]*Log[(-f)^(1/4) - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (p*Log[(g^(1/4)*(e^(1/3) + d^(1/3)*Sqrt[x]))/(d^(1/3)*(-f)^(1/4) + e^(1/3)*g^(1/4))]*Log[(-f)^(1/4) - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (p*Log[(g^(1/4)*((-1)^(2/3)*e^(1/3) + d^(1/3)*Sqrt[x]))/(d^(1/3)*(-f)^(1/4) + (-1)^(2/3)*e^(1/3)*g^(1/4))]*Log[(-f)^(1/4) - g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (Log[c*(d + e/x^(3/2))^p]*Log[Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) + (p*Log[-((g^(1/4)*(e^(1/3) + d^(1/3)*Sqrt[x]))/(d^(1/3)*Sqrt[-Sqrt[-f]] - e^(1/3)*g^(1/4)))]*Log[Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) + (p*Log[-((g^(1/4)*((-1)^(2/3)*e^(1/3) + d^(1/3)*Sqrt[x]))/(d^(1/3)*Sqrt[-Sqrt[-f]] - (-1)^(2/3)*e^(1/3)*g^(1/4)))]*Log[Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) + (p*Log[((-1)^(1/3)*g^(1/4)*(e^(1/3) + (-1)^(2/3)*d^(1/3)*Sqrt[x]))/(d^(1/3)*Sqrt[-Sqrt[-f]] + (-1)^(1/3)*e^(1/3)*g^(1/4))]*Log[Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) + (Log[c*(d + e/x^(3/2))^p]*Log[(-f)^(1/4) + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (p*Log[-((g^(1/4)*(e^(1/3) + d^(1/3)*Sqrt[x]))/(d^(1/3)*(-f)^(1/4) - e^(1/3)*g^(1/4)))]*Log[(-f)^(1/4) + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (p*Log[-((g^(1/4)*((-1)^(2/3)*e^(1/3) + d^(1/3)*Sqrt[x]))/(d^(1/3)*(-f)^(1/4) - (-1)^(2/3)*e^(1/3)*g^(1/4)))]*Log[(-f)^(1/4) + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (p*Log[((-1)^(1/3)*g^(1/4)*(e^(1/3) + (-1)^(2/3)*d^(1/3)*Sqrt[x]))/(d^(1/3)*(-f)^(1/4) + (-1)^(1/3)*e^(1/3)*g^(1/4))]*Log[(-f)^(1/4) + g^(1/4)*Sqrt[x]])/(2*Sqrt[-f]*Sqrt[g]) - (3*p*Log[Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]]*Log[-((g^(1/4)*Sqrt[x])/Sqrt[-Sqrt[-f]])])/(2*Sqrt[-f]*Sqrt[g]) - (3*p*Log[Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]]*Log[(g^(1/4)*Sqrt[x])/Sqrt[-Sqrt[-f]]])/(2*Sqrt[-f]*Sqrt[g]) + (3*p*Log[(-f)^(1/4) + g^(1/4)*Sqrt[x]]*Log[-((g^(1/4)*Sqrt[x])/(-f)^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (3*p*Log[(-f)^(1/4) - g^(1/4)*Sqrt[x]]*Log[(g^(1/4)*Sqrt[x])/(-f)^(1/4)])/(2*Sqrt[-f]*Sqrt[g]) - (3*p*PolyLog[2, (Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x])/Sqrt[-Sqrt[-f]]])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (d^(1/3)*(Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]))/(d^(1/3)*Sqrt[-Sqrt[-f]] + e^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (d^(1/3)*(Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]))/(d^(1/3)*Sqrt[-Sqrt[-f]] - (-1)^(1/3)*e^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (d^(1/3)*(Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]))/(d^(1/3)*Sqrt[-Sqrt[-f]] + (-1)^(2/3)*e^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (3*p*PolyLog[2, ((-f)^(1/4) - g^(1/4)*Sqrt[x])/(-f)^(1/4)])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (d^(1/3)*((-f)^(1/4) - g^(1/4)*Sqrt[x]))/(d^(1/3)*(-f)^(1/4) + e^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (d^(1/3)*((-f)^(1/4) - g^(1/4)*Sqrt[x]))/(d^(1/3)*(-f)^(1/4) - (-1)^(1/3)*e^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (d^(1/3)*((-f)^(1/4) - g^(1/4)*Sqrt[x]))/(d^(1/3)*(-f)^(1/4) + (-1)^(2/3)*e^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) - (3*p*PolyLog[2, (Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x])/Sqrt[-Sqrt[-f]]])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (d^(1/3)*(Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]))/(d^(1/3)*Sqrt[-Sqrt[-f]] - e^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (d^(1/3)*(Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]))/(d^(1/3)*Sqrt[-Sqrt[-f]] + (-1)^(1/3)*e^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (d^(1/3)*(Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]))/(d^(1/3)*Sqrt[-Sqrt[-f]] - (-1)^(2/3)*e^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (3*p*PolyLog[2, ((-f)^(1/4) + g^(1/4)*Sqrt[x])/(-f)^(1/4)])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (d^(1/3)*((-f)^(1/4) + g^(1/4)*Sqrt[x]))/(d^(1/3)*(-f)^(1/4) - e^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (d^(1/3)*((-f)^(1/4) + g^(1/4)*Sqrt[x]))/(d^(1/3)*(-f)^(1/4) + (-1)^(1/3)*e^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (d^(1/3)*((-f)^(1/4) + g^(1/4)*Sqrt[x]))/(d^(1/3)*(-f)^(1/4) - (-1)^(2/3)*e^(1/3)*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g])} 

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

# p>0
[(f+g*x^2)^3*log(c*(d+e*x^2)^p),x,17,-2*f^3*p*x+2*d*f^2*g*p*x/e-6/5*d^2*f*g^2*p*x/e^2+2/7*d^3*g^3*p*x/e^3-2/3*f^2*g*p*x^3+2/5*d*f*g^2*p*x^3/e-2/21*d^2*g^3*p*x^3/e^2-6/25*f*g^2*p*x^5+2/35*d*g^3*p*x^5/e-2/49*g^3*p*x^7-2*d^(3/2)*f^2*g*p*arctan(x*sqrt(e)/sqrt(d))/e^(3/2)+6/5*d^(5/2)*f*g^2*p*arctan(x*sqrt(e)/sqrt(d))/e^(5/2)-2/7*d^(7/2)*g^3*p*arctan(x*sqrt(e)/sqrt(d))/e^(7/2)+f^3*x*log(c*(d+e*x^2)^p)+f^2*g*x^3*log(c*(d+e*x^2)^p)+3/5*f*g^2*x^5*log(c*(d+e*x^2)^p)+1/7*g^3*x^7*log(c*(d+e*x^2)^p)+2*f^3*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)],
[(f+g*x^2)^2*log(c*(d+e*x^2)^p),x,13,-2*f^2*p*x+4/3*d*f*g*p*x/e-2/5*d^2*g^2*p*x/e^2-4/9*f*g*p*x^3+2/15*d*g^2*p*x^3/e-2/25*g^2*p*x^5-4/3*d^(3/2)*f*g*p*arctan(x*sqrt(e)/sqrt(d))/e^(3/2)+2/5*d^(5/2)*g^2*p*arctan(x*sqrt(e)/sqrt(d))/e^(5/2)+f^2*x*log(c*(d+e*x^2)^p)+2/3*f*g*x^3*log(c*(d+e*x^2)^p)+1/5*g^2*x^5*log(c*(d+e*x^2)^p)+2*f^2*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)],
[(f+g*x^2)*log(c*(d+e*x^2)^p),x,9,-2*f*p*x+2/3*d*g*p*x/e-2/9*g*p*x^3-2/3*d^(3/2)*g*p*arctan(x*sqrt(e)/sqrt(d))/e^(3/2)+f*x*log(c*(d+e*x^2)^p)+1/3*g*x^3*log(c*(d+e*x^2)^p)+2*f*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)],
[log(c*(d+e*x^2)^p)/(f+g*x^2),x,12,arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e*x^2)^p)/(sqrt(f)*sqrt(g))+2*p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(sqrt(f)*sqrt(g))-p*arctan(x*sqrt(g)/sqrt(f))*log(-2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/(sqrt(f)*sqrt(g))-p*arctan(x*sqrt(g)/sqrt(f))*log(2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/(sqrt(f)*sqrt(g))-I*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(sqrt(f)*sqrt(g))+1/2*I*p*polylog(2,1+2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/(sqrt(f)*sqrt(g))+1/2*I*p*polylog(2,1-2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/(sqrt(f)*sqrt(g))],
[log(c*(d+e*x^2)^p)/(f+g*x^2)^2,x,26,p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)*sqrt(e)/(f*(e*f-d*g))+1/2*arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e*x^2)^p)/(f^(3/2)*sqrt(g))+p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(f^(3/2)*sqrt(g))-1/2*p*arctan(x*sqrt(g)/sqrt(f))*log(-2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/(f^(3/2)*sqrt(g))-1/2*p*arctan(x*sqrt(g)/sqrt(f))*log(2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/(f^(3/2)*sqrt(g))-1/2*I*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(f^(3/2)*sqrt(g))+1/4*I*p*polylog(2,1+2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/(f^(3/2)*sqrt(g))+1/4*I*p*polylog(2,1-2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/(f^(3/2)*sqrt(g))-1/2*e*p*log(sqrt(-f)-x*sqrt(g))/((e*f-d*g)*sqrt(-f)*sqrt(g))+1/2*e*p*log(sqrt(-f)+x*sqrt(g))/((e*f-d*g)*sqrt(-f)*sqrt(g))-1/4*log(c*(d+e*x^2)^p)/(f*sqrt(g)*(sqrt(-f)-x*sqrt(g)))+1/4*log(c*(d+e*x^2)^p)/(f*sqrt(g)*(sqrt(-f)+x*sqrt(g)))],
[(f+g*x^2)^2*log(c*(d+e*x^2)^p)^2,x,50,8*f^2*p^2*x-64/9*d*f*g*p^2*x/e+184/75*d^2*g^2*p^2*x/e^2+16/27*f*g*p^2*x^3-64/225*d*g^2*p^2*x^3/e+8/125*g^2*p^2*x^5+64/9*d^(3/2)*f*g*p^2*arctan(x*sqrt(e)/sqrt(d))/e^(3/2)-184/75*d^(5/2)*g^2*p^2*arctan(x*sqrt(e)/sqrt(d))/e^(5/2)-8/3*I*d^(3/2)*f*g*p^2*arctan(x*sqrt(e)/sqrt(d))^2/e^(3/2)+4/5*I*d^(5/2)*g^2*p^2*arctan(x*sqrt(e)/sqrt(d))^2/e^(5/2)-4*f^2*p*x*log(c*(d+e*x^2)^p)+8/3*d*f*g*p*x*log(c*(d+e*x^2)^p)/e-4/5*d^2*g^2*p*x*log(c*(d+e*x^2)^p)/e^2-8/9*f*g*p*x^3*log(c*(d+e*x^2)^p)+4/15*d*g^2*p*x^3*log(c*(d+e*x^2)^p)/e-4/25*g^2*p*x^5*log(c*(d+e*x^2)^p)-8/3*d^(3/2)*f*g*p*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)/e^(3/2)+4/5*d^(5/2)*g^2*p*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)/e^(5/2)+f^2*x*log(c*(d+e*x^2)^p)^2+2/3*f*g*x^3*log(c*(d+e*x^2)^p)^2+1/5*g^2*x^5*log(c*(d+e*x^2)^p)^2-16/3*d^(3/2)*f*g*p^2*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(3/2)+8/5*d^(5/2)*g^2*p^2*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(5/2)-8/3*I*d^(3/2)*f*g*p^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(3/2)+4/5*I*d^(5/2)*g^2*p^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(5/2)-8*f^2*p^2*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)+4*I*f^2*p^2*arctan(x*sqrt(e)/sqrt(d))^2*sqrt(d)/sqrt(e)+4*f^2*p*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)*sqrt(d)/sqrt(e)+8*f^2*p^2*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)+4*I*f^2*p^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)],
[(f+g*x^2)*log(c*(d+e*x^2)^p)^2,x,30,8*f*p^2*x-32/9*d*g*p^2*x/e+8/27*g*p^2*x^3+32/9*d^(3/2)*g*p^2*arctan(x*sqrt(e)/sqrt(d))/e^(3/2)-4/3*I*d^(3/2)*g*p^2*arctan(x*sqrt(e)/sqrt(d))^2/e^(3/2)-4*f*p*x*log(c*(d+e*x^2)^p)+4/3*d*g*p*x*log(c*(d+e*x^2)^p)/e-4/9*g*p*x^3*log(c*(d+e*x^2)^p)-4/3*d^(3/2)*g*p*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)/e^(3/2)+f*x*log(c*(d+e*x^2)^p)^2+1/3*g*x^3*log(c*(d+e*x^2)^p)^2-8/3*d^(3/2)*g*p^2*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(3/2)-4/3*I*d^(3/2)*g*p^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(3/2)-8*f*p^2*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)+4*I*f*p^2*arctan(x*sqrt(e)/sqrt(d))^2*sqrt(d)/sqrt(e)+4*f*p*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)*sqrt(d)/sqrt(e)+8*f*p^2*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)+4*I*f*p^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)],
[log(c*(d+e*x^2)^p)^2/(f+g*x^2),x,0,Unintegrable(log(c*(d+e*x^2)^p)^2/(f+g*x^2),x)],
[log(c*(d+e*x^2)^p)^2/(f+g*x^2)^2,x,0,Unintegrable(log(c*(d+e*x^2)^p)^2/(f+g*x^2)^2,x)],
[(f+g*x^2)*log(c*(d+e*x^2)^p)^3,x,48,-48*f*p^3*x+208/9*d*g*p^3*x/e-16/27*g*p^3*x^3-208/9*d^(3/2)*g*p^3*arctan(x*sqrt(e)/sqrt(d))/e^(3/2)+32/3*I*d^(3/2)*g*p^3*arctan(x*sqrt(e)/sqrt(d))^2/e^(3/2)+24*f*p^2*x*log(c*(d+e*x^2)^p)-32/3*d*g*p^2*x*log(c*(d+e*x^2)^p)/e+8/9*g*p^2*x^3*log(c*(d+e*x^2)^p)+32/3*d^(3/2)*g*p^2*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)/e^(3/2)-6*f*p*x*log(c*(d+e*x^2)^p)^2+2*d*g*p*x*log(c*(d+e*x^2)^p)^2/e-2/3*g*p*x^3*log(c*(d+e*x^2)^p)^2+f*x*log(c*(d+e*x^2)^p)^3+1/3*g*x^3*log(c*(d+e*x^2)^p)^3+64/3*d^(3/2)*g*p^3*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(3/2)+32/3*I*d^(3/2)*g*p^3*polylog(2,(-sqrt(d)+I*x*sqrt(e))/(sqrt(d)+I*x*sqrt(e)))/e^(3/2)+48*f*p^3*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)-24*I*f*p^3*arctan(x*sqrt(e)/sqrt(d))^2*sqrt(d)/sqrt(e)-24*f*p^2*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)*sqrt(d)/sqrt(e)-48*f*p^3*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)-24*I*f*p^3*polylog(2,(-sqrt(d)+I*x*sqrt(e))/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)-2*d*(-3*e*f+d*g)*p*Unintegrable(log(c*(d+e*x^2)^p)^2/(d+e*x^2),x)/e,-48*f*p^3*x+208/9*d*g*p^3*x/e-16/27*g*p^3*x^3-208/9*d^(3/2)*g*p^3*arctan(x*sqrt(e)/sqrt(d))/e^(3/2)+32/3*I*d^(3/2)*g*p^3*arctan(x*sqrt(e)/sqrt(d))^2/e^(3/2)+24*f*p^2*x*log(c*(d+e*x^2)^p)-32/3*d*g*p^2*x*log(c*(d+e*x^2)^p)/e+8/9*g*p^2*x^3*log(c*(d+e*x^2)^p)+32/3*d^(3/2)*g*p^2*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)/e^(3/2)-6*f*p*x*log(c*(d+e*x^2)^p)^2+2*d*g*p*x*log(c*(d+e*x^2)^p)^2/e-2/3*g*p*x^3*log(c*(d+e*x^2)^p)^2+f*x*log(c*(d+e*x^2)^p)^3+1/3*g*x^3*log(c*(d+e*x^2)^p)^3+64/3*d^(3/2)*g*p^3*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(3/2)+32/3*I*d^(3/2)*g*p^3*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(3/2)+48*f*p^3*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)-24*I*f*p^3*arctan(x*sqrt(e)/sqrt(d))^2*sqrt(d)/sqrt(e)-24*f*p^2*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)*sqrt(d)/sqrt(e)-48*f*p^3*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)-24*I*f*p^3*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)+6*d*f*p*Unintegrable(log(c*(d+e*x^2)^p)^2/(d+e*x^2),x)-2*d^2*g*p*Unintegrable(log(c*(d+e*x^2)^p)^2/(d+e*x^2),x)/e],
[log(c*(d+e*x^2)^p)^3/(f+g*x^2),x,0,Unintegrable(log(c*(d+e*x^2)^p)^3/(f+g*x^2),x)],
[log(c*(d+e*x^2)^p)^3/(f+g*x^2)^2,x,0,Unintegrable(log(c*(d+e*x^2)^p)^3/(f+g*x^2)^2,x)],

# p<0
[(f+g*x^2)^2/log(c*(d+e*x^2)^p),x,0,Unintegrable((f+g*x^2)^2/log(c*(d+e*x^2)^p),x)],
[(f+g*x^2)/log(c*(d+e*x^2)^p),x,0,Unintegrable((f+g*x^2)/log(c*(d+e*x^2)^p),x)],
[1/((f+g*x^2)*log(c*(d+e*x^2)^p)),x,0,Unintegrable(1/((f+g*x^2)*log(c*(d+e*x^2)^p)),x)],
[1/((f+g*x^2)^2*log(c*(d+e*x^2)^p)),x,0,Unintegrable(1/((f+g*x^2)^2*log(c*(d+e*x^2)^p)),x)],
[(f+g*x^2)^2/log(c*(d+e*x^2)^p)^2,x,0,Unintegrable((f+g*x^2)^2/log(c*(d+e*x^2)^p)^2,x)],
[(f+g*x^2)/log(c*(d+e*x^2)^p)^2,x,0,Unintegrable((f+g*x^2)/log(c*(d+e*x^2)^p)^2,x)],
[1/((f+g*x^2)*log(c*(d+e*x^2)^p)^2),x,0,Unintegrable(1/((f+g*x^2)*log(c*(d+e*x^2)^p)^2),x)],
[1/((f+g*x^2)^2*log(c*(d+e*x^2)^p)^2),x,0,Unintegrable(1/((f+g*x^2)^2*log(c*(d+e*x^2)^p)^2),x)],

# Integrands of the form (f+g x^3)^q Log[c (d+e x^2)^n]^p

# p>0
[(f+g*x^3)^3*log(c*(d+e*x^2)^p),x,17,-2*f^3*p*x+6/7*d^3*f*g^2*p*x/e^3+3/4*d*f^2*g*p*x^2/e-1/10*d^4*g^3*p*x^2/e^4-2/7*d^2*f*g^2*p*x^3/e^2-3/8*f^2*g*p*x^4+1/20*d^3*g^3*p*x^4/e^3+6/35*d*f*g^2*p*x^5/e-1/30*d^2*g^3*p*x^6/e^2-6/49*f*g^2*p*x^7+1/40*d*g^3*p*x^8/e-1/50*g^3*p*x^10-6/7*d^(7/2)*f*g^2*p*arctan(x*sqrt(e)/sqrt(d))/e^(7/2)-3/4*d^2*f^2*g*p*log(d+e*x^2)/e^2+1/10*d^5*g^3*p*log(d+e*x^2)/e^5+f^3*x*log(c*(d+e*x^2)^p)+3/4*f^2*g*x^4*log(c*(d+e*x^2)^p)+3/7*f*g^2*x^7*log(c*(d+e*x^2)^p)+1/10*g^3*x^10*log(c*(d+e*x^2)^p)+2*f^3*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)],
[(f+g*x^3)^2*log(c*(d+e*x^2)^p),x,13,-2*f^2*p*x+2/7*d^3*g^2*p*x/e^3+1/2*d*f*g*p*x^2/e-2/21*d^2*g^2*p*x^3/e^2-1/4*f*g*p*x^4+2/35*d*g^2*p*x^5/e-2/49*g^2*p*x^7-2/7*d^(7/2)*g^2*p*arctan(x*sqrt(e)/sqrt(d))/e^(7/2)-1/2*d^2*f*g*p*log(d+e*x^2)/e^2+f^2*x*log(c*(d+e*x^2)^p)+1/2*f*g*x^4*log(c*(d+e*x^2)^p)+1/7*g^2*x^7*log(c*(d+e*x^2)^p)+2*f^2*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)],
[(f+g*x^3)*log(c*(d+e*x^2)^p),x,9,-2*f*p*x+1/4*d*g*p*x^2/e-1/8*g*p*x^4-1/4*d^2*g*p*log(d+e*x^2)/e^2+f*x*log(c*(d+e*x^2)^p)+1/4*g*x^4*log(c*(d+e*x^2)^p)+2*f*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)],
[log(c*(d+e*x^2)^p)/(f+g*x^3),x,29,1/3*log(-f^(1/3)-g^(1/3)*x)*log(c*(d+e*x^2)^p)/(f^(2/3)*g^(1/3))+1/3*(-1)^(2/3)*log(-f^(1/3)+(-1)^(1/3)*g^(1/3)*x)*log(c*(d+e*x^2)^p)/(f^(2/3)*g^(1/3))-1/3*(-1)^(1/3)*log(-f^(1/3)-(-1)^(2/3)*g^(1/3)*x)*log(c*(d+e*x^2)^p)/(f^(2/3)*g^(1/3))-1/3*p*log(-f^(1/3)-g^(1/3)*x)*log(g^(1/3)*(sqrt(-d)-x*sqrt(e))/(g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(2/3)*g^(1/3))-1/3*(-1)^(2/3)*p*log(-f^(1/3)+(-1)^(1/3)*g^(1/3)*x)*log(-(-1)^(1/3)*g^(1/3)*(sqrt(-d)-x*sqrt(e))/(-(-1)^(1/3)*g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(2/3)*g^(1/3))+1/3*(-1)^(1/3)*p*log(-f^(1/3)-(-1)^(2/3)*g^(1/3)*x)*log((-1)^(2/3)*g^(1/3)*(sqrt(-d)-x*sqrt(e))/((-1)^(2/3)*g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(2/3)*g^(1/3))-1/3*p*log(-f^(1/3)-g^(1/3)*x)*log(-g^(1/3)*(sqrt(-d)+x*sqrt(e))/(-g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(2/3)*g^(1/3))-1/3*(-1)^(2/3)*p*log(-f^(1/3)+(-1)^(1/3)*g^(1/3)*x)*log((-1)^(1/3)*g^(1/3)*(sqrt(-d)+x*sqrt(e))/((-1)^(1/3)*g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(2/3)*g^(1/3))+1/3*(-1)^(1/3)*p*log(-f^(1/3)-(-1)^(2/3)*g^(1/3)*x)*log(-(-1)^(2/3)*g^(1/3)*(sqrt(-d)+x*sqrt(e))/(-(-1)^(2/3)*g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(2/3)*g^(1/3))-1/3*p*polylog(2,(f^(1/3)+g^(1/3)*x)*sqrt(e)/(-g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(2/3)*g^(1/3))-1/3*p*polylog(2,(f^(1/3)+g^(1/3)*x)*sqrt(e)/(g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(2/3)*g^(1/3))-1/3*(-1)^(2/3)*p*polylog(2,(f^(1/3)-(-1)^(1/3)*g^(1/3)*x)*sqrt(e)/(-(-1)^(1/3)*g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(2/3)*g^(1/3))-1/3*(-1)^(2/3)*p*polylog(2,(f^(1/3)-(-1)^(1/3)*g^(1/3)*x)*sqrt(e)/((-1)^(1/3)*g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(2/3)*g^(1/3))+1/3*(-1)^(1/3)*p*polylog(2,(f^(1/3)+(-1)^(2/3)*g^(1/3)*x)*sqrt(e)/(-(-1)^(2/3)*g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(2/3)*g^(1/3))+1/3*(-1)^(1/3)*p*polylog(2,(f^(1/3)+(-1)^(2/3)*g^(1/3)*x)*sqrt(e)/((-1)^(2/3)*g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(2/3)*g^(1/3))],
[log(c*(d+e*x^2)^p)/(f+g*x^3)^2,x,47,-2/9*e*p*log(f^(1/3)+g^(1/3)*x)/(f*(e*f^(2/3)+d*g^(2/3))*g^(1/3))+2*(-1)^(1/3)*e*p*log(f^(1/3)-(-1)^(1/3)*g^(1/3)*x)/((1+(-1)^(1/3))^4*f*(e*f^(2/3)+(-1)^(2/3)*d*g^(2/3))*g^(1/3))+1/9*e*p*log(d+e*x^2)/(f*(e*f^(2/3)+d*g^(2/3))*g^(1/3))-(-1)^(1/3)*e*p*log(d+e*x^2)/((1+(-1)^(1/3))^4*f*(e*f^(2/3)+(-1)^(2/3)*d*g^(2/3))*g^(1/3))-1/9*log(c*(d+e*x^2)^p)/(f^(4/3)*g^(1/3)*(f^(1/3)+g^(1/3)*x))-log(c*(d+e*x^2)^p)/((1+(-1)^(1/3))^4*f^(4/3)*g^(1/3)*((-1)^(2/3)*f^(1/3)+g^(1/3)*x))+1/9*(-1)^(1/3)*log(c*(d+e*x^2)^p)/(f^(4/3)*g^(1/3)*(f^(1/3)+(-1)^(2/3)*g^(1/3)*x))+2/9*log(f^(1/3)+g^(1/3)*x)*log(c*(d+e*x^2)^p)/(f^(5/3)*g^(1/3))-2/9*p*log(f^(1/3)+g^(1/3)*x)*log(g^(1/3)*(sqrt(-d)-x*sqrt(e))/(g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(5/3)*g^(1/3))-2/9*p*log(f^(1/3)+g^(1/3)*x)*log(-g^(1/3)*(sqrt(-d)+x*sqrt(e))/(-g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(5/3)*g^(1/3))-2/9*p*polylog(2,(f^(1/3)+g^(1/3)*x)*sqrt(e)/(-g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(5/3)*g^(1/3))-2/9*p*polylog(2,(f^(1/3)+g^(1/3)*x)*sqrt(e)/(g^(1/3)*sqrt(-d)+f^(1/3)*sqrt(e)))/(f^(5/3)*g^(1/3))+4/9*(-1)^(1/3)*e*p*log(f^(1/3)+(-1)^(2/3)*g^(1/3)*x)/(f*g^(1/3)*(2*e*f^(2/3)-d*g^(2/3)*(1+I*sqrt(3))))-2/9*(-1)^(1/3)*e*p*log(d+e*x^2)/(f*g^(1/3)*(2*e*f^(2/3)-d*g^(2/3)*(1+I*sqrt(3))))-4/9*log(c*(d+e*x^2)^p)*log(2*f^(1/3)-g^(1/3)*x*(1-I*sqrt(3)))/(f^(5/3)*g^(1/3)*(1-I*sqrt(3)))+4/9*p*log(2*f^(1/3)-g^(1/3)*x*(1-I*sqrt(3)))*log(-g^(1/3)*(I+sqrt(3))*(sqrt(-d)-x*sqrt(e))/(-g^(1/3)*(I+sqrt(3))*sqrt(-d)+2*I*f^(1/3)*sqrt(e)))/(f^(5/3)*g^(1/3)*(1-I*sqrt(3)))+4/9*p*log(2*f^(1/3)-g^(1/3)*x*(1-I*sqrt(3)))*log(g^(1/3)*(I+sqrt(3))*(sqrt(-d)+x*sqrt(e))/(g^(1/3)*(I+sqrt(3))*sqrt(-d)+2*I*f^(1/3)*sqrt(e)))/(f^(5/3)*g^(1/3)*(1-I*sqrt(3)))+4/9*p*polylog(2,(2*f^(1/3)-g^(1/3)*x*(1-I*sqrt(3)))*sqrt(e)/(g^(1/3)*(1-I*sqrt(3))*sqrt(-d)+2*f^(1/3)*sqrt(e)))/(f^(5/3)*g^(1/3)*(1-I*sqrt(3)))+4/9*p*polylog(2,(2*f^(1/3)-g^(1/3)*x*(1-I*sqrt(3)))*sqrt(e)/(I*g^(1/3)*(I+sqrt(3))*sqrt(-d)+2*f^(1/3)*sqrt(e)))/(f^(5/3)*g^(1/3)*(1-I*sqrt(3)))-4/9*log(c*(d+e*x^2)^p)*log(2*f^(1/3)-g^(1/3)*x*(1+I*sqrt(3)))/(f^(5/3)*g^(1/3)*(1+I*sqrt(3)))+4/9*p*log(2*f^(1/3)-g^(1/3)*x*(1+I*sqrt(3)))*log(-g^(1/3)*(1+I*sqrt(3))*(sqrt(-d)-x*sqrt(e))/(-g^(1/3)*(1+I*sqrt(3))*sqrt(-d)+2*f^(1/3)*sqrt(e)))/(f^(5/3)*g^(1/3)*(1+I*sqrt(3)))+4/9*p*log(2*f^(1/3)-g^(1/3)*x*(1+I*sqrt(3)))*log(g^(1/3)*(1+I*sqrt(3))*(sqrt(-d)+x*sqrt(e))/(g^(1/3)*(1+I*sqrt(3))*sqrt(-d)+2*f^(1/3)*sqrt(e)))/(f^(5/3)*g^(1/3)*(1+I*sqrt(3)))+4/9*p*polylog(2,(2*f^(1/3)-g^(1/3)*x*(1+I*sqrt(3)))*sqrt(e)/(-g^(1/3)*(1+I*sqrt(3))*sqrt(-d)+2*f^(1/3)*sqrt(e)))/(f^(5/3)*g^(1/3)*(1+I*sqrt(3)))+4/9*p*polylog(2,(2*f^(1/3)-g^(1/3)*x*(1+I*sqrt(3)))*sqrt(e)/(g^(1/3)*(1+I*sqrt(3))*sqrt(-d)+2*f^(1/3)*sqrt(e)))/(f^(5/3)*g^(1/3)*(1+I*sqrt(3)))+2/9*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)*sqrt(e)/(f^(4/3)*(e*f^(2/3)+d*g^(2/3)))+2*(-1)^(2/3)*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)*sqrt(e)/((1+(-1)^(1/3))^4*f^(4/3)*(e*f^(2/3)+(-1)^(2/3)*d*g^(2/3)))+4/9*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)*sqrt(e)/(f^(4/3)*(2*e*f^(2/3)-d*g^(2/3)*(1+I*sqrt(3))))],
[(f+g*x^3)^3*log(c*(d+e*x^2)^p)^2,x,55,8*f^3*p^2*x-1408/245*d^3*f*g^2*p^2*x/e^3-3*d*f^2*g*p^2*x^2/e+d^4*g^3*p^2*x^2/e^4+568/735*d^2*f*g^2*p^2*x^3/e^2-288/1225*d*f*g^2*p^2*x^5/e+24/343*f*g^2*p^2*x^7+3/8*f^2*g*p^2*(d+e*x^2)^2/e^2-1/2*d^3*g^3*p^2*(d+e*x^2)^2/e^5+2/9*d^2*g^3*p^2*(d+e*x^2)^3/e^5-1/16*d*g^3*p^2*(d+e*x^2)^4/e^5+1/125*g^3*p^2*(d+e*x^2)^5/e^5+1408/245*d^(7/2)*f*g^2*p^2*arctan(x*sqrt(e)/sqrt(d))/e^(7/2)-12/7*I*d^(7/2)*f*g^2*p^2*arctan(x*sqrt(e)/sqrt(d))^2/e^(7/2)-1/10*d^5*g^3*p^2*log(d+e*x^2)^2/e^5-4*f^3*p*x*log(c*(d+e*x^2)^p)+12/7*d^3*f*g^2*p*x*log(c*(d+e*x^2)^p)/e^3-4/7*d^2*f*g^2*p*x^3*log(c*(d+e*x^2)^p)/e^2+12/35*d*f*g^2*p*x^5*log(c*(d+e*x^2)^p)/e-12/49*f*g^2*p*x^7*log(c*(d+e*x^2)^p)+3*d*f^2*g*p*(d+e*x^2)*log(c*(d+e*x^2)^p)/e^2-d^4*g^3*p*(d+e*x^2)*log(c*(d+e*x^2)^p)/e^5-3/4*f^2*g*p*(d+e*x^2)^2*log(c*(d+e*x^2)^p)/e^2+d^3*g^3*p*(d+e*x^2)^2*log(c*(d+e*x^2)^p)/e^5-2/3*d^2*g^3*p*(d+e*x^2)^3*log(c*(d+e*x^2)^p)/e^5+1/4*d*g^3*p*(d+e*x^2)^4*log(c*(d+e*x^2)^p)/e^5-1/25*g^3*p*(d+e*x^2)^5*log(c*(d+e*x^2)^p)/e^5-12/7*d^(7/2)*f*g^2*p*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)/e^(7/2)+1/5*d^5*g^3*p*log(d+e*x^2)*log(c*(d+e*x^2)^p)/e^5+f^3*x*log(c*(d+e*x^2)^p)^2+3/7*f*g^2*x^7*log(c*(d+e*x^2)^p)^2+1/10*g^3*x^10*log(c*(d+e*x^2)^p)^2-3/2*d*f^2*g*(d+e*x^2)*log(c*(d+e*x^2)^p)^2/e^2+3/4*f^2*g*(d+e*x^2)^2*log(c*(d+e*x^2)^p)^2/e^2-24/7*d^(7/2)*f*g^2*p^2*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(7/2)-12/7*I*d^(7/2)*f*g^2*p^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(7/2)-8*f^3*p^2*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)+4*I*f^3*p^2*arctan(x*sqrt(e)/sqrt(d))^2*sqrt(d)/sqrt(e)+4*f^3*p*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)*sqrt(d)/sqrt(e)+8*f^3*p^2*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)+4*I*f^3*p^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)],
[(f+g*x^3)^2*log(c*(d+e*x^2)^p)^2,x,47,8*f^2*p^2*x-1408/735*d^3*g^2*p^2*x/e^3-2*d*f*g*p^2*x^2/e+568/2205*d^2*g^2*p^2*x^3/e^2-96/1225*d*g^2*p^2*x^5/e+8/343*g^2*p^2*x^7+1/4*f*g*p^2*(d+e*x^2)^2/e^2+1408/735*d^(7/2)*g^2*p^2*arctan(x*sqrt(e)/sqrt(d))/e^(7/2)-4/7*I*d^(7/2)*g^2*p^2*arctan(x*sqrt(e)/sqrt(d))^2/e^(7/2)-4*f^2*p*x*log(c*(d+e*x^2)^p)+4/7*d^3*g^2*p*x*log(c*(d+e*x^2)^p)/e^3-4/21*d^2*g^2*p*x^3*log(c*(d+e*x^2)^p)/e^2+4/35*d*g^2*p*x^5*log(c*(d+e*x^2)^p)/e-4/49*g^2*p*x^7*log(c*(d+e*x^2)^p)+2*d*f*g*p*(d+e*x^2)*log(c*(d+e*x^2)^p)/e^2-1/2*f*g*p*(d+e*x^2)^2*log(c*(d+e*x^2)^p)/e^2-4/7*d^(7/2)*g^2*p*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)/e^(7/2)+f^2*x*log(c*(d+e*x^2)^p)^2+1/7*g^2*x^7*log(c*(d+e*x^2)^p)^2-d*f*g*(d+e*x^2)*log(c*(d+e*x^2)^p)^2/e^2+1/2*f*g*(d+e*x^2)^2*log(c*(d+e*x^2)^p)^2/e^2-8/7*d^(7/2)*g^2*p^2*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(7/2)-4/7*I*d^(7/2)*g^2*p^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(7/2)-8*f^2*p^2*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)+4*I*f^2*p^2*arctan(x*sqrt(e)/sqrt(d))^2*sqrt(d)/sqrt(e)+4*f^2*p*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)*sqrt(d)/sqrt(e)+8*f^2*p^2*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)+4*I*f^2*p^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)],
[(f+g*x^3)*log(c*(d+e*x^2)^p)^2,x,23,8*f*p^2*x-d*g*p^2*x^2/e+1/8*g*p^2*(d+e*x^2)^2/e^2-4*f*p*x*log(c*(d+e*x^2)^p)+d*g*p*(d+e*x^2)*log(c*(d+e*x^2)^p)/e^2-1/4*g*p*(d+e*x^2)^2*log(c*(d+e*x^2)^p)/e^2+f*x*log(c*(d+e*x^2)^p)^2-1/2*d*g*(d+e*x^2)*log(c*(d+e*x^2)^p)^2/e^2+1/4*g*(d+e*x^2)^2*log(c*(d+e*x^2)^p)^2/e^2-8*f*p^2*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)+4*I*f*p^2*arctan(x*sqrt(e)/sqrt(d))^2*sqrt(d)/sqrt(e)+4*f*p*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)*sqrt(d)/sqrt(e)+8*f*p^2*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)+4*I*f*p^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)],
[log(c*(d+e*x^2)^p)^2/(f+g*x^3),x,0,Unintegrable(log(c*(d+e*x^2)^p)^2/(f+g*x^3),x)],
[log(c*(d+e*x^2)^p)^2/(f+g*x^3)^2,x,0,Unintegrable(log(c*(d+e*x^2)^p)^2/(f+g*x^3)^2,x)],
[(f+g*x^3)^2*log(c*(d+e*x^2)^p)^3,x,103,-48*f^2*p^3*x+351136/25725*d^3*g^2*p^3*x/e^3+6*d*f*g*p^3*x^2/e-55456/77175*d^2*g^2*p^3*x^3/e^2+5232/42875*d*g^2*p^3*x^5/e-48/2401*g^2*p^3*x^7-3/8*f*g*p^3*(d+e*x^2)^2/e^2-351136/25725*d^(7/2)*g^2*p^3*arctan(x*sqrt(e)/sqrt(d))/e^(7/2)+1408/245*I*d^(7/2)*g^2*p^3*arctan(x*sqrt(e)/sqrt(d))^2/e^(7/2)+24*f^2*p^2*x*log(c*(d+e*x^2)^p)-1408/245*d^3*g^2*p^2*x*log(c*(d+e*x^2)^p)/e^3+568/735*d^2*g^2*p^2*x^3*log(c*(d+e*x^2)^p)/e^2-288/1225*d*g^2*p^2*x^5*log(c*(d+e*x^2)^p)/e+24/343*g^2*p^2*x^7*log(c*(d+e*x^2)^p)-6*d*f*g*p^2*(d+e*x^2)*log(c*(d+e*x^2)^p)/e^2+3/4*f*g*p^2*(d+e*x^2)^2*log(c*(d+e*x^2)^p)/e^2+1408/245*d^(7/2)*g^2*p^2*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)/e^(7/2)-6*f^2*p*x*log(c*(d+e*x^2)^p)^2+6/7*d^3*g^2*p*x*log(c*(d+e*x^2)^p)^2/e^3-2/7*d^2*g^2*p*x^3*log(c*(d+e*x^2)^p)^2/e^2+6/35*d*g^2*p*x^5*log(c*(d+e*x^2)^p)^2/e-6/49*g^2*p*x^7*log(c*(d+e*x^2)^p)^2+3*d*f*g*p*(d+e*x^2)*log(c*(d+e*x^2)^p)^2/e^2-3/4*f*g*p*(d+e*x^2)^2*log(c*(d+e*x^2)^p)^2/e^2+f^2*x*log(c*(d+e*x^2)^p)^3+1/7*g^2*x^7*log(c*(d+e*x^2)^p)^3-d*f*g*(d+e*x^2)*log(c*(d+e*x^2)^p)^3/e^2+1/2*f*g*(d+e*x^2)^2*log(c*(d+e*x^2)^p)^3/e^2+2816/245*d^(7/2)*g^2*p^3*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(7/2)+1408/245*I*d^(7/2)*g^2*p^3*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))/e^(7/2)+48*f^2*p^3*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)-24*I*f^2*p^3*arctan(x*sqrt(e)/sqrt(d))^2*sqrt(d)/sqrt(e)-24*f^2*p^2*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)*sqrt(d)/sqrt(e)-48*f^2*p^3*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)-24*I*f^2*p^3*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)+6*d*f^2*p*Unintegrable(log(c*(d+e*x^2)^p)^2/(d+e*x^2),x)-6/7*d^4*g^2*p*Unintegrable(log(c*(d+e*x^2)^p)^2/(d+e*x^2),x)/e^3],
[(f+g*x^3)*log(c*(d+e*x^2)^p)^3,x,28,-48*f*p^3*x+3*d*g*p^3*x^2/e-3/16*g*p^3*(d+e*x^2)^2/e^2+24*f*p^2*x*log(c*(d+e*x^2)^p)-3*d*g*p^2*(d+e*x^2)*log(c*(d+e*x^2)^p)/e^2+3/8*g*p^2*(d+e*x^2)^2*log(c*(d+e*x^2)^p)/e^2-6*f*p*x*log(c*(d+e*x^2)^p)^2+3/2*d*g*p*(d+e*x^2)*log(c*(d+e*x^2)^p)^2/e^2-3/8*g*p*(d+e*x^2)^2*log(c*(d+e*x^2)^p)^2/e^2+f*x*log(c*(d+e*x^2)^p)^3-1/2*d*g*(d+e*x^2)*log(c*(d+e*x^2)^p)^3/e^2+1/4*g*(d+e*x^2)^2*log(c*(d+e*x^2)^p)^3/e^2+48*f*p^3*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)-24*I*f*p^3*arctan(x*sqrt(e)/sqrt(d))^2*sqrt(d)/sqrt(e)-24*f*p^2*arctan(x*sqrt(e)/sqrt(d))*log(c*(d+e*x^2)^p)*sqrt(d)/sqrt(e)-48*f*p^3*arctan(x*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)-24*I*f*p^3*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x*sqrt(e)))*sqrt(d)/sqrt(e)+6*d*f*p*Unintegrable(log(c*(d+e*x^2)^p)^2/(d+e*x^2),x)],
[log(c*(d+e*x^2)^p)^3/(f+g*x^3),x,0,Unintegrable(log(c*(d+e*x^2)^p)^3/(f+g*x^3),x)],
[log(c*(d+e*x^2)^p)^3/(f+g*x^3)^2,x,0,Unintegrable(log(c*(d+e*x^2)^p)^3/(f+g*x^3)^2,x)],

# p<0
[(f+g*x^3)^2/log(c*(d+e*x^2)^p),x,0,Unintegrable((f+g*x^3)^2/log(c*(d+e*x^2)^p),x)],
[(f+g*x^3)/log(c*(d+e*x^2)^p),x,0,Unintegrable((f+g*x^3)/log(c*(d+e*x^2)^p),x)],
[1/((f+g*x^3)*log(c*(d+e*x^2)^p)),x,0,Unintegrable(1/((f+g*x^3)*log(c*(d+e*x^2)^p)),x)],
[1/((f+g*x^3)^2*log(c*(d+e*x^2)^p)),x,0,Unintegrable(1/((f+g*x^3)^2*log(c*(d+e*x^2)^p)),x)],
[(f+g*x^3)^2/log(c*(d+e*x^2)^p)^2,x,0,Unintegrable((f+g*x^3)^2/log(c*(d+e*x^2)^p)^2,x)],
[(f+g*x^3)/log(c*(d+e*x^2)^p)^2,x,0,Unintegrable((f+g*x^3)/log(c*(d+e*x^2)^p)^2,x)],
[1/((f+g*x^3)*log(c*(d+e*x^2)^p)^2),x,0,Unintegrable(1/((f+g*x^3)*log(c*(d+e*x^2)^p)^2),x)],
[1/((f+g*x^3)^2*log(c*(d+e*x^2)^p)^2),x,0,Unintegrable(1/((f+g*x^3)^2*log(c*(d+e*x^2)^p)^2),x)],

# Integrands of the form (h x)^r (f+g x^s)^q Log[c (d+e x^m)^n]^p

# Integrands of the form x^r (f+g x^2)^q Log[c (d+e x^2)^n]

# q>0
[x^5*(f+g*x^2)*log(c*(d+e*x^2)^p),x,5,-1/24*d^2*(4*e*f-3*d*g)*p*x^2/e^3+1/48*d*(4*e*f-3*d*g)*p*x^4/e^2-1/72*(4*e*f-3*d*g)*p*x^6/e-1/32*g*p*x^8+1/24*d^3*(4*e*f-3*d*g)*p*log(d+e*x^2)/e^4+1/6*f*x^6*log(c*(d+e*x^2)^p)+1/8*g*x^8*log(c*(d+e*x^2)^p)],
[x^3*(f+g*x^2)*log(c*(d+e*x^2)^p),x,5,1/12*d*(3*e*f-2*d*g)*p*x^2/e^2-1/24*(3*e*f-2*d*g)*p*x^4/e-1/18*g*p*x^6-1/12*d^2*(3*e*f-2*d*g)*p*log(d+e*x^2)/e^3+1/4*f*x^4*log(c*(d+e*x^2)^p)+1/6*g*x^6*log(c*(d+e*x^2)^p)],
[x*(f+g*x^2)*log(c*(d+e*x^2)^p),x,4,-1/4*(e*f-d*g)*p*x^2/e-1/8*p*(f+g*x^2)^2/g-1/4*(e*f-d*g)^2*p*log(d+e*x^2)/(e^2*g)+1/4*(f+g*x^2)^2*log(c*(d+e*x^2)^p)/g],
[(f+g*x^2)*log(c*(d+e*x^2)^p)/x,x,7,-1/2*g*p*x^2+1/2*g*(d+e*x^2)*log(c*(d+e*x^2)^p)/e+1/2*f*log(-e*x^2/d)*log(c*(d+e*x^2)^p)+1/2*f*p*polylog(2,1+e*x^2/d)],
[(f+g*x^2)*log(c*(d+e*x^2)^p)/x^3,x,9,e*f*p*log(x)/d-1/2*e*f*p*log(d+e*x^2)/d-1/2*f*log(c*(d+e*x^2)^p)/x^2+1/2*g*log(-e*x^2/d)*log(c*(d+e*x^2)^p)+1/2*g*p*polylog(2,1+e*x^2/d)],
[(f+g*x^2)*log(c*(d+e*x^2)^p)/x^5,x,5,-1/4*e*f*p/(d*x^2)-1/2*e*(e*f-2*d*g)*p*log(x)/d^2+1/4*(e*f-d*g)^2*p*log(d+e*x^2)/(d^2*f)-1/4*(f+g*x^2)^2*log(c*(d+e*x^2)^p)/(f*x^4)],
[(f+g*x^2)*log(c*(d+e*x^2)^p)/x^7,x,5,-1/12*e*f*p/(d*x^4)+1/12*e*(2*e*f-3*d*g)*p/(d^2*x^2)+1/6*e^2*(2*e*f-3*d*g)*p*log(x)/d^3-1/12*e^2*(2*e*f-3*d*g)*p*log(d+e*x^2)/d^3-1/6*f*log(c*(d+e*x^2)^p)/x^6-1/4*g*log(c*(d+e*x^2)^p)/x^4],
[(f+g*x^2)*log(c*(d+e*x^2)^p)/x^9,x,5,-1/24*e*f*p/(d*x^6)+1/48*e*(3*e*f-4*d*g)*p/(d^2*x^4)-1/24*e^2*(3*e*f-4*d*g)*p/(d^3*x^2)-1/12*e^3*(3*e*f-4*d*g)*p*log(x)/d^4+1/24*e^3*(3*e*f-4*d*g)*p*log(d+e*x^2)/d^4-1/8*f*log(c*(d+e*x^2)^p)/x^8-1/6*g*log(c*(d+e*x^2)^p)/x^6],
[x^2*(f+g*x^2)*log(c*(d+e*x^2)^p),x,10,2/3*d*f*p*x/e-2/5*d^2*g*p*x/e^2-2/9*f*p*x^3+2/15*d*g*p*x^3/e-2/25*g*p*x^5-2/3*d^(3/2)*f*p*arctan(x*sqrt(e)/sqrt(d))/e^(3/2)+2/5*d^(5/2)*g*p*arctan(x*sqrt(e)/sqrt(d))/e^(5/2)+1/3*f*x^3*log(c*(d+e*x^2)^p)+1/5*g*x^5*log(c*(d+e*x^2)^p)],
[(f+g*x^2)*log(c*(d+e*x^2)^p),x,9,-2*f*p*x+2/3*d*g*p*x/e-2/9*g*p*x^3-2/3*d^(3/2)*g*p*arctan(x*sqrt(e)/sqrt(d))/e^(3/2)+f*x*log(c*(d+e*x^2)^p)+1/3*g*x^3*log(c*(d+e*x^2)^p)+2*f*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)],
[(f+g*x^2)*log(c*(d+e*x^2)^p)/x^2,x,7,-2*g*p*x-f*log(c*(d+e*x^2)^p)/x+g*x*log(c*(d+e*x^2)^p)+2*(e*f+d*g)*p*arctan(x*sqrt(e)/sqrt(d))/(sqrt(d)*sqrt(e)),-2*g*p*x-f*log(c*(d+e*x^2)^p)/x+g*x*log(c*(d+e*x^2)^p)+2*g*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)+2*f*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(e)/sqrt(d)],
[(f+g*x^2)*log(c*(d+e*x^2)^p)/x^4,x,7,-2/3*e*f*p/(d*x)-2/3*e^(3/2)*f*p*arctan(x*sqrt(e)/sqrt(d))/d^(3/2)-1/3*f*log(c*(d+e*x^2)^p)/x^3-g*log(c*(d+e*x^2)^p)/x+2*g*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(e)/sqrt(d)],
[(f+g*x^2)*log(c*(d+e*x^2)^p)/x^6,x,9,-2/15*e*f*p/(d*x^3)+2/5*e^2*f*p/(d^2*x)-2/3*e*g*p/(d*x)+2/5*e^(5/2)*f*p*arctan(x*sqrt(e)/sqrt(d))/d^(5/2)-2/3*e^(3/2)*g*p*arctan(x*sqrt(e)/sqrt(d))/d^(3/2)-1/5*f*log(c*(d+e*x^2)^p)/x^5-1/3*g*log(c*(d+e*x^2)^p)/x^3],
[x^5*(f+g*x^2)^2*log(c*(d+e*x^2)^p),x,5,-1/2*d^2*(e*f-d*g)^2*p*x^2/e^4+1/4*d*(e*f-2*d*g)*(e*f-d*g)*p*(d+e*x^2)^2/e^5-1/18*(e^2*f^2-6*d*e*f*g+6*d^2*g^2)*p*(d+e*x^2)^3/e^5-1/16*g*(e*f-2*d*g)*p*(d+e*x^2)^4/e^5-1/50*g^2*p*(d+e*x^2)^5/e^5+1/60*d^3*(10*e^2*f^2-15*d*e*f*g+6*d^2*g^2)*p*log(d+e*x^2)/e^5+1/6*f^2*x^6*log(c*(d+e*x^2)^p)+1/4*f*g*x^8*log(c*(d+e*x^2)^p)+1/10*g^2*x^10*log(c*(d+e*x^2)^p)],
[x^3*(f+g*x^2)^2*log(c*(d+e*x^2)^p),x,5,1/2*d*(e*f-d*g)^2*p*x^2/e^3-1/8*(e*f-3*d*g)*(e*f-d*g)*p*(d+e*x^2)^2/e^4-1/18*g*(2*e*f-3*d*g)*p*(d+e*x^2)^3/e^4-1/32*g^2*p*(d+e*x^2)^4/e^4-1/24*d^2*(6*e^2*f^2-8*d*e*f*g+3*d^2*g^2)*p*log(d+e*x^2)/e^4+1/4*f^2*x^4*log(c*(d+e*x^2)^p)+1/3*f*g*x^6*log(c*(d+e*x^2)^p)+1/8*g^2*x^8*log(c*(d+e*x^2)^p)],
[x*(f+g*x^2)^2*log(c*(d+e*x^2)^p),x,4,-1/6*(e*f-d*g)^2*p*x^2/e^2-1/12*(e*f-d*g)*p*(f+g*x^2)^2/(e*g)-1/18*p*(f+g*x^2)^3/g-1/6*(e*f-d*g)^3*p*log(d+e*x^2)/(e^3*g)+1/6*(f+g*x^2)^3*log(c*(d+e*x^2)^p)/g],
[(f+g*x^2)^2*log(c*(d+e*x^2)^p)/x,x,10,-f*g*p*x^2+1/4*d*g^2*p*x^2/e-1/8*g^2*p*x^4-1/4*d^2*g^2*p*log(d+e*x^2)/e^2+1/4*g^2*x^4*log(c*(d+e*x^2)^p)+f*g*(d+e*x^2)*log(c*(d+e*x^2)^p)/e+1/2*f^2*log(-e*x^2/d)*log(c*(d+e*x^2)^p)+1/2*f^2*p*polylog(2,1+e*x^2/d)],
[(f+g*x^2)^2*log(c*(d+e*x^2)^p)/x^3,x,11,-1/2*g^2*p*x^2+e*f^2*p*log(x)/d-1/2*e*f^2*p*log(d+e*x^2)/d-1/2*f^2*log(c*(d+e*x^2)^p)/x^2+1/2*g^2*(d+e*x^2)*log(c*(d+e*x^2)^p)/e+f*g*log(-e*x^2/d)*log(c*(d+e*x^2)^p)+f*g*p*polylog(2,1+e*x^2/d)],
[(f+g*x^2)^2*log(c*(d+e*x^2)^p)/x^5,x,12,-1/4*e*f^2*p/(d*x^2)-1/2*e^2*f^2*p*log(x)/d^2+2*e*f*g*p*log(x)/d+1/4*e^2*f^2*p*log(d+e*x^2)/d^2-e*f*g*p*log(d+e*x^2)/d-1/4*f^2*log(c*(d+e*x^2)^p)/x^4-f*g*log(c*(d+e*x^2)^p)/x^2+1/2*g^2*log(-e*x^2/d)*log(c*(d+e*x^2)^p)+1/2*g^2*p*polylog(2,1+e*x^2/d)],
[(f+g*x^2)^2*log(c*(d+e*x^2)^p)/x^7,x,5,-1/12*e*f^2*p/(d*x^4)+1/6*e*f*(e*f-3*d*g)*p/(d^2*x^2)+1/3*e*(e^2*f^2-3*d*e*f*g+3*d^2*g^2)*p*log(x)/d^3-1/6*(e*f-d*g)^3*p*log(d+e*x^2)/(d^3*f)-1/6*(f+g*x^2)^3*log(c*(d+e*x^2)^p)/(f*x^6)],
[(f+g*x^2)^2*log(c*(d+e*x^2)^p)/x^9,x,5,-1/24*e*f^2*p/(d*x^6)+1/48*e*f*(3*e*f-8*d*g)*p/(d^2*x^4)-1/24*e*(3*e^2*f^2-8*d*e*f*g+6*d^2*g^2)*p/(d^3*x^2)-1/12*e^2*(3*e^2*f^2-8*d*e*f*g+6*d^2*g^2)*p*log(x)/d^4+1/24*e^2*(3*e^2*f^2-8*d*e*f*g+6*d^2*g^2)*p*log(d+e*x^2)/d^4-1/8*f^2*log(c*(d+e*x^2)^p)/x^8-1/3*f*g*log(c*(d+e*x^2)^p)/x^6-1/4*g^2*log(c*(d+e*x^2)^p)/x^4],
[(f+g*x^2)^2*log(c*(d+e*x^2)^p)/x^11,x,5,-1/40*e*f^2*p/(d*x^8)+1/60*e*f*(2*e*f-5*d*g)*p/(d^2*x^6)-1/120*e*(6*e^2*f^2-15*d*e*f*g+10*d^2*g^2)*p/(d^3*x^4)+1/60*e^2*(6*e^2*f^2-15*d*e*f*g+10*d^2*g^2)*p/(d^4*x^2)+1/30*e^3*(6*e^2*f^2-15*d*e*f*g+10*d^2*g^2)*p*log(x)/d^5-1/60*e^3*(6*e^2*f^2-15*d*e*f*g+10*d^2*g^2)*p*log(d+e*x^2)/d^5-1/10*f^2*log(c*(d+e*x^2)^p)/x^10-1/4*f*g*log(c*(d+e*x^2)^p)/x^8-1/6*g^2*log(c*(d+e*x^2)^p)/x^6],
[x^2*(f+g*x^2)^2*log(c*(d+e*x^2)^p),x,14,2/3*d*f^2*p*x/e-4/5*d^2*f*g*p*x/e^2+2/7*d^3*g^2*p*x/e^3-2/9*f^2*p*x^3+4/15*d*f*g*p*x^3/e-2/21*d^2*g^2*p*x^3/e^2-4/25*f*g*p*x^5+2/35*d*g^2*p*x^5/e-2/49*g^2*p*x^7-2/3*d^(3/2)*f^2*p*arctan(x*sqrt(e)/sqrt(d))/e^(3/2)+4/5*d^(5/2)*f*g*p*arctan(x*sqrt(e)/sqrt(d))/e^(5/2)-2/7*d^(7/2)*g^2*p*arctan(x*sqrt(e)/sqrt(d))/e^(7/2)+1/3*f^2*x^3*log(c*(d+e*x^2)^p)+2/5*f*g*x^5*log(c*(d+e*x^2)^p)+1/7*g^2*x^7*log(c*(d+e*x^2)^p)],
[(f+g*x^2)^2*log(c*(d+e*x^2)^p),x,13,-2*f^2*p*x+4/3*d*f*g*p*x/e-2/5*d^2*g^2*p*x/e^2-4/9*f*g*p*x^3+2/15*d*g^2*p*x^3/e-2/25*g^2*p*x^5-4/3*d^(3/2)*f*g*p*arctan(x*sqrt(e)/sqrt(d))/e^(3/2)+2/5*d^(5/2)*g^2*p*arctan(x*sqrt(e)/sqrt(d))/e^(5/2)+f^2*x*log(c*(d+e*x^2)^p)+2/3*f*g*x^3*log(c*(d+e*x^2)^p)+1/5*g^2*x^5*log(c*(d+e*x^2)^p)+2*f^2*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)],
[(f+g*x^2)^2*log(c*(d+e*x^2)^p)/x^2,x,11,-4*f*g*p*x+2/3*d*g^2*p*x/e-2/9*g^2*p*x^3-2/3*d^(3/2)*g^2*p*arctan(x*sqrt(e)/sqrt(d))/e^(3/2)-f^2*log(c*(d+e*x^2)^p)/x+2*f*g*x*log(c*(d+e*x^2)^p)+1/3*g^2*x^3*log(c*(d+e*x^2)^p)+4*f*g*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)+2*f^2*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(e)/sqrt(d)],
[(f+g*x^2)^2*log(c*(d+e*x^2)^p)/x^4,x,10,-2/3*e*f^2*p/(d*x)-2*g^2*p*x-2/3*e^(3/2)*f^2*p*arctan(x*sqrt(e)/sqrt(d))/d^(3/2)-1/3*f^2*log(c*(d+e*x^2)^p)/x^3-2*f*g*log(c*(d+e*x^2)^p)/x+g^2*x*log(c*(d+e*x^2)^p)+2*g^2*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/sqrt(e)+4*f*g*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(e)/sqrt(d)],
[(f+g*x^2)^2*log(c*(d+e*x^2)^p)/x^6,x,11,-2/15*e*f^2*p/(d*x^3)+2/5*e^2*f^2*p/(d^2*x)-4/3*e*f*g*p/(d*x)+2/5*e^(5/2)*f^2*p*arctan(x*sqrt(e)/sqrt(d))/d^(5/2)-4/3*e^(3/2)*f*g*p*arctan(x*sqrt(e)/sqrt(d))/d^(3/2)-1/5*f^2*log(c*(d+e*x^2)^p)/x^5-2/3*f*g*log(c*(d+e*x^2)^p)/x^3-g^2*log(c*(d+e*x^2)^p)/x+2*g^2*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(e)/sqrt(d)],
[(f+g*x^2)^2*log(c*(d+e*x^2)^p)/x^8,x,14,-2/35*e*f^2*p/(d*x^5)+2/21*e^2*f^2*p/(d^2*x^3)-4/15*e*f*g*p/(d*x^3)-2/7*e^3*f^2*p/(d^3*x)+4/5*e^2*f*g*p/(d^2*x)-2/3*e*g^2*p/(d*x)-2/7*e^(7/2)*f^2*p*arctan(x*sqrt(e)/sqrt(d))/d^(7/2)+4/5*e^(5/2)*f*g*p*arctan(x*sqrt(e)/sqrt(d))/d^(5/2)-2/3*e^(3/2)*g^2*p*arctan(x*sqrt(e)/sqrt(d))/d^(3/2)-1/7*f^2*log(c*(d+e*x^2)^p)/x^7-2/5*f*g*log(c*(d+e*x^2)^p)/x^5-1/3*g^2*log(c*(d+e*x^2)^p)/x^3],

# q<0
[x^5*log(c*(d+e*x^2)^p)/(f+g*x^2),x,11,1/2*f*p*x^2/g^2+1/4*d*p*x^2/(e*g)-1/8*p*x^4/g-1/4*d^2*p*log(d+e*x^2)/(e^2*g)+1/4*x^4*log(c*(d+e*x^2)^p)/g-1/2*f*(d+e*x^2)*log(c*(d+e*x^2)^p)/(e*g^2)+1/2*f^2*log(c*(d+e*x^2)^p)*log(e*(f+g*x^2)/(e*f-d*g))/g^3+1/2*f^2*p*polylog(2,-g*(d+e*x^2)/(e*f-d*g))/g^3],
[x^3*log(c*(d+e*x^2)^p)/(f+g*x^2),x,8,-1/2*p*x^2/g+1/2*(d+e*x^2)*log(c*(d+e*x^2)^p)/(e*g)-1/2*f*log(c*(d+e*x^2)^p)*log(e*(f+g*x^2)/(e*f-d*g))/g^2-1/2*f*p*polylog(2,-g*(d+e*x^2)/(e*f-d*g))/g^2],
[x*log(c*(d+e*x^2)^p)/(f+g*x^2),x,4,1/2*log(c*(d+e*x^2)^p)*log(e*(f+g*x^2)/(e*f-d*g))/g+1/2*p*polylog(2,-g*(d+e*x^2)/(e*f-d*g))/g],
[log(c*(d+e*x^2)^p)/(x*(f+g*x^2)),x,8,1/2*log(-e*x^2/d)*log(c*(d+e*x^2)^p)/f-1/2*log(c*(d+e*x^2)^p)*log(e*(f+g*x^2)/(e*f-d*g))/f-1/2*p*polylog(2,-g*(d+e*x^2)/(e*f-d*g))/f+1/2*p*polylog(2,1+e*x^2/d)/f],
[log(c*(d+e*x^2)^p)/(x^3*(f+g*x^2)),x,12,e*p*log(x)/(d*f)-1/2*e*p*log(d+e*x^2)/(d*f)-1/2*log(c*(d+e*x^2)^p)/(f*x^2)-1/2*g*log(-e*x^2/d)*log(c*(d+e*x^2)^p)/f^2+1/2*g*log(c*(d+e*x^2)^p)*log(e*(f+g*x^2)/(e*f-d*g))/f^2+1/2*g*p*polylog(2,-g*(d+e*x^2)/(e*f-d*g))/f^2-1/2*g*p*polylog(2,1+e*x^2/d)/f^2],
[x^4*log(c*(d+e*x^2)^p)/(f+g*x^2),x,21,2*f*p*x/g^2+2/3*d*p*x/(e*g)-2/9*p*x^3/g-2/3*d^(3/2)*p*arctan(x*sqrt(e)/sqrt(d))/(e^(3/2)*g)-f*x*log(c*(d+e*x^2)^p)/g^2+1/3*x^3*log(c*(d+e*x^2)^p)/g+f^(3/2)*arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e*x^2)^p)/g^(5/2)+2*f^(3/2)*p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/g^(5/2)-f^(3/2)*p*arctan(x*sqrt(g)/sqrt(f))*log(-2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/g^(5/2)-f^(3/2)*p*arctan(x*sqrt(g)/sqrt(f))*log(2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/g^(5/2)-I*f^(3/2)*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/g^(5/2)+1/2*I*f^(3/2)*p*polylog(2,1+2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/g^(5/2)+1/2*I*f^(3/2)*p*polylog(2,1-2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/g^(5/2)-2*f*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/(g^2*sqrt(e))],
[x^2*log(c*(d+e*x^2)^p)/(f+g*x^2),x,17,-2*p*x/g+x*log(c*(d+e*x^2)^p)/g+2*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/(g*sqrt(e))-arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e*x^2)^p)*sqrt(f)/g^(3/2)-2*p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))*sqrt(f)/g^(3/2)+p*arctan(x*sqrt(g)/sqrt(f))*log(-2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))*sqrt(f)/g^(3/2)+p*arctan(x*sqrt(g)/sqrt(f))*log(2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))*sqrt(f)/g^(3/2)+I*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))*sqrt(f)/g^(3/2)-1/2*I*p*polylog(2,1+2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))*sqrt(f)/g^(3/2)-1/2*I*p*polylog(2,1-2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))*sqrt(f)/g^(3/2)],
[log(c*(d+e*x^2)^p)/(f+g*x^2),x,12,arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e*x^2)^p)/(sqrt(f)*sqrt(g))+2*p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(sqrt(f)*sqrt(g))-p*arctan(x*sqrt(g)/sqrt(f))*log(-2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/(sqrt(f)*sqrt(g))-p*arctan(x*sqrt(g)/sqrt(f))*log(2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/(sqrt(f)*sqrt(g))-I*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(sqrt(f)*sqrt(g))+1/2*I*p*polylog(2,1+2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/(sqrt(f)*sqrt(g))+1/2*I*p*polylog(2,1-2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/(sqrt(f)*sqrt(g))],
[log(c*(d+e*x^2)^p)/(x^2*(f+g*x^2)),x,16,-log(c*(d+e*x^2)^p)/(f*x)+2*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(e)/(f*sqrt(d))-arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e*x^2)^p)*sqrt(g)/f^(3/2)-2*p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))*sqrt(g)/f^(3/2)+p*arctan(x*sqrt(g)/sqrt(f))*log(-2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))*sqrt(g)/f^(3/2)+p*arctan(x*sqrt(g)/sqrt(f))*log(2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))*sqrt(g)/f^(3/2)+I*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))*sqrt(g)/f^(3/2)-1/2*I*p*polylog(2,1+2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))*sqrt(g)/f^(3/2)-1/2*I*p*polylog(2,1-2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))*sqrt(g)/f^(3/2)],
[log(c*(d+e*x^2)^p)/(x^4*(f+g*x^2)),x,19,-2/3*e*p/(d*f*x)-2/3*e^(3/2)*p*arctan(x*sqrt(e)/sqrt(d))/(d^(3/2)*f)-1/3*log(c*(d+e*x^2)^p)/(f*x^3)+g*log(c*(d+e*x^2)^p)/(f^2*x)+g^(3/2)*arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e*x^2)^p)/f^(5/2)+2*g^(3/2)*p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/f^(5/2)-g^(3/2)*p*arctan(x*sqrt(g)/sqrt(f))*log(-2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/f^(5/2)-g^(3/2)*p*arctan(x*sqrt(g)/sqrt(f))*log(2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/f^(5/2)-I*g^(3/2)*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/f^(5/2)+1/2*I*g^(3/2)*p*polylog(2,1+2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/f^(5/2)+1/2*I*g^(3/2)*p*polylog(2,1-2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/f^(5/2)-2*g*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(e)/(f^2*sqrt(d))],
[x^5*log(c*(d+e*x^2)^p)/(f+g*x^2)^2,x,12,-1/2*p*x^2/g^2+1/2*e*f^2*p*log(d+e*x^2)/(g^3*(e*f-d*g))+1/2*(d+e*x^2)*log(c*(d+e*x^2)^p)/(e*g^2)-1/2*f^2*log(c*(d+e*x^2)^p)/(g^3*(f+g*x^2))-1/2*e*f^2*p*log(f+g*x^2)/(g^3*(e*f-d*g))-f*log(c*(d+e*x^2)^p)*log(e*(f+g*x^2)/(e*f-d*g))/g^3-f*p*polylog(2,-g*(d+e*x^2)/(e*f-d*g))/g^3],
[x^3*log(c*(d+e*x^2)^p)/(f+g*x^2)^2,x,10,-1/2*e*f*p*log(d+e*x^2)/(g^2*(e*f-d*g))+1/2*f*log(c*(d+e*x^2)^p)/(g^2*(f+g*x^2))+1/2*e*f*p*log(f+g*x^2)/(g^2*(e*f-d*g))+1/2*log(c*(d+e*x^2)^p)*log(e*(f+g*x^2)/(e*f-d*g))/g^2+1/2*p*polylog(2,-g*(d+e*x^2)/(e*f-d*g))/g^2],
[x*log(c*(d+e*x^2)^p)/(f+g*x^2)^2,x,5,1/2*e*p*log(d+e*x^2)/(g*(e*f-d*g))-1/2*log(c*(d+e*x^2)^p)/(g*(f+g*x^2))-1/2*e*p*log(f+g*x^2)/(g*(e*f-d*g))],
[log(c*(d+e*x^2)^p)/(x*(f+g*x^2)^2),x,12,-1/2*e*p*log(d+e*x^2)/(f*(e*f-d*g))+1/2*log(c*(d+e*x^2)^p)/(f*(f+g*x^2))+1/2*log(-e*x^2/d)*log(c*(d+e*x^2)^p)/f^2+1/2*e*p*log(f+g*x^2)/(f*(e*f-d*g))-1/2*log(c*(d+e*x^2)^p)*log(e*(f+g*x^2)/(e*f-d*g))/f^2-1/2*p*polylog(2,-g*(d+e*x^2)/(e*f-d*g))/f^2+1/2*p*polylog(2,1+e*x^2/d)/f^2],
[log(c*(d+e*x^2)^p)/(x^3*(f+g*x^2)^2),x,16,e*p*log(x)/(d*f^2)-1/2*e*p*log(d+e*x^2)/(d*f^2)+1/2*e*g*p*log(d+e*x^2)/(f^2*(e*f-d*g))-1/2*log(c*(d+e*x^2)^p)/(f^2*x^2)-1/2*g*log(c*(d+e*x^2)^p)/(f^2*(f+g*x^2))-g*log(-e*x^2/d)*log(c*(d+e*x^2)^p)/f^3-1/2*e*g*p*log(f+g*x^2)/(f^2*(e*f-d*g))+g*log(c*(d+e*x^2)^p)*log(e*(f+g*x^2)/(e*f-d*g))/f^3+g*p*polylog(2,-g*(d+e*x^2)/(e*f-d*g))/f^3-g*p*polylog(2,1+e*x^2/d)/f^3],
[x^4*log(c*(d+e*x^2)^p)/(f+g*x^2)^2,x,43,-2*p*x/g^2+x*log(c*(d+e*x^2)^p)/g^2-1/2*e*(-f)^(3/2)*p*log(sqrt(-f)-x*sqrt(g))/(g^(5/2)*(e*f-d*g))+1/2*e*(-f)^(3/2)*p*log(sqrt(-f)+x*sqrt(g))/(g^(5/2)*(e*f-d*g))+2*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)/(g^2*sqrt(e))+f*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)*sqrt(e)/(g^2*(e*f-d*g))-3/2*arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e*x^2)^p)*sqrt(f)/g^(5/2)-3*p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))*sqrt(f)/g^(5/2)+3/2*p*arctan(x*sqrt(g)/sqrt(f))*log(-2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))*sqrt(f)/g^(5/2)+3/2*p*arctan(x*sqrt(g)/sqrt(f))*log(2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))*sqrt(f)/g^(5/2)+3/2*I*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))*sqrt(f)/g^(5/2)-3/4*I*p*polylog(2,1+2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))*sqrt(f)/g^(5/2)-3/4*I*p*polylog(2,1-2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))*sqrt(f)/g^(5/2)-1/4*f*log(c*(d+e*x^2)^p)/(g^(5/2)*(sqrt(-f)-x*sqrt(g)))+1/4*f*log(c*(d+e*x^2)^p)/(g^(5/2)*(sqrt(-f)+x*sqrt(g)))],
[x^2*log(c*(d+e*x^2)^p)/(f+g*x^2)^2,x,40,-p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)*sqrt(e)/(g*(e*f-d*g))-1/2*e*p*log(sqrt(-f)-x*sqrt(g))*sqrt(-f)/(g^(3/2)*(e*f-d*g))+1/2*e*p*log(sqrt(-f)+x*sqrt(g))*sqrt(-f)/(g^(3/2)*(e*f-d*g))+1/2*arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e*x^2)^p)/(g^(3/2)*sqrt(f))+p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(g^(3/2)*sqrt(f))-1/2*p*arctan(x*sqrt(g)/sqrt(f))*log(-2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/(g^(3/2)*sqrt(f))-1/2*p*arctan(x*sqrt(g)/sqrt(f))*log(2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/(g^(3/2)*sqrt(f))-1/2*I*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(g^(3/2)*sqrt(f))+1/4*I*p*polylog(2,1+2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/(g^(3/2)*sqrt(f))+1/4*I*p*polylog(2,1-2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/(g^(3/2)*sqrt(f))+1/4*log(c*(d+e*x^2)^p)/(g^(3/2)*(sqrt(-f)-x*sqrt(g)))-1/4*log(c*(d+e*x^2)^p)/(g^(3/2)*(sqrt(-f)+x*sqrt(g)))],
[log(c*(d+e*x^2)^p)/(f+g*x^2)^2,x,26,p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)*sqrt(e)/(f*(e*f-d*g))+1/2*arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e*x^2)^p)/(f^(3/2)*sqrt(g))+p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(f^(3/2)*sqrt(g))-1/2*p*arctan(x*sqrt(g)/sqrt(f))*log(-2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/(f^(3/2)*sqrt(g))-1/2*p*arctan(x*sqrt(g)/sqrt(f))*log(2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/(f^(3/2)*sqrt(g))-1/2*I*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))/(f^(3/2)*sqrt(g))+1/4*I*p*polylog(2,1+2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))/(f^(3/2)*sqrt(g))+1/4*I*p*polylog(2,1-2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))/(f^(3/2)*sqrt(g))-1/2*e*p*log(sqrt(-f)-x*sqrt(g))/((e*f-d*g)*sqrt(-f)*sqrt(g))+1/2*e*p*log(sqrt(-f)+x*sqrt(g))/((e*f-d*g)*sqrt(-f)*sqrt(g))-1/4*log(c*(d+e*x^2)^p)/(f*sqrt(g)*(sqrt(-f)-x*sqrt(g)))+1/4*log(c*(d+e*x^2)^p)/(f*sqrt(g)*(sqrt(-f)+x*sqrt(g)))],
[log(c*(d+e*x^2)^p)/(x^2*(f+g*x^2)^2),x,42,-log(c*(d+e*x^2)^p)/(f^2*x)+2*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(e)/(f^2*sqrt(d))-g*p*arctan(x*sqrt(e)/sqrt(d))*sqrt(d)*sqrt(e)/(f^2*(e*f-d*g))-3/2*arctan(x*sqrt(g)/sqrt(f))*log(c*(d+e*x^2)^p)*sqrt(g)/f^(5/2)-1/2*e*p*log(sqrt(-f)-x*sqrt(g))*sqrt(g)/((-f)^(3/2)*(e*f-d*g))-3*p*arctan(x*sqrt(g)/sqrt(f))*log(2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))*sqrt(g)/f^(5/2)+1/2*e*p*log(sqrt(-f)+x*sqrt(g))*sqrt(g)/((-f)^(3/2)*(e*f-d*g))+3/2*p*arctan(x*sqrt(g)/sqrt(f))*log(-2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))*sqrt(g)/f^(5/2)+3/2*p*arctan(x*sqrt(g)/sqrt(f))*log(2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))*sqrt(g)/f^(5/2)+3/2*I*p*polylog(2,1-2*sqrt(f)/(sqrt(f)-I*x*sqrt(g)))*sqrt(g)/f^(5/2)-3/4*I*p*polylog(2,1+2*(sqrt(-d)-x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)-sqrt(-d)*sqrt(g))))*sqrt(g)/f^(5/2)-3/4*I*p*polylog(2,1-2*(sqrt(-d)+x*sqrt(e))*sqrt(f)*sqrt(g)/((sqrt(f)-I*x*sqrt(g))*(I*sqrt(e)*sqrt(f)+sqrt(-d)*sqrt(g))))*sqrt(g)/f^(5/2)+1/4*log(c*(d+e*x^2)^p)*sqrt(g)/(f^2*(sqrt(-f)-x*sqrt(g)))-1/4*log(c*(d+e*x^2)^p)*sqrt(g)/(f^2*(sqrt(-f)+x*sqrt(g)))],
[log(c*(a+b*x^2)^n)/(a+b*x^2),x,6,I*n*arctan(x*sqrt(b)/sqrt(a))^2/(sqrt(a)*sqrt(b))+arctan(x*sqrt(b)/sqrt(a))*log(c*(a+b*x^2)^n)/(sqrt(a)*sqrt(b))+2*n*arctan(x*sqrt(b)/sqrt(a))*log(2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/(sqrt(a)*sqrt(b))+I*n*polylog(2,1-2*sqrt(a)/(sqrt(a)+I*x*sqrt(b)))/(sqrt(a)*sqrt(b))],
[log(1-x^2)/(2-x^2),x,12,arctanh(x/sqrt(2))*log(1-x^2)/sqrt(2)-arctanh(x/sqrt(2))*log(-4*(1-x)/((2-sqrt(2))*(x+sqrt(2))))/sqrt(2)-arctanh(x/sqrt(2))*log(4*(1+x)/((2+sqrt(2))*(x+sqrt(2))))/sqrt(2)+1/2*polylog(2,1+4*(1-x)/((2-sqrt(2))*(x+sqrt(2))))/sqrt(2)-polylog(2,1-2*sqrt(2)/(x+sqrt(2)))/sqrt(2)+1/2*polylog(2,1-4*(1+x)/((2+sqrt(2))*(x+sqrt(2))))/sqrt(2)+arctanh(x/sqrt(2))*log(2*sqrt(2)/(x+sqrt(2)))*sqrt(2)],
[log(d+e*x^2)/(1-x^2),x,11,2*arctanh(x)*log(2/(1+x))+arctanh(x)*log(d+e*x^2)-arctanh(x)*log(2*(sqrt(-d)-x*sqrt(e))/((1+x)*(sqrt(-d)-sqrt(e))))-arctanh(x)*log(2*(sqrt(-d)+x*sqrt(e))/((1+x)*(sqrt(-d)+sqrt(e))))-polylog(2,1+(-2)/(1+x))+1/2*polylog(2,1-2*(sqrt(-d)-x*sqrt(e))/((1+x)*(sqrt(-d)-sqrt(e))))+1/2*polylog(2,1-2*(sqrt(-d)+x*sqrt(e))/((1+x)*(sqrt(-d)+sqrt(e))))],

# Integrands of the form x^r (f+g x^s)^q Log[c (d+e x^m)^n] when s=k n and s symbolic

# r>0
[(f+g*x^(3*n))*log(c*(d+e*x^n)^p)/x,x,8,-1/3*d^2*g*p*x^n/(e^2*n)+1/6*d*g*p*x^(2*n)/(e*n)-1/9*g*p*x^(3*n)/n+1/3*d^3*g*p*log(d+e*x^n)/(e^3*n)+1/3*g*x^(3*n)*log(c*(d+e*x^n)^p)/n+f*log(-e*x^n/d)*log(c*(d+e*x^n)^p)/n+f*p*polylog(2,1+e*x^n/d)/n],
[(f+g*x^(2*n))*log(c*(d+e*x^n)^p)/x,x,8,1/2*d*g*p*x^n/(e*n)-1/4*g*p*x^(2*n)/n-1/2*d^2*g*p*log(d+e*x^n)/(e^2*n)+1/2*g*x^(2*n)*log(c*(d+e*x^n)^p)/n+f*log(-e*x^n/d)*log(c*(d+e*x^n)^p)/n+f*p*polylog(2,1+e*x^n/d)/n],
[(f+g*x^n)*log(c*(d+e*x^n)^p)/x,x,7,-g*p*x^n/n+g*(d+e*x^n)*log(c*(d+e*x^n)^p)/(e*n)+f*log(-e*x^n/d)*log(c*(d+e*x^n)^p)/n+f*p*polylog(2,1+e*x^n/d)/n],
[(f+g/x^n)*log(c*(d+e*x^n)^p)/x,x,9,e*g*p*log(x)/d-e*g*p*log(d+e*x^n)/(d*n)-g*log(c*(d+e*x^n)^p)/(n*x^n)+f*log(-e*x^n/d)*log(c*(d+e*x^n)^p)/n+f*p*polylog(2,1+e*x^n/d)/n],
[(f+g/x^(2*n))*log(c*(d+e*x^n)^p)/x,x,8,-1/2*e*g*p/(d*n*x^n)-1/2*e^2*g*p*log(x)/d^2+1/2*e^2*g*p*log(d+e*x^n)/(d^2*n)-1/2*g*log(c*(d+e*x^n)^p)/(n*x^(2*n))+f*log(-e*x^n/d)*log(c*(d+e*x^n)^p)/n+f*p*polylog(2,1+e*x^n/d)/n],
[(f+g*x^(3*n))^2*log(c*(d+e*x^n)^p)/x,x,11,-2/3*d^2*f*g*p*x^n/(e^2*n)+1/6*d^5*g^2*p*x^n/(e^5*n)+1/3*d*f*g*p*x^(2*n)/(e*n)-1/12*d^4*g^2*p*x^(2*n)/(e^4*n)-2/9*f*g*p*x^(3*n)/n+1/18*d^3*g^2*p*x^(3*n)/(e^3*n)-1/24*d^2*g^2*p*x^(4*n)/(e^2*n)+1/30*d*g^2*p*x^(5*n)/(e*n)-1/36*g^2*p*x^(6*n)/n+2/3*d^3*f*g*p*log(d+e*x^n)/(e^3*n)-1/6*d^6*g^2*p*log(d+e*x^n)/(e^6*n)+2/3*f*g*x^(3*n)*log(c*(d+e*x^n)^p)/n+1/6*g^2*x^(6*n)*log(c*(d+e*x^n)^p)/n+f^2*log(-e*x^n/d)*log(c*(d+e*x^n)^p)/n+f^2*p*polylog(2,1+e*x^n/d)/n],
[(f+g*x^(2*n))^2*log(c*(d+e*x^n)^p)/x,x,11,d*f*g*p*x^n/(e*n)+1/4*d^3*g^2*p*x^n/(e^3*n)-1/2*f*g*p*x^(2*n)/n-1/8*d^2*g^2*p*x^(2*n)/(e^2*n)+1/12*d*g^2*p*x^(3*n)/(e*n)-1/16*g^2*p*x^(4*n)/n-d^2*f*g*p*log(d+e*x^n)/(e^2*n)-1/4*d^4*g^2*p*log(d+e*x^n)/(e^4*n)+f*g*x^(2*n)*log(c*(d+e*x^n)^p)/n+1/4*g^2*x^(4*n)*log(c*(d+e*x^n)^p)/n+f^2*log(-e*x^n/d)*log(c*(d+e*x^n)^p)/n+f^2*p*polylog(2,1+e*x^n/d)/n],
[(f+g*x^n)^2*log(c*(d+e*x^n)^p)/x,x,10,-2*f*g*p*x^n/n+1/2*d*g^2*p*x^n/(e*n)-1/4*g^2*p*x^(2*n)/n-1/2*d^2*g^2*p*log(d+e*x^n)/(e^2*n)+1/2*g^2*x^(2*n)*log(c*(d+e*x^n)^p)/n+2*f*g*(d+e*x^n)*log(c*(d+e*x^n)^p)/(e*n)+f^2*log(-e*x^n/d)*log(c*(d+e*x^n)^p)/n+f^2*p*polylog(2,1+e*x^n/d)/n],
[(f+g/x^n)^2*log(c*(d+e*x^n)^p)/x,x,12,-1/2*e*g^2*p/(d*n*x^n)+2*e*f*g*p*log(x)/d-1/2*e^2*g^2*p*log(x)/d^2-2*e*f*g*p*log(d+e*x^n)/(d*n)+1/2*e^2*g^2*p*log(d+e*x^n)/(d^2*n)-1/2*g^2*log(c*(d+e*x^n)^p)/(n*x^(2*n))-2*f*g*log(c*(d+e*x^n)^p)/(n*x^n)+f^2*log(-e*x^n/d)*log(c*(d+e*x^n)^p)/n+f^2*p*polylog(2,1+e*x^n/d)/n],
[(f+g/x^(2*n))^2*log(c*(d+e*x^n)^p)/x,x,11,-1/12*e*g^2*p/(d*n*x^(3*n))+1/8*e^2*g^2*p/(d^2*n*x^(2*n))-e*f*g*p/(d*n*x^n)-1/4*e^3*g^2*p/(d^3*n*x^n)-e^2*f*g*p*log(x)/d^2-1/4*e^4*g^2*p*log(x)/d^4+e^2*f*g*p*log(d+e*x^n)/(d^2*n)+1/4*e^4*g^2*p*log(d+e*x^n)/(d^4*n)-1/4*g^2*log(c*(d+e*x^n)^p)/(n*x^(4*n))-f*g*log(c*(d+e*x^n)^p)/(n*x^(2*n))+f^2*log(-e*x^n/d)*log(c*(d+e*x^n)^p)/n+f^2*p*polylog(2,1+e*x^n/d)/n],

# r<0
[log(c*(d+e*x^n)^p)/(x*(f+g*x^(2*n))),x,13,log(-e*x^n/d)*log(c*(d+e*x^n)^p)/(f*n)-1/2*log(c*(d+e*x^n)^p)*log(e*(sqrt(-f)-x^n*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/(f*n)-1/2*log(c*(d+e*x^n)^p)*log(e*(sqrt(-f)+x^n*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/(f*n)+p*polylog(2,1+e*x^n/d)/(f*n)-1/2*p*polylog(2,-(d+e*x^n)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(f*n)-1/2*p*polylog(2,(d+e*x^n)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(f*n)],
[log(c*(d+e*x^n)^p)/(x*(f+g*x^n)),x,8,log(-e*x^n/d)*log(c*(d+e*x^n)^p)/(f*n)-log(c*(d+e*x^n)^p)*log(e*(f+g*x^n)/(e*f-d*g))/(f*n)-p*polylog(2,-g*(d+e*x^n)/(e*f-d*g))/(f*n)+p*polylog(2,1+e*x^n/d)/(f*n)],
[log(c*(d+e*x^n)^p)/(x*(f+g/x^n)),x,5,log(c*(d+e*x^n)^p)*log(-e*(g+f*x^n)/(d*f-e*g))/(f*n)+p*polylog(2,f*(d+e*x^n)/(d*f-e*g))/(f*n)],
[log(c*(d+e*x^n)^p)/(x*(f+g/x^(2*n))),x,9,1/2*log(c*(d+e*x^n)^p)*log(-e*(x^n*sqrt(-f)+sqrt(g))/(d*sqrt(-f)-e*sqrt(g)))/(f*n)+1/2*log(c*(d+e*x^n)^p)*log(e*(-x^n*sqrt(-f)+sqrt(g))/(d*sqrt(-f)+e*sqrt(g)))/(f*n)+1/2*p*polylog(2,(d+e*x^n)*sqrt(-f)/(d*sqrt(-f)-e*sqrt(g)))/(f*n)+1/2*p*polylog(2,(d+e*x^n)*sqrt(-f)/(d*sqrt(-f)+e*sqrt(g)))/(f*n)],
[log(c*(d+e*x^n)^p)/(x*(f+g*x^(2*n))^2),x,19,-1/2*e^2*p*log(d+e*x^n)/(f*(e^2*f+d^2*g)*n)+1/2*log(c*(d+e*x^n)^p)/(f*n*(f+g*x^(2*n)))+log(-e*x^n/d)*log(c*(d+e*x^n)^p)/(f^2*n)+1/4*e^2*p*log(f+g*x^(2*n))/(f*(e^2*f+d^2*g)*n)-1/2*log(c*(d+e*x^n)^p)*log(e*(sqrt(-f)-x^n*sqrt(g))/(e*sqrt(-f)+d*sqrt(g)))/(f^2*n)-1/2*log(c*(d+e*x^n)^p)*log(e*(sqrt(-f)+x^n*sqrt(g))/(e*sqrt(-f)-d*sqrt(g)))/(f^2*n)+p*polylog(2,1+e*x^n/d)/(f^2*n)-1/2*p*polylog(2,-(d+e*x^n)*sqrt(g)/(e*sqrt(-f)-d*sqrt(g)))/(f^2*n)-1/2*p*polylog(2,(d+e*x^n)*sqrt(g)/(e*sqrt(-f)+d*sqrt(g)))/(f^2*n)-1/2*d*e*p*arctan(x^n*sqrt(g)/sqrt(f))*sqrt(g)/(f^(3/2)*(e^2*f+d^2*g)*n)],
[log(c*(d+e*x^n)^p)/(x*(f+g*x^n)^2),x,12,-e*p*log(d+e*x^n)/(f*(e*f-d*g)*n)+log(c*(d+e*x^n)^p)/(f*n*(f+g*x^n))+log(-e*x^n/d)*log(c*(d+e*x^n)^p)/(f^2*n)+e*p*log(f+g*x^n)/(f*(e*f-d*g)*n)-log(c*(d+e*x^n)^p)*log(e*(f+g*x^n)/(e*f-d*g))/(f^2*n)-p*polylog(2,-g*(d+e*x^n)/(e*f-d*g))/(f^2*n)+p*polylog(2,1+e*x^n/d)/(f^2*n)],
[log(c*(d+e*x^n)^p)/(x*(f+g/x^n)^2),x,10,e*g*p*log(d+e*x^n)/(f^2*(d*f-e*g)*n)+g*log(c*(d+e*x^n)^p)/(f^2*n*(g+f*x^n))-e*g*p*log(g+f*x^n)/(f^2*(d*f-e*g)*n)+log(c*(d+e*x^n)^p)*log(-e*(g+f*x^n)/(d*f-e*g))/(f^2*n)+p*polylog(2,f*(d+e*x^n)/(d*f-e*g))/(f^2*n)],
[log(c*(d+e*x^n)^p)/(x*(f+g/x^(2*n))^2),x,17,-1/2*e^2*g*p*log(d+e*x^n)/(f^2*(d^2*f+e^2*g)*n)+1/2*g*log(c*(d+e*x^n)^p)/(f^2*n*(g+f*x^(2*n)))+1/4*e^2*g*p*log(g+f*x^(2*n))/(f^2*(d^2*f+e^2*g)*n)+1/2*log(c*(d+e*x^n)^p)*log(-e*(x^n*sqrt(-f)+sqrt(g))/(d*sqrt(-f)-e*sqrt(g)))/(f^2*n)+1/2*log(c*(d+e*x^n)^p)*log(e*(-x^n*sqrt(-f)+sqrt(g))/(d*sqrt(-f)+e*sqrt(g)))/(f^2*n)+1/2*p*polylog(2,(d+e*x^n)*sqrt(-f)/(d*sqrt(-f)-e*sqrt(g)))/(f^2*n)+1/2*p*polylog(2,(d+e*x^n)*sqrt(-f)/(d*sqrt(-f)+e*sqrt(g)))/(f^2*n)-1/2*d*e*p*arctan(x^n*sqrt(f)/sqrt(g))*sqrt(g)/(f^(3/2)*(d^2*f+e^2*g)*n)],
[log(c*(d+e*x^n))/(x*(c*e+(-1+c*d)/x^n)),x,4,-polylog(2,1-c*(d+e*x^n))/(c*e*n)],
[x^(-1+n)*log(c*(d+e*x^n))/(-1+c*d+c*e*x^n),x,3,-polylog(2,1-c*(d+e*x^n))/(c*e*n)],
[log(c*(d+e/x^n))/(x*(c*e-(1-c*d)*x^n)),x,4,polylog(2,1-c*(d+e/x^n))/(c*e*n)],

# Integrands of the form x^r (f+g x^s)^q Log[c (d+e x^m)^n]^q when q symbolic

# r>0
[(f+g*x^(2*n))^2*log(c*(d+e*x^n)^p)^q/x,x,0,4^(-1-q)*g^2*(d+e*x^n)^4*GAMMA(1+q,-4*log(c*(d+e*x^n)^p)/p)*log(c*(d+e*x^n)^p)^q/(e^4*n*(c*(d+e*x^n)^p)^(4/p)*(-log(c*(d+e*x^n)^p)/p)^q)-d*g^2*(d+e*x^n)^3*GAMMA(1+q,-3*log(c*(d+e*x^n)^p)/p)*log(c*(d+e*x^n)^p)^q/(3^q*e^4*n*(c*(d+e*x^n)^p)^(3/p)*(-log(c*(d+e*x^n)^p)/p)^q)+f*g*(d+e*x^n)^2*GAMMA(1+q,-2*log(c*(d+e*x^n)^p)/p)*log(c*(d+e*x^n)^p)^q/(2^q*e^2*n*(c*(d+e*x^n)^p)^(2/p)*(-log(c*(d+e*x^n)^p)/p)^q)+3*2^(-1-q)*d^2*g^2*(d+e*x^n)^2*GAMMA(1+q,-2*log(c*(d+e*x^n)^p)/p)*log(c*(d+e*x^n)^p)^q/(e^4*n*(c*(d+e*x^n)^p)^(2/p)*(-log(c*(d+e*x^n)^p)/p)^q)-2*d*f*g*(d+e*x^n)*GAMMA(1+q,-log(c*(d+e*x^n)^p)/p)*log(c*(d+e*x^n)^p)^q/(e^2*n*(c*(d+e*x^n)^p)^(1/p)*(-log(c*(d+e*x^n)^p)/p)^q)-d^3*g^2*(d+e*x^n)*GAMMA(1+q,-log(c*(d+e*x^n)^p)/p)*log(c*(d+e*x^n)^p)^q/(e^4*n*(c*(d+e*x^n)^p)^(1/p)*(-log(c*(d+e*x^n)^p)/p)^q)+f^2*Unintegrable(log(c*(d+e*x^n)^p)^q/x,x),Unintegrable((f+g*x^(2*n))^2*log(c*(d+e*x^n)^p)^q/x,x)],
[(f+g*x^n)^2*log(c*(d+e*x^n)^p)^q/x,x,0,2^(-1-q)*g^2*(d+e*x^n)^2*GAMMA(1+q,-2*log(c*(d+e*x^n)^p)/p)*log(c*(d+e*x^n)^p)^q/(e^2*n*(c*(d+e*x^n)^p)^(2/p)*(-log(c*(d+e*x^n)^p)/p)^q)+2*f*g*(d+e*x^n)*GAMMA(1+q,-log(c*(d+e*x^n)^p)/p)*log(c*(d+e*x^n)^p)^q/(e*n*(c*(d+e*x^n)^p)^(1/p)*(-log(c*(d+e*x^n)^p)/p)^q)-d*g^2*(d+e*x^n)*GAMMA(1+q,-log(c*(d+e*x^n)^p)/p)*log(c*(d+e*x^n)^p)^q/(e^2*n*(c*(d+e*x^n)^p)^(1/p)*(-log(c*(d+e*x^n)^p)/p)^q)+f^2*Unintegrable(log(c*(d+e*x^n)^p)^q/x,x),Unintegrable((f+g*x^n)^2*log(c*(d+e*x^n)^p)^q/x,x)],
[(f+g/x^n)^2*log(c*(d+e*x^n)^p)^q/x,x,0,Unintegrable((f+g/x^n)^2*log(c*(d+e*x^n)^p)^q/x,x)],
[(f+g/x^(2*n))^2*log(c*(d+e*x^n)^p)^q/x,x,0,Unintegrable((f+g/x^(2*n))^2*log(c*(d+e*x^n)^p)^q/x,x)],

# r<0
[log(c*(d+e*x^n)^p)^q/(x*(f+g*x^(2*n))),x,0,Unintegrable(log(c*(d+e*x^n)^p)^q/(x*(f+g*x^(2*n))),x)],
[log(c*(d+e*x^n)^p)^q/(x*(f+g*x^n)),x,0,Unintegrable(log(c*(d+e*x^n)^p)^q/(x*(f+g*x^n)),x)],
[log(c*(d+e*x^n)^p)^q/(x*(f+g/x^n)),x,0,Unintegrable(log(c*(d+e*x^n)^p)^q/(x*(f+g/x^n)),x)],
[log(c*(d+e*x^n)^p)^q/(x*(f+g/x^(2*n))),x,0,Unintegrable(log(c*(d+e*x^n)^p)^q/(x*(f+g/x^(2*n))),x)],

# Integrands of the form (h x)^r Log[f x^s]^q Log[c (d+e x^m)^n]^p
[log(x)*log(d+e*x^m)/x,x,4,1/2*log(x)^2*log(d+e*x^m)-1/2*log(x)^2*log(1+e*x^m/d)-log(x)*polylog(2,-e*x^m/d)/m+polylog(3,-e*x^m/d)/m^2],

# Integrands of the form (f+g x)^q Log[c (d+e x^m)/x^n]
[log((a+x)/x)/x,x,1,polylog(2,-a/x),polylog(2,1+(-a-x)/x)],
[log((a+x^2)/x^2)/x,x,2,1/2*polylog(2,-a/x^2)],
[log((a+x^n)/x^n)/x,x,2,polylog(2,-a/x^n)/n],
[log((a+b*x)/x)/x,x,4,-log(b+a/x)*log(-a/(b*x))-polylog(2,1+a/(b*x))],
[log((a+b*x^2)/x^2)/x,x,4,-1/2*log(b+a/x^2)*log(-a/(b*x^2))-1/2*polylog(2,1+a/(b*x^2))],
[log((a+b*x^n)/x^n)/x,x,4,-log(-a/(b*x^n))*log(b+a/x^n)/n-polylog(2,1+a/(b*x^n))/n],
[log((a+b*x)/x)/(c+d*x),x,9,log(b+a/x)*log(c+d*x)/d+log(-d*x/c)*log(c+d*x)/d-log(-d*(a+b*x)/(b*c-a*d))*log(c+d*x)/d-polylog(2,b*(c+d*x)/(b*c-a*d))/d+polylog(2,1+d*x/c)/d],
[log((a+b*x^2)/x^2)/(c+d*x),x,14,log(b+a/x^2)*log(c+d*x)/d+2*log(-d*x/c)*log(c+d*x)/d-log(c+d*x)*log(d*(sqrt(-a)-x*sqrt(b))/(d*sqrt(-a)+c*sqrt(b)))/d-log(c+d*x)*log(-d*(sqrt(-a)+x*sqrt(b))/(-d*sqrt(-a)+c*sqrt(b)))/d+2*polylog(2,1+d*x/c)/d-polylog(2,(c+d*x)*sqrt(b)/(-d*sqrt(-a)+c*sqrt(b)))/d-polylog(2,(c+d*x)*sqrt(b)/(d*sqrt(-a)+c*sqrt(b)))/d],
[log((a+b*x^n)/x^n)/(c+d*x),x,1,Unintegrable(log(b+a/x^n)/(c+d*x),x)],

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

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

# Integrands of the form (f x)^q (a+b Log[c (d+e x^m)^n]) when q symbolic
[(f*x)^q*(a+b*log(c*(d+e*x^m)^n)),x,3,-b*e*m*n*x^(1+m)*(f*x)^q*hypergeom([1,(1+m+q)/m],[(1+2*m+q)/m],-e*x^m/d)/(d*(1+q)*(1+m+q))+(f*x)^(1+q)*(a+b*log(c*(d+e*x^m)^n))/(f*(1+q))],

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

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

# m=1
[x^3*(a+b*log(c*(d+e*sqrt(x))^n)),x,4,-1/8*b*d^6*n*x/e^6+1/12*b*d^5*n*x^(3/2)/e^5-1/16*b*d^4*n*x^2/e^4+1/20*b*d^3*n*x^(5/2)/e^3-1/24*b*d^2*n*x^3/e^2+1/28*b*d*n*x^(7/2)/e-1/32*b*n*x^4-1/4*b*d^8*n*log(d+e*sqrt(x))/e^8+1/4*x^4*(a+b*log(c*(d+e*sqrt(x))^n))+1/4*b*d^7*n*sqrt(x)/e^7],
[x^2*(a+b*log(c*(d+e*sqrt(x))^n)),x,4,-1/6*b*d^4*n*x/e^4+1/9*b*d^3*n*x^(3/2)/e^3-1/12*b*d^2*n*x^2/e^2+1/15*b*d*n*x^(5/2)/e-1/18*b*n*x^3-1/3*b*d^6*n*log(d+e*sqrt(x))/e^6+1/3*x^3*(a+b*log(c*(d+e*sqrt(x))^n))+1/3*b*d^5*n*sqrt(x)/e^5],
[x*(a+b*log(c*(d+e*sqrt(x))^n)),x,4,-1/4*b*d^2*n*x/e^2+1/6*b*d*n*x^(3/2)/e-1/8*b*n*x^2-1/2*b*d^4*n*log(d+e*sqrt(x))/e^4+1/2*x^2*(a+b*log(c*(d+e*sqrt(x))^n))+1/2*b*d^3*n*sqrt(x)/e^3],
[a+b*log(c*(d+e*sqrt(x))^n),x,5,a*x-1/2*b*n*x-b*d^2*n*log(d+e*sqrt(x))/e^2+b*x*log(c*(d+e*sqrt(x))^n)+b*d*n*sqrt(x)/e],
[(a+b*log(c*(d+e*sqrt(x))^n))/x,x,3,2*log(-e*sqrt(x)/d)*(a+b*log(c*(d+e*sqrt(x))^n))+2*b*n*polylog(2,1+e*sqrt(x)/d)],
[(a+b*log(c*(d+e*sqrt(x))^n))/x^2,x,4,-1/2*b*e^2*n*log(x)/d^2+b*e^2*n*log(d+e*sqrt(x))/d^2+(-a-b*log(c*(d+e*sqrt(x))^n))/x-b*e*n/(d*sqrt(x))],
[(a+b*log(c*(d+e*sqrt(x))^n))/x^3,x,4,-1/6*b*e*n/(d*x^(3/2))+1/4*b*e^2*n/(d^2*x)-1/4*b*e^4*n*log(x)/d^4+1/2*b*e^4*n*log(d+e*sqrt(x))/d^4+1/2*(-a-b*log(c*(d+e*sqrt(x))^n))/x^2-1/2*b*e^3*n/(d^3*sqrt(x))],
[(a+b*log(c*(d+e*sqrt(x))^n))/x^4,x,4,-1/15*b*e*n/(d*x^(5/2))+1/12*b*e^2*n/(d^2*x^2)-1/9*b*e^3*n/(d^3*x^(3/2))+1/6*b*e^4*n/(d^4*x)-1/6*b*e^6*n*log(x)/d^6+1/3*b*e^6*n*log(d+e*sqrt(x))/d^6+1/3*(-a-b*log(c*(d+e*sqrt(x))^n))/x^3-1/3*b*e^5*n/(d^5*sqrt(x))],
[x^2*(a+b*log(c*(d+e*sqrt(x))^n))^2,x,8,1/3*b^2*d^6*n^2*log(d+e*sqrt(x))^2/e^6-2/3*b*d^6*n*log(d+e*sqrt(x))*(a+b*log(c*(d+e*sqrt(x))^n))/e^6+1/3*x^3*(a+b*log(c*(d+e*sqrt(x))^n))^2-4*b^2*d^5*n^2*sqrt(x)/e^5+4*b*d^5*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))/e^6+5/2*b^2*d^4*n^2*(d+e*sqrt(x))^2/e^6-5*b*d^4*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^2/e^6-40/27*b^2*d^3*n^2*(d+e*sqrt(x))^3/e^6+40/9*b*d^3*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^3/e^6+5/8*b^2*d^2*n^2*(d+e*sqrt(x))^4/e^6-5/2*b*d^2*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^4/e^6-4/25*b^2*d*n^2*(d+e*sqrt(x))^5/e^6+4/5*b*d*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^5/e^6+1/54*b^2*n^2*(d+e*sqrt(x))^6/e^6-1/9*b*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^6/e^6],
[x*(a+b*log(c*(d+e*sqrt(x))^n))^2,x,8,1/2*b^2*d^4*n^2*log(d+e*sqrt(x))^2/e^4-b*d^4*n*log(d+e*sqrt(x))*(a+b*log(c*(d+e*sqrt(x))^n))/e^4+1/2*x^2*(a+b*log(c*(d+e*sqrt(x))^n))^2-4*b^2*d^3*n^2*sqrt(x)/e^3+4*b*d^3*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))/e^4+3/2*b^2*d^2*n^2*(d+e*sqrt(x))^2/e^4-3*b*d^2*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^2/e^4-4/9*b^2*d*n^2*(d+e*sqrt(x))^3/e^4+4/3*b*d*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^3/e^4+1/16*b^2*n^2*(d+e*sqrt(x))^4/e^4-1/4*b*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^4/e^4],
[(a+b*log(c*(d+e*sqrt(x))^n))^2,x,10,4*a*b*d*n*sqrt(x)/e-4*b^2*d*n^2*sqrt(x)/e+4*b^2*d*n*log(c*(d+e*sqrt(x))^n)*(d+e*sqrt(x))/e^2-2*d*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))/e^2+1/2*b^2*n^2*(d+e*sqrt(x))^2/e^2-b*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^2/e^2+(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))^2/e^2],
[(a+b*log(c*(d+e*sqrt(x))^n))^2/x,x,5,2*log(-e*sqrt(x)/d)*(a+b*log(c*(d+e*sqrt(x))^n))^2+4*b*n*(a+b*log(c*(d+e*sqrt(x))^n))*polylog(2,1+e*sqrt(x)/d)-4*b^2*n^2*polylog(3,1+e*sqrt(x)/d)],
[(a+b*log(c*(d+e*sqrt(x))^n))^2/x^2,x,8,b^2*e^2*n^2*log(x)/d^2-(a+b*log(c*(d+e*sqrt(x))^n))^2/x-2*b*e^2*n*(a+b*log(c*(d+e*sqrt(x))^n))*log(1-d/(d+e*sqrt(x)))/d^2+2*b^2*e^2*n^2*polylog(2,d/(d+e*sqrt(x)))/d^2-2*b*e*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))/(d^2*sqrt(x))],
[(a+b*log(c*(d+e*sqrt(x))^n))^2/x^3,x,16,-1/6*b^2*e^2*n^2/(d^2*x)+11/12*b^2*e^4*n^2*log(x)/d^4-5/6*b^2*e^4*n^2*log(d+e*sqrt(x))/d^4-1/3*b*e*n*(a+b*log(c*(d+e*sqrt(x))^n))/(d*x^(3/2))+1/2*b*e^2*n*(a+b*log(c*(d+e*sqrt(x))^n))/(d^2*x)-1/2*(a+b*log(c*(d+e*sqrt(x))^n))^2/x^2-b*e^4*n*(a+b*log(c*(d+e*sqrt(x))^n))*log(1-d/(d+e*sqrt(x)))/d^4+b^2*e^4*n^2*polylog(2,d/(d+e*sqrt(x)))/d^4+5/6*b^2*e^3*n^2/(d^3*sqrt(x))-b*e^3*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))/(d^4*sqrt(x))],
[(a+b*log(c*(d+e*sqrt(x))^n))^2/x^4,x,24,-1/30*b^2*e^2*n^2/(d^2*x^2)+1/10*b^2*e^3*n^2/(d^3*x^(3/2))-47/180*b^2*e^4*n^2/(d^4*x)+137/180*b^2*e^6*n^2*log(x)/d^6-77/90*b^2*e^6*n^2*log(d+e*sqrt(x))/d^6-2/15*b*e*n*(a+b*log(c*(d+e*sqrt(x))^n))/(d*x^(5/2))+1/6*b*e^2*n*(a+b*log(c*(d+e*sqrt(x))^n))/(d^2*x^2)-2/9*b*e^3*n*(a+b*log(c*(d+e*sqrt(x))^n))/(d^3*x^(3/2))+1/3*b*e^4*n*(a+b*log(c*(d+e*sqrt(x))^n))/(d^4*x)-1/3*(a+b*log(c*(d+e*sqrt(x))^n))^2/x^3-2/3*b*e^6*n*(a+b*log(c*(d+e*sqrt(x))^n))*log(1-d/(d+e*sqrt(x)))/d^6+2/3*b^2*e^6*n^2*polylog(2,d/(d+e*sqrt(x)))/d^6+77/90*b^2*e^5*n^2/(d^5*sqrt(x))-2/3*b*e^5*n*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))/(d^6*sqrt(x))],
[x^2*(a+b*log(c*(d+e*sqrt(x))^n))^3,x,28,-12*a*b^2*d^5*n^2*sqrt(x)/e^5+12*b^3*d^5*n^3*sqrt(x)/e^5-12*b^3*d^5*n^2*log(c*(d+e*sqrt(x))^n)*(d+e*sqrt(x))/e^6+6*b*d^5*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))/e^6-2*d^5*(a+b*log(c*(d+e*sqrt(x))^n))^3*(d+e*sqrt(x))/e^6-15/4*b^3*d^4*n^3*(d+e*sqrt(x))^2/e^6+15/2*b^2*d^4*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^2/e^6-15/2*b*d^4*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))^2/e^6+5*d^4*(a+b*log(c*(d+e*sqrt(x))^n))^3*(d+e*sqrt(x))^2/e^6+40/27*b^3*d^3*n^3*(d+e*sqrt(x))^3/e^6-40/9*b^2*d^3*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^3/e^6+20/3*b*d^3*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))^3/e^6-20/3*d^3*(a+b*log(c*(d+e*sqrt(x))^n))^3*(d+e*sqrt(x))^3/e^6-15/32*b^3*d^2*n^3*(d+e*sqrt(x))^4/e^6+15/8*b^2*d^2*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^4/e^6-15/4*b*d^2*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))^4/e^6+5*d^2*(a+b*log(c*(d+e*sqrt(x))^n))^3*(d+e*sqrt(x))^4/e^6+12/125*b^3*d*n^3*(d+e*sqrt(x))^5/e^6-12/25*b^2*d*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^5/e^6+6/5*b*d*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))^5/e^6-2*d*(a+b*log(c*(d+e*sqrt(x))^n))^3*(d+e*sqrt(x))^5/e^6-1/108*b^3*n^3*(d+e*sqrt(x))^6/e^6+1/18*b^2*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^6/e^6-1/6*b*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))^6/e^6+1/3*(a+b*log(c*(d+e*sqrt(x))^n))^3*(d+e*sqrt(x))^6/e^6],
[x*(a+b*log(c*(d+e*sqrt(x))^n))^3,x,20,-12*a*b^2*d^3*n^2*sqrt(x)/e^3+12*b^3*d^3*n^3*sqrt(x)/e^3-12*b^3*d^3*n^2*log(c*(d+e*sqrt(x))^n)*(d+e*sqrt(x))/e^4+6*b*d^3*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))/e^4-2*d^3*(a+b*log(c*(d+e*sqrt(x))^n))^3*(d+e*sqrt(x))/e^4-9/4*b^3*d^2*n^3*(d+e*sqrt(x))^2/e^4+9/2*b^2*d^2*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^2/e^4-9/2*b*d^2*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))^2/e^4+3*d^2*(a+b*log(c*(d+e*sqrt(x))^n))^3*(d+e*sqrt(x))^2/e^4+4/9*b^3*d*n^3*(d+e*sqrt(x))^3/e^4-4/3*b^2*d*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^3/e^4+2*b*d*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))^3/e^4-2*d*(a+b*log(c*(d+e*sqrt(x))^n))^3*(d+e*sqrt(x))^3/e^4-3/64*b^3*n^3*(d+e*sqrt(x))^4/e^4+3/16*b^2*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^4/e^4-3/8*b*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))^4/e^4+1/2*(a+b*log(c*(d+e*sqrt(x))^n))^3*(d+e*sqrt(x))^4/e^4],
[(a+b*log(c*(d+e*sqrt(x))^n))^3,x,12,-12*a*b^2*d*n^2*sqrt(x)/e+12*b^3*d*n^3*sqrt(x)/e-12*b^3*d*n^2*log(c*(d+e*sqrt(x))^n)*(d+e*sqrt(x))/e^2+6*b*d*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))/e^2-2*d*(a+b*log(c*(d+e*sqrt(x))^n))^3*(d+e*sqrt(x))/e^2-3/4*b^3*n^3*(d+e*sqrt(x))^2/e^2+3/2*b^2*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))^2/e^2-3/2*b*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))^2/e^2+(a+b*log(c*(d+e*sqrt(x))^n))^3*(d+e*sqrt(x))^2/e^2],
[(a+b*log(c*(d+e*sqrt(x))^n))^3/x,x,6,2*log(-e*sqrt(x)/d)*(a+b*log(c*(d+e*sqrt(x))^n))^3+6*b*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*polylog(2,1+e*sqrt(x)/d)-12*b^2*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*polylog(3,1+e*sqrt(x)/d)+12*b^3*n^3*polylog(4,1+e*sqrt(x)/d)],
[(a+b*log(c*(d+e*sqrt(x))^n))^3/x^2,x,10,6*b^2*e^2*n^2*log(-e*sqrt(x)/d)*(a+b*log(c*(d+e*sqrt(x))^n))/d^2-(a+b*log(c*(d+e*sqrt(x))^n))^3/x-3*b*e^2*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*log(1-d/(d+e*sqrt(x)))/d^2+6*b^2*e^2*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*polylog(2,d/(d+e*sqrt(x)))/d^2+6*b^3*e^2*n^3*polylog(2,1+e*sqrt(x)/d)/d^2+6*b^3*e^2*n^3*polylog(3,d/(d+e*sqrt(x)))/d^2-3*b*e*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))/(d^2*sqrt(x))],
[(a+b*log(c*(d+e*sqrt(x))^n))^3/x^3,x,28,-3/2*b^3*e^4*n^3*log(x)/d^4+1/2*b^3*e^4*n^3*log(d+e*sqrt(x))/d^4-1/2*b^2*e^2*n^2*(a+b*log(c*(d+e*sqrt(x))^n))/(d^2*x)+3*b^2*e^4*n^2*log(-e*sqrt(x)/d)*(a+b*log(c*(d+e*sqrt(x))^n))/d^4-1/2*b*e*n*(a+b*log(c*(d+e*sqrt(x))^n))^2/(d*x^(3/2))+3/4*b*e^2*n*(a+b*log(c*(d+e*sqrt(x))^n))^2/(d^2*x)-1/2*(a+b*log(c*(d+e*sqrt(x))^n))^3/x^2+5/2*b^2*e^4*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*log(1-d/(d+e*sqrt(x)))/d^4-3/2*b*e^4*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*log(1-d/(d+e*sqrt(x)))/d^4-5/2*b^3*e^4*n^3*polylog(2,d/(d+e*sqrt(x)))/d^4+3*b^2*e^4*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*polylog(2,d/(d+e*sqrt(x)))/d^4+3*b^3*e^4*n^3*polylog(2,1+e*sqrt(x)/d)/d^4+3*b^3*e^4*n^3*polylog(3,d/(d+e*sqrt(x)))/d^4-1/2*b^3*e^3*n^3/(d^3*sqrt(x))+5/2*b^2*e^3*n^2*(a+b*log(c*(d+e*sqrt(x))^n))*(d+e*sqrt(x))/(d^4*sqrt(x))-3/2*b*e^3*n*(a+b*log(c*(d+e*sqrt(x))^n))^2*(d+e*sqrt(x))/(d^4*sqrt(x))],

# m=-1
[x^3*(a+b*log(c*(d+e/sqrt(x))^n)),x,4,-1/8*b*e^6*n*x/d^6+1/12*b*e^5*n*x^(3/2)/d^5-1/16*b*e^4*n*x^2/d^4+1/20*b*e^3*n*x^(5/2)/d^3-1/24*b*e^2*n*x^3/d^2+1/28*b*e*n*x^(7/2)/d-1/8*b*e^8*n*log(x)/d^8-1/4*b*e^8*n*log(d+e/sqrt(x))/d^8+1/4*x^4*(a+b*log(c*(d+e/sqrt(x))^n))+1/4*b*e^7*n*sqrt(x)/d^7],
[x^2*(a+b*log(c*(d+e/sqrt(x))^n)),x,4,-1/6*b*e^4*n*x/d^4+1/9*b*e^3*n*x^(3/2)/d^3-1/12*b*e^2*n*x^2/d^2+1/15*b*e*n*x^(5/2)/d-1/6*b*e^6*n*log(x)/d^6-1/3*b*e^6*n*log(d+e/sqrt(x))/d^6+1/3*x^3*(a+b*log(c*(d+e/sqrt(x))^n))+1/3*b*e^5*n*sqrt(x)/d^5],
[x*(a+b*log(c*(d+e/sqrt(x))^n)),x,4,-1/4*b*e^2*n*x/d^2+1/6*b*e*n*x^(3/2)/d-1/4*b*e^4*n*log(x)/d^4-1/2*b*e^4*n*log(d+e/sqrt(x))/d^4+1/2*x^2*(a+b*log(c*(d+e/sqrt(x))^n))+1/2*b*e^3*n*sqrt(x)/d^3],
[a+b*log(c*(d+e/sqrt(x))^n),x,6,a*x+b*x*log(c*(d+e/sqrt(x))^n)-b*e^2*n*log(e+d*sqrt(x))/d^2+b*e*n*sqrt(x)/d],
[(a+b*log(c*(d+e/sqrt(x))^n))/x,x,3,-2*(a+b*log(c*(d+e/sqrt(x))^n))*log(-e/(d*sqrt(x)))-2*b*n*polylog(2,1+e/(d*sqrt(x)))],
[(a+b*log(c*(d+e/sqrt(x))^n))/x^2,x,4,1/2*b*n/x+b*d^2*n*log(d+e/sqrt(x))/e^2+(-a-b*log(c*(d+e/sqrt(x))^n))/x-b*d*n/(e*sqrt(x))],
[(a+b*log(c*(d+e/sqrt(x))^n))/x^3,x,4,1/8*b*n/x^2-1/6*b*d*n/(e*x^(3/2))+1/4*b*d^2*n/(e^2*x)+1/2*b*d^4*n*log(d+e/sqrt(x))/e^4+1/2*(-a-b*log(c*(d+e/sqrt(x))^n))/x^2-1/2*b*d^3*n/(e^3*sqrt(x))],
[(a+b*log(c*(d+e/sqrt(x))^n))/x^4,x,4,1/18*b*n/x^3-1/15*b*d*n/(e*x^(5/2))+1/12*b*d^2*n/(e^2*x^2)-1/9*b*d^3*n/(e^3*x^(3/2))+1/6*b*d^4*n/(e^4*x)+1/3*b*d^6*n*log(d+e/sqrt(x))/e^6+1/3*(-a-b*log(c*(d+e/sqrt(x))^n))/x^3-1/3*b*d^5*n/(e^5*sqrt(x))],
[x^2*(a+b*log(c*(d+e/sqrt(x))^n))^2,x,24,47/180*b^2*e^4*n^2*x/d^4-1/10*b^2*e^3*n^2*x^(3/2)/d^3+1/30*b^2*e^2*n^2*x^2/d^2+137/180*b^2*e^6*n^2*log(x)/d^6+77/90*b^2*e^6*n^2*log(d+e/sqrt(x))/d^6-1/3*b*e^4*n*x*(a+b*log(c*(d+e/sqrt(x))^n))/d^4+2/9*b*e^3*n*x^(3/2)*(a+b*log(c*(d+e/sqrt(x))^n))/d^3-1/6*b*e^2*n*x^2*(a+b*log(c*(d+e/sqrt(x))^n))/d^2+2/15*b*e*n*x^(5/2)*(a+b*log(c*(d+e/sqrt(x))^n))/d+2/3*b*e^6*n*log(1-d/(d+e/sqrt(x)))*(a+b*log(c*(d+e/sqrt(x))^n))/d^6+1/3*x^3*(a+b*log(c*(d+e/sqrt(x))^n))^2-2/3*b^2*e^6*n^2*polylog(2,d/(d+e/sqrt(x)))/d^6-77/90*b^2*e^5*n^2*sqrt(x)/d^5+2/3*b*e^5*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))*sqrt(x)/d^6],
[x*(a+b*log(c*(d+e/sqrt(x))^n))^2,x,16,1/6*b^2*e^2*n^2*x/d^2+11/12*b^2*e^4*n^2*log(x)/d^4+5/6*b^2*e^4*n^2*log(d+e/sqrt(x))/d^4-1/2*b*e^2*n*x*(a+b*log(c*(d+e/sqrt(x))^n))/d^2+1/3*b*e*n*x^(3/2)*(a+b*log(c*(d+e/sqrt(x))^n))/d+b*e^4*n*log(1-d/(d+e/sqrt(x)))*(a+b*log(c*(d+e/sqrt(x))^n))/d^4+1/2*x^2*(a+b*log(c*(d+e/sqrt(x))^n))^2-b^2*e^4*n^2*polylog(2,d/(d+e/sqrt(x)))/d^4-5/6*b^2*e^3*n^2*sqrt(x)/d^3+b*e^3*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))*sqrt(x)/d^4],
[(a+b*log(c*(d+e/sqrt(x))^n))^2,x,9,b^2*e^2*n^2*log(x)/d^2+2*b*e^2*n*log(1-d/(d+e/sqrt(x)))*(a+b*log(c*(d+e/sqrt(x))^n))/d^2+x*(a+b*log(c*(d+e/sqrt(x))^n))^2-2*b^2*e^2*n^2*polylog(2,d/(d+e/sqrt(x)))/d^2+2*b*e*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))*sqrt(x)/d^2],
[(a+b*log(c*(d+e/sqrt(x))^n))^2/x,x,5,-2*(a+b*log(c*(d+e/sqrt(x))^n))^2*log(-e/(d*sqrt(x)))-4*b*n*(a+b*log(c*(d+e/sqrt(x))^n))*polylog(2,1+e/(d*sqrt(x)))+4*b^2*n^2*polylog(3,1+e/(d*sqrt(x)))],
[(a+b*log(c*(d+e/sqrt(x))^n))^2/x^2,x,10,-4*b^2*d*n*log(c*(d+e/sqrt(x))^n)*(d+e/sqrt(x))/e^2+2*d*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))/e^2-1/2*b^2*n^2*(d+e/sqrt(x))^2/e^2+b*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^2/e^2-(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))^2/e^2-4*a*b*d*n/(e*sqrt(x))+4*b^2*d*n^2/(e*sqrt(x))],
[(a+b*log(c*(d+e/sqrt(x))^n))^2/x^3,x,8,-1/2*b^2*d^4*n^2*log(d+e/sqrt(x))^2/e^4+b*d^4*n*log(d+e/sqrt(x))*(a+b*log(c*(d+e/sqrt(x))^n))/e^4-1/2*(a+b*log(c*(d+e/sqrt(x))^n))^2/x^2-4*b*d^3*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))/e^4-3/2*b^2*d^2*n^2*(d+e/sqrt(x))^2/e^4+3*b*d^2*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^2/e^4+4/9*b^2*d*n^2*(d+e/sqrt(x))^3/e^4-4/3*b*d*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^3/e^4-1/16*b^2*n^2*(d+e/sqrt(x))^4/e^4+1/4*b*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^4/e^4+4*b^2*d^3*n^2/(e^3*sqrt(x))],
[(a+b*log(c*(d+e/sqrt(x))^n))^2/x^4,x,8,-1/3*b^2*d^6*n^2*log(d+e/sqrt(x))^2/e^6+2/3*b*d^6*n*log(d+e/sqrt(x))*(a+b*log(c*(d+e/sqrt(x))^n))/e^6-1/3*(a+b*log(c*(d+e/sqrt(x))^n))^2/x^3-4*b*d^5*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))/e^6-5/2*b^2*d^4*n^2*(d+e/sqrt(x))^2/e^6+5*b*d^4*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^2/e^6+40/27*b^2*d^3*n^2*(d+e/sqrt(x))^3/e^6-40/9*b*d^3*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^3/e^6-5/8*b^2*d^2*n^2*(d+e/sqrt(x))^4/e^6+5/2*b*d^2*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^4/e^6+4/25*b^2*d*n^2*(d+e/sqrt(x))^5/e^6-4/5*b*d*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^5/e^6-1/54*b^2*n^2*(d+e/sqrt(x))^6/e^6+1/9*b*n*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^6/e^6+4*b^2*d^5*n^2/(e^5*sqrt(x))],
[x*(a+b*log(c*(d+e/sqrt(x))^n))^3,x,28,-3/2*b^3*e^4*n^3*log(x)/d^4-1/2*b^3*e^4*n^3*log(d+e/sqrt(x))/d^4+1/2*b^2*e^2*n^2*x*(a+b*log(c*(d+e/sqrt(x))^n))/d^2-5/2*b^2*e^4*n^2*log(1-d/(d+e/sqrt(x)))*(a+b*log(c*(d+e/sqrt(x))^n))/d^4-3/4*b*e^2*n*x*(a+b*log(c*(d+e/sqrt(x))^n))^2/d^2+1/2*b*e*n*x^(3/2)*(a+b*log(c*(d+e/sqrt(x))^n))^2/d+3/2*b*e^4*n*log(1-d/(d+e/sqrt(x)))*(a+b*log(c*(d+e/sqrt(x))^n))^2/d^4+1/2*x^2*(a+b*log(c*(d+e/sqrt(x))^n))^3-3*b^2*e^4*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*log(-e/(d*sqrt(x)))/d^4+5/2*b^3*e^4*n^3*polylog(2,d/(d+e/sqrt(x)))/d^4-3*b^2*e^4*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*polylog(2,d/(d+e/sqrt(x)))/d^4-3*b^3*e^4*n^3*polylog(2,1+e/(d*sqrt(x)))/d^4-3*b^3*e^4*n^3*polylog(3,d/(d+e/sqrt(x)))/d^4+1/2*b^3*e^3*n^3*sqrt(x)/d^3-5/2*b^2*e^3*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))*sqrt(x)/d^4+3/2*b*e^3*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))*sqrt(x)/d^4],
[(a+b*log(c*(d+e/sqrt(x))^n))^3,x,11,3*b*e^2*n*log(1-d/(d+e/sqrt(x)))*(a+b*log(c*(d+e/sqrt(x))^n))^2/d^2+x*(a+b*log(c*(d+e/sqrt(x))^n))^3-6*b^2*e^2*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*log(-e/(d*sqrt(x)))/d^2-6*b^2*e^2*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*polylog(2,d/(d+e/sqrt(x)))/d^2-6*b^3*e^2*n^3*polylog(2,1+e/(d*sqrt(x)))/d^2-6*b^3*e^2*n^3*polylog(3,d/(d+e/sqrt(x)))/d^2+3*b*e*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))*sqrt(x)/d^2],
[(a+b*log(c*(d+e/sqrt(x))^n))^3/x,x,6,-2*(a+b*log(c*(d+e/sqrt(x))^n))^3*log(-e/(d*sqrt(x)))-6*b*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*polylog(2,1+e/(d*sqrt(x)))+12*b^2*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*polylog(3,1+e/(d*sqrt(x)))-12*b^3*n^3*polylog(4,1+e/(d*sqrt(x)))],
[(a+b*log(c*(d+e/sqrt(x))^n))^3/x^2,x,12,12*b^3*d*n^2*log(c*(d+e/sqrt(x))^n)*(d+e/sqrt(x))/e^2-6*b*d*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))/e^2+2*d*(a+b*log(c*(d+e/sqrt(x))^n))^3*(d+e/sqrt(x))/e^2+3/4*b^3*n^3*(d+e/sqrt(x))^2/e^2-3/2*b^2*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^2/e^2+3/2*b*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))^2/e^2-(a+b*log(c*(d+e/sqrt(x))^n))^3*(d+e/sqrt(x))^2/e^2+12*a*b^2*d*n^2/(e*sqrt(x))-12*b^3*d*n^3/(e*sqrt(x))],
[(a+b*log(c*(d+e/sqrt(x))^n))^3/x^3,x,20,12*b^3*d^3*n^2*log(c*(d+e/sqrt(x))^n)*(d+e/sqrt(x))/e^4-6*b*d^3*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))/e^4+2*d^3*(a+b*log(c*(d+e/sqrt(x))^n))^3*(d+e/sqrt(x))/e^4+9/4*b^3*d^2*n^3*(d+e/sqrt(x))^2/e^4-9/2*b^2*d^2*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^2/e^4+9/2*b*d^2*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))^2/e^4-3*d^2*(a+b*log(c*(d+e/sqrt(x))^n))^3*(d+e/sqrt(x))^2/e^4-4/9*b^3*d*n^3*(d+e/sqrt(x))^3/e^4+4/3*b^2*d*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^3/e^4-2*b*d*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))^3/e^4+2*d*(a+b*log(c*(d+e/sqrt(x))^n))^3*(d+e/sqrt(x))^3/e^4+3/64*b^3*n^3*(d+e/sqrt(x))^4/e^4-3/16*b^2*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^4/e^4+3/8*b*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))^4/e^4-1/2*(a+b*log(c*(d+e/sqrt(x))^n))^3*(d+e/sqrt(x))^4/e^4+12*a*b^2*d^3*n^2/(e^3*sqrt(x))-12*b^3*d^3*n^3/(e^3*sqrt(x))],
[(a+b*log(c*(d+e/sqrt(x))^n))^3/x^4,x,28,12*b^3*d^5*n^2*log(c*(d+e/sqrt(x))^n)*(d+e/sqrt(x))/e^6-6*b*d^5*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))/e^6+2*d^5*(a+b*log(c*(d+e/sqrt(x))^n))^3*(d+e/sqrt(x))/e^6+15/4*b^3*d^4*n^3*(d+e/sqrt(x))^2/e^6-15/2*b^2*d^4*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^2/e^6+15/2*b*d^4*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))^2/e^6-5*d^4*(a+b*log(c*(d+e/sqrt(x))^n))^3*(d+e/sqrt(x))^2/e^6-40/27*b^3*d^3*n^3*(d+e/sqrt(x))^3/e^6+40/9*b^2*d^3*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^3/e^6-20/3*b*d^3*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))^3/e^6+20/3*d^3*(a+b*log(c*(d+e/sqrt(x))^n))^3*(d+e/sqrt(x))^3/e^6+15/32*b^3*d^2*n^3*(d+e/sqrt(x))^4/e^6-15/8*b^2*d^2*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^4/e^6+15/4*b*d^2*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))^4/e^6-5*d^2*(a+b*log(c*(d+e/sqrt(x))^n))^3*(d+e/sqrt(x))^4/e^6-12/125*b^3*d*n^3*(d+e/sqrt(x))^5/e^6+12/25*b^2*d*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^5/e^6-6/5*b*d*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))^5/e^6+2*d*(a+b*log(c*(d+e/sqrt(x))^n))^3*(d+e/sqrt(x))^5/e^6+1/108*b^3*n^3*(d+e/sqrt(x))^6/e^6-1/18*b^2*n^2*(a+b*log(c*(d+e/sqrt(x))^n))*(d+e/sqrt(x))^6/e^6+1/6*b*n*(a+b*log(c*(d+e/sqrt(x))^n))^2*(d+e/sqrt(x))^6/e^6-1/3*(a+b*log(c*(d+e/sqrt(x))^n))^3*(d+e/sqrt(x))^6/e^6+12*a*b^2*d^5*n^2/(e^5*sqrt(x))-12*b^3*d^5*n^3/(e^5*sqrt(x))],

# Integrands of the form x^q (a+b Log[c (d+e x^(m/3))^n])^p when n symbolic

# m=1
[x^3*(a+b*log(c*(d+e*x^(1/3))^n)),x,4,1/4*b*d^11*n*x^(1/3)/e^11-1/8*b*d^10*n*x^(2/3)/e^10+1/12*b*d^9*n*x/e^9-1/16*b*d^8*n*x^(4/3)/e^8+1/20*b*d^7*n*x^(5/3)/e^7-1/24*b*d^6*n*x^2/e^6+1/28*b*d^5*n*x^(7/3)/e^5-1/32*b*d^4*n*x^(8/3)/e^4+1/36*b*d^3*n*x^3/e^3-1/40*b*d^2*n*x^(10/3)/e^2+1/44*b*d*n*x^(11/3)/e-1/48*b*n*x^4-1/4*b*d^12*n*log(d+e*x^(1/3))/e^12+1/4*x^4*(a+b*log(c*(d+e*x^(1/3))^n))],
[x^2*(a+b*log(c*(d+e*x^(1/3))^n)),x,4,-1/3*b*d^8*n*x^(1/3)/e^8+1/6*b*d^7*n*x^(2/3)/e^7-1/9*b*d^6*n*x/e^6+1/12*b*d^5*n*x^(4/3)/e^5-1/15*b*d^4*n*x^(5/3)/e^4+1/18*b*d^3*n*x^2/e^3-1/21*b*d^2*n*x^(7/3)/e^2+1/24*b*d*n*x^(8/3)/e-1/27*b*n*x^3+1/3*b*d^9*n*log(d+e*x^(1/3))/e^9+1/3*x^3*(a+b*log(c*(d+e*x^(1/3))^n))],
[x*(a+b*log(c*(d+e*x^(1/3))^n)),x,4,1/2*b*d^5*n*x^(1/3)/e^5-1/4*b*d^4*n*x^(2/3)/e^4+1/6*b*d^3*n*x/e^3-1/8*b*d^2*n*x^(4/3)/e^2+1/10*b*d*n*x^(5/3)/e-1/12*b*n*x^2-1/2*b*d^6*n*log(d+e*x^(1/3))/e^6+1/2*x^2*(a+b*log(c*(d+e*x^(1/3))^n))],
[a+b*log(c*(d+e*x^(1/3))^n),x,5,-b*d^2*n*x^(1/3)/e^2+1/2*b*d*n*x^(2/3)/e+a*x-1/3*b*n*x+b*d^3*n*log(d+e*x^(1/3))/e^3+b*x*log(c*(d+e*x^(1/3))^n)],
[(a+b*log(c*(d+e*x^(1/3))^n))/x,x,3,3*(a+b*log(c*(d+e*x^(1/3))^n))*log(-e*x^(1/3)/d)+3*b*n*polylog(2,1+e*x^(1/3)/d)],
[(a+b*log(c*(d+e*x^(1/3))^n))/x^2,x,4,-1/2*b*e*n/(d*x^(2/3))+b*e^2*n/(d^2*x^(1/3))-b*e^3*n*log(d+e*x^(1/3))/d^3+(-a-b*log(c*(d+e*x^(1/3))^n))/x+1/3*b*e^3*n*log(x)/d^3],
[(a+b*log(c*(d+e*x^(1/3))^n))/x^3,x,4,-1/10*b*e*n/(d*x^(5/3))+1/8*b*e^2*n/(d^2*x^(4/3))-1/6*b*e^3*n/(d^3*x)+1/4*b*e^4*n/(d^4*x^(2/3))-1/2*b*e^5*n/(d^5*x^(1/3))+1/2*b*e^6*n*log(d+e*x^(1/3))/d^6+1/2*(-a-b*log(c*(d+e*x^(1/3))^n))/x^2-1/6*b*e^6*n*log(x)/d^6],
[(a+b*log(c*(d+e*x^(1/3))^n))/x^4,x,4,-1/24*b*e*n/(d*x^(8/3))+1/21*b*e^2*n/(d^2*x^(7/3))-1/18*b*e^3*n/(d^3*x^2)+1/15*b*e^4*n/(d^4*x^(5/3))-1/12*b*e^5*n/(d^5*x^(4/3))+1/9*b*e^6*n/(d^6*x)-1/6*b*e^7*n/(d^7*x^(2/3))+1/3*b*e^8*n/(d^8*x^(1/3))-1/3*b*e^9*n*log(d+e*x^(1/3))/d^9+1/3*(-a-b*log(c*(d+e*x^(1/3))^n))/x^3+1/9*b*e^9*n*log(x)/d^9],
[x^2*(a+b*log(c*(d+e*x^(1/3))^n))^2,x,8,-6*b^2*d^7*n^2*(d+e*x^(1/3))^2/e^9+56/9*b^2*d^6*n^2*(d+e*x^(1/3))^3/e^9-21/4*b^2*d^5*n^2*(d+e*x^(1/3))^4/e^9+84/25*b^2*d^4*n^2*(d+e*x^(1/3))^5/e^9-14/9*b^2*d^3*n^2*(d+e*x^(1/3))^6/e^9+24/49*b^2*d^2*n^2*(d+e*x^(1/3))^7/e^9-3/32*b^2*d*n^2*(d+e*x^(1/3))^8/e^9+2/243*b^2*n^2*(d+e*x^(1/3))^9/e^9+6*b^2*d^8*n^2*x^(1/3)/e^8-1/3*b^2*d^9*n^2*log(d+e*x^(1/3))^2/e^9-6*b*d^8*n*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))/e^9+12*b*d^7*n*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))/e^9-56/3*b*d^6*n*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))/e^9+21*b*d^5*n*(d+e*x^(1/3))^4*(a+b*log(c*(d+e*x^(1/3))^n))/e^9-84/5*b*d^4*n*(d+e*x^(1/3))^5*(a+b*log(c*(d+e*x^(1/3))^n))/e^9+28/3*b*d^3*n*(d+e*x^(1/3))^6*(a+b*log(c*(d+e*x^(1/3))^n))/e^9-24/7*b*d^2*n*(d+e*x^(1/3))^7*(a+b*log(c*(d+e*x^(1/3))^n))/e^9+3/4*b*d*n*(d+e*x^(1/3))^8*(a+b*log(c*(d+e*x^(1/3))^n))/e^9-2/27*b*n*(d+e*x^(1/3))^9*(a+b*log(c*(d+e*x^(1/3))^n))/e^9+2/3*b*d^9*n*log(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))/e^9+1/3*x^3*(a+b*log(c*(d+e*x^(1/3))^n))^2],
[x*(a+b*log(c*(d+e*x^(1/3))^n))^2,x,8,15/4*b^2*d^4*n^2*(d+e*x^(1/3))^2/e^6-20/9*b^2*d^3*n^2*(d+e*x^(1/3))^3/e^6+15/16*b^2*d^2*n^2*(d+e*x^(1/3))^4/e^6-6/25*b^2*d*n^2*(d+e*x^(1/3))^5/e^6+1/36*b^2*n^2*(d+e*x^(1/3))^6/e^6-6*b^2*d^5*n^2*x^(1/3)/e^5+1/2*b^2*d^6*n^2*log(d+e*x^(1/3))^2/e^6+6*b*d^5*n*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))/e^6-15/2*b*d^4*n*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))/e^6+20/3*b*d^3*n*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))/e^6-15/4*b*d^2*n*(d+e*x^(1/3))^4*(a+b*log(c*(d+e*x^(1/3))^n))/e^6+6/5*b*d*n*(d+e*x^(1/3))^5*(a+b*log(c*(d+e*x^(1/3))^n))/e^6-1/6*b*n*(d+e*x^(1/3))^6*(a+b*log(c*(d+e*x^(1/3))^n))/e^6-b*d^6*n*log(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))/e^6+1/2*x^2*(a+b*log(c*(d+e*x^(1/3))^n))^2],
[(a+b*log(c*(d+e*x^(1/3))^n))^2,x,8,-3/2*b^2*d*n^2*(d+e*x^(1/3))^2/e^3+2/9*b^2*n^2*(d+e*x^(1/3))^3/e^3+6*b^2*d^2*n^2*x^(1/3)/e^2-b^2*d^3*n^2*log(d+e*x^(1/3))^2/e^3-6*b*d^2*n*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))/e^3+3*b*d*n*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))/e^3-2/3*b*n*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))/e^3+2*b*d^3*n*log(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))/e^3+x*(a+b*log(c*(d+e*x^(1/3))^n))^2],
[(a+b*log(c*(d+e*x^(1/3))^n))^2/x,x,5,3*(a+b*log(c*(d+e*x^(1/3))^n))^2*log(-e*x^(1/3)/d)+6*b*n*(a+b*log(c*(d+e*x^(1/3))^n))*polylog(2,1+e*x^(1/3)/d)-6*b^2*n^2*polylog(3,1+e*x^(1/3)/d)],
[(a+b*log(c*(d+e*x^(1/3))^n))^2/x^2,x,12,-b^2*e^2*n^2/(d^2*x^(1/3))+b^2*e^3*n^2*log(d+e*x^(1/3))/d^3-b*e*n*(a+b*log(c*(d+e*x^(1/3))^n))/(d*x^(2/3))+2*b*e^2*n*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))/(d^3*x^(1/3))+2*b*e^3*n*log(1-d/(d+e*x^(1/3)))*(a+b*log(c*(d+e*x^(1/3))^n))/d^3-(a+b*log(c*(d+e*x^(1/3))^n))^2/x-b^2*e^3*n^2*log(x)/d^3-2*b^2*e^3*n^2*polylog(2,d/(d+e*x^(1/3)))/d^3],
[(a+b*log(c*(d+e*x^(1/3))^n))^2/x^3,x,24,-1/20*b^2*e^2*n^2/(d^2*x^(4/3))+3/20*b^2*e^3*n^2/(d^3*x)-47/120*b^2*e^4*n^2/(d^4*x^(2/3))+77/60*b^2*e^5*n^2/(d^5*x^(1/3))-77/60*b^2*e^6*n^2*log(d+e*x^(1/3))/d^6-1/5*b*e*n*(a+b*log(c*(d+e*x^(1/3))^n))/(d*x^(5/3))+1/4*b*e^2*n*(a+b*log(c*(d+e*x^(1/3))^n))/(d^2*x^(4/3))-1/3*b*e^3*n*(a+b*log(c*(d+e*x^(1/3))^n))/(d^3*x)+1/2*b*e^4*n*(a+b*log(c*(d+e*x^(1/3))^n))/(d^4*x^(2/3))-b*e^5*n*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))/(d^6*x^(1/3))-b*e^6*n*log(1-d/(d+e*x^(1/3)))*(a+b*log(c*(d+e*x^(1/3))^n))/d^6-1/2*(a+b*log(c*(d+e*x^(1/3))^n))^2/x^2+137/180*b^2*e^6*n^2*log(x)/d^6+b^2*e^6*n^2*polylog(2,d/(d+e*x^(1/3)))/d^6],
[x^3*(a+b*log(c*(d+e*x^(1/3))^n))^3,x,52,-99/8*b^3*d^10*n^3*(d+e*x^(1/3))^2/e^12+110/9*b^3*d^9*n^3*(d+e*x^(1/3))^3/e^12-1485/128*b^3*d^8*n^3*(d+e*x^(1/3))^4/e^12+1188/125*b^3*d^7*n^3*(d+e*x^(1/3))^5/e^12-77/12*b^3*d^6*n^3*(d+e*x^(1/3))^6/e^12+1188/343*b^3*d^5*n^3*(d+e*x^(1/3))^7/e^12-1485/1024*b^3*d^4*n^3*(d+e*x^(1/3))^8/e^12+110/243*b^3*d^3*n^3*(d+e*x^(1/3))^9/e^12-99/1000*b^3*d^2*n^3*(d+e*x^(1/3))^10/e^12+18/1331*b^3*d*n^3*(d+e*x^(1/3))^11/e^12-1/1152*b^3*n^3*(d+e*x^(1/3))^12/e^12-18*a*b^2*d^11*n^2*x^(1/3)/e^11+18*b^3*d^11*n^3*x^(1/3)/e^11-18*b^3*d^11*n^2*(d+e*x^(1/3))*log(c*(d+e*x^(1/3))^n)/e^12+99/4*b^2*d^10*n^2*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))/e^12-110/3*b^2*d^9*n^2*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))/e^12+1485/32*b^2*d^8*n^2*(d+e*x^(1/3))^4*(a+b*log(c*(d+e*x^(1/3))^n))/e^12-1188/25*b^2*d^7*n^2*(d+e*x^(1/3))^5*(a+b*log(c*(d+e*x^(1/3))^n))/e^12+77/2*b^2*d^6*n^2*(d+e*x^(1/3))^6*(a+b*log(c*(d+e*x^(1/3))^n))/e^12-1188/49*b^2*d^5*n^2*(d+e*x^(1/3))^7*(a+b*log(c*(d+e*x^(1/3))^n))/e^12+1485/128*b^2*d^4*n^2*(d+e*x^(1/3))^8*(a+b*log(c*(d+e*x^(1/3))^n))/e^12-110/27*b^2*d^3*n^2*(d+e*x^(1/3))^9*(a+b*log(c*(d+e*x^(1/3))^n))/e^12+99/100*b^2*d^2*n^2*(d+e*x^(1/3))^10*(a+b*log(c*(d+e*x^(1/3))^n))/e^12-18/121*b^2*d*n^2*(d+e*x^(1/3))^11*(a+b*log(c*(d+e*x^(1/3))^n))/e^12+1/96*b^2*n^2*(d+e*x^(1/3))^12*(a+b*log(c*(d+e*x^(1/3))^n))/e^12+9*b*d^11*n*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^12-99/4*b*d^10*n*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^12+55*b*d^9*n*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^12-1485/16*b*d^8*n*(d+e*x^(1/3))^4*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^12+594/5*b*d^7*n*(d+e*x^(1/3))^5*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^12-231/2*b*d^6*n*(d+e*x^(1/3))^6*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^12+594/7*b*d^5*n*(d+e*x^(1/3))^7*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^12-1485/32*b*d^4*n*(d+e*x^(1/3))^8*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^12+55/3*b*d^3*n*(d+e*x^(1/3))^9*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^12-99/20*b*d^2*n*(d+e*x^(1/3))^10*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^12+9/11*b*d*n*(d+e*x^(1/3))^11*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^12-1/16*b*n*(d+e*x^(1/3))^12*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^12-3*d^11*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^12+33/2*d^10*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^12-55*d^9*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^12+495/4*d^8*(d+e*x^(1/3))^4*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^12-198*d^7*(d+e*x^(1/3))^5*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^12+231*d^6*(d+e*x^(1/3))^6*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^12-198*d^5*(d+e*x^(1/3))^7*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^12+495/4*d^4*(d+e*x^(1/3))^8*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^12-55*d^3*(d+e*x^(1/3))^9*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^12+33/2*d^2*(d+e*x^(1/3))^10*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^12-3*d*(d+e*x^(1/3))^11*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^12+1/4*(d+e*x^(1/3))^12*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^12],
[x^2*(a+b*log(c*(d+e*x^(1/3))^n))^3,x,40,9*b^3*d^7*n^3*(d+e*x^(1/3))^2/e^9-56/9*b^3*d^6*n^3*(d+e*x^(1/3))^3/e^9+63/16*b^3*d^5*n^3*(d+e*x^(1/3))^4/e^9-252/125*b^3*d^4*n^3*(d+e*x^(1/3))^5/e^9+7/9*b^3*d^3*n^3*(d+e*x^(1/3))^6/e^9-72/343*b^3*d^2*n^3*(d+e*x^(1/3))^7/e^9+9/256*b^3*d*n^3*(d+e*x^(1/3))^8/e^9-2/729*b^3*n^3*(d+e*x^(1/3))^9/e^9+18*a*b^2*d^8*n^2*x^(1/3)/e^8-18*b^3*d^8*n^3*x^(1/3)/e^8+18*b^3*d^8*n^2*(d+e*x^(1/3))*log(c*(d+e*x^(1/3))^n)/e^9-18*b^2*d^7*n^2*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))/e^9+56/3*b^2*d^6*n^2*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))/e^9-63/4*b^2*d^5*n^2*(d+e*x^(1/3))^4*(a+b*log(c*(d+e*x^(1/3))^n))/e^9+252/25*b^2*d^4*n^2*(d+e*x^(1/3))^5*(a+b*log(c*(d+e*x^(1/3))^n))/e^9-14/3*b^2*d^3*n^2*(d+e*x^(1/3))^6*(a+b*log(c*(d+e*x^(1/3))^n))/e^9+72/49*b^2*d^2*n^2*(d+e*x^(1/3))^7*(a+b*log(c*(d+e*x^(1/3))^n))/e^9-9/32*b^2*d*n^2*(d+e*x^(1/3))^8*(a+b*log(c*(d+e*x^(1/3))^n))/e^9+2/81*b^2*n^2*(d+e*x^(1/3))^9*(a+b*log(c*(d+e*x^(1/3))^n))/e^9-9*b*d^8*n*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^9+18*b*d^7*n*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^9-28*b*d^6*n*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^9+63/2*b*d^5*n*(d+e*x^(1/3))^4*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^9-126/5*b*d^4*n*(d+e*x^(1/3))^5*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^9+14*b*d^3*n*(d+e*x^(1/3))^6*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^9-36/7*b*d^2*n*(d+e*x^(1/3))^7*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^9+9/8*b*d*n*(d+e*x^(1/3))^8*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^9-1/9*b*n*(d+e*x^(1/3))^9*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^9+3*d^8*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^9-12*d^7*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^9+28*d^6*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^9-42*d^5*(d+e*x^(1/3))^4*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^9+42*d^4*(d+e*x^(1/3))^5*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^9-28*d^3*(d+e*x^(1/3))^6*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^9+12*d^2*(d+e*x^(1/3))^7*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^9-3*d*(d+e*x^(1/3))^8*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^9+1/3*(d+e*x^(1/3))^9*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^9],
[x*(a+b*log(c*(d+e*x^(1/3))^n))^3,x,28,-45/8*b^3*d^4*n^3*(d+e*x^(1/3))^2/e^6+20/9*b^3*d^3*n^3*(d+e*x^(1/3))^3/e^6-45/64*b^3*d^2*n^3*(d+e*x^(1/3))^4/e^6+18/125*b^3*d*n^3*(d+e*x^(1/3))^5/e^6-1/72*b^3*n^3*(d+e*x^(1/3))^6/e^6-18*a*b^2*d^5*n^2*x^(1/3)/e^5+18*b^3*d^5*n^3*x^(1/3)/e^5-18*b^3*d^5*n^2*(d+e*x^(1/3))*log(c*(d+e*x^(1/3))^n)/e^6+45/4*b^2*d^4*n^2*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))/e^6-20/3*b^2*d^3*n^2*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))/e^6+45/16*b^2*d^2*n^2*(d+e*x^(1/3))^4*(a+b*log(c*(d+e*x^(1/3))^n))/e^6-18/25*b^2*d*n^2*(d+e*x^(1/3))^5*(a+b*log(c*(d+e*x^(1/3))^n))/e^6+1/12*b^2*n^2*(d+e*x^(1/3))^6*(a+b*log(c*(d+e*x^(1/3))^n))/e^6+9*b*d^5*n*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^6-45/4*b*d^4*n*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^6+10*b*d^3*n*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^6-45/8*b*d^2*n*(d+e*x^(1/3))^4*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^6+9/5*b*d*n*(d+e*x^(1/3))^5*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^6-1/4*b*n*(d+e*x^(1/3))^6*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^6-3*d^5*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^6+15/2*d^4*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^6-10*d^3*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^6+15/2*d^2*(d+e*x^(1/3))^4*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^6-3*d*(d+e*x^(1/3))^5*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^6+1/2*(d+e*x^(1/3))^6*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^6],
[(a+b*log(c*(d+e*x^(1/3))^n))^3,x,16,9/4*b^3*d*n^3*(d+e*x^(1/3))^2/e^3-2/9*b^3*n^3*(d+e*x^(1/3))^3/e^3+18*a*b^2*d^2*n^2*x^(1/3)/e^2-18*b^3*d^2*n^3*x^(1/3)/e^2+18*b^3*d^2*n^2*(d+e*x^(1/3))*log(c*(d+e*x^(1/3))^n)/e^3-9/2*b^2*d*n^2*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))/e^3+2/3*b^2*n^2*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))/e^3-9*b*d^2*n*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^3+9/2*b*d*n*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^3-b*n*(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))^2/e^3+3*d^2*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^3-3*d*(d+e*x^(1/3))^2*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^3+(d+e*x^(1/3))^3*(a+b*log(c*(d+e*x^(1/3))^n))^3/e^3],
[(a+b*log(c*(d+e*x^(1/3))^n))^3/x,x,6,3*(a+b*log(c*(d+e*x^(1/3))^n))^3*log(-e*x^(1/3)/d)+9*b*n*(a+b*log(c*(d+e*x^(1/3))^n))^2*polylog(2,1+e*x^(1/3)/d)-18*b^2*n^2*(a+b*log(c*(d+e*x^(1/3))^n))*polylog(3,1+e*x^(1/3)/d)+18*b^3*n^3*polylog(4,1+e*x^(1/3)/d)],
[(a+b*log(c*(d+e*x^(1/3))^n))^3/x^2,x,17,-3*b^2*e^2*n^2*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))/(d^3*x^(1/3))-3*b^2*e^3*n^2*log(1-d/(d+e*x^(1/3)))*(a+b*log(c*(d+e*x^(1/3))^n))/d^3-3/2*b*e*n*(a+b*log(c*(d+e*x^(1/3))^n))^2/(d*x^(2/3))+3*b*e^2*n*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))^2/(d^3*x^(1/3))+3*b*e^3*n*log(1-d/(d+e*x^(1/3)))*(a+b*log(c*(d+e*x^(1/3))^n))^2/d^3-(a+b*log(c*(d+e*x^(1/3))^n))^3/x-6*b^2*e^3*n^2*(a+b*log(c*(d+e*x^(1/3))^n))*log(-e*x^(1/3)/d)/d^3+b^3*e^3*n^3*log(x)/d^3+3*b^3*e^3*n^3*polylog(2,d/(d+e*x^(1/3)))/d^3-6*b^2*e^3*n^2*(a+b*log(c*(d+e*x^(1/3))^n))*polylog(2,d/(d+e*x^(1/3)))/d^3-6*b^3*e^3*n^3*polylog(2,1+e*x^(1/3)/d)/d^3-6*b^3*e^3*n^3*polylog(3,d/(d+e*x^(1/3)))/d^3],
[(a+b*log(c*(d+e*x^(1/3))^n))^3/x^3,x,62,-1/20*b^3*e^3*n^3/(d^3*x)+3/10*b^3*e^4*n^3/(d^4*x^(2/3))-71/40*b^3*e^5*n^3/(d^5*x^(1/3))+71/40*b^3*e^6*n^3*log(d+e*x^(1/3))/d^6-3/20*b^2*e^2*n^2*(a+b*log(c*(d+e*x^(1/3))^n))/(d^2*x^(4/3))+9/20*b^2*e^3*n^2*(a+b*log(c*(d+e*x^(1/3))^n))/(d^3*x)-47/40*b^2*e^4*n^2*(a+b*log(c*(d+e*x^(1/3))^n))/(d^4*x^(2/3))+77/20*b^2*e^5*n^2*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))/(d^6*x^(1/3))+77/20*b^2*e^6*n^2*log(1-d/(d+e*x^(1/3)))*(a+b*log(c*(d+e*x^(1/3))^n))/d^6-3/10*b*e*n*(a+b*log(c*(d+e*x^(1/3))^n))^2/(d*x^(5/3))+3/8*b*e^2*n*(a+b*log(c*(d+e*x^(1/3))^n))^2/(d^2*x^(4/3))-1/2*b*e^3*n*(a+b*log(c*(d+e*x^(1/3))^n))^2/(d^3*x)+3/4*b*e^4*n*(a+b*log(c*(d+e*x^(1/3))^n))^2/(d^4*x^(2/3))-3/2*b*e^5*n*(d+e*x^(1/3))*(a+b*log(c*(d+e*x^(1/3))^n))^2/(d^6*x^(1/3))-3/2*b*e^6*n*log(1-d/(d+e*x^(1/3)))*(a+b*log(c*(d+e*x^(1/3))^n))^2/d^6-1/2*(a+b*log(c*(d+e*x^(1/3))^n))^3/x^2+3*b^2*e^6*n^2*(a+b*log(c*(d+e*x^(1/3))^n))*log(-e*x^(1/3)/d)/d^6-15/8*b^3*e^6*n^3*log(x)/d^6-77/20*b^3*e^6*n^3*polylog(2,d/(d+e*x^(1/3)))/d^6+3*b^2*e^6*n^2*(a+b*log(c*(d+e*x^(1/3))^n))*polylog(2,d/(d+e*x^(1/3)))/d^6+3*b^3*e^6*n^3*polylog(2,1+e*x^(1/3)/d)/d^6+3*b^3*e^6*n^3*polylog(3,d/(d+e*x^(1/3)))/d^6],

# m=2
[x^3*(a+b*log(c*(d+e*x^(2/3))^n)),x,4,1/4*b*d^5*n*x^(2/3)/e^5-1/8*b*d^4*n*x^(4/3)/e^4+1/12*b*d^3*n*x^2/e^3-1/16*b*d^2*n*x^(8/3)/e^2+1/20*b*d*n*x^(10/3)/e-1/24*b*n*x^4-1/4*b*d^6*n*log(d+e*x^(2/3))/e^6+1/4*x^4*(a+b*log(c*(d+e*x^(2/3))^n))],
[x^2*(a+b*log(c*(d+e*x^(2/3))^n)),x,5,-2/3*b*d^4*n*x^(1/3)/e^4+2/9*b*d^3*n*x/e^3-2/15*b*d^2*n*x^(5/3)/e^2+2/21*b*d*n*x^(7/3)/e-2/27*b*n*x^3+2/3*b*d^(9/2)*n*arctan(x^(1/3)*sqrt(e)/sqrt(d))/e^(9/2)+1/3*x^3*(a+b*log(c*(d+e*x^(2/3))^n))],
[x*(a+b*log(c*(d+e*x^(2/3))^n)),x,4,-1/2*b*d^2*n*x^(2/3)/e^2+1/4*b*d*n*x^(4/3)/e-1/6*b*n*x^2+1/2*b*d^3*n*log(d+e*x^(2/3))/e^3+1/2*x^2*(a+b*log(c*(d+e*x^(2/3))^n))],
[a+b*log(c*(d+e*x^(2/3))^n),x,6,2*b*d*n*x^(1/3)/e+a*x-2/3*b*n*x-2*b*d^(3/2)*n*arctan(x^(1/3)*sqrt(e)/sqrt(d))/e^(3/2)+b*x*log(c*(d+e*x^(2/3))^n)],
[(a+b*log(c*(d+e*x^(2/3))^n))/x,x,3,3/2*(a+b*log(c*(d+e*x^(2/3))^n))*log(-e*x^(2/3)/d)+3/2*b*n*polylog(2,1+e*x^(2/3)/d)],
[(a+b*log(c*(d+e*x^(2/3))^n))/x^2,x,4,-2*b*e*n/(d*x^(1/3))-2*b*e^(3/2)*n*arctan(x^(1/3)*sqrt(e)/sqrt(d))/d^(3/2)+(-a-b*log(c*(d+e*x^(2/3))^n))/x],
[(a+b*log(c*(d+e*x^(2/3))^n))/x^3,x,4,-1/4*b*e*n/(d*x^(4/3))+1/2*b*e^2*n/(d^2*x^(2/3))-1/2*b*e^3*n*log(d+e*x^(2/3))/d^3+1/2*(-a-b*log(c*(d+e*x^(2/3))^n))/x^2+1/3*b*e^3*n*log(x)/d^3],
[(a+b*log(c*(d+e*x^(2/3))^n))/x^4,x,7,-2/21*b*e*n/(d*x^(7/3))+2/15*b*e^2*n/(d^2*x^(5/3))-2/9*b*e^3*n/(d^3*x)+2/3*b*e^4*n/(d^4*x^(1/3))+2/3*b*e^(9/2)*n*arctan(x^(1/3)*sqrt(e)/sqrt(d))/d^(9/2)+1/3*(-a-b*log(c*(d+e*x^(2/3))^n))/x^3],
[x^3*(a+b*log(c*(d+e*x^(2/3))^n))^2,x,8,15/8*b^2*d^4*n^2*(d+e*x^(2/3))^2/e^6-10/9*b^2*d^3*n^2*(d+e*x^(2/3))^3/e^6+15/32*b^2*d^2*n^2*(d+e*x^(2/3))^4/e^6-3/25*b^2*d*n^2*(d+e*x^(2/3))^5/e^6+1/72*b^2*n^2*(d+e*x^(2/3))^6/e^6-3*b^2*d^5*n^2*x^(2/3)/e^5+1/4*b^2*d^6*n^2*log(d+e*x^(2/3))^2/e^6+3*b*d^5*n*(d+e*x^(2/3))*(a+b*log(c*(d+e*x^(2/3))^n))/e^6-15/4*b*d^4*n*(d+e*x^(2/3))^2*(a+b*log(c*(d+e*x^(2/3))^n))/e^6+10/3*b*d^3*n*(d+e*x^(2/3))^3*(a+b*log(c*(d+e*x^(2/3))^n))/e^6-15/8*b*d^2*n*(d+e*x^(2/3))^4*(a+b*log(c*(d+e*x^(2/3))^n))/e^6+3/5*b*d*n*(d+e*x^(2/3))^5*(a+b*log(c*(d+e*x^(2/3))^n))/e^6-1/12*b*n*(d+e*x^(2/3))^6*(a+b*log(c*(d+e*x^(2/3))^n))/e^6-1/2*b*d^6*n*log(d+e*x^(2/3))*(a+b*log(c*(d+e*x^(2/3))^n))/e^6+1/4*x^4*(a+b*log(c*(d+e*x^(2/3))^n))^2],
[x*(a+b*log(c*(d+e*x^(2/3))^n))^2,x,8,-3/4*b^2*d*n^2*(d+e*x^(2/3))^2/e^3+1/9*b^2*n^2*(d+e*x^(2/3))^3/e^3+3*b^2*d^2*n^2*x^(2/3)/e^2-1/2*b^2*d^3*n^2*log(d+e*x^(2/3))^2/e^3-3*b*d^2*n*(d+e*x^(2/3))*(a+b*log(c*(d+e*x^(2/3))^n))/e^3+3/2*b*d*n*(d+e*x^(2/3))^2*(a+b*log(c*(d+e*x^(2/3))^n))/e^3-1/3*b*n*(d+e*x^(2/3))^3*(a+b*log(c*(d+e*x^(2/3))^n))/e^3+b*d^3*n*log(d+e*x^(2/3))*(a+b*log(c*(d+e*x^(2/3))^n))/e^3+1/2*x^2*(a+b*log(c*(d+e*x^(2/3))^n))^2],
[(a+b*log(c*(d+e*x^(2/3))^n))^2/x,x,5,3/2*(a+b*log(c*(d+e*x^(2/3))^n))^2*log(-e*x^(2/3)/d)+3*b*n*(a+b*log(c*(d+e*x^(2/3))^n))*polylog(2,1+e*x^(2/3)/d)-3*b^2*n^2*polylog(3,1+e*x^(2/3)/d)],
[(a+b*log(c*(d+e*x^(2/3))^n))^2/x^3,x,12,-1/2*b^2*e^2*n^2/(d^2*x^(2/3))+1/2*b^2*e^3*n^2*log(d+e*x^(2/3))/d^3-1/2*b*e*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d*x^(4/3))+b*e^2*n*(d+e*x^(2/3))*(a+b*log(c*(d+e*x^(2/3))^n))/(d^3*x^(2/3))+b*e^3*n*log(1-d/(d+e*x^(2/3)))*(a+b*log(c*(d+e*x^(2/3))^n))/d^3-1/2*(a+b*log(c*(d+e*x^(2/3))^n))^2/x^2-b^2*e^3*n^2*log(x)/d^3-b^2*e^3*n^2*polylog(2,d/(d+e*x^(2/3)))/d^3],
[(a+b*log(c*(d+e*x^(2/3))^n))^2/x^5,x,24,-1/40*b^2*e^2*n^2/(d^2*x^(8/3))+3/40*b^2*e^3*n^2/(d^3*x^2)-47/240*b^2*e^4*n^2/(d^4*x^(4/3))+77/120*b^2*e^5*n^2/(d^5*x^(2/3))-77/120*b^2*e^6*n^2*log(d+e*x^(2/3))/d^6-1/10*b*e*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d*x^(10/3))+1/8*b*e^2*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d^2*x^(8/3))-1/6*b*e^3*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d^3*x^2)+1/4*b*e^4*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d^4*x^(4/3))-1/2*b*e^5*n*(d+e*x^(2/3))*(a+b*log(c*(d+e*x^(2/3))^n))/(d^6*x^(2/3))-1/2*b*e^6*n*log(1-d/(d+e*x^(2/3)))*(a+b*log(c*(d+e*x^(2/3))^n))/d^6-1/4*(a+b*log(c*(d+e*x^(2/3))^n))^2/x^4+137/180*b^2*e^6*n^2*log(x)/d^6+1/2*b^2*e^6*n^2*polylog(2,d/(d+e*x^(2/3)))/d^6],
[x^2*(a+b*log(c*(d+e*x^(2/3))^n))^2,x,30,-4/3*a*b*d^4*n*x^(1/3)/e^4+4504/945*b^2*d^4*n^2*x^(1/3)/e^4-1984/2835*b^2*d^3*n^2*x/e^3+1144/4725*b^2*d^2*n^2*x^(5/3)/e^2-128/1323*b^2*d*n^2*x^(7/3)/e+8/243*b^2*n^2*x^3-4504/945*b^2*d^(9/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))/e^(9/2)+4/3*I*b^2*d^(9/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))^2/e^(9/2)-4/3*b^2*d^4*n*x^(1/3)*log(c*(d+e*x^(2/3))^n)/e^4+4/9*b*d^3*n*x*(a+b*log(c*(d+e*x^(2/3))^n))/e^3-4/15*b*d^2*n*x^(5/3)*(a+b*log(c*(d+e*x^(2/3))^n))/e^2+4/21*b*d*n*x^(7/3)*(a+b*log(c*(d+e*x^(2/3))^n))/e-4/27*b*n*x^3*(a+b*log(c*(d+e*x^(2/3))^n))+4/3*b*d^(9/2)*n*arctan(x^(1/3)*sqrt(e)/sqrt(d))*(a+b*log(c*(d+e*x^(2/3))^n))/e^(9/2)+1/3*x^3*(a+b*log(c*(d+e*x^(2/3))^n))^2+8/3*b^2*d^(9/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/e^(9/2)+4/3*I*b^2*d^(9/2)*n^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/e^(9/2)],
[(a+b*log(c*(d+e*x^(2/3))^n))^2,x,18,4*a*b*d*n*x^(1/3)/e-32/3*b^2*d*n^2*x^(1/3)/e+8/9*b^2*n^2*x+32/3*b^2*d^(3/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))/e^(3/2)-4*I*b^2*d^(3/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))^2/e^(3/2)+4*b^2*d*n*x^(1/3)*log(c*(d+e*x^(2/3))^n)/e-4/3*b*n*x*(a+b*log(c*(d+e*x^(2/3))^n))-4*b*d^(3/2)*n*arctan(x^(1/3)*sqrt(e)/sqrt(d))*(a+b*log(c*(d+e*x^(2/3))^n))/e^(3/2)+x*(a+b*log(c*(d+e*x^(2/3))^n))^2-8*b^2*d^(3/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/e^(3/2)-4*I*b^2*d^(3/2)*n^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/e^(3/2)],
[(a+b*log(c*(d+e*x^(2/3))^n))^2/x^2,x,12,8*b^2*e^(3/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))/d^(3/2)-4*I*b^2*e^(3/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))^2/d^(3/2)-4*b*e*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d*x^(1/3))-4*b*e^(3/2)*n*arctan(x^(1/3)*sqrt(e)/sqrt(d))*(a+b*log(c*(d+e*x^(2/3))^n))/d^(3/2)-(a+b*log(c*(d+e*x^(2/3))^n))^2/x-8*b^2*e^(3/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/d^(3/2)-4*I*b^2*e^(3/2)*n^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/d^(3/2)],
[(a+b*log(c*(d+e*x^(2/3))^n))^2/x^4,x,24,-8/105*b^2*e^2*n^2/(d^2*x^(5/3))+32/105*b^2*e^3*n^2/(d^3*x)-568/315*b^2*e^4*n^2/(d^4*x^(1/3))-1408/315*b^2*e^(9/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))/d^(9/2)+4/3*I*b^2*e^(9/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))^2/d^(9/2)-4/21*b*e*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d*x^(7/3))+4/15*b*e^2*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d^2*x^(5/3))-4/9*b*e^3*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d^3*x)+4/3*b*e^4*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d^4*x^(1/3))+4/3*b*e^(9/2)*n*arctan(x^(1/3)*sqrt(e)/sqrt(d))*(a+b*log(c*(d+e*x^(2/3))^n))/d^(9/2)-1/3*(a+b*log(c*(d+e*x^(2/3))^n))^2/x^3+8/3*b^2*e^(9/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/d^(9/2)+4/3*I*b^2*e^(9/2)*n^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/d^(9/2)],
[(a+b*log(c*(d+e*x^(2/3))^n))^2/x^6,x,45,-8/715*b^2*e^2*n^2/(d^2*x^(11/3))+64/2145*b^2*e^3*n^2/(d^3*x^3)-2872/45045*b^2*e^4*n^2/(d^4*x^(7/3))+1216/9009*b^2*e^5*n^2/(d^5*x^(5/3))-224072/675675*b^2*e^6*n^2/(d^6*x)+344192/225225*b^2*e^7*n^2/(d^7*x^(1/3))+704552/225225*b^2*e^(15/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))/d^(15/2)-4/5*I*b^2*e^(15/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))^2/d^(15/2)-4/65*b*e*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d*x^(13/3))+4/55*b*e^2*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d^2*x^(11/3))-4/45*b*e^3*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d^3*x^3)+4/35*b*e^4*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d^4*x^(7/3))-4/25*b*e^5*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d^5*x^(5/3))+4/15*b*e^6*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d^6*x)-4/5*b*e^7*n*(a+b*log(c*(d+e*x^(2/3))^n))/(d^7*x^(1/3))-4/5*b*e^(15/2)*n*arctan(x^(1/3)*sqrt(e)/sqrt(d))*(a+b*log(c*(d+e*x^(2/3))^n))/d^(15/2)-1/5*(a+b*log(c*(d+e*x^(2/3))^n))^2/x^5-8/5*b^2*e^(15/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/d^(15/2)-4/5*I*b^2*e^(15/2)*n^2*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/d^(15/2)],
[x^3*(a+b*log(c*(d+e*x^(2/3))^n))^3,x,28,-45/16*b^3*d^4*n^3*(d+e*x^(2/3))^2/e^6+10/9*b^3*d^3*n^3*(d+e*x^(2/3))^3/e^6-45/128*b^3*d^2*n^3*(d+e*x^(2/3))^4/e^6+9/125*b^3*d*n^3*(d+e*x^(2/3))^5/e^6-1/144*b^3*n^3*(d+e*x^(2/3))^6/e^6-9*a*b^2*d^5*n^2*x^(2/3)/e^5+9*b^3*d^5*n^3*x^(2/3)/e^5-9*b^3*d^5*n^2*(d+e*x^(2/3))*log(c*(d+e*x^(2/3))^n)/e^6+45/8*b^2*d^4*n^2*(d+e*x^(2/3))^2*(a+b*log(c*(d+e*x^(2/3))^n))/e^6-10/3*b^2*d^3*n^2*(d+e*x^(2/3))^3*(a+b*log(c*(d+e*x^(2/3))^n))/e^6+45/32*b^2*d^2*n^2*(d+e*x^(2/3))^4*(a+b*log(c*(d+e*x^(2/3))^n))/e^6-9/25*b^2*d*n^2*(d+e*x^(2/3))^5*(a+b*log(c*(d+e*x^(2/3))^n))/e^6+1/24*b^2*n^2*(d+e*x^(2/3))^6*(a+b*log(c*(d+e*x^(2/3))^n))/e^6+9/2*b*d^5*n*(d+e*x^(2/3))*(a+b*log(c*(d+e*x^(2/3))^n))^2/e^6-45/8*b*d^4*n*(d+e*x^(2/3))^2*(a+b*log(c*(d+e*x^(2/3))^n))^2/e^6+5*b*d^3*n*(d+e*x^(2/3))^3*(a+b*log(c*(d+e*x^(2/3))^n))^2/e^6-45/16*b*d^2*n*(d+e*x^(2/3))^4*(a+b*log(c*(d+e*x^(2/3))^n))^2/e^6+9/10*b*d*n*(d+e*x^(2/3))^5*(a+b*log(c*(d+e*x^(2/3))^n))^2/e^6-1/8*b*n*(d+e*x^(2/3))^6*(a+b*log(c*(d+e*x^(2/3))^n))^2/e^6-3/2*d^5*(d+e*x^(2/3))*(a+b*log(c*(d+e*x^(2/3))^n))^3/e^6+15/4*d^4*(d+e*x^(2/3))^2*(a+b*log(c*(d+e*x^(2/3))^n))^3/e^6-5*d^3*(d+e*x^(2/3))^3*(a+b*log(c*(d+e*x^(2/3))^n))^3/e^6+15/4*d^2*(d+e*x^(2/3))^4*(a+b*log(c*(d+e*x^(2/3))^n))^3/e^6-3/2*d*(d+e*x^(2/3))^5*(a+b*log(c*(d+e*x^(2/3))^n))^3/e^6+1/4*(d+e*x^(2/3))^6*(a+b*log(c*(d+e*x^(2/3))^n))^3/e^6],
[x*(a+b*log(c*(d+e*x^(2/3))^n))^3,x,16,9/8*b^3*d*n^3*(d+e*x^(2/3))^2/e^3-1/9*b^3*n^3*(d+e*x^(2/3))^3/e^3+9*a*b^2*d^2*n^2*x^(2/3)/e^2-9*b^3*d^2*n^3*x^(2/3)/e^2+9*b^3*d^2*n^2*(d+e*x^(2/3))*log(c*(d+e*x^(2/3))^n)/e^3-9/4*b^2*d*n^2*(d+e*x^(2/3))^2*(a+b*log(c*(d+e*x^(2/3))^n))/e^3+1/3*b^2*n^2*(d+e*x^(2/3))^3*(a+b*log(c*(d+e*x^(2/3))^n))/e^3-9/2*b*d^2*n*(d+e*x^(2/3))*(a+b*log(c*(d+e*x^(2/3))^n))^2/e^3+9/4*b*d*n*(d+e*x^(2/3))^2*(a+b*log(c*(d+e*x^(2/3))^n))^2/e^3-1/2*b*n*(d+e*x^(2/3))^3*(a+b*log(c*(d+e*x^(2/3))^n))^2/e^3+3/2*d^2*(d+e*x^(2/3))*(a+b*log(c*(d+e*x^(2/3))^n))^3/e^3-3/2*d*(d+e*x^(2/3))^2*(a+b*log(c*(d+e*x^(2/3))^n))^3/e^3+1/2*(d+e*x^(2/3))^3*(a+b*log(c*(d+e*x^(2/3))^n))^3/e^3],
[(a+b*log(c*(d+e*x^(2/3))^n))^3/x,x,6,3/2*(a+b*log(c*(d+e*x^(2/3))^n))^3*log(-e*x^(2/3)/d)+9/2*b*n*(a+b*log(c*(d+e*x^(2/3))^n))^2*polylog(2,1+e*x^(2/3)/d)-9*b^2*n^2*(a+b*log(c*(d+e*x^(2/3))^n))*polylog(3,1+e*x^(2/3)/d)+9*b^3*n^3*polylog(4,1+e*x^(2/3)/d)],
[(a+b*log(c*(d+e*x^(2/3))^n))^3/x^3,x,17,-3/2*b^2*e^2*n^2*(d+e*x^(2/3))*(a+b*log(c*(d+e*x^(2/3))^n))/(d^3*x^(2/3))-3/2*b^2*e^3*n^2*log(1-d/(d+e*x^(2/3)))*(a+b*log(c*(d+e*x^(2/3))^n))/d^3-3/4*b*e*n*(a+b*log(c*(d+e*x^(2/3))^n))^2/(d*x^(4/3))+3/2*b*e^2*n*(d+e*x^(2/3))*(a+b*log(c*(d+e*x^(2/3))^n))^2/(d^3*x^(2/3))+3/2*b*e^3*n*log(1-d/(d+e*x^(2/3)))*(a+b*log(c*(d+e*x^(2/3))^n))^2/d^3-1/2*(a+b*log(c*(d+e*x^(2/3))^n))^3/x^2-3*b^2*e^3*n^2*(a+b*log(c*(d+e*x^(2/3))^n))*log(-e*x^(2/3)/d)/d^3+b^3*e^3*n^3*log(x)/d^3+3/2*b^3*e^3*n^3*polylog(2,d/(d+e*x^(2/3)))/d^3-3*b^2*e^3*n^2*(a+b*log(c*(d+e*x^(2/3))^n))*polylog(2,d/(d+e*x^(2/3)))/d^3-3*b^3*e^3*n^3*polylog(2,1+e*x^(2/3)/d)/d^3-3*b^3*e^3*n^3*polylog(3,d/(d+e*x^(2/3)))/d^3],
[x^2*(a+b*log(c*(d+e*x^(2/3))^n))^3,x,109,4504/315*a*b^2*d^4*n^2*x^(1/3)/e^4-3475504/99225*b^3*d^4*n^3*x^(1/3)/e^4+637984/297675*b^3*d^3*n^3*x/e^3-221344/496125*b^3*d^2*n^3*x^(5/3)/e^2+3088/27783*b^3*d*n^3*x^(7/3)/e-16/729*b^3*n^3*x^3+3475504/99225*b^3*d^(9/2)*n^3*arctan(x^(1/3)*sqrt(e)/sqrt(d))/e^(9/2)-4504/315*I*b^3*d^(9/2)*n^3*arctan(x^(1/3)*sqrt(e)/sqrt(d))^2/e^(9/2)+4504/315*b^3*d^4*n^2*x^(1/3)*log(c*(d+e*x^(2/3))^n)/e^4-1984/945*b^2*d^3*n^2*x*(a+b*log(c*(d+e*x^(2/3))^n))/e^3+1144/1575*b^2*d^2*n^2*x^(5/3)*(a+b*log(c*(d+e*x^(2/3))^n))/e^2-128/441*b^2*d*n^2*x^(7/3)*(a+b*log(c*(d+e*x^(2/3))^n))/e+8/81*b^2*n^2*x^3*(a+b*log(c*(d+e*x^(2/3))^n))-4504/315*b^2*d^(9/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))*(a+b*log(c*(d+e*x^(2/3))^n))/e^(9/2)-2*b*d^4*n*x^(1/3)*(a+b*log(c*(d+e*x^(2/3))^n))^2/e^4+2/3*b*d^3*n*x*(a+b*log(c*(d+e*x^(2/3))^n))^2/e^3-2/5*b*d^2*n*x^(5/3)*(a+b*log(c*(d+e*x^(2/3))^n))^2/e^2+2/7*b*d*n*x^(7/3)*(a+b*log(c*(d+e*x^(2/3))^n))^2/e-2/9*b*n*x^3*(a+b*log(c*(d+e*x^(2/3))^n))^2+1/3*x^3*(a+b*log(c*(d+e*x^(2/3))^n))^3-9008/315*b^3*d^(9/2)*n^3*arctan(x^(1/3)*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/e^(9/2)-4504/315*I*b^3*d^(9/2)*n^3*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/e^(9/2)+2/3*b*d^5*n*Unintegrable((a+b*log(c*(d+e*x^(2/3))^n))^2/((d+e*x^(2/3))*x^(2/3)),x)/e^4],
[(a+b*log(c*(d+e*x^(2/3))^n))^3,x,34,-32*a*b^2*d*n^2*x^(1/3)/e+208/3*b^3*d*n^3*x^(1/3)/e-16/9*b^3*n^3*x-208/3*b^3*d^(3/2)*n^3*arctan(x^(1/3)*sqrt(e)/sqrt(d))/e^(3/2)+32*I*b^3*d^(3/2)*n^3*arctan(x^(1/3)*sqrt(e)/sqrt(d))^2/e^(3/2)-32*b^3*d*n^2*x^(1/3)*log(c*(d+e*x^(2/3))^n)/e+8/3*b^2*n^2*x*(a+b*log(c*(d+e*x^(2/3))^n))+32*b^2*d^(3/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))*(a+b*log(c*(d+e*x^(2/3))^n))/e^(3/2)+6*b*d*n*x^(1/3)*(a+b*log(c*(d+e*x^(2/3))^n))^2/e-2*b*n*x*(a+b*log(c*(d+e*x^(2/3))^n))^2+x*(a+b*log(c*(d+e*x^(2/3))^n))^3+64*b^3*d^(3/2)*n^3*arctan(x^(1/3)*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/e^(3/2)+32*I*b^3*d^(3/2)*n^3*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/e^(3/2)-2*b*d^2*n*Unintegrable((a+b*log(c*(d+e*x^(2/3))^n))^2/((d+e*x^(2/3))*x^(2/3)),x)/e],
[(a+b*log(c*(d+e*x^(2/3))^n))^3/x^2,x,11,24*I*b^3*e^(3/2)*n^3*arctan(x^(1/3)*sqrt(e)/sqrt(d))^2/d^(3/2)+24*b^2*e^(3/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))*(a+b*log(c*(d+e*x^(2/3))^n))/d^(3/2)-6*b*e*n*(a+b*log(c*(d+e*x^(2/3))^n))^2/(d*x^(1/3))-(a+b*log(c*(d+e*x^(2/3))^n))^3/x+48*b^3*e^(3/2)*n^3*arctan(x^(1/3)*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/d^(3/2)+24*I*b^3*e^(3/2)*n^3*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/d^(3/2)-2*b*e^2*n*Unintegrable((a+b*log(c*(d+e*x^(2/3))^n))^2/((d+e*x^(2/3))*x^(2/3)),x)/d],
[(a+b*log(c*(d+e*x^(2/3))^n))^3/x^4,x,54,-16/105*b^3*e^3*n^3/(d^3*x)+16/7*b^3*e^4*n^3/(d^4*x^(1/3))+1376/105*b^3*e^(9/2)*n^3*arctan(x^(1/3)*sqrt(e)/sqrt(d))/d^(9/2)-1408/105*I*b^3*e^(9/2)*n^3*arctan(x^(1/3)*sqrt(e)/sqrt(d))^2/d^(9/2)-8/35*b^2*e^2*n^2*(a+b*log(c*(d+e*x^(2/3))^n))/(d^2*x^(5/3))+32/35*b^2*e^3*n^2*(a+b*log(c*(d+e*x^(2/3))^n))/(d^3*x)-568/105*b^2*e^4*n^2*(a+b*log(c*(d+e*x^(2/3))^n))/(d^4*x^(1/3))-1408/105*b^2*e^(9/2)*n^2*arctan(x^(1/3)*sqrt(e)/sqrt(d))*(a+b*log(c*(d+e*x^(2/3))^n))/d^(9/2)-2/7*b*e*n*(a+b*log(c*(d+e*x^(2/3))^n))^2/(d*x^(7/3))+2/5*b*e^2*n*(a+b*log(c*(d+e*x^(2/3))^n))^2/(d^2*x^(5/3))-2/3*b*e^3*n*(a+b*log(c*(d+e*x^(2/3))^n))^2/(d^3*x)+2*b*e^4*n*(a+b*log(c*(d+e*x^(2/3))^n))^2/(d^4*x^(1/3))-1/3*(a+b*log(c*(d+e*x^(2/3))^n))^3/x^3-2816/105*b^3*e^(9/2)*n^3*arctan(x^(1/3)*sqrt(e)/sqrt(d))*log(2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/d^(9/2)-1408/105*I*b^3*e^(9/2)*n^3*polylog(2,1-2*sqrt(d)/(sqrt(d)+I*x^(1/3)*sqrt(e)))/d^(9/2)+2/3*b*e^5*n*Unintegrable((a+b*log(c*(d+e*x^(2/3))^n))^2/((d+e*x^(2/3))*x^(2/3)),x)/d^4],

# m=-1
[x^3*(a+b*log(c*(d+e/x^(1/3))^n)),x,4,1/4*b*e^11*n*x^(1/3)/d^11-1/8*b*e^10*n*x^(2/3)/d^10+1/12*b*e^9*n*x/d^9-1/16*b*e^8*n*x^(4/3)/d^8+1/20*b*e^7*n*x^(5/3)/d^7-1/24*b*e^6*n*x^2/d^6+1/28*b*e^5*n*x^(7/3)/d^5-1/32*b*e^4*n*x^(8/3)/d^4+1/36*b*e^3*n*x^3/d^3-1/40*b*e^2*n*x^(10/3)/d^2+1/44*b*e*n*x^(11/3)/d-1/4*b*e^12*n*log(d+e/x^(1/3))/d^12+1/4*x^4*(a+b*log(c*(d+e/x^(1/3))^n))-1/12*b*e^12*n*log(x)/d^12],
[x^2*(a+b*log(c*(d+e/x^(1/3))^n)),x,4,-1/3*b*e^8*n*x^(1/3)/d^8+1/6*b*e^7*n*x^(2/3)/d^7-1/9*b*e^6*n*x/d^6+1/12*b*e^5*n*x^(4/3)/d^5-1/15*b*e^4*n*x^(5/3)/d^4+1/18*b*e^3*n*x^2/d^3-1/21*b*e^2*n*x^(7/3)/d^2+1/24*b*e*n*x^(8/3)/d+1/3*b*e^9*n*log(d+e/x^(1/3))/d^9+1/3*x^3*(a+b*log(c*(d+e/x^(1/3))^n))+1/9*b*e^9*n*log(x)/d^9],
[x*(a+b*log(c*(d+e/x^(1/3))^n)),x,4,1/2*b*e^5*n*x^(1/3)/d^5-1/4*b*e^4*n*x^(2/3)/d^4+1/6*b*e^3*n*x/d^3-1/8*b*e^2*n*x^(4/3)/d^2+1/10*b*e*n*x^(5/3)/d-1/2*b*e^6*n*log(d+e/x^(1/3))/d^6+1/2*x^2*(a+b*log(c*(d+e/x^(1/3))^n))-1/6*b*e^6*n*log(x)/d^6],
[a+b*log(c*(d+e/x^(1/3))^n),x,6,-b*e^2*n*x^(1/3)/d^2+1/2*b*e*n*x^(2/3)/d+a*x+b*x*log(c*(d+e/x^(1/3))^n)+b*e^3*n*log(e+d*x^(1/3))/d^3],
[(a+b*log(c*(d+e/x^(1/3))^n))/x,x,3,-3*(a+b*log(c*(d+e/x^(1/3))^n))*log(-e/(d*x^(1/3)))-3*b*n*polylog(2,1+e/(d*x^(1/3)))],
[(a+b*log(c*(d+e/x^(1/3))^n))/x^2,x,4,1/3*b*n/x-1/2*b*d*n/(e*x^(2/3))+b*d^2*n/(e^2*x^(1/3))-b*d^3*n*log(d+e/x^(1/3))/e^3+(-a-b*log(c*(d+e/x^(1/3))^n))/x],
[(a+b*log(c*(d+e/x^(1/3))^n))/x^3,x,4,1/12*b*n/x^2-1/10*b*d*n/(e*x^(5/3))+1/8*b*d^2*n/(e^2*x^(4/3))-1/6*b*d^3*n/(e^3*x)+1/4*b*d^4*n/(e^4*x^(2/3))-1/2*b*d^5*n/(e^5*x^(1/3))+1/2*b*d^6*n*log(d+e/x^(1/3))/e^6+1/2*(-a-b*log(c*(d+e/x^(1/3))^n))/x^2],
[(a+b*log(c*(d+e/x^(1/3))^n))/x^4,x,4,1/27*b*n/x^3-1/24*b*d*n/(e*x^(8/3))+1/21*b*d^2*n/(e^2*x^(7/3))-1/18*b*d^3*n/(e^3*x^2)+1/15*b*d^4*n/(e^4*x^(5/3))-1/12*b*d^5*n/(e^5*x^(4/3))+1/9*b*d^6*n/(e^6*x)-1/6*b*d^7*n/(e^7*x^(2/3))+1/3*b*d^8*n/(e^8*x^(1/3))-1/3*b*d^9*n*log(d+e/x^(1/3))/e^9+1/3*(-a-b*log(c*(d+e/x^(1/3))^n))/x^3],
[x^2*(a+b*log(c*(d+e/x^(1/3))^n))^2,x,36,481/420*b^2*e^8*n^2*x^(1/3)/d^8-341/840*b^2*e^7*n^2*x^(2/3)/d^7+743/3780*b^2*e^6*n^2*x/d^6-533/5040*b^2*e^5*n^2*x^(4/3)/d^5+73/1260*b^2*e^4*n^2*x^(5/3)/d^4-5/168*b^2*e^3*n^2*x^2/d^3+1/84*b^2*e^2*n^2*x^(7/3)/d^2-481/420*b^2*e^9*n^2*log(d+e/x^(1/3))/d^9-2/3*b*e^8*n*(d+e/x^(1/3))*x^(1/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d^9+1/3*b*e^7*n*x^(2/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d^7-2/9*b*e^6*n*x*(a+b*log(c*(d+e/x^(1/3))^n))/d^6+1/6*b*e^5*n*x^(4/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d^5-2/15*b*e^4*n*x^(5/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d^4+1/9*b*e^3*n*x^2*(a+b*log(c*(d+e/x^(1/3))^n))/d^3-2/21*b*e^2*n*x^(7/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d^2+1/12*b*e*n*x^(8/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d-2/3*b*e^9*n*log(1-d/(d+e/x^(1/3)))*(a+b*log(c*(d+e/x^(1/3))^n))/d^9+1/3*x^3*(a+b*log(c*(d+e/x^(1/3))^n))^2-761/1260*b^2*e^9*n^2*log(x)/d^9+2/3*b^2*e^9*n^2*polylog(2,d/(d+e/x^(1/3)))/d^9],
[x*(a+b*log(c*(d+e/x^(1/3))^n))^2,x,24,-77/60*b^2*e^5*n^2*x^(1/3)/d^5+47/120*b^2*e^4*n^2*x^(2/3)/d^4-3/20*b^2*e^3*n^2*x/d^3+1/20*b^2*e^2*n^2*x^(4/3)/d^2+77/60*b^2*e^6*n^2*log(d+e/x^(1/3))/d^6+b*e^5*n*(d+e/x^(1/3))*x^(1/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d^6-1/2*b*e^4*n*x^(2/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d^4+1/3*b*e^3*n*x*(a+b*log(c*(d+e/x^(1/3))^n))/d^3-1/4*b*e^2*n*x^(4/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d^2+1/5*b*e*n*x^(5/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d+b*e^6*n*log(1-d/(d+e/x^(1/3)))*(a+b*log(c*(d+e/x^(1/3))^n))/d^6+1/2*x^2*(a+b*log(c*(d+e/x^(1/3))^n))^2+137/180*b^2*e^6*n^2*log(x)/d^6-b^2*e^6*n^2*polylog(2,d/(d+e/x^(1/3)))/d^6],
[(a+b*log(c*(d+e/x^(1/3))^n))^2,x,13,b^2*e^2*n^2*x^(1/3)/d^2-b^2*e^3*n^2*log(d+e/x^(1/3))/d^3-2*b*e^2*n*(d+e/x^(1/3))*x^(1/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d^3+b*e*n*x^(2/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d-2*b*e^3*n*log(1-d/(d+e/x^(1/3)))*(a+b*log(c*(d+e/x^(1/3))^n))/d^3+x*(a+b*log(c*(d+e/x^(1/3))^n))^2-b^2*e^3*n^2*log(x)/d^3+2*b^2*e^3*n^2*polylog(2,d/(d+e/x^(1/3)))/d^3],
[(a+b*log(c*(d+e/x^(1/3))^n))^2/x,x,5,-3*(a+b*log(c*(d+e/x^(1/3))^n))^2*log(-e/(d*x^(1/3)))-6*b*n*(a+b*log(c*(d+e/x^(1/3))^n))*polylog(2,1+e/(d*x^(1/3)))+6*b^2*n^2*polylog(3,1+e/(d*x^(1/3)))],
[(a+b*log(c*(d+e/x^(1/3))^n))^2/x^2,x,8,3/2*b^2*d*n^2*(d+e/x^(1/3))^2/e^3-2/9*b^2*n^2*(d+e/x^(1/3))^3/e^3-6*b^2*d^2*n^2/(e^2*x^(1/3))+b^2*d^3*n^2*log(d+e/x^(1/3))^2/e^3+6*b*d^2*n*(d+e/x^(1/3))*(a+b*log(c*(d+e/x^(1/3))^n))/e^3-3*b*d*n*(d+e/x^(1/3))^2*(a+b*log(c*(d+e/x^(1/3))^n))/e^3+2/3*b*n*(d+e/x^(1/3))^3*(a+b*log(c*(d+e/x^(1/3))^n))/e^3-2*b*d^3*n*log(d+e/x^(1/3))*(a+b*log(c*(d+e/x^(1/3))^n))/e^3-(a+b*log(c*(d+e/x^(1/3))^n))^2/x],
[(a+b*log(c*(d+e/x^(1/3))^n))^2/x^3,x,8,-15/4*b^2*d^4*n^2*(d+e/x^(1/3))^2/e^6+20/9*b^2*d^3*n^2*(d+e/x^(1/3))^3/e^6-15/16*b^2*d^2*n^2*(d+e/x^(1/3))^4/e^6+6/25*b^2*d*n^2*(d+e/x^(1/3))^5/e^6-1/36*b^2*n^2*(d+e/x^(1/3))^6/e^6+6*b^2*d^5*n^2/(e^5*x^(1/3))-1/2*b^2*d^6*n^2*log(d+e/x^(1/3))^2/e^6-6*b*d^5*n*(d+e/x^(1/3))*(a+b*log(c*(d+e/x^(1/3))^n))/e^6+15/2*b*d^4*n*(d+e/x^(1/3))^2*(a+b*log(c*(d+e/x^(1/3))^n))/e^6-20/3*b*d^3*n*(d+e/x^(1/3))^3*(a+b*log(c*(d+e/x^(1/3))^n))/e^6+15/4*b*d^2*n*(d+e/x^(1/3))^4*(a+b*log(c*(d+e/x^(1/3))^n))/e^6-6/5*b*d*n*(d+e/x^(1/3))^5*(a+b*log(c*(d+e/x^(1/3))^n))/e^6+1/6*b*n*(d+e/x^(1/3))^6*(a+b*log(c*(d+e/x^(1/3))^n))/e^6+b*d^6*n*log(d+e/x^(1/3))*(a+b*log(c*(d+e/x^(1/3))^n))/e^6-1/2*(a+b*log(c*(d+e/x^(1/3))^n))^2/x^2],
[x*(a+b*log(c*(d+e/x^(1/3))^n))^3,x,62,71/40*b^3*e^5*n^3*x^(1/3)/d^5-3/10*b^3*e^4*n^3*x^(2/3)/d^4+1/20*b^3*e^3*n^3*x/d^3-71/40*b^3*e^6*n^3*log(d+e/x^(1/3))/d^6-77/20*b^2*e^5*n^2*(d+e/x^(1/3))*x^(1/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d^6+47/40*b^2*e^4*n^2*x^(2/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d^4-9/20*b^2*e^3*n^2*x*(a+b*log(c*(d+e/x^(1/3))^n))/d^3+3/20*b^2*e^2*n^2*x^(4/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d^2-77/20*b^2*e^6*n^2*log(1-d/(d+e/x^(1/3)))*(a+b*log(c*(d+e/x^(1/3))^n))/d^6+3/2*b*e^5*n*(d+e/x^(1/3))*x^(1/3)*(a+b*log(c*(d+e/x^(1/3))^n))^2/d^6-3/4*b*e^4*n*x^(2/3)*(a+b*log(c*(d+e/x^(1/3))^n))^2/d^4+1/2*b*e^3*n*x*(a+b*log(c*(d+e/x^(1/3))^n))^2/d^3-3/8*b*e^2*n*x^(4/3)*(a+b*log(c*(d+e/x^(1/3))^n))^2/d^2+3/10*b*e*n*x^(5/3)*(a+b*log(c*(d+e/x^(1/3))^n))^2/d+3/2*b*e^6*n*log(1-d/(d+e/x^(1/3)))*(a+b*log(c*(d+e/x^(1/3))^n))^2/d^6+1/2*x^2*(a+b*log(c*(d+e/x^(1/3))^n))^3-3*b^2*e^6*n^2*(a+b*log(c*(d+e/x^(1/3))^n))*log(-e/(d*x^(1/3)))/d^6-15/8*b^3*e^6*n^3*log(x)/d^6+77/20*b^3*e^6*n^3*polylog(2,d/(d+e/x^(1/3)))/d^6-3*b^2*e^6*n^2*(a+b*log(c*(d+e/x^(1/3))^n))*polylog(2,d/(d+e/x^(1/3)))/d^6-3*b^3*e^6*n^3*polylog(2,1+e/(d*x^(1/3)))/d^6-3*b^3*e^6*n^3*polylog(3,d/(d+e/x^(1/3)))/d^6],
[(a+b*log(c*(d+e/x^(1/3))^n))^3,x,18,3*b^2*e^2*n^2*(d+e/x^(1/3))*x^(1/3)*(a+b*log(c*(d+e/x^(1/3))^n))/d^3+3*b^2*e^3*n^2*log(1-d/(d+e/x^(1/3)))*(a+b*log(c*(d+e/x^(1/3))^n))/d^3-3*b*e^2*n*(d+e/x^(1/3))*x^(1/3)*(a+b*log(c*(d+e/x^(1/3))^n))^2/d^3+3/2*b*e*n*x^(2/3)*(a+b*log(c*(d+e/x^(1/3))^n))^2/d-3*b*e^3*n*log(1-d/(d+e/x^(1/3)))*(a+b*log(c*(d+e/x^(1/3))^n))^2/d^3+x*(a+b*log(c*(d+e/x^(1/3))^n))^3+6*b^2*e^3*n^2*(a+b*log(c*(d+e/x^(1/3))^n))*log(-e/(d*x^(1/3)))/d^3+b^3*e^3*n^3*log(x)/d^3-3*b^3*e^3*n^3*polylog(2,d/(d+e/x^(1/3)))/d^3+6*b^2*e^3*n^2*(a+b*log(c*(d+e/x^(1/3))^n))*polylog(2,d/(d+e/x^(1/3)))/d^3+6*b^3*e^3*n^3*polylog(2,1+e/(d*x^(1/3)))/d^3+6*b^3*e^3*n^3*polylog(3,d/(d+e/x^(1/3)))/d^3],
[(a+b*log(c*(d+e/x^(1/3))^n))^3/x,x,6,-3*(a+b*log(c*(d+e/x^(1/3))^n))^3*log(-e/(d*x^(1/3)))-9*b*n*(a+b*log(c*(d+e/x^(1/3))^n))^2*polylog(2,1+e/(d*x^(1/3)))+18*b^2*n^2*(a+b*log(c*(d+e/x^(1/3))^n))*polylog(3,1+e/(d*x^(1/3)))-18*b^3*n^3*polylog(4,1+e/(d*x^(1/3)))],
[(a+b*log(c*(d+e/x^(1/3))^n))^3/x^2,x,16,-9/4*b^3*d*n^3*(d+e/x^(1/3))^2/e^3+2/9*b^3*n^3*(d+e/x^(1/3))^3/e^3-18*a*b^2*d^2*n^2/(e^2*x^(1/3))+18*b^3*d^2*n^3/(e^2*x^(1/3))-18*b^3*d^2*n^2*(d+e/x^(1/3))*log(c*(d+e/x^(1/3))^n)/e^3+9/2*b^2*d*n^2*(d+e/x^(1/3))^2*(a+b*log(c*(d+e/x^(1/3))^n))/e^3-2/3*b^2*n^2*(d+e/x^(1/3))^3*(a+b*log(c*(d+e/x^(1/3))^n))/e^3+9*b*d^2*n*(d+e/x^(1/3))*(a+b*log(c*(d+e/x^(1/3))^n))^2/e^3-9/2*b*d*n*(d+e/x^(1/3))^2*(a+b*log(c*(d+e/x^(1/3))^n))^2/e^3+b*n*(d+e/x^(1/3))^3*(a+b*log(c*(d+e/x^(1/3))^n))^2/e^3-3*d^2*(d+e/x^(1/3))*(a+b*log(c*(d+e/x^(1/3))^n))^3/e^3+3*d*(d+e/x^(1/3))^2*(a+b*log(c*(d+e/x^(1/3))^n))^3/e^3-(d+e/x^(1/3))^3*(a+b*log(c*(d+e/x^(1/3))^n))^3/e^3],
[(a+b*log(c*(d+e/x^(1/3))^n))^3/x^3,x,28,45/8*b^3*d^4*n^3*(d+e/x^(1/3))^2/e^6-20/9*b^3*d^3*n^3*(d+e/x^(1/3))^3/e^6+45/64*b^3*d^2*n^3*(d+e/x^(1/3))^4/e^6-18/125*b^3*d*n^3*(d+e/x^(1/3))^5/e^6+1/72*b^3*n^3*(d+e/x^(1/3))^6/e^6+18*a*b^2*d^5*n^2/(e^5*x^(1/3))-18*b^3*d^5*n^3/(e^5*x^(1/3))+18*b^3*d^5*n^2*(d+e/x^(1/3))*log(c*(d+e/x^(1/3))^n)/e^6-45/4*b^2*d^4*n^2*(d+e/x^(1/3))^2*(a+b*log(c*(d+e/x^(1/3))^n))/e^6+20/3*b^2*d^3*n^2*(d+e/x^(1/3))^3*(a+b*log(c*(d+e/x^(1/3))^n))/e^6-45/16*b^2*d^2*n^2*(d+e/x^(1/3))^4*(a+b*log(c*(d+e/x^(1/3))^n))/e^6+18/25*b^2*d*n^2*(d+e/x^(1/3))^5*(a+b*log(c*(d+e/x^(1/3))^n))/e^6-1/12*b^2*n^2*(d+e/x^(1/3))^6*(a+b*log(c*(d+e/x^(1/3))^n))/e^6-9*b*d^5*n*(d+e/x^(1/3))*(a+b*log(c*(d+e/x^(1/3))^n))^2/e^6+45/4*b*d^4*n*(d+e/x^(1/3))^2*(a+b*log(c*(d+e/x^(1/3))^n))^2/e^6-10*b*d^3*n*(d+e/x^(1/3))^3*(a+b*log(c*(d+e/x^(1/3))^n))^2/e^6+45/8*b*d^2*n*(d+e/x^(1/3))^4*(a+b*log(c*(d+e/x^(1/3))^n))^2/e^6-9/5*b*d*n*(d+e/x^(1/3))^5*(a+b*log(c*(d+e/x^(1/3))^n))^2/e^6+1/4*b*n*(d+e/x^(1/3))^6*(a+b*log(c*(d+e/x^(1/3))^n))^2/e^6+3*d^5*(d+e/x^(1/3))*(a+b*log(c*(d+e/x^(1/3))^n))^3/e^6-15/2*d^4*(d+e/x^(1/3))^2*(a+b*log(c*(d+e/x^(1/3))^n))^3/e^6+10*d^3*(d+e/x^(1/3))^3*(a+b*log(c*(d+e/x^(1/3))^n))^3/e^6-15/2*d^2*(d+e/x^(1/3))^4*(a+b*log(c*(d+e/x^(1/3))^n))^3/e^6+3*d*(d+e/x^(1/3))^5*(a+b*log(c*(d+e/x^(1/3))^n))^3/e^6-1/2*(d+e/x^(1/3))^6*(a+b*log(c*(d+e/x^(1/3))^n))^3/e^6],

# m=-2
[x^3*(a+b*log(c*(d+e/x^(2/3))^n)),x,4,1/4*b*e^5*n*x^(2/3)/d^5-1/8*b*e^4*n*x^(4/3)/d^4+1/12*b*e^3*n*x^2/d^3-1/16*b*e^2*n*x^(8/3)/d^2+1/20*b*e*n*x^(10/3)/d-1/4*b*e^6*n*log(d+e/x^(2/3))/d^6+1/4*x^4*(a+b*log(c*(d+e/x^(2/3))^n))-1/6*b*e^6*n*log(x)/d^6],
[x^2*(a+b*log(c*(d+e/x^(2/3))^n)),x,6,-2/3*b*e^4*n*x^(1/3)/d^4+2/9*b*e^3*n*x/d^3-2/15*b*e^2*n*x^(5/3)/d^2+2/21*b*e*n*x^(7/3)/d+2/3*b*e^(9/2)*n*arctan(x^(1/3)*sqrt(d)/sqrt(e))/d^(9/2)+1/3*x^3*(a+b*log(c*(d+e/x^(2/3))^n))],
[x*(a+b*log(c*(d+e/x^(2/3))^n)),x,4,-1/2*b*e^2*n*x^(2/3)/d^2+1/4*b*e*n*x^(4/3)/d+1/2*b*e^3*n*log(d+e/x^(2/3))/d^3+1/2*x^2*(a+b*log(c*(d+e/x^(2/3))^n))+1/3*b*e^3*n*log(x)/d^3],
[a+b*log(c*(d+e/x^(2/3))^n),x,6,2*b*e*n*x^(1/3)/d+a*x-2*b*e^(3/2)*n*arctan(x^(1/3)*sqrt(d)/sqrt(e))/d^(3/2)+b*x*log(c*(d+e/x^(2/3))^n)],
[(a+b*log(c*(d+e/x^(2/3))^n))/x,x,3,-3/2*(a+b*log(c*(d+e/x^(2/3))^n))*log(-e/(d*x^(2/3)))-3/2*b*n*polylog(2,1+e/(d*x^(2/3)))],
[(a+b*log(c*(d+e/x^(2/3))^n))/x^2,x,6,2/3*b*n/x-2*b*d*n/(e*x^(1/3))-2*b*d^(3/2)*n*arctan(x^(1/3)*sqrt(d)/sqrt(e))/e^(3/2)+(-a-b*log(c*(d+e/x^(2/3))^n))/x],
[(a+b*log(c*(d+e/x^(2/3))^n))/x^3,x,4,1/6*b*n/x^2-1/4*b*d*n/(e*x^(4/3))+1/2*b*d^2*n/(e^2*x^(2/3))-1/2*b*d^3*n*log(d+e/x^(2/3))/e^3+1/2*(-a-b*log(c*(d+e/x^(2/3))^n))/x^2],
[(a+b*log(c*(d+e/x^(2/3))^n))/x^4,x,9,2/27*b*n/x^3-2/21*b*d*n/(e*x^(7/3))+2/15*b*d^2*n/(e^2*x^(5/3))-2/9*b*d^3*n/(e^3*x)+2/3*b*d^4*n/(e^4*x^(1/3))+2/3*b*d^(9/2)*n*arctan(x^(1/3)*sqrt(d)/sqrt(e))/e^(9/2)+1/3*(-a-b*log(c*(d+e/x^(2/3))^n))/x^3],
[x^3*(a+b*log(c*(d+e/x^(2/3))^n))^2,x,24,-77/120*b^2*e^5*n^2*x^(2/3)/d^5+47/240*b^2*e^4*n^2*x^(4/3)/d^4-3/40*b^2*e^3*n^2*x^2/d^3+1/40*b^2*e^2*n^2*x^(8/3)/d^2+77/120*b^2*e^6*n^2*log(d+e/x^(2/3))/d^6+1/2*b*e^5*n*(d+e/x^(2/3))*x^(2/3)*(a+b*log(c*(d+e/x^(2/3))^n))/d^6-1/4*b*e^4*n*x^(4/3)*(a+b*log(c*(d+e/x^(2/3))^n))/d^4+1/6*b*e^3*n*x^2*(a+b*log(c*(d+e/x^(2/3))^n))/d^3-1/8*b*e^2*n*x^(8/3)*(a+b*log(c*(d+e/x^(2/3))^n))/d^2+1/10*b*e*n*x^(10/3)*(a+b*log(c*(d+e/x^(2/3))^n))/d+1/2*b*e^6*n*log(1-d/(d+e/x^(2/3)))*(a+b*log(c*(d+e/x^(2/3))^n))/d^6+1/4*x^4*(a+b*log(c*(d+e/x^(2/3))^n))^2+137/180*b^2*e^6*n^2*log(x)/d^6-1/2*b^2*e^6*n^2*polylog(2,d/(d+e/x^(2/3)))/d^6],
[x*(a+b*log(c*(d+e/x^(2/3))^n))^2,x,12,1/2*b^2*e^2*n^2*x^(2/3)/d^2-1/2*b^2*e^3*n^2*log(d+e/x^(2/3))/d^3-b*e^2*n*(d+e/x^(2/3))*x^(2/3)*(a+b*log(c*(d+e/x^(2/3))^n))/d^3+1/2*b*e*n*x^(4/3)*(a+b*log(c*(d+e/x^(2/3))^n))/d-b*e^3*n*log(1-d/(d+e/x^(2/3)))*(a+b*log(c*(d+e/x^(2/3))^n))/d^3+1/2*x^2*(a+b*log(c*(d+e/x^(2/3))^n))^2-b^2*e^3*n^2*log(x)/d^3+b^2*e^3*n^2*polylog(2,d/(d+e/x^(2/3)))/d^3],
[(a+b*log(c*(d+e/x^(2/3))^n))^2/x,x,5,-3/2*(a+b*log(c*(d+e/x^(2/3))^n))^2*log(-e/(d*x^(2/3)))-3*b*n*(a+b*log(c*(d+e/x^(2/3))^n))*polylog(2,1+e/(d*x^(2/3)))+3*b^2*n^2*polylog(3,1+e/(d*x^(2/3)))],
[(a+b*log(c*(d+e/x^(2/3))^n))^2/x^3,x,8,3/4*b^2*d*n^2*(d+e/x^(2/3))^2/e^3-1/9*b^2*n^2*(d+e/x^(2/3))^3/e^3-3*b^2*d^2*n^2/(e^2*x^(2/3))+1/2*b^2*d^3*n^2*log(d+e/x^(2/3))^2/e^3+3*b*d^2*n*(d+e/x^(2/3))*(a+b*log(c*(d+e/x^(2/3))^n))/e^3-3/2*b*d*n*(d+e/x^(2/3))^2*(a+b*log(c*(d+e/x^(2/3))^n))/e^3+1/3*b*n*(d+e/x^(2/3))^3*(a+b*log(c*(d+e/x^(2/3))^n))/e^3-b*d^3*n*log(d+e/x^(2/3))*(a+b*log(c*(d+e/x^(2/3))^n))/e^3-1/2*(a+b*log(c*(d+e/x^(2/3))^n))^2/x^2],
[(a+b*log(c*(d+e/x^(2/3))^n))^2/x^5,x,8,-15/8*b^2*d^4*n^2*(d+e/x^(2/3))^2/e^6+10/9*b^2*d^3*n^2*(d+e/x^(2/3))^3/e^6-15/32*b^2*d^2*n^2*(d+e/x^(2/3))^4/e^6+3/25*b^2*d*n^2*(d+e/x^(2/3))^5/e^6-1/72*b^2*n^2*(d+e/x^(2/3))^6/e^6+3*b^2*d^5*n^2/(e^5*x^(2/3))-1/4*b^2*d^6*n^2*log(d+e/x^(2/3))^2/e^6-3*b*d^5*n*(d+e/x^(2/3))*(a+b*log(c*(d+e/x^(2/3))^n))/e^6+15/4*b*d^4*n*(d+e/x^(2/3))^2*(a+b*log(c*(d+e/x^(2/3))^n))/e^6-10/3*b*d^3*n*(d+e/x^(2/3))^3*(a+b*log(c*(d+e/x^(2/3))^n))/e^6+15/8*b*d^2*n*(d+e/x^(2/3))^4*(a+b*log(c*(d+e/x^(2/3))^n))/e^6-3/5*b*d*n*(d+e/x^(2/3))^5*(a+b*log(c*(d+e/x^(2/3))^n))/e^6+1/12*b*n*(d+e/x^(2/3))^6*(a+b*log(c*(d+e/x^(2/3))^n))/e^6+1/2*b*d^6*n*log(d+e/x^(2/3))*(a+b*log(c*(d+e/x^(2/3))^n))/e^6-1/4*(a+b*log(c*(d+e/x^(2/3))^n))^2/x^4],
[x^2*(a+b*log(c*(d+e/x^(2/3))^n))^2,x,28,-4/3*a*b*e^4*n*x^(1/3)/d^4+568/315*b^2*e^4*n^2*x^(1/3)/d^4-32/105*b^2*e^3*n^2*x/d^3+8/105*b^2*e^2*n^2*x^(5/3)/d^2-1408/315*b^2*e^(9/2)*n^2*arctan(x^(1/3)*sqrt(d)/sqrt(e))/d^(9/2)-4/3*I*b^2*e^(9/2)*n^2*arctan(x^(1/3)*sqrt(d)/sqrt(e))^2/d^(9/2)-4/3*b^2*e^4*n*x^(1/3)*log(c*(d+e/x^(2/3))^n)/d^4+4/9*b*e^3*n*x*(a+b*log(c*(d+e/x^(2/3))^n))/d^3-4/15*b*e^2*n*x^(5/3)*(a+b*log(c*(d+e/x^(2/3))^n))/d^2+4/21*b*e*n*x^(7/3)*(a+b*log(c*(d+e/x^(2/3))^n))/d+4/3*b*e^(9/2)*n*arctan(x^(1/3)*sqrt(d)/sqrt(e))*(a+b*log(c*(d+e/x^(2/3))^n))/d^(9/2)+1/3*x^3*(a+b*log(c*(d+e/x^(2/3))^n))^2+8/3*b^2*e^(9/2)*n^2*arctan(x^(1/3)*sqrt(d)/sqrt(e))*log(2-2*sqrt(e)/(-I*x^(1/3)*sqrt(d)+sqrt(e)))/d^(9/2)-4/3*I*b^2*e^(9/2)*n^2*polylog(2,-1+2*sqrt(e)/(-I*x^(1/3)*sqrt(d)+sqrt(e)))/d^(9/2)],
[(a+b*log(c*(d+e/x^(2/3))^n))^2,x,14,4*a*b*e*n*x^(1/3)/d+8*b^2*e^(3/2)*n^2*arctan(x^(1/3)*sqrt(d)/sqrt(e))/d^(3/2)+4*I*b^2*e^(3/2)*n^2*arctan(x^(1/3)*sqrt(d)/sqrt(e))^2/d^(3/2)+4*b^2*e*n*x^(1/3)*log(c*(d+e/x^(2/3))^n)/d-4*b*e^(3/2)*n*arctan(x^(1/3)*sqrt(d)/sqrt(e))*(a+b*log(c*(d+e/x^(2/3))^n))/d^(3/2)+x*(a+b*log(c*(d+e/x^(2/3))^n))^2-8*b^2*e^(3/2)*n^2*arctan(x^(1/3)*sqrt(d)/sqrt(e))*log(2-2*sqrt(e)/(-I*x^(1/3)*sqrt(d)+sqrt(e)))/d^(3/2)+4*I*b^2*e^(3/2)*n^2*polylog(2,-1+2*sqrt(e)/(-I*x^(1/3)*sqrt(d)+sqrt(e)))/d^(3/2)],
[(a+b*log(c*(d+e/x^(2/3))^n))^2/x^2,x,19,-8/9*b^2*n^2/x+32/3*b^2*d*n^2/(e*x^(1/3))+32/3*b^2*d^(3/2)*n^2*arctan(x^(1/3)*sqrt(d)/sqrt(e))/e^(3/2)+4*I*b^2*d^(3/2)*n^2*arctan(x^(1/3)*sqrt(d)/sqrt(e))^2/e^(3/2)+4/3*b*n*(a+b*log(c*(d+e/x^(2/3))^n))/x-4*b*d*n*(a+b*log(c*(d+e/x^(2/3))^n))/(e*x^(1/3))-4*b*d^(3/2)*n*arctan(x^(1/3)*sqrt(d)/sqrt(e))*(a+b*log(c*(d+e/x^(2/3))^n))/e^(3/2)-(a+b*log(c*(d+e/x^(2/3))^n))^2/x-8*b^2*d^(3/2)*n^2*arctan(x^(1/3)*sqrt(d)/sqrt(e))*log(2-2*sqrt(e)/(-I*x^(1/3)*sqrt(d)+sqrt(e)))/e^(3/2)+4*I*b^2*d^(3/2)*n^2*polylog(2,-1+2*sqrt(e)/(-I*x^(1/3)*sqrt(d)+sqrt(e)))/e^(3/2)],

#  {(a + b*Log[c*(d + e/x^(2/3))^n])^2/x^4, x, 40, -((8*b^2*n^2)/(243*x^3)) + (128*b^2*d*n^2)/(1323*e*x^(7/3)) - (1144*b^2*d^2*n^2)/(4725*e^2*x^(5/3)) + (1984*b^2*d^3*n^2)/(2835*e^3*x) - (4504*b^2*d^4*n^2)/(945*e^4*x^(1/3)) - (4504*b^2*d^(9/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]])/(945*e^(9/2)) - (4*I*b^2*d^(9/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]^2)/(3*e^(9/2)) + (8*b^2*d^(9/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*Log[2 - (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/(3*e^(9/2)) + (4*b*n*(a + b*Log[c*(d + e/x^(2/3))^n]))/(27*x^3) - (4*b*d*n*(a + b*Log[c*(d + e/x^(2/3))^n]))/(21*e*x^(7/3)) + (4*b*d^2*n*(a + b*Log[c*(d + e/x^(2/3))^n]))/(15*e^2*x^(5/3)) - (4*b*d^3*n*(a + b*Log[c*(d + e/x^(2/3))^n]))/(9*e^3*x) + (4*b*d^4*n*(a + b*Log[c*(d + e/x^(2/3))^n]))/(3*e^4*x^(1/3)) + (4*b*d^(9/2)*n*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*(a + b*Log[c*(d + e/x^(2/3))^n]))/(3*e^(9/2)) - (a + b*Log[c*(d + e/x^(2/3))^n])^2/(3*x^3) - (4*I*b^2*d^(9/2)*n^2*PolyLog[2, -1 + (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/(3*e^(9/2))} 
[x^3*(a+b*log(c*(d+e/x^(2/3))^n))^3,x,62,71/80*b^3*e^5*n^3*x^(2/3)/d^5-3/20*b^3*e^4*n^3*x^(4/3)/d^4+1/40*b^3*e^3*n^3*x^2/d^3-71/80*b^3*e^6*n^3*log(d+e/x^(2/3))/d^6-77/40*b^2*e^5*n^2*(d+e/x^(2/3))*x^(2/3)*(a+b*log(c*(d+e/x^(2/3))^n))/d^6+47/80*b^2*e^4*n^2*x^(4/3)*(a+b*log(c*(d+e/x^(2/3))^n))/d^4-9/40*b^2*e^3*n^2*x^2*(a+b*log(c*(d+e/x^(2/3))^n))/d^3+3/40*b^2*e^2*n^2*x^(8/3)*(a+b*log(c*(d+e/x^(2/3))^n))/d^2-77/40*b^2*e^6*n^2*log(1-d/(d+e/x^(2/3)))*(a+b*log(c*(d+e/x^(2/3))^n))/d^6+3/4*b*e^5*n*(d+e/x^(2/3))*x^(2/3)*(a+b*log(c*(d+e/x^(2/3))^n))^2/d^6-3/8*b*e^4*n*x^(4/3)*(a+b*log(c*(d+e/x^(2/3))^n))^2/d^4+1/4*b*e^3*n*x^2*(a+b*log(c*(d+e/x^(2/3))^n))^2/d^3-3/16*b*e^2*n*x^(8/3)*(a+b*log(c*(d+e/x^(2/3))^n))^2/d^2+3/20*b*e*n*x^(10/3)*(a+b*log(c*(d+e/x^(2/3))^n))^2/d+3/4*b*e^6*n*log(1-d/(d+e/x^(2/3)))*(a+b*log(c*(d+e/x^(2/3))^n))^2/d^6+1/4*x^4*(a+b*log(c*(d+e/x^(2/3))^n))^3-3/2*b^2*e^6*n^2*(a+b*log(c*(d+e/x^(2/3))^n))*log(-e/(d*x^(2/3)))/d^6-15/8*b^3*e^6*n^3*log(x)/d^6+77/40*b^3*e^6*n^3*polylog(2,d/(d+e/x^(2/3)))/d^6-3/2*b^2*e^6*n^2*(a+b*log(c*(d+e/x^(2/3))^n))*polylog(2,d/(d+e/x^(2/3)))/d^6-3/2*b^3*e^6*n^3*polylog(2,1+e/(d*x^(2/3)))/d^6-3/2*b^3*e^6*n^3*polylog(3,d/(d+e/x^(2/3)))/d^6],
[x*(a+b*log(c*(d+e/x^(2/3))^n))^3,x,17,3/2*b^2*e^2*n^2*(d+e/x^(2/3))*x^(2/3)*(a+b*log(c*(d+e/x^(2/3))^n))/d^3+3/2*b^2*e^3*n^2*log(1-d/(d+e/x^(2/3)))*(a+b*log(c*(d+e/x^(2/3))^n))/d^3-3/2*b*e^2*n*(d+e/x^(2/3))*x^(2/3)*(a+b*log(c*(d+e/x^(2/3))^n))^2/d^3+3/4*b*e*n*x^(4/3)*(a+b*log(c*(d+e/x^(2/3))^n))^2/d-3/2*b*e^3*n*log(1-d/(d+e/x^(2/3)))*(a+b*log(c*(d+e/x^(2/3))^n))^2/d^3+1/2*x^2*(a+b*log(c*(d+e/x^(2/3))^n))^3+3*b^2*e^3*n^2*(a+b*log(c*(d+e/x^(2/3))^n))*log(-e/(d*x^(2/3)))/d^3+b^3*e^3*n^3*log(x)/d^3-3/2*b^3*e^3*n^3*polylog(2,d/(d+e/x^(2/3)))/d^3+3*b^2*e^3*n^2*(a+b*log(c*(d+e/x^(2/3))^n))*polylog(2,d/(d+e/x^(2/3)))/d^3+3*b^3*e^3*n^3*polylog(2,1+e/(d*x^(2/3)))/d^3+3*b^3*e^3*n^3*polylog(3,d/(d+e/x^(2/3)))/d^3],
[(a+b*log(c*(d+e/x^(2/3))^n))^3/x,x,6,-3/2*(a+b*log(c*(d+e/x^(2/3))^n))^3*log(-e/(d*x^(2/3)))-9/2*b*n*(a+b*log(c*(d+e/x^(2/3))^n))^2*polylog(2,1+e/(d*x^(2/3)))+9*b^2*n^2*(a+b*log(c*(d+e/x^(2/3))^n))*polylog(3,1+e/(d*x^(2/3)))-9*b^3*n^3*polylog(4,1+e/(d*x^(2/3)))],
[(a+b*log(c*(d+e/x^(2/3))^n))^3/x^3,x,16,-9/8*b^3*d*n^3*(d+e/x^(2/3))^2/e^3+1/9*b^3*n^3*(d+e/x^(2/3))^3/e^3-9*a*b^2*d^2*n^2/(e^2*x^(2/3))+9*b^3*d^2*n^3/(e^2*x^(2/3))-9*b^3*d^2*n^2*(d+e/x^(2/3))*log(c*(d+e/x^(2/3))^n)/e^3+9/4*b^2*d*n^2*(d+e/x^(2/3))^2*(a+b*log(c*(d+e/x^(2/3))^n))/e^3-1/3*b^2*n^2*(d+e/x^(2/3))^3*(a+b*log(c*(d+e/x^(2/3))^n))/e^3+9/2*b*d^2*n*(d+e/x^(2/3))*(a+b*log(c*(d+e/x^(2/3))^n))^2/e^3-9/4*b*d*n*(d+e/x^(2/3))^2*(a+b*log(c*(d+e/x^(2/3))^n))^2/e^3+1/2*b*n*(d+e/x^(2/3))^3*(a+b*log(c*(d+e/x^(2/3))^n))^2/e^3-3/2*d^2*(d+e/x^(2/3))*(a+b*log(c*(d+e/x^(2/3))^n))^3/e^3+3/2*d*(d+e/x^(2/3))^2*(a+b*log(c*(d+e/x^(2/3))^n))^3/e^3-1/2*(d+e/x^(2/3))^3*(a+b*log(c*(d+e/x^(2/3))^n))^3/e^3],
[x^2*(a+b*log(c*(d+e/x^(2/3))^n))^3,x,83,568/105*a*b^2*e^4*n^2*x^(1/3)/d^4-16/7*b^3*e^4*n^3*x^(1/3)/d^4+16/105*b^3*e^3*n^3*x/d^3+1376/105*b^3*e^(9/2)*n^3*arctan(x^(1/3)*sqrt(d)/sqrt(e))/d^(9/2)+568/105*I*b^3*e^(9/2)*n^3*arctan(x^(1/3)*sqrt(d)/sqrt(e))^2/d^(9/2)+568/105*b^3*e^4*n^2*x^(1/3)*log(c*(d+e/x^(2/3))^n)/d^4-32/35*b^2*e^3*n^2*x*(a+b*log(c*(d+e/x^(2/3))^n))/d^3+8/35*b^2*e^2*n^2*x^(5/3)*(a+b*log(c*(d+e/x^(2/3))^n))/d^2-568/105*b^2*e^(9/2)*n^2*arctan(x^(1/3)*sqrt(d)/sqrt(e))*(a+b*log(c*(d+e/x^(2/3))^n))/d^(9/2)-2*b*e^4*n*x^(1/3)*(a+b*log(c*(d+e/x^(2/3))^n))^2/d^4+2/3*b*e^3*n*x*(a+b*log(c*(d+e/x^(2/3))^n))^2/d^3-2/5*b*e^2*n*x^(5/3)*(a+b*log(c*(d+e/x^(2/3))^n))^2/d^2+2/7*b*e*n*x^(7/3)*(a+b*log(c*(d+e/x^(2/3))^n))^2/d+1/3*x^3*(a+b*log(c*(d+e/x^(2/3))^n))^3+4*b^2*e^(9/2)*n^2*(a+b*log(c*(d+e/x^(2/3))^n))*log(-x^(1/3)*sqrt(-d)+sqrt(e))/(-d)^(9/2)-4*b^3*e^(9/2)*n^3*log(1/2*(1+x^(1/3)*sqrt(-d)/sqrt(e)))*log(-x^(1/3)*sqrt(-d)+sqrt(e))/(-d)^(9/2)+8*b^3*e^(9/2)*n^3*log(x^(1/3)*sqrt(-d)/sqrt(e))*log(-x^(1/3)*sqrt(-d)+sqrt(e))/(-d)^(9/2)-2*b^3*e^(9/2)*n^3*log(-x^(1/3)*sqrt(-d)+sqrt(e))^2/(-d)^(9/2)-4*b^2*e^(9/2)*n^2*(a+b*log(c*(d+e/x^(2/3))^n))*log(x^(1/3)*sqrt(-d)+sqrt(e))/(-d)^(9/2)+4*b^3*e^(9/2)*n^3*log(1/2-1/2*x^(1/3)*sqrt(-d)/sqrt(e))*log(x^(1/3)*sqrt(-d)+sqrt(e))/(-d)^(9/2)-8*b^3*e^(9/2)*n^3*log(-x^(1/3)*sqrt(-d)/sqrt(e))*log(x^(1/3)*sqrt(-d)+sqrt(e))/(-d)^(9/2)+2*b^3*e^(9/2)*n^3*log(x^(1/3)*sqrt(-d)+sqrt(e))^2/(-d)^(9/2)-1136/105*b^3*e^(9/2)*n^3*arctan(x^(1/3)*sqrt(d)/sqrt(e))*log(2-2*sqrt(e)/(-I*x^(1/3)*sqrt(d)+sqrt(e)))/d^(9/2)+8*b^3*e^(9/2)*n^3*polylog(2,1-x^(1/3)*sqrt(-d)/sqrt(e))/(-d)^(9/2)-4*b^3*e^(9/2)*n^3*polylog(2,1/2-1/2*x^(1/3)*sqrt(-d)/sqrt(e))/(-d)^(9/2)+4*b^3*e^(9/2)*n^3*polylog(2,1/2*(1+x^(1/3)*sqrt(-d)/sqrt(e)))/(-d)^(9/2)-8*b^3*e^(9/2)*n^3*polylog(2,1+x^(1/3)*sqrt(-d)/sqrt(e))/(-d)^(9/2)+568/105*I*b^3*e^(9/2)*n^3*polylog(2,-1+2*sqrt(e)/(-I*x^(1/3)*sqrt(d)+sqrt(e)))/d^(9/2)+2/3*b*e^5*n*Unintegrable((a+b*log(c*(d+e/x^(2/3))^n))^2/((e+d*x^(2/3))*x^(2/3)),x)/d^4],
[(a+b*log(c*(d+e/x^(2/3))^n))^3,x,31,6*b*e*n*x^(1/3)*(a+b*log(c*(d+e/x^(2/3))^n))^2/d+x*(a+b*log(c*(d+e/x^(2/3))^n))^3+12*b^2*e^(3/2)*n^2*(a+b*log(c*(d+e/x^(2/3))^n))*log(-x^(1/3)*sqrt(-d)+sqrt(e))/(-d)^(3/2)-12*b^3*e^(3/2)*n^3*log(1/2*(1+x^(1/3)*sqrt(-d)/sqrt(e)))*log(-x^(1/3)*sqrt(-d)+sqrt(e))/(-d)^(3/2)+24*b^3*e^(3/2)*n^3*log(x^(1/3)*sqrt(-d)/sqrt(e))*log(-x^(1/3)*sqrt(-d)+sqrt(e))/(-d)^(3/2)-6*b^3*e^(3/2)*n^3*log(-x^(1/3)*sqrt(-d)+sqrt(e))^2/(-d)^(3/2)-12*b^2*e^(3/2)*n^2*(a+b*log(c*(d+e/x^(2/3))^n))*log(x^(1/3)*sqrt(-d)+sqrt(e))/(-d)^(3/2)+12*b^3*e^(3/2)*n^3*log(1/2-1/2*x^(1/3)*sqrt(-d)/sqrt(e))*log(x^(1/3)*sqrt(-d)+sqrt(e))/(-d)^(3/2)-24*b^3*e^(3/2)*n^3*log(-x^(1/3)*sqrt(-d)/sqrt(e))*log(x^(1/3)*sqrt(-d)+sqrt(e))/(-d)^(3/2)+6*b^3*e^(3/2)*n^3*log(x^(1/3)*sqrt(-d)+sqrt(e))^2/(-d)^(3/2)+24*b^3*e^(3/2)*n^3*polylog(2,1-x^(1/3)*sqrt(-d)/sqrt(e))/(-d)^(3/2)-12*b^3*e^(3/2)*n^3*polylog(2,1/2-1/2*x^(1/3)*sqrt(-d)/sqrt(e))/(-d)^(3/2)+12*b^3*e^(3/2)*n^3*polylog(2,1/2*(1+x^(1/3)*sqrt(-d)/sqrt(e)))/(-d)^(3/2)-24*b^3*e^(3/2)*n^3*polylog(2,1+x^(1/3)*sqrt(-d)/sqrt(e))/(-d)^(3/2)-2*b*e^2*n*Unintegrable((a+b*log(c*(d+e/x^(2/3))^n))^2/((e+d*x^(2/3))*x^(2/3)),x)/d],
[(a+b*log(c*(d+e/x^(2/3))^n))^3/x^2,x,35,16/9*b^3*n^3/x-208/3*b^3*d*n^3/(e*x^(1/3))-208/3*b^3*d^(3/2)*n^3*arctan(x^(1/3)*sqrt(d)/sqrt(e))/e^(3/2)-32*I*b^3*d^(3/2)*n^3*arctan(x^(1/3)*sqrt(d)/sqrt(e))^2/e^(3/2)-8/3*b^2*n^2*(a+b*log(c*(d+e/x^(2/3))^n))/x+32*b^2*d*n^2*(a+b*log(c*(d+e/x^(2/3))^n))/(e*x^(1/3))+32*b^2*d^(3/2)*n^2*arctan(x^(1/3)*sqrt(d)/sqrt(e))*(a+b*log(c*(d+e/x^(2/3))^n))/e^(3/2)+2*b*n*(a+b*log(c*(d+e/x^(2/3))^n))^2/x-6*b*d*n*(a+b*log(c*(d+e/x^(2/3))^n))^2/(e*x^(1/3))-(a+b*log(c*(d+e/x^(2/3))^n))^3/x+64*b^3*d^(3/2)*n^3*arctan(x^(1/3)*sqrt(d)/sqrt(e))*log(2-2*sqrt(e)/(-I*x^(1/3)*sqrt(d)+sqrt(e)))/e^(3/2)-32*I*b^3*d^(3/2)*n^3*polylog(2,-1+2*sqrt(e)/(-I*x^(1/3)*sqrt(d)+sqrt(e)))/e^(3/2)-2*b*d^2*n*Unintegrable((a+b*log(c*(d+e/x^(2/3))^n))^2/((e+d*x^(2/3))*x^(2/3)),x)/e],
[(a+b*log(c*(d+e/x^(2/3))^n))^3/x^4,x,129,16/729*b^3*n^3/x^3-3088/27783*b^3*d*n^3/(e*x^(7/3))+221344/496125*b^3*d^2*n^3/(e^2*x^(5/3))-637984/297675*b^3*d^3*n^3/(e^3*x)+3475504/99225*b^3*d^4*n^3/(e^4*x^(1/3))+3475504/99225*b^3*d^(9/2)*n^3*arctan(x^(1/3)*sqrt(d)/sqrt(e))/e^(9/2)+4504/315*I*b^3*d^(9/2)*n^3*arctan(x^(1/3)*sqrt(d)/sqrt(e))^2/e^(9/2)-8/81*b^2*n^2*(a+b*log(c*(d+e/x^(2/3))^n))/x^3+128/441*b^2*d*n^2*(a+b*log(c*(d+e/x^(2/3))^n))/(e*x^(7/3))-1144/1575*b^2*d^2*n^2*(a+b*log(c*(d+e/x^(2/3))^n))/(e^2*x^(5/3))+1984/945*b^2*d^3*n^2*(a+b*log(c*(d+e/x^(2/3))^n))/(e^3*x)-4504/315*b^2*d^4*n^2*(a+b*log(c*(d+e/x^(2/3))^n))/(e^4*x^(1/3))-4504/315*b^2*d^(9/2)*n^2*arctan(x^(1/3)*sqrt(d)/sqrt(e))*(a+b*log(c*(d+e/x^(2/3))^n))/e^(9/2)+2/9*b*n*(a+b*log(c*(d+e/x^(2/3))^n))^2/x^3-2/7*b*d*n*(a+b*log(c*(d+e/x^(2/3))^n))^2/(e*x^(7/3))+2/5*b*d^2*n*(a+b*log(c*(d+e/x^(2/3))^n))^2/(e^2*x^(5/3))-2/3*b*d^3*n*(a+b*log(c*(d+e/x^(2/3))^n))^2/(e^3*x)+2*b*d^4*n*(a+b*log(c*(d+e/x^(2/3))^n))^2/(e^4*x^(1/3))-1/3*(a+b*log(c*(d+e/x^(2/3))^n))^3/x^3-9008/315*b^3*d^(9/2)*n^3*arctan(x^(1/3)*sqrt(d)/sqrt(e))*log(2-2*sqrt(e)/(-I*x^(1/3)*sqrt(d)+sqrt(e)))/e^(9/2)+4504/315*I*b^3*d^(9/2)*n^3*polylog(2,-1+2*sqrt(e)/(-I*x^(1/3)*sqrt(d)+sqrt(e)))/e^(9/2)+2/3*b*d^5*n*Unintegrable((a+b*log(c*(d+e/x^(2/3))^n))^2/((e+d*x^(2/3))*x^(2/3)),x)/e^4],

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

# m=1
[x^3*(a+b*log(c*(d+e*sqrt(x))))^p,x,27,2^(-2-3*p)*GAMMA(1+p,-8*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(c^8*e^8*exp(8*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)-2*d*GAMMA(1+p,-7*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(7^p*c^7*e^8*exp(7*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)+7*d^2*GAMMA(1+p,-6*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(6^p*c^6*e^8*exp(6*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)-14*d^3*GAMMA(1+p,-5*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(5^p*c^5*e^8*exp(5*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)+35*2^(-1-2*p)*d^4*GAMMA(1+p,-4*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(c^4*e^8*exp(4*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)-14*d^5*GAMMA(1+p,-3*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(3^p*c^3*e^8*exp(3*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)+7*d^6*GAMMA(1+p,-2*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(2^p*c^2*e^8*exp(2*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)-2*d^7*GAMMA(1+p,(-a-b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(c*e^8*exp(a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)],
[x^2*(a+b*log(c*(d+e*sqrt(x))))^p,x,21,3^(-1-p)*GAMMA(1+p,-6*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(2^p*c^6*e^6*exp(6*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)-2*d*GAMMA(1+p,-5*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(5^p*c^5*e^6*exp(5*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)+5*d^2*GAMMA(1+p,-4*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(4^p*c^4*e^6*exp(4*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)-20*3^(-1-p)*d^3*GAMMA(1+p,-3*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(c^3*e^6*exp(3*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)+5*d^4*GAMMA(1+p,-2*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(2^p*c^2*e^6*exp(2*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)-2*d^5*GAMMA(1+p,(-a-b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(c*e^6*exp(a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)],
[x*(a+b*log(c*(d+e*sqrt(x))))^p,x,15,2^(-1-2*p)*GAMMA(1+p,-4*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(c^4*e^4*exp(4*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)-2*d*GAMMA(1+p,-3*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(3^p*c^3*e^4*exp(3*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)+3*d^2*GAMMA(1+p,-2*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(2^p*c^2*e^4*exp(2*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)-2*d^3*GAMMA(1+p,(-a-b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(c*e^4*exp(a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)],
[(a+b*log(c*(d+e*sqrt(x))))^p,x,9,GAMMA(1+p,-2*(a+b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(2^p*c^2*e^2*exp(2*a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)-2*d*GAMMA(1+p,(-a-b*log(c*(d+e*sqrt(x))))/b)*(a+b*log(c*(d+e*sqrt(x))))^p/(c*e^2*exp(a/b)*((-a-b*log(c*(d+e*sqrt(x))))/b)^p)],
[(a+b*log(c*(d+e*sqrt(x))))^p/x,x,1,Unintegrable((a+b*log(c*(d+e*sqrt(x))))^p/x,x)],
[(a+b*log(c*(d+e*sqrt(x))))^p/x^2,x,1,Unintegrable((a+b*log(c*(d+e*sqrt(x))))^p/x^2,x)],
[x^3*(a+b*log(c*(d+e*sqrt(x))^2))^p,x,27,GAMMA(1+p,-4*(a+b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p/(2^(2*(1+p))*c^4*e^8*exp(4*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p)+7*d^2*GAMMA(1+p,-3*(a+b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p/(3^p*c^3*e^8*exp(3*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p)+35*2^(-1-p)*d^4*GAMMA(1+p,-2*(a+b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p/(c^2*e^8*exp(2*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p)+7*d^6*GAMMA(1+p,(-a-b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p/(c*e^8*exp(a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p)-2^(1+p)*d*GAMMA(1+p,-7/2*(a+b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p*(d+e*sqrt(x))^7/(7^p*e^8*exp(7/2*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p*(c*(d+e*sqrt(x))^2)^(7/2))-7*2^(1+p)*d^3*GAMMA(1+p,-5/2*(a+b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p*(d+e*sqrt(x))^5/(5^p*e^8*exp(5/2*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p*(c*(d+e*sqrt(x))^2)^(5/2))-7*2^(1+p)*d^5*GAMMA(1+p,-3/2*(a+b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p*(d+e*sqrt(x))^3/(3^p*e^8*exp(3/2*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p*(c*(d+e*sqrt(x))^2)^(3/2))-2^(1+p)*d^7*GAMMA(1+p,1/2*(-a-b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p*(d+e*sqrt(x))/(e^8*exp(1/2*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p*sqrt(c*(d+e*sqrt(x))^2))],
[x^2*(a+b*log(c*(d+e*sqrt(x))^2))^p,x,21,3^(-1-p)*GAMMA(1+p,-3*(a+b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p/(c^3*e^6*exp(3*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p)+5*d^2*GAMMA(1+p,-2*(a+b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p/(2^p*c^2*e^6*exp(2*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p)+5*d^4*GAMMA(1+p,(-a-b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p/(c*e^6*exp(a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p)-2^(1+p)*d*GAMMA(1+p,-5/2*(a+b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p*(d+e*sqrt(x))^5/(5^p*e^6*exp(5/2*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p*(c*(d+e*sqrt(x))^2)^(5/2))-5*2^(2+p)*3^(-1-p)*d^3*GAMMA(1+p,-3/2*(a+b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p*(d+e*sqrt(x))^3/(e^6*exp(3/2*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p*(c*(d+e*sqrt(x))^2)^(3/2))-2^(1+p)*d^5*GAMMA(1+p,1/2*(-a-b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p*(d+e*sqrt(x))/(e^6*exp(1/2*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p*sqrt(c*(d+e*sqrt(x))^2))],
[x*(a+b*log(c*(d+e*sqrt(x))^2))^p,x,15,2^(-1-p)*GAMMA(1+p,-2*(a+b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p/(c^2*e^4*exp(2*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p)+3*d^2*GAMMA(1+p,(-a-b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p/(c*e^4*exp(a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p)-2^(1+p)*d*GAMMA(1+p,-3/2*(a+b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p*(d+e*sqrt(x))^3/(3^p*e^4*exp(3/2*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p*(c*(d+e*sqrt(x))^2)^(3/2))-2^(1+p)*d^3*GAMMA(1+p,1/2*(-a-b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p*(d+e*sqrt(x))/(e^4*exp(1/2*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p*sqrt(c*(d+e*sqrt(x))^2))],
[(a+b*log(c*(d+e*sqrt(x))^2))^p,x,9,GAMMA(1+p,(-a-b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p/(c*e^2*exp(a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p)-2^(1+p)*d*GAMMA(1+p,1/2*(-a-b*log(c*(d+e*sqrt(x))^2))/b)*(a+b*log(c*(d+e*sqrt(x))^2))^p*(d+e*sqrt(x))/(e^2*exp(1/2*a/b)*((-a-b*log(c*(d+e*sqrt(x))^2))/b)^p*sqrt(c*(d+e*sqrt(x))^2))],
[(a+b*log(c*(d+e*sqrt(x))^2))^p/x,x,1,Unintegrable((a+b*log(c*(d+e*sqrt(x))^2))^p/x,x)],
[(a+b*log(c*(d+e*sqrt(x))^2))^p/x^2,x,1,Unintegrable((a+b*log(c*(d+e*sqrt(x))^2))^p/x^2,x)],

# m=-1
[x*(a+b*log(c*(d+e/sqrt(x))))^p,x,1,Unintegrable(x*(a+b*log(c*(d+e/sqrt(x))))^p,x)],
[(a+b*log(c*(d+e/sqrt(x))))^p,x,1,Unintegrable((a+b*log(c*(d+e/sqrt(x))))^p,x)],
[(a+b*log(c*(d+e/sqrt(x))))^p/x,x,1,Unintegrable((a+b*log(c*(d+e/sqrt(x))))^p/x,x)],
[(a+b*log(c*(d+e/sqrt(x))))^p/x^2,x,9,-GAMMA(1+p,-2*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(2^p*c^2*e^2*exp(2*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)+2*d*GAMMA(1+p,(-a-b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(c*e^2*exp(a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)],
[(a+b*log(c*(d+e/sqrt(x))))^p/x^4,x,21,-3^(-1-p)*GAMMA(1+p,-6*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(2^p*c^6*e^6*exp(6*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)+2*d*GAMMA(1+p,-5*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(5^p*c^5*e^6*exp(5*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)-5*d^2*GAMMA(1+p,-4*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(4^p*c^4*e^6*exp(4*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)+20*3^(-1-p)*d^3*GAMMA(1+p,-3*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(c^3*e^6*exp(3*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)-5*d^4*GAMMA(1+p,-2*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(2^p*c^2*e^6*exp(2*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)+2*d^5*GAMMA(1+p,(-a-b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(c*e^6*exp(a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)],
[(a+b*log(c*(d+e/sqrt(x))))^p/x^6,x,33,-5^(-1-p)*GAMMA(1+p,-10*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(2^p*c^10*e^10*exp(10*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)+2*d*GAMMA(1+p,-9*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(9^p*c^9*e^10*exp(9*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)-9*d^2*GAMMA(1+p,-8*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(8^p*c^8*e^10*exp(8*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)+24*d^3*GAMMA(1+p,-7*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(7^p*c^7*e^10*exp(7*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)-7*6^(1-p)*d^4*GAMMA(1+p,-6*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(c^6*e^10*exp(6*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)+252*5^(-1-p)*d^5*GAMMA(1+p,-5*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(c^5*e^10*exp(5*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)-21*2^(1-2*p)*d^6*GAMMA(1+p,-4*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(c^4*e^10*exp(4*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)+8*3^(1-p)*d^7*GAMMA(1+p,-3*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(c^3*e^10*exp(3*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)-9*d^8*GAMMA(1+p,-2*(a+b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(2^p*c^2*e^10*exp(2*a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)+2*d^9*GAMMA(1+p,(-a-b*log(c*(d+e/sqrt(x))))/b)*(a+b*log(c*(d+e/sqrt(x))))^p/(c*e^10*exp(a/b)*((-a-b*log(c*(d+e/sqrt(x))))/b)^p)],
[x*(a+b*log(c*(d+e/sqrt(x))^2))^p,x,1,Unintegrable(x*(a+b*log(c*(d+e/sqrt(x))^2))^p,x)],
[(a+b*log(c*(d+e/sqrt(x))^2))^p,x,1,Unintegrable((a+b*log(c*(d+e/sqrt(x))^2))^p,x)],
[(a+b*log(c*(d+e/sqrt(x))^2))^p/x,x,1,Unintegrable((a+b*log(c*(d+e/sqrt(x))^2))^p/x,x)],
[(a+b*log(c*(d+e/sqrt(x))^2))^p/x^2,x,9,-GAMMA(1+p,(-a-b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p/(c*e^2*exp(a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p)+2^(1+p)*d*GAMMA(1+p,1/2*(-a-b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p*(d+e/sqrt(x))/(e^2*exp(1/2*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p*sqrt(c*(d+e/sqrt(x))^2))],
[(a+b*log(c*(d+e/sqrt(x))^2))^p/x^4,x,21,-3^(-1-p)*GAMMA(1+p,-3*(a+b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p/(c^3*e^6*exp(3*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p)-5*d^2*GAMMA(1+p,-2*(a+b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p/(2^p*c^2*e^6*exp(2*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p)-5*d^4*GAMMA(1+p,(-a-b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p/(c*e^6*exp(a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p)+2^(1+p)*d*GAMMA(1+p,-5/2*(a+b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p*(d+e/sqrt(x))^5/(5^p*e^6*exp(5/2*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p*(c*(d+e/sqrt(x))^2)^(5/2))+5*2^(2+p)*3^(-1-p)*d^3*GAMMA(1+p,-3/2*(a+b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p*(d+e/sqrt(x))^3/(e^6*exp(3/2*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p*(c*(d+e/sqrt(x))^2)^(3/2))+2^(1+p)*d^5*GAMMA(1+p,1/2*(-a-b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p*(d+e/sqrt(x))/(e^6*exp(1/2*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p*sqrt(c*(d+e/sqrt(x))^2))],
[(a+b*log(c*(d+e/sqrt(x))^2))^p/x^6,x,33,-5^(-1-p)*GAMMA(1+p,-5*(a+b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p/(c^5*e^10*exp(5*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p)-9*d^2*GAMMA(1+p,-4*(a+b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p/(4^p*c^4*e^10*exp(4*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p)-14*3^(1-p)*d^4*GAMMA(1+p,-3*(a+b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p/(c^3*e^10*exp(3*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p)-21*2^(1-p)*d^6*GAMMA(1+p,-2*(a+b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p/(c^2*e^10*exp(2*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p)-9*d^8*GAMMA(1+p,(-a-b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p/(c*e^10*exp(a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p)+2^(1+p)*d*GAMMA(1+p,-9/2*(a+b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p*(d+e/sqrt(x))^9/(9^p*e^10*exp(9/2*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p*(c*(d+e/sqrt(x))^2)^(9/2))+3*2^(3+p)*d^3*GAMMA(1+p,-7/2*(a+b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p*(d+e/sqrt(x))^7/(7^p*e^10*exp(7/2*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p*(c*(d+e/sqrt(x))^2)^(7/2))+63*2^(2+p)*5^(-1-p)*d^5*GAMMA(1+p,-5/2*(a+b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p*(d+e/sqrt(x))^5/(e^10*exp(5/2*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p*(c*(d+e/sqrt(x))^2)^(5/2))+2^(3+p)*3^(1-p)*d^7*GAMMA(1+p,-3/2*(a+b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p*(d+e/sqrt(x))^3/(e^10*exp(3/2*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p*(c*(d+e/sqrt(x))^2)^(3/2))+2^(1+p)*d^9*GAMMA(1+p,1/2*(-a-b*log(c*(d+e/sqrt(x))^2))/b)*(a+b*log(c*(d+e/sqrt(x))^2))^p*(d+e/sqrt(x))/(e^10*exp(1/2*a/b)*((-a-b*log(c*(d+e/sqrt(x))^2))/b)^p*sqrt(c*(d+e/sqrt(x))^2))],

# Integrands of the form x^q (a+b Log[c (d+e x^(m/3))^n])^p when p symbolic

# m=1
[x^3*(a+b*log(c*(d+e*x^(1/3))))^p,x,39,4^(-1-p)*GAMMA(1+p,-12*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(3^p*c^12*e^12*exp(12*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-3*d*GAMMA(1+p,-11*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(11^p*c^11*e^12*exp(11*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)+33*2^(-1-p)*d^2*GAMMA(1+p,-10*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(5^p*c^10*e^12*exp(10*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-55*d^3*GAMMA(1+p,-9*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(9^p*c^9*e^12*exp(9*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)+495*2^(-2-3*p)*d^4*GAMMA(1+p,-8*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(c^8*e^12*exp(8*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-198*d^5*GAMMA(1+p,-7*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(7^p*c^7*e^12*exp(7*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)+77*3^(1-p)*d^6*GAMMA(1+p,-6*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(2^p*c^6*e^12*exp(6*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-198*d^7*GAMMA(1+p,-5*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(5^p*c^5*e^12*exp(5*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)+495*4^(-1-p)*d^8*GAMMA(1+p,-4*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(c^4*e^12*exp(4*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-55*d^9*GAMMA(1+p,-3*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(3^p*c^3*e^12*exp(3*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)+33*2^(-1-p)*d^10*GAMMA(1+p,-2*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(c^2*e^12*exp(2*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-3*d^11*GAMMA(1+p,(-a-b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(c*e^12*exp(a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)],
[x^2*(a+b*log(c*(d+e*x^(1/3))))^p,x,30,3^(-1-2*p)*GAMMA(1+p,-9*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(c^9*e^9*exp(9*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-3*d*GAMMA(1+p,-8*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(8^p*c^8*e^9*exp(8*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)+12*d^2*GAMMA(1+p,-7*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(7^p*c^7*e^9*exp(7*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-7*2^(2-p)*d^3*GAMMA(1+p,-6*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(3^p*c^6*e^9*exp(6*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)+42*d^4*GAMMA(1+p,-5*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(5^p*c^5*e^9*exp(5*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-21*2^(1-2*p)*d^5*GAMMA(1+p,-4*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(c^4*e^9*exp(4*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)+28*d^6*GAMMA(1+p,-3*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(3^p*c^3*e^9*exp(3*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-3*2^(2-p)*d^7*GAMMA(1+p,-2*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(c^2*e^9*exp(2*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)+3*d^8*GAMMA(1+p,(-a-b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(c*e^9*exp(a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)],
[x*(a+b*log(c*(d+e*x^(1/3))))^p,x,21,2^(-1-p)*GAMMA(1+p,-6*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(3^p*c^6*e^6*exp(6*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-3*d*GAMMA(1+p,-5*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(5^p*c^5*e^6*exp(5*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)+15*2^(-1-2*p)*d^2*GAMMA(1+p,-4*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(c^4*e^6*exp(4*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-10*d^3*GAMMA(1+p,-3*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(3^p*c^3*e^6*exp(3*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)+15*2^(-1-p)*d^4*GAMMA(1+p,-2*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(c^2*e^6*exp(2*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-3*d^5*GAMMA(1+p,(-a-b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(c*e^6*exp(a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)],
[(a+b*log(c*(d+e*x^(1/3))))^p,x,12,GAMMA(1+p,-3*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(3^p*c^3*e^3*exp(3*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)-3*d*GAMMA(1+p,-2*(a+b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(2^p*c^2*e^3*exp(2*a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)+3*d^2*GAMMA(1+p,(-a-b*log(c*(d+e*x^(1/3))))/b)*(a+b*log(c*(d+e*x^(1/3))))^p/(c*e^3*exp(a/b)*((-a-b*log(c*(d+e*x^(1/3))))/b)^p)],
[(a+b*log(c*(d+e*x^(1/3))))^p/x,x,1,Unintegrable((a+b*log(c*(d+e*x^(1/3))))^p/x,x)],
[(a+b*log(c*(d+e*x^(1/3))))^p/x^2,x,1,Unintegrable((a+b*log(c*(d+e*x^(1/3))))^p/x^2,x)],
[x^3*(a+b*log(c*(d+e*x^(1/3))^2))^p,x,39,2^(-2-p)*GAMMA(1+p,-6*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(3^p*c^6*e^12*exp(6*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-3*(2/11)^p*d*(d+e*x^(1/3))^11*GAMMA(1+p,-11/2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(e^12*exp(11/2*a/b)*(c*(d+e*x^(1/3))^2)^(11/2)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)+33/2*d^2*GAMMA(1+p,-5*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(5^p*c^5*e^12*exp(5*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-55*(2/9)^p*d^3*(d+e*x^(1/3))^9*GAMMA(1+p,-9/2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(e^12*exp(9/2*a/b)*(c*(d+e*x^(1/3))^2)^(9/2)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)+495*d^4*GAMMA(1+p,-4*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(2^(2*(1+p))*c^4*e^12*exp(4*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-99*2^(1+p)*d^5*(d+e*x^(1/3))^7*GAMMA(1+p,-7/2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(7^p*e^12*exp(7/2*a/b)*(c*(d+e*x^(1/3))^2)^(7/2)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)+77*3^(1-p)*d^6*GAMMA(1+p,-3*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(c^3*e^12*exp(3*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-99*2^(1+p)*d^7*(d+e*x^(1/3))^5*GAMMA(1+p,-5/2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(5^p*e^12*exp(5/2*a/b)*(c*(d+e*x^(1/3))^2)^(5/2)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)+495*2^(-2-p)*d^8*GAMMA(1+p,-2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(c^2*e^12*exp(2*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-55*(2/3)^p*d^9*(d+e*x^(1/3))^3*GAMMA(1+p,-3/2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(e^12*exp(3/2*a/b)*(c*(d+e*x^(1/3))^2)^(3/2)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)+33/2*d^10*GAMMA(1+p,(-a-b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(c*e^12*exp(a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-3*2^p*d^11*(d+e*x^(1/3))*GAMMA(1+p,1/2*(-a-b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(e^12*exp(1/2*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p*sqrt(c*(d+e*x^(1/3))^2))],
[x^2*(a+b*log(c*(d+e*x^(1/3))^2))^p,x,30,2^p*3^(-1-2*p)*(d+e*x^(1/3))^9*GAMMA(1+p,-9/2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(e^9*exp(9/2*a/b)*(c*(d+e*x^(1/3))^2)^(9/2)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-3*d*GAMMA(1+p,-4*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(4^p*c^4*e^9*exp(4*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)+3*2^(2+p)*d^2*(d+e*x^(1/3))^7*GAMMA(1+p,-7/2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(7^p*e^9*exp(7/2*a/b)*(c*(d+e*x^(1/3))^2)^(7/2)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-28*d^3*GAMMA(1+p,-3*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(3^p*c^3*e^9*exp(3*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)+21*2^(1+p)*d^4*(d+e*x^(1/3))^5*GAMMA(1+p,-5/2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(5^p*e^9*exp(5/2*a/b)*(c*(d+e*x^(1/3))^2)^(5/2)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-21*2^(1-p)*d^5*GAMMA(1+p,-2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(c^2*e^9*exp(2*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)+7*2^(2+p)*d^6*(d+e*x^(1/3))^3*GAMMA(1+p,-3/2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(3^p*e^9*exp(3/2*a/b)*(c*(d+e*x^(1/3))^2)^(3/2)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-12*d^7*GAMMA(1+p,(-a-b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(c*e^9*exp(a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)+3*2^p*d^8*(d+e*x^(1/3))*GAMMA(1+p,1/2*(-a-b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(e^9*exp(1/2*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p*sqrt(c*(d+e*x^(1/3))^2))],
[x*(a+b*log(c*(d+e*x^(1/3))^2))^p,x,21,1/2*GAMMA(1+p,-3*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(3^p*c^3*e^6*exp(3*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-3*(2/5)^p*d*(d+e*x^(1/3))^5*GAMMA(1+p,-5/2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(e^6*exp(5/2*a/b)*(c*(d+e*x^(1/3))^2)^(5/2)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)+15*2^(-1-p)*d^2*GAMMA(1+p,-2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(c^2*e^6*exp(2*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-5*2^(1+p)*d^3*(d+e*x^(1/3))^3*GAMMA(1+p,-3/2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(3^p*e^6*exp(3/2*a/b)*(c*(d+e*x^(1/3))^2)^(3/2)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)+15/2*d^4*GAMMA(1+p,(-a-b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(c*e^6*exp(a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-3*2^p*d^5*(d+e*x^(1/3))*GAMMA(1+p,1/2*(-a-b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(e^6*exp(1/2*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p*sqrt(c*(d+e*x^(1/3))^2))],
[(a+b*log(c*(d+e*x^(1/3))^2))^p,x,12,(2/3)^p*(d+e*x^(1/3))^3*GAMMA(1+p,-3/2*(a+b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(e^3*exp(3/2*a/b)*(c*(d+e*x^(1/3))^2)^(3/2)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)-3*d*GAMMA(1+p,(-a-b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(c*e^3*exp(a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p)+3*2^p*d^2*(d+e*x^(1/3))*GAMMA(1+p,1/2*(-a-b*log(c*(d+e*x^(1/3))^2))/b)*(a+b*log(c*(d+e*x^(1/3))^2))^p/(e^3*exp(1/2*a/b)*((-a-b*log(c*(d+e*x^(1/3))^2))/b)^p*sqrt(c*(d+e*x^(1/3))^2))],
[(a+b*log(c*(d+e*x^(1/3))^2))^p/x,x,1,Unintegrable((a+b*log(c*(d+e*x^(1/3))^2))^p/x,x)],
[(a+b*log(c*(d+e*x^(1/3))^2))^p/x^2,x,1,Unintegrable((a+b*log(c*(d+e*x^(1/3))^2))^p/x^2,x)],

# m=2
[x^3*(a+b*log(c*(d+e*x^(2/3))))^p,x,21,2^(-2-p)*GAMMA(1+p,-6*(a+b*log(c*(d+e*x^(2/3))))/b)*(a+b*log(c*(d+e*x^(2/3))))^p/(3^p*c^6*e^6*exp(6*a/b)*((-a-b*log(c*(d+e*x^(2/3))))/b)^p)-3/2*d*GAMMA(1+p,-5*(a+b*log(c*(d+e*x^(2/3))))/b)*(a+b*log(c*(d+e*x^(2/3))))^p/(5^p*c^5*e^6*exp(5*a/b)*((-a-b*log(c*(d+e*x^(2/3))))/b)^p)+15*d^2*GAMMA(1+p,-4*(a+b*log(c*(d+e*x^(2/3))))/b)*(a+b*log(c*(d+e*x^(2/3))))^p/(2^(2*(1+p))*c^4*e^6*exp(4*a/b)*((-a-b*log(c*(d+e*x^(2/3))))/b)^p)-5*d^3*GAMMA(1+p,-3*(a+b*log(c*(d+e*x^(2/3))))/b)*(a+b*log(c*(d+e*x^(2/3))))^p/(3^p*c^3*e^6*exp(3*a/b)*((-a-b*log(c*(d+e*x^(2/3))))/b)^p)+15*2^(-2-p)*d^4*GAMMA(1+p,-2*(a+b*log(c*(d+e*x^(2/3))))/b)*(a+b*log(c*(d+e*x^(2/3))))^p/(c^2*e^6*exp(2*a/b)*((-a-b*log(c*(d+e*x^(2/3))))/b)^p)-3/2*d^5*GAMMA(1+p,(-a-b*log(c*(d+e*x^(2/3))))/b)*(a+b*log(c*(d+e*x^(2/3))))^p/(c*e^6*exp(a/b)*((-a-b*log(c*(d+e*x^(2/3))))/b)^p)],
[x*(a+b*log(c*(d+e*x^(2/3))))^p,x,12,1/2*GAMMA(1+p,-3*(a+b*log(c*(d+e*x^(2/3))))/b)*(a+b*log(c*(d+e*x^(2/3))))^p/(3^p*c^3*e^3*exp(3*a/b)*((-a-b*log(c*(d+e*x^(2/3))))/b)^p)-3*2^(-1-p)*d*GAMMA(1+p,-2*(a+b*log(c*(d+e*x^(2/3))))/b)*(a+b*log(c*(d+e*x^(2/3))))^p/(c^2*e^3*exp(2*a/b)*((-a-b*log(c*(d+e*x^(2/3))))/b)^p)+3/2*d^2*GAMMA(1+p,(-a-b*log(c*(d+e*x^(2/3))))/b)*(a+b*log(c*(d+e*x^(2/3))))^p/(c*e^3*exp(a/b)*((-a-b*log(c*(d+e*x^(2/3))))/b)^p)],
[(a+b*log(c*(d+e*x^(2/3))))^p/x,x,1,Unintegrable((a+b*log(c*(d+e*x^(2/3))))^p/x,x)],
[(a+b*log(c*(d+e*x^(2/3))))^p/x^3,x,1,Unintegrable((a+b*log(c*(d+e*x^(2/3))))^p/x^3,x)],
[x^2*(a+b*log(c*(d+e*x^(2/3))))^p,x,1,Unintegrable(x^2*(a+b*log(c*(d+e*x^(2/3))))^p,x)],
[(a+b*log(c*(d+e*x^(2/3))))^p,x,1,Unintegrable((a+b*log(c*(d+e*x^(2/3))))^p,x)],
[(a+b*log(c*(d+e*x^(2/3))))^p/x^2,x,1,Unintegrable((a+b*log(c*(d+e*x^(2/3))))^p/x^2,x)],
[x^3*(a+b*log(c*(d+e*x^(2/3))^2))^p,x,21,1/4*GAMMA(1+p,-3*(a+b*log(c*(d+e*x^(2/3))^2))/b)*(a+b*log(c*(d+e*x^(2/3))^2))^p/(3^p*c^3*e^6*exp(3*a/b)*((-a-b*log(c*(d+e*x^(2/3))^2))/b)^p)-3*2^(-1+p)*d*(d+e*x^(2/3))^5*GAMMA(1+p,-5/2*(a+b*log(c*(d+e*x^(2/3))^2))/b)*(a+b*log(c*(d+e*x^(2/3))^2))^p/(5^p*e^6*exp(5/2*a/b)*(c*(d+e*x^(2/3))^2)^(5/2)*((-a-b*log(c*(d+e*x^(2/3))^2))/b)^p)+15*2^(-2-p)*d^2*GAMMA(1+p,-2*(a+b*log(c*(d+e*x^(2/3))^2))/b)*(a+b*log(c*(d+e*x^(2/3))^2))^p/(c^2*e^6*exp(2*a/b)*((-a-b*log(c*(d+e*x^(2/3))^2))/b)^p)-5*(2/3)^p*d^3*(d+e*x^(2/3))^3*GAMMA(1+p,-3/2*(a+b*log(c*(d+e*x^(2/3))^2))/b)*(a+b*log(c*(d+e*x^(2/3))^2))^p/(e^6*exp(3/2*a/b)*(c*(d+e*x^(2/3))^2)^(3/2)*((-a-b*log(c*(d+e*x^(2/3))^2))/b)^p)+15/4*d^4*GAMMA(1+p,(-a-b*log(c*(d+e*x^(2/3))^2))/b)*(a+b*log(c*(d+e*x^(2/3))^2))^p/(c*e^6*exp(a/b)*((-a-b*log(c*(d+e*x^(2/3))^2))/b)^p)-3*2^(-1+p)*d^5*(d+e*x^(2/3))*GAMMA(1+p,1/2*(-a-b*log(c*(d+e*x^(2/3))^2))/b)*(a+b*log(c*(d+e*x^(2/3))^2))^p/(e^6*exp(1/2*a/b)*((-a-b*log(c*(d+e*x^(2/3))^2))/b)^p*sqrt(c*(d+e*x^(2/3))^2))],
[x*(a+b*log(c*(d+e*x^(2/3))^2))^p,x,12,2^(-1+p)*(d+e*x^(2/3))^3*GAMMA(1+p,-3/2*(a+b*log(c*(d+e*x^(2/3))^2))/b)*(a+b*log(c*(d+e*x^(2/3))^2))^p/(3^p*e^3*exp(3/2*a/b)*(c*(d+e*x^(2/3))^2)^(3/2)*((-a-b*log(c*(d+e*x^(2/3))^2))/b)^p)-3/2*d*GAMMA(1+p,(-a-b*log(c*(d+e*x^(2/3))^2))/b)*(a+b*log(c*(d+e*x^(2/3))^2))^p/(c*e^3*exp(a/b)*((-a-b*log(c*(d+e*x^(2/3))^2))/b)^p)+3*2^(-1+p)*d^2*(d+e*x^(2/3))*GAMMA(1+p,1/2*(-a-b*log(c*(d+e*x^(2/3))^2))/b)*(a+b*log(c*(d+e*x^(2/3))^2))^p/(e^3*exp(1/2*a/b)*((-a-b*log(c*(d+e*x^(2/3))^2))/b)^p*sqrt(c*(d+e*x^(2/3))^2))],
[(a+b*log(c*(d+e*x^(2/3))^2))^p/x,x,1,Unintegrable((a+b*log(c*(d+e*x^(2/3))^2))^p/x,x)],
[(a+b*log(c*(d+e*x^(2/3))^2))^p/x^3,x,1,Unintegrable((a+b*log(c*(d+e*x^(2/3))^2))^p/x^3,x)],
[x^2*(a+b*log(c*(d+e*x^(2/3))^2))^p,x,1,Unintegrable(x^2*(a+b*log(c*(d+e*x^(2/3))^2))^p,x)],
[(a+b*log(c*(d+e*x^(2/3))^2))^p,x,1,Unintegrable((a+b*log(c*(d+e*x^(2/3))^2))^p,x)],
[(a+b*log(c*(d+e*x^(2/3))^2))^p/x^2,x,1,Unintegrable((a+b*log(c*(d+e*x^(2/3))^2))^p/x^2,x)],

# m=-1
[x*(a+b*log(c*(d+e/x^(1/3))))^p,x,1,Unintegrable(x*(a+b*log(c*(d+e/x^(1/3))))^p,x)],
[(a+b*log(c*(d+e/x^(1/3))))^p,x,1,Unintegrable((a+b*log(c*(d+e/x^(1/3))))^p,x)],
[(a+b*log(c*(d+e/x^(1/3))))^p/x,x,1,Unintegrable((a+b*log(c*(d+e/x^(1/3))))^p/x,x)],
[(a+b*log(c*(d+e/x^(1/3))))^p/x^2,x,12,-GAMMA(1+p,-3*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(3^p*c^3*e^3*exp(3*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)+3*d*GAMMA(1+p,-2*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(2^p*c^2*e^3*exp(2*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)-3*d^2*GAMMA(1+p,(-a-b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(c*e^3*exp(a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)],
[(a+b*log(c*(d+e/x^(1/3))))^p/x^3,x,21,-2^(-1-p)*GAMMA(1+p,-6*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(3^p*c^6*e^6*exp(6*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)+3*d*GAMMA(1+p,-5*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(5^p*c^5*e^6*exp(5*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)-15*2^(-1-2*p)*d^2*GAMMA(1+p,-4*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(c^4*e^6*exp(4*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)+10*d^3*GAMMA(1+p,-3*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(3^p*c^3*e^6*exp(3*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)-15*2^(-1-p)*d^4*GAMMA(1+p,-2*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(c^2*e^6*exp(2*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)+3*d^5*GAMMA(1+p,(-a-b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(c*e^6*exp(a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)],
[(a+b*log(c*(d+e/x^(1/3))))^p/x^4,x,30,-3^(-1-2*p)*GAMMA(1+p,-9*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(c^9*e^9*exp(9*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)+3*d*GAMMA(1+p,-8*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(8^p*c^8*e^9*exp(8*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)-12*d^2*GAMMA(1+p,-7*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(7^p*c^7*e^9*exp(7*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)+7*2^(2-p)*d^3*GAMMA(1+p,-6*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(3^p*c^6*e^9*exp(6*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)-42*d^4*GAMMA(1+p,-5*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(5^p*c^5*e^9*exp(5*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)+21*2^(1-2*p)*d^5*GAMMA(1+p,-4*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(c^4*e^9*exp(4*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)-28*d^6*GAMMA(1+p,-3*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(3^p*c^3*e^9*exp(3*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)+3*2^(2-p)*d^7*GAMMA(1+p,-2*(a+b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(c^2*e^9*exp(2*a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)-3*d^8*GAMMA(1+p,(-a-b*log(c*(d+e/x^(1/3))))/b)*(a+b*log(c*(d+e/x^(1/3))))^p/(c*e^9*exp(a/b)*((-a-b*log(c*(d+e/x^(1/3))))/b)^p)],
[x*(a+b*log(c*(d+e/x^(1/3))^2))^p,x,1,Unintegrable(x*(a+b*log(c*(d+e/x^(1/3))^2))^p,x)],
[(a+b*log(c*(d+e/x^(1/3))^2))^p,x,1,Unintegrable((a+b*log(c*(d+e/x^(1/3))^2))^p,x)],
[(a+b*log(c*(d+e/x^(1/3))^2))^p/x,x,1,Unintegrable((a+b*log(c*(d+e/x^(1/3))^2))^p/x,x)],
[(a+b*log(c*(d+e/x^(1/3))^2))^p/x^2,x,12,-(2/3)^p*(d+e/x^(1/3))^3*GAMMA(1+p,-3/2*(a+b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(e^3*exp(3/2*a/b)*(c*(d+e/x^(1/3))^2)^(3/2)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)+3*d*GAMMA(1+p,(-a-b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(c*e^3*exp(a/b)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)-3*2^p*d^2*(d+e/x^(1/3))*GAMMA(1+p,1/2*(-a-b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(e^3*exp(1/2*a/b)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p*sqrt(c*(d+e/x^(1/3))^2))],
[(a+b*log(c*(d+e/x^(1/3))^2))^p/x^3,x,21,-1/2*GAMMA(1+p,-3*(a+b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(3^p*c^3*e^6*exp(3*a/b)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)+3*(2/5)^p*d*(d+e/x^(1/3))^5*GAMMA(1+p,-5/2*(a+b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(e^6*exp(5/2*a/b)*(c*(d+e/x^(1/3))^2)^(5/2)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)-15*2^(-1-p)*d^2*GAMMA(1+p,-2*(a+b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(c^2*e^6*exp(2*a/b)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)+5*2^(1+p)*d^3*(d+e/x^(1/3))^3*GAMMA(1+p,-3/2*(a+b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(3^p*e^6*exp(3/2*a/b)*(c*(d+e/x^(1/3))^2)^(3/2)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)-15/2*d^4*GAMMA(1+p,(-a-b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(c*e^6*exp(a/b)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)+3*2^p*d^5*(d+e/x^(1/3))*GAMMA(1+p,1/2*(-a-b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(e^6*exp(1/2*a/b)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p*sqrt(c*(d+e/x^(1/3))^2))],
[(a+b*log(c*(d+e/x^(1/3))^2))^p/x^4,x,30,-2^p*3^(-1-2*p)*(d+e/x^(1/3))^9*GAMMA(1+p,-9/2*(a+b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(e^9*exp(9/2*a/b)*(c*(d+e/x^(1/3))^2)^(9/2)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)+3*d*GAMMA(1+p,-4*(a+b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(4^p*c^4*e^9*exp(4*a/b)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)-3*2^(2+p)*d^2*(d+e/x^(1/3))^7*GAMMA(1+p,-7/2*(a+b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(7^p*e^9*exp(7/2*a/b)*(c*(d+e/x^(1/3))^2)^(7/2)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)+28*d^3*GAMMA(1+p,-3*(a+b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(3^p*c^3*e^9*exp(3*a/b)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)-21*2^(1+p)*d^4*(d+e/x^(1/3))^5*GAMMA(1+p,-5/2*(a+b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(5^p*e^9*exp(5/2*a/b)*(c*(d+e/x^(1/3))^2)^(5/2)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)+21*2^(1-p)*d^5*GAMMA(1+p,-2*(a+b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(c^2*e^9*exp(2*a/b)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)-7*2^(2+p)*d^6*(d+e/x^(1/3))^3*GAMMA(1+p,-3/2*(a+b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(3^p*e^9*exp(3/2*a/b)*(c*(d+e/x^(1/3))^2)^(3/2)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)+12*d^7*GAMMA(1+p,(-a-b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(c*e^9*exp(a/b)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p)-3*2^p*d^8*(d+e/x^(1/3))*GAMMA(1+p,1/2*(-a-b*log(c*(d+e/x^(1/3))^2))/b)*(a+b*log(c*(d+e/x^(1/3))^2))^p/(e^9*exp(1/2*a/b)*((-a-b*log(c*(d+e/x^(1/3))^2))/b)^p*sqrt(c*(d+e/x^(1/3))^2))],

# m=-2
[x^3*(a+b*log(c*(d+e/x^(2/3))))^p,x,1,Unintegrable(x^3*(a+b*log(c*(d+e/x^(2/3))))^p,x)],
[x^2*(a+b*log(c*(d+e/x^(2/3))))^p,x,1,Unintegrable(x^2*(a+b*log(c*(d+e/x^(2/3))))^p,x)],
[x*(a+b*log(c*(d+e/x^(2/3))))^p,x,1,Unintegrable(x*(a+b*log(c*(d+e/x^(2/3))))^p,x)],
[(a+b*log(c*(d+e/x^(2/3))))^p,x,1,Unintegrable((a+b*log(c*(d+e/x^(2/3))))^p,x)],
[(a+b*log(c*(d+e/x^(2/3))))^p/x,x,1,Unintegrable((a+b*log(c*(d+e/x^(2/3))))^p/x,x)],
[(a+b*log(c*(d+e/x^(2/3))))^p/x^2,x,1,Unintegrable((a+b*log(c*(d+e/x^(2/3))))^p/x^2,x)],
[x^3*(a+b*log(c*(d+e/x^(2/3))^2))^p,x,1,Unintegrable(x^3*(a+b*log(c*(d+e/x^(2/3))^2))^p,x)],
[x^2*(a+b*log(c*(d+e/x^(2/3))^2))^p,x,1,Unintegrable(x^2*(a+b*log(c*(d+e/x^(2/3))^2))^p,x)],
[x*(a+b*log(c*(d+e/x^(2/3))^2))^p,x,1,Unintegrable(x*(a+b*log(c*(d+e/x^(2/3))^2))^p,x)],
[(a+b*log(c*(d+e/x^(2/3))^2))^p,x,1,Unintegrable((a+b*log(c*(d+e/x^(2/3))^2))^p,x)],
[(a+b*log(c*(d+e/x^(2/3))^2))^p/x,x,1,Unintegrable((a+b*log(c*(d+e/x^(2/3))^2))^p/x,x)],
[(a+b*log(c*(d+e/x^(2/3))^2))^p/x^2,x,1,Unintegrable((a+b*log(c*(d+e/x^(2/3))^2))^p/x^2,x)],

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

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

# r>0
[(f+g*x)*(a+b*log(c*(d+e*x^2)^p))/(h*x)^(1/2),x,26,-8/9*b*g*p*(h*x)^(3/2)/h^2+2/3*g*(h*x)^(3/2)*(a+b*log(c*(d+e*x^2)^p))/h^2-2*b*d^(1/4)*f*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(1/4)*sqrt(h))-2/3*b*d^(3/4)*g*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(3/4)*sqrt(h))+2*b*d^(1/4)*f*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(1/4)*sqrt(h))+2/3*b*d^(3/4)*g*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(3/4)*sqrt(h))-b*d^(1/4)*f*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(1/4)*sqrt(h))+1/3*b*d^(3/4)*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(3/4)*sqrt(h))+b*d^(1/4)*f*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(1/4)*sqrt(h))-1/3*b*d^(3/4)*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(3/4)*sqrt(h))+2*a*f*sqrt(h*x)/h-8*b*f*p*sqrt(h*x)/h+2*b*f*log(c*(d+e*x^2)^p)*sqrt(h*x)/h],
[(f+g*x)*(a+b*log(c*(d+e*x^2)^p))/(h*x)^(3/2),x,25,-2*b*e^(1/4)*f*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(1/4)*h^(3/2))-2*b*d^(1/4)*g*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(1/4)*h^(3/2))+2*b*e^(1/4)*f*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(1/4)*h^(3/2))+2*b*d^(1/4)*g*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(1/4)*h^(3/2))+b*e^(1/4)*f*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(1/4)*h^(3/2))-b*d^(1/4)*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(1/4)*h^(3/2))-b*e^(1/4)*f*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(1/4)*h^(3/2))+b*d^(1/4)*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(1/4)*h^(3/2))-2*f*(a+b*log(c*(d+e*x^2)^p))/(h*sqrt(h*x))+2*a*g*sqrt(h*x)/h^2-8*b*g*p*sqrt(h*x)/h^2+2*b*g*log(c*(d+e*x^2)^p)*sqrt(h*x)/h^2],
[(f+g*x)*(a+b*log(c*(d+e*x^2)^p))/(h*x)^(5/2),x,23,-2/3*f*(a+b*log(c*(d+e*x^2)^p))/(h*(h*x)^(3/2))-2/3*b*e^(3/4)*f*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(3/4)*h^(5/2))-2*b*e^(1/4)*g*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(1/4)*h^(5/2))+2/3*b*e^(3/4)*f*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(3/4)*h^(5/2))+2*b*e^(1/4)*g*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(1/4)*h^(5/2))-1/3*b*e^(3/4)*f*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(3/4)*h^(5/2))+b*e^(1/4)*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(1/4)*h^(5/2))+1/3*b*e^(3/4)*f*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(3/4)*h^(5/2))-b*e^(1/4)*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(1/4)*h^(5/2))-2*g*(a+b*log(c*(d+e*x^2)^p))/(h^2*sqrt(h*x))],
[(f+g*x)*(a+b*log(c*(d+e*x^2)^p))/(h*x)^(7/2),x,24,-2/5*f*(a+b*log(c*(d+e*x^2)^p))/(h*(h*x)^(5/2))-2/3*g*(a+b*log(c*(d+e*x^2)^p))/(h^2*(h*x)^(3/2))+2/5*b*e^(5/4)*f*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(5/4)*h^(7/2))-2/3*b*e^(3/4)*g*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(3/4)*h^(7/2))-2/5*b*e^(5/4)*f*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(5/4)*h^(7/2))+2/3*b*e^(3/4)*g*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(3/4)*h^(7/2))-1/5*b*e^(5/4)*f*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(5/4)*h^(7/2))-1/3*b*e^(3/4)*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(3/4)*h^(7/2))+1/5*b*e^(5/4)*f*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(5/4)*h^(7/2))+1/3*b*e^(3/4)*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(3/4)*h^(7/2))-8/5*b*e*f*p/(d*h^3*sqrt(h*x))],
[(f+g*x)*(a+b*log(c*(d+e*x^2)^p))/(h*x)^(9/2),x,25,-8/21*b*e*f*p/(d*h^3*(h*x)^(3/2))-2/7*f*(a+b*log(c*(d+e*x^2)^p))/(h*(h*x)^(7/2))-2/5*g*(a+b*log(c*(d+e*x^2)^p))/(h^2*(h*x)^(5/2))+2/7*b*e^(7/4)*f*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(7/4)*h^(9/2))+2/5*b*e^(5/4)*g*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(5/4)*h^(9/2))-2/7*b*e^(7/4)*f*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(7/4)*h^(9/2))-2/5*b*e^(5/4)*g*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(5/4)*h^(9/2))+1/7*b*e^(7/4)*f*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(7/4)*h^(9/2))-1/5*b*e^(5/4)*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(5/4)*h^(9/2))-1/7*b*e^(7/4)*f*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(7/4)*h^(9/2))+1/5*b*e^(5/4)*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(5/4)*h^(9/2))-8/5*b*e*g*p/(d*h^4*sqrt(h*x))],
[(f+g*x)^2*(a+b*log(c*(d+e*x^2)^p))/(h*x)^(1/2),x,38,-16/9*b*f*g*p*(h*x)^(3/2)/h^2-8/25*b*g^2*p*(h*x)^(5/2)/h^3+4/3*f*g*(h*x)^(3/2)*(a+b*log(c*(d+e*x^2)^p))/h^2+2/5*g^2*(h*x)^(5/2)*(a+b*log(c*(d+e*x^2)^p))/h^3-2*b*d^(1/4)*f^2*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(1/4)*sqrt(h))-4/3*b*d^(3/4)*f*g*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(3/4)*sqrt(h))+2/5*b*d^(5/4)*g^2*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(5/4)*sqrt(h))+2*b*d^(1/4)*f^2*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(1/4)*sqrt(h))+4/3*b*d^(3/4)*f*g*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(3/4)*sqrt(h))-2/5*b*d^(5/4)*g^2*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(5/4)*sqrt(h))-b*d^(1/4)*f^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(1/4)*sqrt(h))+2/3*b*d^(3/4)*f*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(3/4)*sqrt(h))+1/5*b*d^(5/4)*g^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(5/4)*sqrt(h))+b*d^(1/4)*f^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(1/4)*sqrt(h))-2/3*b*d^(3/4)*f*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(3/4)*sqrt(h))-1/5*b*d^(5/4)*g^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(5/4)*sqrt(h))+2*a*f^2*sqrt(h*x)/h-8*b*f^2*p*sqrt(h*x)/h+8/5*b*d*g^2*p*sqrt(h*x)/(e*h)+2*b*f^2*log(c*(d+e*x^2)^p)*sqrt(h*x)/h],
[(f+g*x)^2*(a+b*log(c*(d+e*x^2)^p))/(h*x)^(3/2),x,36,-8/9*b*g^2*p*(h*x)^(3/2)/h^3+2/3*g^2*(h*x)^(3/2)*(a+b*log(c*(d+e*x^2)^p))/h^3-2*b*e^(1/4)*f^2*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(1/4)*h^(3/2))-4*b*d^(1/4)*f*g*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(1/4)*h^(3/2))-2/3*b*d^(3/4)*g^2*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(3/4)*h^(3/2))+2*b*e^(1/4)*f^2*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(1/4)*h^(3/2))+4*b*d^(1/4)*f*g*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(1/4)*h^(3/2))+2/3*b*d^(3/4)*g^2*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(3/4)*h^(3/2))+b*e^(1/4)*f^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(1/4)*h^(3/2))-2*b*d^(1/4)*f*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(1/4)*h^(3/2))+1/3*b*d^(3/4)*g^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(3/4)*h^(3/2))-b*e^(1/4)*f^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(1/4)*h^(3/2))+2*b*d^(1/4)*f*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(1/4)*h^(3/2))-1/3*b*d^(3/4)*g^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(3/4)*h^(3/2))-2*f^2*(a+b*log(c*(d+e*x^2)^p))/(h*sqrt(h*x))+4*a*f*g*sqrt(h*x)/h^2-16*b*f*g*p*sqrt(h*x)/h^2+4*b*f*g*log(c*(d+e*x^2)^p)*sqrt(h*x)/h^2],
[(f+g*x)^2*(a+b*log(c*(d+e*x^2)^p))/(h*x)^(5/2),x,35,-2/3*f^2*(a+b*log(c*(d+e*x^2)^p))/(h*(h*x)^(3/2))-2/3*b*e^(3/4)*f^2*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(3/4)*h^(5/2))-4*b*e^(1/4)*f*g*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(1/4)*h^(5/2))-2*b*d^(1/4)*g^2*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(1/4)*h^(5/2))+2/3*b*e^(3/4)*f^2*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(3/4)*h^(5/2))+4*b*e^(1/4)*f*g*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(1/4)*h^(5/2))+2*b*d^(1/4)*g^2*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(e^(1/4)*h^(5/2))-1/3*b*e^(3/4)*f^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(3/4)*h^(5/2))+2*b*e^(1/4)*f*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(1/4)*h^(5/2))-b*d^(1/4)*g^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(1/4)*h^(5/2))+1/3*b*e^(3/4)*f^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(3/4)*h^(5/2))-2*b*e^(1/4)*f*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(1/4)*h^(5/2))+b*d^(1/4)*g^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(e^(1/4)*h^(5/2))-4*f*g*(a+b*log(c*(d+e*x^2)^p))/(h^2*sqrt(h*x))+2*a*g^2*sqrt(h*x)/h^3-8*b*g^2*p*sqrt(h*x)/h^3+2*b*g^2*log(c*(d+e*x^2)^p)*sqrt(h*x)/h^3],
[(f+g*x)^2*(a+b*log(c*(d+e*x^2)^p))/(h*x)^(7/2),x,34,-2/5*f^2*(a+b*log(c*(d+e*x^2)^p))/(h*(h*x)^(5/2))-4/3*f*g*(a+b*log(c*(d+e*x^2)^p))/(h^2*(h*x)^(3/2))+2/5*b*e^(5/4)*f^2*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(5/4)*h^(7/2))-4/3*b*e^(3/4)*f*g*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(3/4)*h^(7/2))-2*b*e^(1/4)*g^2*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(1/4)*h^(7/2))-2/5*b*e^(5/4)*f^2*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(5/4)*h^(7/2))+4/3*b*e^(3/4)*f*g*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(3/4)*h^(7/2))+2*b*e^(1/4)*g^2*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(1/4)*h^(7/2))-1/5*b*e^(5/4)*f^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(5/4)*h^(7/2))-2/3*b*e^(3/4)*f*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(3/4)*h^(7/2))+b*e^(1/4)*g^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(1/4)*h^(7/2))+1/5*b*e^(5/4)*f^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(5/4)*h^(7/2))+2/3*b*e^(3/4)*f*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(3/4)*h^(7/2))-b*e^(1/4)*g^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(1/4)*h^(7/2))-8/5*b*e*f^2*p/(d*h^3*sqrt(h*x))-2*g^2*(a+b*log(c*(d+e*x^2)^p))/(h^3*sqrt(h*x))],
[(f+g*x)^2*(a+b*log(c*(d+e*x^2)^p))/(h*x)^(9/2),x,35,-8/21*b*e*f^2*p/(d*h^3*(h*x)^(3/2))-2/7*f^2*(a+b*log(c*(d+e*x^2)^p))/(h*(h*x)^(7/2))-4/5*f*g*(a+b*log(c*(d+e*x^2)^p))/(h^2*(h*x)^(5/2))-2/3*g^2*(a+b*log(c*(d+e*x^2)^p))/(h^3*(h*x)^(3/2))+2/7*b*e^(7/4)*f^2*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(7/4)*h^(9/2))+4/5*b*e^(5/4)*f*g*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(5/4)*h^(9/2))-2/3*b*e^(3/4)*g^2*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(3/4)*h^(9/2))-2/7*b*e^(7/4)*f^2*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(7/4)*h^(9/2))-4/5*b*e^(5/4)*f*g*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(5/4)*h^(9/2))+2/3*b*e^(3/4)*g^2*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(3/4)*h^(9/2))+1/7*b*e^(7/4)*f^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(7/4)*h^(9/2))-2/5*b*e^(5/4)*f*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(5/4)*h^(9/2))-1/3*b*e^(3/4)*g^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(3/4)*h^(9/2))-1/7*b*e^(7/4)*f^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(7/4)*h^(9/2))+2/5*b*e^(5/4)*f*g*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(5/4)*h^(9/2))+1/3*b*e^(3/4)*g^2*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(3/4)*h^(9/2))-16/5*b*e*f*g*p/(d*h^4*sqrt(h*x))],

# r<0
[(h*x)^(1/2)*(a+b*log(c*(d+e*x^2)^p))/(f+g*x),x,39,-2*b*d^(1/4)*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)*sqrt(h)/(e^(1/4)*g)+2*b*d^(1/4)*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)*sqrt(h)/(e^(1/4)*g)-b*d^(1/4)*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)*sqrt(h)/(e^(1/4)*g)+b*d^(1/4)*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)*sqrt(h)/(e^(1/4)*g)-2*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*(a+b*log(c*(d+e*x^2)^p))*sqrt(f)*sqrt(h)/g^(3/2)-8*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(2*sqrt(f)*sqrt(h)/(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x)))*sqrt(f)*sqrt(h)/g^(3/2)+2*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h)-e^(1/4)*sqrt(h*x))/(((-d)^(1/4)*sqrt(g)*sqrt(-h)-I*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(f)*sqrt(h)/g^(3/2)+2*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(-2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h)-e^(1/4)*sqrt(h*x))/((I*e^(1/4)*sqrt(f)-(-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(f)*sqrt(h)/g^(3/2)+2*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h)+e^(1/4)*sqrt(h*x))/(((-d)^(1/4)*sqrt(g)*sqrt(-h)+I*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(f)*sqrt(h)/g^(3/2)+2*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h)+e^(1/4)*sqrt(h*x))/((I*e^(1/4)*sqrt(f)+(-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(f)*sqrt(h)/g^(3/2)+4*I*b*p*polylog(2,1-2*sqrt(f)*sqrt(h)/(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x)))*sqrt(f)*sqrt(h)/g^(3/2)-I*b*p*polylog(2,1-2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h)-e^(1/4)*sqrt(h*x))/(((-d)^(1/4)*sqrt(g)*sqrt(-h)-I*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(f)*sqrt(h)/g^(3/2)-I*b*p*polylog(2,1+2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h)-e^(1/4)*sqrt(h*x))/((I*e^(1/4)*sqrt(f)-(-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(f)*sqrt(h)/g^(3/2)-I*b*p*polylog(2,1-2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h)+e^(1/4)*sqrt(h*x))/(((-d)^(1/4)*sqrt(g)*sqrt(-h)+I*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(f)*sqrt(h)/g^(3/2)-I*b*p*polylog(2,1-2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h)+e^(1/4)*sqrt(h*x))/((I*e^(1/4)*sqrt(f)+(-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(f)*sqrt(h)/g^(3/2)+2*a*sqrt(h*x)/g-8*b*p*sqrt(h*x)/g+2*b*log(c*(d+e*x^2)^p)*sqrt(h*x)/g],
[(a+b*log(c*(d+e*x^2)^p))/((h*x)^(1/2)*(f+g*x)),x,25,2*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*(a+b*log(c*(d+e*x^2)^p))/(sqrt(f)*sqrt(g)*sqrt(h))+8*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(2*sqrt(f)*sqrt(h)/(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x)))/(sqrt(f)*sqrt(g)*sqrt(h))-2*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h)-e^(1/4)*sqrt(h*x))/(((-d)^(1/4)*sqrt(g)*sqrt(-h)-I*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))/(sqrt(f)*sqrt(g)*sqrt(h))-2*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(-2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h)-e^(1/4)*sqrt(h*x))/((I*e^(1/4)*sqrt(f)-(-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))/(sqrt(f)*sqrt(g)*sqrt(h))-2*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h)+e^(1/4)*sqrt(h*x))/(((-d)^(1/4)*sqrt(g)*sqrt(-h)+I*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))/(sqrt(f)*sqrt(g)*sqrt(h))-2*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h)+e^(1/4)*sqrt(h*x))/((I*e^(1/4)*sqrt(f)+(-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))/(sqrt(f)*sqrt(g)*sqrt(h))-4*I*b*p*polylog(2,1-2*sqrt(f)*sqrt(h)/(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x)))/(sqrt(f)*sqrt(g)*sqrt(h))+I*b*p*polylog(2,1-2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h)-e^(1/4)*sqrt(h*x))/(((-d)^(1/4)*sqrt(g)*sqrt(-h)-I*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))/(sqrt(f)*sqrt(g)*sqrt(h))+I*b*p*polylog(2,1+2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h)-e^(1/4)*sqrt(h*x))/((I*e^(1/4)*sqrt(f)-(-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))/(sqrt(f)*sqrt(g)*sqrt(h))+I*b*p*polylog(2,1-2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h)+e^(1/4)*sqrt(h*x))/(((-d)^(1/4)*sqrt(g)*sqrt(-h)+I*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))/(sqrt(f)*sqrt(g)*sqrt(h))+I*b*p*polylog(2,1-2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h)+e^(1/4)*sqrt(h*x))/((I*e^(1/4)*sqrt(f)+(-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))/(sqrt(f)*sqrt(g)*sqrt(h))],
[(a+b*log(c*(d+e*x^2)^p))/((h*x)^(3/2)*(f+g*x)),x,37,-2*b*e^(1/4)*p*arctan(1-e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(1/4)*f*h^(3/2))+2*b*e^(1/4)*p*arctan(1+e^(1/4)*sqrt(2)*sqrt(h*x)/(d^(1/4)*sqrt(h)))*sqrt(2)/(d^(1/4)*f*h^(3/2))+b*e^(1/4)*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)-d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(1/4)*f*h^(3/2))-b*e^(1/4)*p*log(sqrt(d)*sqrt(h)+x*sqrt(e)*sqrt(h)+d^(1/4)*e^(1/4)*sqrt(2)*sqrt(h*x))*sqrt(2)/(d^(1/4)*f*h^(3/2))-2*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*(a+b*log(c*(d+e*x^2)^p))*sqrt(g)/(f^(3/2)*h^(3/2))-8*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(2*sqrt(f)*sqrt(h)/(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x)))*sqrt(g)/(f^(3/2)*h^(3/2))+2*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h)-e^(1/4)*sqrt(h*x))/(((-d)^(1/4)*sqrt(g)*sqrt(-h)-I*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(g)/(f^(3/2)*h^(3/2))+2*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(-2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h)-e^(1/4)*sqrt(h*x))/((I*e^(1/4)*sqrt(f)-(-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(g)/(f^(3/2)*h^(3/2))+2*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h)+e^(1/4)*sqrt(h*x))/(((-d)^(1/4)*sqrt(g)*sqrt(-h)+I*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(g)/(f^(3/2)*h^(3/2))+2*b*p*arctan(sqrt(g)*sqrt(h*x)/(sqrt(f)*sqrt(h)))*log(2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h)+e^(1/4)*sqrt(h*x))/((I*e^(1/4)*sqrt(f)+(-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(g)/(f^(3/2)*h^(3/2))+4*I*b*p*polylog(2,1-2*sqrt(f)*sqrt(h)/(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x)))*sqrt(g)/(f^(3/2)*h^(3/2))-I*b*p*polylog(2,1-2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h)-e^(1/4)*sqrt(h*x))/(((-d)^(1/4)*sqrt(g)*sqrt(-h)-I*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(g)/(f^(3/2)*h^(3/2))-I*b*p*polylog(2,1+2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h)-e^(1/4)*sqrt(h*x))/((I*e^(1/4)*sqrt(f)-(-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(g)/(f^(3/2)*h^(3/2))-I*b*p*polylog(2,1-2*sqrt(f)*sqrt(g)*sqrt(h)*((-d)^(1/4)*sqrt(-h)+e^(1/4)*sqrt(h*x))/(((-d)^(1/4)*sqrt(g)*sqrt(-h)+I*e^(1/4)*sqrt(f)*sqrt(h))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(g)/(f^(3/2)*h^(3/2))-I*b*p*polylog(2,1-2*sqrt(f)*sqrt(g)*((-d)^(1/4)*sqrt(h)+e^(1/4)*sqrt(h*x))/((I*e^(1/4)*sqrt(f)+(-d)^(1/4)*sqrt(g))*(sqrt(f)*sqrt(h)-I*sqrt(g)*sqrt(h*x))))*sqrt(g)/(f^(3/2)*h^(3/2))-2*(a+b*log(c*(d+e*x^2)^p))/(f*h*sqrt(h*x))],

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

# Integrands of the form (h x)^s Log[f x^r]^q (a+b Log[c (d+e x^m)^n])
[log(f*x^p)*log(1+e*x^m)/x,x,2,-log(f*x^p)*polylog(2,-e*x^m)/m+p*polylog(3,-e*x^m)/m^2],
[x^(-1+m)*log(f*x^p)^2/(d+e*x^m),x,3,log(f*x^p)^2*log(1+e*x^m/d)/(e*m)+2*p*log(f*x^p)*polylog(2,-e*x^m/d)/(e*m^2)-2*p^2*polylog(3,-e*x^m/d)/(e*m^3)],
[log(f*x^p)^3*(a+b*log(c*(d+e*x^m)^n))/x,x,6,1/4*log(f*x^p)^4*(a+b*log(c*(d+e*x^m)^n))/p-1/4*b*n*log(f*x^p)^4*log(1+e*x^m/d)/p-b*n*log(f*x^p)^3*polylog(2,-e*x^m/d)/m+3*b*n*p*log(f*x^p)^2*polylog(3,-e*x^m/d)/m^2-6*b*n*p^2*log(f*x^p)*polylog(4,-e*x^m/d)/m^3+6*b*n*p^3*polylog(5,-e*x^m/d)/m^4],
[log(f*x^p)^2*(a+b*log(c*(d+e*x^m)^n))/x,x,5,1/3*log(f*x^p)^3*(a+b*log(c*(d+e*x^m)^n))/p-1/3*b*n*log(f*x^p)^3*log(1+e*x^m/d)/p-b*n*log(f*x^p)^2*polylog(2,-e*x^m/d)/m+2*b*n*p*log(f*x^p)*polylog(3,-e*x^m/d)/m^2-2*b*n*p^2*polylog(4,-e*x^m/d)/m^3],
[log(f*x^p)*(a+b*log(c*(d+e*x^m)^n))/x,x,4,1/2*log(f*x^p)^2*(a+b*log(c*(d+e*x^m)^n))/p-1/2*b*n*log(f*x^p)^2*log(1+e*x^m/d)/p-b*n*log(f*x^p)*polylog(2,-e*x^m/d)/m+b*n*p*polylog(3,-e*x^m/d)/m^2],
[(a+b*log(c*(d+e*x^m)^n))/x,x,3,log(-e*x^m/d)*(a+b*log(c*(d+e*x^m)^n))/m+b*n*polylog(2,1+e*x^m/d)/m],
[(a+b*log(c*(d+e*x^m)^n))/(x*log(f*x^p)),x,4,a*log(log(f*x^p))/p+b*Unintegrable(log(c*(d+e*x^m)^n)/(x*log(f*x^p)),x)],
[(a+b*log(c*(d+e*x^m)^n))/(x*log(f*x^p)^2),x,1,(-a-b*log(c*(d+e*x^m)^n))/(p*log(f*x^p))+b*e*m*n*Unintegrable(x^(-1+m)/((d+e*x^m)*log(f*x^p)),x)/p],
[(a+b*log(c*(d+e*x^m)^n))/(x*log(f*x^p)^3),x,1,1/2*(-a-b*log(c*(d+e*x^m)^n))/(p*log(f*x^p)^2)+1/2*b*e*m*n*Unintegrable(x^(-1+m)/((d+e*x^m)*log(f*x^p)^2),x)/p],

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

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

# Integrands of the form Log[c (d+e (f+g x)^m)^n]
[log(c*(d+e*(f+g*x)^p)^q),x,3,-e*p*q*(f+g*x)^(1+p)*hypergeom([1,1+1/p],[2+1/p],-e*(f+g*x)^p/d)/(d*g*(1+p))+(f+g*x)*log(c*(d+e*(f+g*x)^p)^q)/g],
[log(c*(d+e*(f+g*x)^3)^q),x,9,-3*q*x+d^(1/3)*q*log(d^(1/3)+e^(1/3)*(f+g*x))/(e^(1/3)*g)-1/2*d^(1/3)*q*log(d^(2/3)-d^(1/3)*e^(1/3)*(f+g*x)+e^(2/3)*(f+g*x)^2)/(e^(1/3)*g)+(f+g*x)*log(c*(d+e*(f+g*x)^3)^q)/g-d^(1/3)*q*arctan((d^(1/3)-2*e^(1/3)*(f+g*x))/(d^(1/3)*sqrt(3)))*sqrt(3)/(e^(1/3)*g)],
[log(c*(d+e*(f+g*x)^2)^q),x,4,-2*q*x+(f+g*x)*log(c*(d+e*(f+g*x)^2)^q)/g+2*q*arctan((f+g*x)*sqrt(e)/sqrt(d))*sqrt(d)/(g*sqrt(e))],
[log(c*(d+e*(f+g*x))^q),x,3,-q*x+(d+e*f+e*g*x)*log(c*(d+e*(f+g*x))^q)/(e*g)],
[log(c*(d+e/(f+g*x))^q),x,4,(f+g*x)*log(c*(d+e/(f+g*x))^q)/g+e*q*log(e+d*(f+g*x))/(d*g)],
[log(c*(d+e/(f+g*x)^2)^q),x,4,(f+g*x)*log(c*(d+e/(f+g*x)^2)^q)/g+2*q*arctan((f+g*x)*sqrt(d)/sqrt(e))*sqrt(e)/(g*sqrt(d))],
[log(c*(d+e/(f+g*x)^3)^q),x,9,(f+g*x)*log(c*(d+e/(f+g*x)^3)^q)/g+e^(1/3)*q*log(e^(1/3)+d^(1/3)*(f+g*x))/(d^(1/3)*g)-1/2*e^(1/3)*q*log(e^(2/3)-d^(1/3)*e^(1/3)*(f+g*x)+d^(2/3)*(f+g*x)^2)/(d^(1/3)*g)-e^(1/3)*q*arctan((e^(1/3)-2*d^(1/3)*(f+g*x))/(e^(1/3)*sqrt(3)))*sqrt(3)/(d^(1/3)*g)],

# Integrands of the form (a+b Log[c (d+e/(f+g x))^n])^p
[(a+b*log(c*(d+e/(f+g*x))^p))^n,x,0,Unintegrable((a+b*log(c*(d+e/(f+g*x))^p))^n,x)],
[(a+b*log(c*(d+e/(f+g*x))^p))^4,x,8,-4*b*e*p*log(-e/(d*(f+g*x)))*(a+b*log(c*(d+e/(f+g*x))^p))^3/(d*g)+(e+d*(f+g*x))*(a+b*log(c*(d+e/(f+g*x))^p))^4/(d*g)-12*b^2*e*p^2*(a+b*log(c*(d+e/(f+g*x))^p))^2*polylog(2,1+e/(d*(f+g*x)))/(d*g)+24*b^3*e*p^3*(a+b*log(c*(d+e/(f+g*x))^p))*polylog(3,1+e/(d*(f+g*x)))/(d*g)-24*b^4*e*p^4*polylog(4,1+e/(d*(f+g*x)))/(d*g)],
[(a+b*log(c*(d+e/(f+g*x))^p))^3,x,7,-3*b*e*p*log(-e/(d*(f+g*x)))*(a+b*log(c*(d+e/(f+g*x))^p))^2/(d*g)+(e+d*(f+g*x))*(a+b*log(c*(d+e/(f+g*x))^p))^3/(d*g)-6*b^2*e*p^2*(a+b*log(c*(d+e/(f+g*x))^p))*polylog(2,1+e/(d*(f+g*x)))/(d*g)+6*b^3*e*p^3*polylog(3,1+e/(d*(f+g*x)))/(d*g)],
[(a+b*log(c*(d+e/(f+g*x))^p))^2,x,5,-2*b*e*p*log(-e/(d*(f+g*x)))*(a+b*log(c*(d+e/(f+g*x))^p))/(d*g)+(e+d*(f+g*x))*(a+b*log(c*(d+e/(f+g*x))^p))^2/(d*g)-2*b^2*e*p^2*polylog(2,1+e/(d*(f+g*x)))/(d*g)],
[a+b*log(c*(d+e/(f+g*x))^p),x,5,a*x+b*(f+g*x)*log(c*(d+e/(f+g*x))^p)/g+b*e*p*log(e+d*(f+g*x))/(d*g)],
[1/(a+b*log(c*(d+e/(f+g*x))^p)),x,0,Unintegrable(1/(a+b*log(c*(d+e/(f+g*x))^p)),x)],
[1/(a+b*log(c*(d+e/(f+g*x))^p))^2,x,0,Unintegrable(1/(a+b*log(c*(d+e/(f+g*x))^p))^2,x)]]:
