\[ \int e^{\text {sech}^{-1}(a x)} x^m \, dx \]
Optimal antiderivative \[ \frac {x^{m}}{a m \left (1+m \right )}+\frac {\left (\frac {1}{a x}+\sqrt {\frac {1}{a x}-1}\, \sqrt {1+\frac {1}{a x}}\right ) x^{1+m}}{1+m}+\frac {x^{m} \hypergeom \! \left (\left [\frac {1}{2}, \frac {m}{2}\right ], \left [1+\frac {m}{2}\right ], a^{2} x^{2}\right ) \sqrt {\frac {1}{a x +1}}\, \sqrt {a x +1}}{a m \left (1+m \right )} \]
command
Integrate[E^ArcSech[a*x]*x^m,x]
Mathematica 13.1 output
\[ \int e^{\text {sech}^{-1}(a x)} x^m \, dx \]
Mathematica 12.3 output
\[ -\frac {2^{m+1} x^m (a x)^{-m} e^{2 \text {sech}^{-1}(a x)} \left (\frac {e^{\text {sech}^{-1}(a x)}}{e^{2 \text {sech}^{-1}(a x)}+1}\right )^m \left (e^{2 \text {sech}^{-1}(a x)}+1\right )^m \left ((m+2) e^{2 \text {sech}^{-1}(a x)} \, _2F_1\left (\frac {m}{2}+2,m+2;\frac {m}{2}+3;-e^{2 \text {sech}^{-1}(a x)}\right )-(m+4) \, _2F_1\left (\frac {m}{2}+1,m+2;\frac {m}{2}+2;-e^{2 \text {sech}^{-1}(a x)}\right )\right )}{a (m+2) (m+4)} \]