The value of the integral  ∫0π xsin⁡x1+cos2⁡xdx, is

# The value of the integral  ${\int }_{0}^{\pi } \frac{x\mathrm{sin}x}{1+{\mathrm{cos}}^{2}x}dx$, is

1. A

$\frac{{\pi }^{2}}{2}$

2. B

$\frac{{\pi }^{2}}{4}$

3. C

$\frac{{\pi }^{2}}{8}$

4. D

$\frac{{\pi }^{2}}{16}$

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### Solution:

Let $I={\int }_{0}^{\pi } \frac{x\mathrm{sin}x}{1+{\mathrm{cos}}^{2}x}dx$

Then,

Adding (i) and (ii), we get

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