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Evaluate the value of the trignometric function

Source: Bangladesh National Mathematical Olympiad 2018

February 23, 2019
calculuscontestsInteresting problemgeometrytrigonometryfunction

Problem Statement

Evaluate
∫0π/2cos⁡4x+sin⁡xcos⁡3x+sin⁡2xcos⁡2x+sin⁡3xcos⁡xsin⁡4x+cos⁡4x+2 sinxcos⁡3x+2sin⁡2xcos⁡2x+2sin⁡3xcos⁡xdx\int^{\pi/2}_0 \frac{\cos^4x + \sin x \cos^3 x + \sin^2x\cos^2x + \sin^3x\cos x}{\sin^4x + \cos^4x + 2\ sinx\cos^3x + 2\sin^2x\cos^2x + 2\sin^3x\cos x} dx
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