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Evaluate: int1/(e^x+e^(-x))\ dx...

Evaluate: `int1/(e^x+e^(-x))\ dx`

Text Solution

Verified by Experts

The correct Answer is:
`tan^(-1)(e^(x))+C`
`I=int(dx)/(e^(x)+e^(-x))=int(e^(x)dx)/(e^(2x)+1)`
Let `e^(x)=t.`
` :. e^(x)dx=dt`
` :. I=int(dt)/(t^(2)+1)=tan^(-1)t+C=tan^(-1)(e^(x))+C`
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