\[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^3 \, dx \]
Optimal antiderivative \[ -\frac {a \,{\mathrm e}^{\left (b x +a \right )^{3}}}{b^{4}}+\frac {a^{3} \left (b x +a \right ) \Gamma \! \left (\frac {1}{3}, -\left (b x +a \right )^{3}\right )}{3 b^{4} \left (-\left (b x +a \right )^{3}\right )^{\frac {1}{3}}}-\frac {a^{2} \left (b x +a \right )^{2} \Gamma \! \left (\frac {2}{3}, -\left (b x +a \right )^{3}\right )}{b^{4} \left (-\left (b x +a \right )^{3}\right )^{\frac {2}{3}}}-\frac {\left (b x +a \right )^{4} \Gamma \! \left (\frac {4}{3}, -\left (b x +a \right )^{3}\right )}{3 b^{4} \left (-\left (b x +a \right )^{3}\right )^{\frac {4}{3}}} \]
command
Int[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^3,x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^3 \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {a^3 (a+b x) \Gamma \left (\frac {1}{3},-(a+b x)^3\right )}{3 b^4 \sqrt [3]{-(a+b x)^3}}-\frac {a^2 (a+b x)^2 \Gamma \left (\frac {2}{3},-(a+b x)^3\right )}{b^4 \left (-(a+b x)^3\right )^{2/3}}-\frac {a e^{(a+b x)^3}}{b^4}-\frac {(a+b x)^4 \Gamma \left (\frac {4}{3},-(a+b x)^3\right )}{3 b^4 \left (-(a+b x)^3\right )^{4/3}} \]