`int_(0)^(1)(dx)/(e^(x)+e^(-x))`

Explanation

Let `I=int_(0)^(1)(dx)/(e^(x)+e^(-1))=int_(0)^(1)(e^(x))/(1+e^(2x))dx`
Put `e^(x)=t`
`impliese^(x)dx=dt`
When `xto0`, then `t to1`
and `xto1`, then `t to e`
`:.I=int_(1)^(e)(dt)/(1+t^(2))=[tan^(-1)t]_(1)^(e)`
`=tan^(-1)e-tan^(-1)1`
`=tan^(-1)e-(pi)/4`