Simple Yet Challenging Integral

Calculus Level 3

Evaluate the definite integral 0π4ln(tanx+1)dx.\displaystyle{\int _{ 0 }^{ \frac{\pi}{4}}{ \ln { (\tan { x+1)\, dx } } } .} The answer must be a decimal in terms of π\pi. For example, if the calculation result is 2.654π,2.654\pi, then the answer should be 2.6542.654.

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