\( \int \frac{\operatorname{Sin}^{-1} \sqrt{x}-\cos ^{-1} \sqrt{x}}{\operatorname{Sin}^{-1} \sqr....

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\( \int \frac{\operatorname{Sin}^{-1} \sqrt{x}-\cos ^{-1} \sqrt{x}}{\operatorname{Sin}^{-1} \sqrt{x}+\cos ^{-1} \sqrt{x}} d x= \)
\( \mathrm{P} \)
(1) \( \frac{4}{\pi}\left[\frac{\sqrt{x-x^{2}}}{2}+x \sin ^{-1} \sqrt{x}+\frac{1}{2} \sin ^{-1} \sqrt{1-x}\right]-x+c \)
(2) \( \frac{2}{\pi}\left[\sqrt{x-x^{2}}+x \operatorname{Sin}^{-1} x-\operatorname{Sin}^{-1} \sqrt{1-x}\right]-x+c \)
(3) \( \frac{2}{\pi}\left[\sqrt{x-x^{2}}+x \operatorname{Sin}^{-1} x-\frac{1}{2} \operatorname{Sin}^{-1} \sqrt{1-x}\right]-x+c \)
(4) \( \frac{2}{\pi}\left[\sqrt{x-x^{2}}+x \operatorname{Sin}^{-1} x+\frac{1}{2} \operatorname{Sin}^{-1} \sqrt{1-x}-x\right]+c \)



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