Tricky Integrals [Part 1]

Calculus Level 4

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

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

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