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

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

Text Solution

Verified by Experts

The correct Answer is:
`e^(x)sqrt((1+x)/(1-x))+C`
`int (e^(x)(2-x^(2)))/((1-x)sqrt(1-x^(2)))dx=int(e^(x)(1-x^(2)+1))/((1-x)sqrt(1-x^(2)))dx`
`=int e^(x)[((1-x^(2)))/((1-x)sqrt(1-x^(2)))+(1)/((1-x)sqrt(1-x^(2)))]dx`
`=int e^(x)[(1+x)/(sqrt(1-x^(2)))+(1)/((1-x)sqrt(1-x^(2)))]dx`
`=int e^(x)[sqrt((1+x)/(1-x))+(d)/(dx)(sqrt((1+x)/(1-x)))]dx`
`=e^(x)sqrt((1+x)/(1-x))+C`
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