I would need some help to work with the following integral:
$$f(x) = \int_2^\infty \log (1-x^t) dt ,\ \ \ \ \ \ \ \ \ |x|<1$$
I would like to get a closed form or something similar (which seems to be impossible), but any other type of exact equivalent expression to work with would be great.
Making a change of variables seems not to help much. I also tried to evaluate it as a complex integral, but the path of integration $[2, \infty)$ is not the easiest to work with.
Any idea will be welcomed. Thank you in advantage.