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

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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