integration - The closed form representations of Integrals of logarithm functions

I wish to find a closed form representations of the following integral
$$\int\limits_{0}^1\frac{\log^p(x)\log^r\left(\frac{1-x}{1+x}\right)}{x}dx=?$$
Here $p\ge 1$ and $r\ge 0$ are nonnegative integers. It can be expressed in terms of a linear combination of well known constants (such as: Riemann zeta values,$\pi$ et. al.)?