The value of the integral ∫ x+π/4 / 2-cos2x dx; x ∈ [-π/4, π/4] is:

Question

The value of the integral \(\int \limits_{-\frac \pi 4}^{\frac \pi 4} \frac{x+\frac \pi 4}{2 -\cos 2x} dx\) is:

(1) \(\frac {\pi^2}6\)

(2) \(\frac {\pi^2}{12\sqrt 3}\)

(3) \(\frac {\pi^2}{3\sqrt 3}\)

(4) \(\frac{\pi^2}{6\sqrt 3}\)

Answer 1

Correct option is (4) \(\frac{\pi^2}{6\sqrt 3}\)