Day 16: The Powers of Trigonometric Integrals

Calculus Level 4

\[\large \int^{{\pi} / {4}}_0 (\cos^8\theta +\sin^8\theta+(\cos^4\theta+\sin^4\theta)\cos^2\theta \sin^2\theta ) \, d\theta\]

If the value of the integral above is of the form \(\dfrac{a\pi}{b}\) where \(a\) and \(b\) are positive coprime integers, find the value of \(a+b\).


This problem is part of the Advent Calendar 2015. Adapted from a maths test question so credit to my maths teacher!
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