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Evaluate: int(dx)/(sqrt(x)-sqrt(x-3))...

Evaluate: `int(dx)/(sqrt(x)-sqrt(x-3))`

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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Knowledge Check

  • int(dx)/(sqrt(1-2x)+sqrt(3-2x)) =

    A
    `1/2{1/sqrt(1-2x)-1/sqrt(3-2x)}+c`
    B
    `1/6{(1-2x)^(3//2)-(3-2x)^(3//2)}+c`
    C
    `1/6{(1-2x)^(3//2)+(3-2x)^(3//2)}+c`
    D
    `1/2{(1-2x)^(3//2)+(3-2x)^(3//2)}+c`

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