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Evaluate int(0)^(4)(e^(x))/(1+e^(2x))dx...

Evaluate `int_(0)^(4)(e^(x))/(1+e^(2x))dx`

Text Solution

Verified by Experts

Here, Put `e^(x)=timpliese^(x)dx=dt`
When `x=0`, `t=1` and when `x=1`, `t=e`
So, `int_(0)^(1)(e^(x))/(1+e^(2x))dx=int_(1)^(e)(dt)1+t^(2)=[tan^(-1)e-tan^(-1)1]=tan^(-1)e-(pi)/(4)`
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