# Terrible Integrals!

Calculus Level 4

$\large \displaystyle \int _{ 0 }^{ \frac { \pi }{ 2 } }{ \sin ^{ 5 }{ (x) } \cos ^{ 3 }{ (x) } \ dx } = \ ?$

If the closed form of the integral above is in the form of $$\dfrac{a}{b}$$, where $$a$$ and $$b$$ are natural numbers and $$\gcd(a,b)=1$$, find $$a+b$$.

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