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Evaluate: int(sqrt(x)dx)/(1+x)...

Evaluate: `int(sqrt(x)dx)/(1+x)`

Text Solution

Verified by Experts

The correct Answer is:
`2sqrt(x)-2tan^(-1)sqrt(x)+C`
` " Put " x=t^(2) or dx=2tdt.` Then,
`int(sqrt(x)dx)/(1+x)=2int(t^(2)dt)/(1+t^(2)) `
` =2int(1-(1)/(1+t^(2)))dt `
`=2(t-tan^(-1)t)+C`
` =2sqrt(x)-2tan^(-1)sqrt(x)+C`
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