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Evaluate the following : int(0)^(pi)(dx)...

Evaluate the following : `int_(0)^(pi)(dx)/(1+sinx)`

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`int_(0)^(pi)(dx)/(1+sinx)=int_(0)^(pi)(1-sinx)/(1-sin^(2)x) dx=int_(0)^(pi)(1-sin x)/(cos^(2)x) dx`
`=int_(0)^(pi)(sec^(2)x-sec x tan x)dx`
`=|tanx-secx|_(0)^(pi)`
`=(tanpi-secpi)-(tan 0-sec0)`
`=0-(-1)-(0-1)=1+1=2`
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