Tricky integral

Calculus Level 3

0ln(1+x2)1+x2dx=πln(k),k= ?\large \int _{ 0 }^{ \infty }{ \frac { \ln { (1+{ x }^{ 2 }) } }{ 1+{ x }^{ 2 } } } \, dx =\pi \ln {( k) } \quad , \quad k = \ ?

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