Recent content by The Lord

Great! This was my approach as well. (Yes)

Prove that $$ \int_0^\infty \frac{\log x}{(1+x^2)^2}dx = \frac{-\pi}{4}$$

Prove that $$\int_0^{\pi/2} (\log \sin x )^2 dx = \frac{1}{24} \left(\pi ^3+12 \pi \log^2(2)\right)$$

I explored the challenge forums today and found it very interesting. I thought it would be a good idea to share a problem with this excellent community. Show that $$ \int_0^\infty \frac{\ln(\tan^2 (x))}{1+x^2}dx = \pi \ln(\tanh(1))$$