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Evaluate: int0^(pi//2)x/(sinx+cosx)dx...

Evaluate: `int_0^(pi//2)x/(sinx+cosx)dx`

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`int_0^(pi//2)x/(sinx+cosx)dx ---(1)`
`f(pi/2 - x)=frac{}{sin(pi/2-x)+cos(pi/2 - x)}`
`=frac{pi/2 -x}{cosx+sinx}--(2)`
Adding 1 and 2
`f(x)+f(pi/2-x)=pi/2 . frac{1}{cosx+sinx}`
`=pi/(2 sqrt2) sec(x-pi/4)`
`I=int_0^(pi//2) f(x)dx`
`2I=int_0^(pi//2)[f(x)+f(pi/2 - x)]dx` ...
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