Note on an integral by Anatolii Prudnikov

Closed expressions for the integral \begin{document}$ \begin{equation*} \int_{0}^{\infty}\frac{x^{m-1} \log ^k(a x)}{\left(x^{2 u}+1\right) \left(x^{3 u}+1\right)}dx \end{equation*} $\end{document} are given where the variables $ a $, $ k $, $ m $ and $ u $ are general complex numbers. Some of these closed expressions are given in [ 4 ] . Some special cases of the integral are derived and discussed.