So I encountered this problem while trying to solve another problem(which I can post if requested) and this step is omitted (perhaps as being trivial) in the solution booklet. $$\int_{0}^{1}ln[(1-t)t]dt$$ The answer given is -2,kindly show the steps in arriving at this solution without solving integral!
Edit: Apologies for not mentioning what all I had tried,the only excuse I have is that it as 3am and I was tired :P. I tried using KING and QUEEN(after multiplying $(1+t) * t$ inside ln() itself) but the thought of expanding ln() never crossed my mind. Lesson learnt, maths with a sleepy mind is never a good idea.
HINT:
$\displaystyle\int_0^1\ln((1-t)t)\,dt = \int_0^1\ln(1-t)+\ln(t)\,dt=\int_0^1\ln(1-t)\,dt+\int_0^1\ln(t)\,dt$
Use integration by parts to obtain your required answer.