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Evaluate int(dx)/(x+sqrt(x))...

Evaluate ` int(dx)/(x+sqrt(x))`

Text Solution

Verified by Experts

The correct Answer is:
`2log(sqrt(x)+1)+C`
` I=int(dx)/(x+sqrt(x))=int(dx)/(sqrt(x)(sqrt(x)+1)). `
` " Put " sqrtx=z `
` :. (1)/(2sqrt(x))dx=dz `
` :. I=int(2dz)/(z+1)`
`=2log|z+1|+C`
` =2log(sqrt(x)+1)+C`
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