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Evaluate:int-pi^pi ((2x)(1+sinx)/(1+cos^...

Evaluate:`int_-pi^pi ((2x)(1+sinx)/(1+cos^2x))dx`

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`I=∫_(−π)^π​ (2x​)/(1+cos^2x)dx+∫_(−π)^π​(2xsinx)/(1+cos^2x)​dx`
`I=∫_0^π​ (2(π−x)sinx​dx)/(1+cos^2x)`
`2I=2π∫_0^π(sinx)/(​1+cos^2x)​`
`I=π∫_(−1)^1​(dt)/(1+t^2​) `
...
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