Prove-that-0-2-0-1-arctan-sinx-u-cosx-dudx-pi-2-16-3-2-ln-2-pi-4-

Question Number 164125 by HongKing last updated on 14/Jan/22

Prove that :

\underset{0}{\int^{\frac{π}{2}}} \underset{0}{\int^{1}} \arctan (\frac{\sin x}{u + \cos x}) dudx = \frac{π^{2}}{16} + \frac{3}{2} \ln (2) - \frac{π}{4}

Answered by Kamel last updated on 14/Jan/22

Commented by HongKing last updated on 15/Jan/22

thank you so much my dear Sir cool