Prove that ∫ x cot x dx=π/4(log 2), x ∈[0,π/2]

Question

Prove that  

\(\int\limits_0^{\pi/2}x\,cot\,x\,dx=\cfrac{\pi}{4}(log\,2)\)

∫ x cot x dx=π/4(log 2), x ∈[0,π/2]

Answer 1

Use integration by parts