\int { \sin ^{-1} \sqrt{x}-\cos ^{-1} \sqrt{x}}/{\sqrt{x} ( \sin ^{-1} \sqrt{x}+\cos ^{-1} \sqrt{x}) } \dx=

Correct Answer is : 8π((√xsin−1√x−√1−x))−2√x+C

\frac{2}{\pi} [ \sin ^{-1} \sqrt{x}(2 x-1)+\sqrt{x(1-x)}] +x+C

\frac{8}{\pi} ( (\sqrt{x} \sin ^{-1} \sqrt{x}-\sqrt{1-x}) ) -2 \sqrt{x}+C

\frac{2}{\pi} [(2 x-1) \sin ^{-1} \sqrt{x}-\sqrt{x(1-x)}] -x+C

\frac{2}{\pi} [(2 x-1) \sin ^{-1} \sqrt{x}-\sqrt{x(1-x)}] +x+C

AP EAPCET 16th May 2023 Shift 2 Solved Paper

Section: Mathematics

Question : 69 of 160

Marks: +1, -0

∫‌

sin‌−1√x−cos−1√x

√x(sin‌−1√x+cos−1√x)

‌dx=

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