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Evaluate: int(dx)/((x-p)sqrt((x-p)(x-q))...

Evaluate: `int(dx)/((x-p)sqrt((x-p)(x-q)))`

Text Solution

Verified by Experts

The correct Answer is:
`-(2)/(p-q)sqrt((x-q)/(x-p))+C`
`sqrt((x-q)/(x-p))=t`
` :. (1)/(2)((x-p)/(x-q))^(1//2)((x-p)1-(x-q)1)/((x-p)^(2))dx=dt.`
`or (1)/(2)(q-p)/(sqrt(x-q)(x-p)^(3//2))dx=dt`
`or (dx)/((x-p)^(3//2)sqrt((x-q)))=(2dt)/(q-p)`
`or I=-int(2dt)/(p-q)t= -(2)/(p-q)sqrt((x-q)/(x-p))+C`
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