Evaluate: ∫ sin x/(sin x+ cos x) dx, x ∈ [π/5, 3π/10]

Question

Evaluate:

\(\int_{\pi/5}^{3\pi/10} \cfrac{sin\,x }{sin\,x +cos\,x}dx\)

∫ sin x/(sin x+ cos x) dx,  x ∈ [π/5, 3π/10]

Answer 1

Let \(I\) = \(\int_{\pi/5}^{3\pi/10} \cfrac{sin\,x }{sin\,x +cos\,x}dx\)

Adding (1) and (2) we get,