# This needs more care!

Calculus Level 5

$\int_{0}^{\infty}\sin^{-1}\left(\dfrac{e^{-x}}{\sqrt{2}}\right)\, dx=\dfrac{\pi^P}Q \ln R + \dfrac GR$

The equation above holds true for positive integers $$P,Q,R$$ with $$R$$ being a prime. Find $$P+Q+R$$

 Notation: $$\displaystyle G = \sum_{n=0}^\infty \dfrac{ (-1)^n}{(2n+1)^2} \approx 0.916$$ denotes the Catalan's constant.

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