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$\int_0^{\pi / 2} \frac{\sin x}{1+\cos x+\sin x} d x=$
$\int_{-1}^3 \left(\tan^{-1}\left(\frac{x}{x^2+1}\right) + \tan^{-1}\left(\frac{x^2+1}{x}\right)\right) dx =$
$\int_0^{\pi / 2} \frac{1}{1+\sqrt{\tan x}} d x=$
$\int_{-\pi}^{\pi} |\pi - |x|| \, dx$ is equal to :
$ \int_{0}^{\frac{\pi}{2}} \frac{\sin ^{1000} x}{\sin ^{1000} x+\cos ^{1000} x} \, dx $ is equal to
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