While I was practicing calculus today ,I was held up by this guy.
$$I=\int_0^1 \ln x \space\cdot\ln(1-x)\space dx$$ I have no idea where to start , I think $$\lim_{x\to \infty}\space \sum_{r=1}^n\frac{1}{r^2}\space= \frac{\pi^2}{6}$$ might be helpful . Any suggestion are appreciated . Cheers!