$\int \frac{d x}{(x-\beta) \sqrt{(x-\alpha)(\beta-x)}}$ is

$\frac{2}{\alpha-\beta} \sqrt{(x-\alpha)(\beta-x)}+c$

$\frac{\alpha-\beta}{2}(x-\alpha) \sqrt{\beta-x}$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{d x}{(x-\beta) \sqrt{(x-\alpha)(\beta-x)}}

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Correct option: A

\frac{2}{\alpha-\beta} \sqrt{\frac{x-\alpha}{\beta-x}}+c

Option A is correct because the integral evaluates to (2/(α-β)) * sqrt((x-α)/(β-x)) + c after using the appropriate substitution and trigonometric identities.

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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