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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