On the Mellin transform of $\frac{\log^{n}(1+x)}{(1+x)^{m+1}}$

Abstract

We use the Ramanujan's master theorem to evaluate the integral $$\int_{0}^{\infty}\frac{x^{l-1}}{(1+x)^{m+1}}\log^{n}(1+x)\, dx$$ in terms of the digamma function, the gamma function, and the Hurwitz zeta function.