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Evaluate: int(e^x)/(sqrt(4-e^(2x)))\ dx...

Evaluate: `int(e^x)/(sqrt(4-e^(2x)))\ dx`

Text Solution

Verified by Experts

`I=int(e^(x))/(sqrt(4-e^(2x)))dx=int(e^(x))/(sqrt(2^(2)-(e^(x))^(2)))dx`
Let `e^(x)=t " or " e^(x)dx=dt`
`:. I=int(dt)/(sqrt(4-t^(2)))=int(dt)/(sqrt(2^(2)-t^(2)))`
`=sin^(-1)((t)/(2))+C=sin^(-1)((e^(x))/(2))+C`
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