# Inspired by Abhishek Singh's Integral!

Calculus Level 4

$\int_{0}^{\infty} \frac{\lbrace x \rbrace^{\lfloor x \rfloor}}{\lceil x \rceil} \ \mathrm{d}x$

If the above integral is of the form $$\frac{a\pi^{b}}{c}$$ where $$a$$ and $$c$$ are coprime and $$a,b,c \in \mathbb{Z}^{+}$$, find $$a+b+c$$.

Details and Assumptions

$$\lbrace x \rbrace$$ denotes the fractional part of $$x$$ such that $$\lbrace x \rbrace = x-\lfloor x \rfloor$$.

You might want to try this problem first.

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