# 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 $$a+b$$.

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