∫ 0 π / 2 x + sin x 1 + cos x d x =

Step-by-step solution

I = ∫ 0 π 2 x + sin x 1 + cos x .   d x ( 1 + cos x = 2 cos 2 x 2 as cos 2 x = 2 cos 2 x - 1 ) I = ∫ 0 π 2 x + sin x 2 cos 2 x 2 .   d x sin 2 x = 2 sin x   cos x   &   1 cos x = sec x I = ∫ 0 π 2 x sec 2 x 2 2 + 2 sin x 2 cos x 2 2   cos 2 x 2 . d x I = ∫ 0 π 2 1 2 x . sec 2 x 2 d x   + ∫ 0 π 2 tan x 2 . d x Using chain rule intergration, we get I = 1 2 ( x ∫ 0 π 2   sec 2 x 2 .   d x - ∫ 0 &#96