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

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

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2)log(e^(2x)+1)-2 tan^(-1)(e^(x))+C`
`int(e^(2x)-2e^(x))/(e^(2x)+1)dx=(1)/(2)int(2e^(2x))/(e^(2x)+1)dx-2int(e^(x)dx)/((e^(x))^(2)+1) `
`=(1)/(2)log(e^(2x)+1)-2int(dz)/(z^(2)+1), " where " z=e^(x) `
` =(1)/(2)log(e^(2x)+1)-2 tan^(-1)(e^(x))+C`
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