I have this integral
$\int_0^\infty \frac{x^{2 m}\;\ln^n (x) }{e^{\frac{2 p +1}{2}x}} dx\;\; m,n,p \in \mathbb{N}$
and I'like to know the general solution.
From WolframAlpha I got some solutions, e.g.
$\int_0^\infty \frac{x^2\ln(x)}{e^{\frac{3x}{2}}} dx = \frac{8}{27}\left(3-2\gamma-\ln\left(\frac{9}{4}\right)\right) $ and
$\int_0^\infty \frac{x^{2}\ln^{2}(x)}{e^{\frac{3x}{2}}} dx = \frac{8}{81}\left(6-18\gamma+6\gamma^{2}+\pi^{2}-6 \ln \left(\frac{3}{2}\right)\left(3-2\gamma-\ln\left(\frac{3}{2}\right)\right) \right) $
etc... but I'd like to know the general form of the solution and the process/method to get there. Note that $\gamma$ is the Euler-Mascheroni constant.
Thanks.