\[ \int e^{\frac {x}{2}+x z} x^4 \sin ^4(\pi z) \, dz \]
Optimal antiderivative \[ \frac {24 \,{\mathrm e}^{\frac {1}{2} x +x z} \pi ^{4} x^{3}}{64 \pi ^{4}+20 \pi ^{2} x^{2}+x^{4}}-\frac {24 \,{\mathrm e}^{\frac {1}{2} x +x z} \pi ^{3} x^{4} \cos \left (\pi z \right ) \sin \left (\pi z \right )}{64 \pi ^{4}+20 \pi ^{2} x^{2}+x^{4}}+\frac {12 \,{\mathrm e}^{\frac {1}{2} x +x z} \pi ^{2} x^{5} \left (\sin ^{2}\left (\pi z \right )\right )}{64 \pi ^{4}+20 \pi ^{2} x^{2}+x^{4}}-\frac {4 \,{\mathrm e}^{\frac {1}{2} x +x z} \pi \,x^{4} \cos \left (\pi z \right ) \left (\sin ^{3}\left (\pi z \right )\right )}{16 \pi ^{2}+x^{2}}+\frac {{\mathrm e}^{\frac {1}{2} x +x z} x^{5} \left (\sin ^{4}\left (\pi z \right )\right )}{16 \pi ^{2}+x^{2}} \]
command
integrate(x**4*exp(1/2*x+x*z)*sin(pi*z)**4,z)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________