Question

Evaluate the following integral using properties of integration.

∫(x sin x)/(1 + sin x) dx for x ∈ [0,π]

Answer 1

From the integral 

Let I = ∫(x sin x)/(1 + sin x) dx for x ∈ [0,π] ... (1)

2I = π² - 2π

I = (π²/2) - π