# Arctan and Tan inverse!

Calculus Level 4

$\large \int_1^{16} \arctan \sqrt{\sqrt x-1}\, dx$

The above integral can be written as $$\dfrac{A\pi^B}C-D\sqrt E$$, where $$A$$, $$B$$, $$C$$, $$D$$ and $$E$$ are positive integers with $$A,C$$ coprime and $$E$$ square-free. Find $$A+B+C+D+E$$.

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