\[ \int \frac {x^8}{\log ^2\left (c \left (d+e x^3\right )^p\right )} \, dx \]
Optimal antiderivative \[ \frac {d^{2} \left (e \,x^{3}+d \right ) \expIntegral \left (\frac {\ln \left (c \left (e \,x^{3}+d \right )^{p}\right )}{p}\right ) \left (c \left (e \,x^{3}+d \right )^{p}\right )^{-\frac {1}{p}}}{3 e^{3} p^{2}}-\frac {4 d \left (e \,x^{3}+d \right )^{2} \expIntegral \left (\frac {2 \ln \left (c \left (e \,x^{3}+d \right )^{p}\right )}{p}\right ) \left (c \left (e \,x^{3}+d \right )^{p}\right )^{-\frac {2}{p}}}{3 e^{3} p^{2}}+\frac {\left (e \,x^{3}+d \right )^{3} \expIntegral \left (\frac {3 \ln \left (c \left (e \,x^{3}+d \right )^{p}\right )}{p}\right ) \left (c \left (e \,x^{3}+d \right )^{p}\right )^{-\frac {3}{p}}}{e^{3} p^{2}}-\frac {x^{6} \left (e \,x^{3}+d \right )}{3 e p \ln \left (c \left (e \,x^{3}+d \right )^{p}\right )} \]
command
int(x^8/ln(c*(e*x^3+d)^p)^2,x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(2564\) |
Maple 2021.1 output
\[ \int \frac {x^{8}}{\ln \left (c \left (e \,x^{3}+d \right )^{p}\right )^{2}}\, dx \]________________________________________________________________________________________