Tricky Integrals [Part 1]

Calculus Level 4

\[\large \int _{ 0 }^{ { \pi }/{ 4 } }{ \ln { \left( \tan { x } +1 \right) } }~ {dx} \]

If the integral above is equal to \(\dfrac{\pi}{A}\ln{B}\), where \(A\) and \(B\) are integers and \(B\) is prime, find \({A}^{B}\).

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