# Whose integrals is it?

Calculus Level 5

$\displaystyle \large\sum\limits_{k=1}^{2018} \int_0^{\infty} \sin^{2k} \bigg(\frac{1}{x}\bigg) \mathrm{d}x = \displaystyle a \sqrt{\pi} \cdot \dfrac{ \Gamma \big(\frac{b}{c} \big)}{\Gamma (d) }$

The equation above holds true for positive integers $$a$$, $$b$$, $$c$$ and $$d$$ with $$\gcd(b,c) = 1$$. Find $$a+b+c+d$$.


Notation: $$\Gamma(\cdot)$$ denotes the Gamma function.

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