# Only one more for today

Calculus Level 3

$\large \int_0^{\pi /2} \dfrac{ (\sin x)^m }{(\sin x)^m + ( \cos x)^m} \, dx$

$$\forall m\in \mathbb R$$, the integral above is equal to $$\text{arctan} (b)$$. Find $$b$$.

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