The primitive of $$1(x$$−$$a)3/2(b$$−$$x)1/2$$ is

Correct option is 4none of these

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The primitive of $\frac{1}{(x - a)^{3 / 2} (b - x)^{1 / 2}}$ is

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1b−ab−xx−a1/2+C

34(b−a)b−xx−a1/2+C

1b−ax−ab−a1/2+C

none of these

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detailed solution

Correct option is D

putting x−a=(1/t) we have dx=−1/t2dt and the given integral can be written as ∫−1t2dt(1/t)3/2b−a−1t1/2=−∫dt(b−a)t−1=−2(b−a)t−1b−a+C=−2b−ab−a−(x−a)x−a+C=2a−bb−xx−a+C

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The primitive of 1(x−a)3/2(b−x)1/2 is

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The primitive of $\frac{1}{(x - a)^{3 / 2} (b - x)^{1 / 2}}$ is