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Evaluate: int(e^x)/(sqrt(16-e^(2x)))...

Evaluate: `int(e^x)/(sqrt(16-e^(2x)))`

Text Solution

Verified by Experts

I=`int(e^x)/(sqrt(16-e^(2x)))`
let `e^x=t`
`e^xdx=dt`
So,
I=`int(t)/(sqrt(4^2-t^2))`
`I=sin^(-1)(t/4)`
`I=sin^(-1)((e^x)/4)+C`
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