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Evaluate: 1/(sqrt(1-e^(2x)))dx...

Evaluate: `1/(sqrt(1-e^(2x)))dx`

Text Solution

Verified by Experts

I=`1/(sqrt(1-e^(2x)))dx`
I=`(e^(-x))/(sqrt(e^(-2x)-1))dx`
let `e^-x=t`

so,
on differentiation and we get,
`−e^(−x)dx=dt`
`I=int(dt)/(sqrt(t^2-1))`
`I=ln∣​t+sqrt(t^2−1)∣​+c`
...
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