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## Main Question or Discussion Point

Hello everyone

I need some help in performing the following integration (not HW):

[tex]\int_{0}^{\pi/4}\left(\frac{x}{x\sin x + \cos x}\right)^{2}dx[/tex]

I tried integration by parts, but it leads nowhere. Any suggestions would be appreciated.

Thanks

Vivek

PS--Mathematica gives the answer as [itex](4-\pi)/(4+\pi)[/itex] but is unable to perform the integration with the [itex]x^2[/itex] term in the numerator replaced by unity.

I need some help in performing the following integration (not HW):

[tex]\int_{0}^{\pi/4}\left(\frac{x}{x\sin x + \cos x}\right)^{2}dx[/tex]

I tried integration by parts, but it leads nowhere. Any suggestions would be appreciated.

Thanks

Vivek

PS--Mathematica gives the answer as [itex](4-\pi)/(4+\pi)[/itex] but is unable to perform the integration with the [itex]x^2[/itex] term in the numerator replaced by unity.