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Evaluate: int1/(sqrt(x)+x)dx...

Evaluate: `int1/(sqrt(x)+x)dx`

Text Solution

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`int(1)/((sqrt(x)+x))dx=int(1)/(sqrt(x)(1+sqrt(x)))dx`
Now, put `(1+sqrt(x))` =t so that `(1)/(sqrt(x))dx=2dt`.
`:.int(1)/(sqrt(x)+x)dx=int(1)/(sqrt(x)(1+sqrt(x)))dx`
`=2intdt=2log|t|+C=2log|{:(1+sqrt(x)):}|+C`.
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