\[ \int x \log \left (e^x \log (x) \sin (x)\right ) \, dx \]
Optimal antiderivative \[ \left (-\frac {1}{6}+\frac {i}{6}\right ) x^{3}-\frac {\expIntegral \left (2 \ln \left (x \right )\right )}{2}-\frac {x^{2} \ln \left (1-{\mathrm e}^{2 i x}\right )}{2}+\frac {x^{2} \ln \left ({\mathrm e}^{x} \ln \left (x \right ) \sin \left (x \right )\right )}{2}+\frac {i x \polylog \left (2, {\mathrm e}^{2 i x}\right )}{2}-\frac {\polylog \left (3, {\mathrm e}^{2 i x}\right )}{4} \]
command
int(x*ln(exp(x)*ln(x)*sin(x)),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(663\) |
Maple 2021.1 output
\[ \int x \ln \left ({\mathrm e}^{x} \ln \left (x \right ) \sin \left (x \right )\right )\, dx \]________________________________________________________________________________________