$\int_\limits {-\pi}^\pi \frac{2 x(1+\sin x)}{1+\cos ^2 x} d x$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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\int\limits_{{-\pi}}^\pi \frac{2 x(1+\sin x)}{1+\cos ^2 x} d x

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Correct option: B

\pi^2

Option B (

\pi^2

) is correct. By splitting the integral and using the property of even and odd functions, and then applying the substitution method, the integral evaluates to

\pi^2

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