\[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^4 \, dx \]
Optimal antiderivative \[ \frac {2 a^{2} {\mathrm e}^{\left (b x +a \right )^{3}}}{b^{5}}-\frac {a^{4} \left (b x +a \right ) \Gamma \! \left (\frac {1}{3}, -\left (b x +a \right )^{3}\right )}{3 b^{5} \left (-\left (b x +a \right )^{3}\right )^{\frac {1}{3}}}+\frac {4 a^{3} \left (b x +a \right )^{2} \Gamma \! \left (\frac {2}{3}, -\left (b x +a \right )^{3}\right )}{3 b^{5} \left (-\left (b x +a \right )^{3}\right )^{\frac {2}{3}}}+\frac {4 a \left (b x +a \right )^{4} \Gamma \! \left (\frac {4}{3}, -\left (b x +a \right )^{3}\right )}{3 b^{5} \left (-\left (b x +a \right )^{3}\right )^{\frac {4}{3}}}-\frac {\left (b x +a \right )^{5} \Gamma \! \left (\frac {5}{3}, -\left (b x +a \right )^{3}\right )}{3 b^{5} \left (-\left (b x +a \right )^{3}\right )^{\frac {5}{3}}} \]
command
Int[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^4,x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^4 \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ -\frac {a^4 (a+b x) \Gamma \left (\frac {1}{3},-(a+b x)^3\right )}{3 b^5 \sqrt [3]{-(a+b x)^3}}+\frac {4 a^3 (a+b x)^2 \Gamma \left (\frac {2}{3},-(a+b x)^3\right )}{3 b^5 \left (-(a+b x)^3\right )^{2/3}}+\frac {2 a^2 e^{(a+b x)^3}}{b^5}-\frac {(a+b x)^5 \Gamma \left (\frac {5}{3},-(a+b x)^3\right )}{3 b^5 \left (-(a+b x)^3\right )^{5/3}}+\frac {4 a (a+b x)^4 \Gamma \left (\frac {4}{3},-(a+b x)^3\right )}{3 b^5 \left (-(a+b x)^3\right )^{4/3}} \]