# Nefarious Integral

Calculus Level 5

$\LARGE{\int_0^1}\large {\frac1x \tan^{-1} \left( \frac{\cot^{-1} \left(\frac1x\right) - \coth^{-1} \left( \frac1x\right)}{\text{cs}^{-1}\left( \frac1x | 0\right) - \coth^{-1} \left(\frac1x\right) -\pi} \right) \, dx}$

Given that the integral above equals to $$\dfrac{\pi}{a}\ln\bigg(\dfrac{\pi^b}{c}\bigg)$$ for constants $$a,b$$ and $$c,$$ evaluate $$a+b+c$$.

Note: $$\text{cs}(x)$$ is a Jacobi elliptic function.

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