As homework, I have to solve this integral using the gamma and beta functions. I was unable to find it online, so could anyone help me? $$ \int_{0}^{\infty}x^{\alpha-1}\ln^{2}{x}dx, {\alpha}< {0} $$
I have tried the following substitutions until now: $$ t=\ln{x};t=\ln{(1-x)}; t=\ln{(1/x)}; t=\ln{(x+1)} $$
I got stuck either at ln(0) or when I had to find a function that can be transformed to the gamma function.
This is the beta function: https://en.wikipedia.org/wiki/Beta_function And this is the gamma function: https://en.wikipedia.org/wiki/Gamma_function