Question

$\int \frac{\operatorname{Sin}^{-1} \sqrt{x}-\operatorname{Cos}^{-1} \sqrt{x}}{\operatorname{Sin}^{-1} \sqrt{x}+\operatorname{Cos}^{-1} \sqrt{x}} d x=$

Accepted Answer

$\frac{4}{\pi}\left[\frac{\sqrt{x-x^2}}{2}+x \operatorname{Sin}^{-1} \sqrt{x}-\frac{1}{2} \operatorname{Sin}^{-1} \sqrt{1-x}\right]-x+c$

Answer

$\frac{2}{\pi}\left[\sqrt{x-x^2}+x \operatorname{Sin}^{-1} x-\operatorname{Sin}^{-1} \sqrt{1-x}\right]-x+c$

Answer

$\frac{2}{\pi}\left[\sqrt{x-x^2}+x \operatorname{Sin}^{-1} x-\frac{1}{2} \operatorname{Sin}^{-1} \sqrt{1-x}\right]-x+c$

Answer

$\frac{2}{\pi}\left[\sqrt{x-x^2}+x \operatorname{Sin}^{-1} x+\frac{1}{2} \operatorname{Sin}^{-1} \sqrt{1-x}-x\right]+c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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