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Evaluate: int(dx)/(sqrt(x)+sqrt(x-2))...

Evaluate: `int(dx)/(sqrt(x)+sqrt(x-2))`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(3){x^(3//2)-(x-2)^(3//2)}+C `
`int(dx)/(sqrt(x)+sqrt(x-2))=int(sqrt(x)-sqrt(x-2)dx)/(x-(x-2)) " (rationalizing) " `
`=(1)/(2)int(sqrt(x)-sqrt(x-2))dx `
`=(1)/(3){x^(3//2)-(x-2)^(3//2)}+C `
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