Not Trigonometric Substitution

Calculus Level 3

ππ2x(1+sinx)1+cos2x dx=πm,    m= ? \displaystyle \int_{-\pi} ^\pi \frac {2x (1 + \sin x)}{1 + \cos^2 x} \ \mathrm d x = \pi^m, \ \ \ \ m = \ ?

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