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int(0)^(pi)(x tanx)/((secx+cosx))dx=(pi^...

`int_(0)^(pi)(x tanx)/((secx+cosx))dx=(pi^(2))/(4)`

Text Solution

Verified by Experts

`I=int_(0)^(pi)(xsinx)/((1+cos^(2)x))dx` and `I=int_(0)^(pi)((pi-x)sinx)/((1+cos^(2)x))dx`.
`:.2I=pi*int_(0)^(pi)(sinx)/((1+cos^(2)x))dx`. Now, put `cosx=t`.
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