\[ \int \frac {x^3}{\log ^2\left (c \left (a+b x^2\right )^p\right )} \, dx \]
Optimal antiderivative \[ -\frac {a \left (b \,x^{2}+a \right ) \expIntegral \left (\frac {\ln \left (c \left (b \,x^{2}+a \right )^{p}\right )}{p}\right ) \left (c \left (b \,x^{2}+a \right )^{p}\right )^{-\frac {1}{p}}}{2 b^{2} p^{2}}+\frac {\left (b \,x^{2}+a \right )^{2} \expIntegral \left (\frac {2 \ln \left (c \left (b \,x^{2}+a \right )^{p}\right )}{p}\right ) \left (c \left (b \,x^{2}+a \right )^{p}\right )^{-\frac {2}{p}}}{b^{2} p^{2}}-\frac {x^{2} \left (b \,x^{2}+a \right )}{2 b p \ln \left (c \left (b \,x^{2}+a \right )^{p}\right )} \]
command
int(x^3/ln(c*(b*x^2+a)^p)^2,x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(1474\) |
Maple 2021.1 output
\[ \int \frac {x^{3}}{\ln \left (c \left (b \,x^{2}+a \right )^{p}\right )^{2}}\, dx \]________________________________________________________________________________________