The value of 120/π^3 |∫ x^2 sin x. cos x / (sin x)^4 + (cos x)^4 dx | ; x ∈ (0,π)

Question

The value of \(\frac {120}{\pi ^3}\left|\int ^\pi _ 0 \frac{x^2 sin \,x .cos \,x}{(sin\,x)^4 +(cos \,x)^4}dx\right|\) is 

Answer 1

Correct answer is : 15

Let cos2x = t