If \int e^x ( {x \sin ^{-1} x}/{\sqrt{1-x^2}}+ { \sin ^{-1} x}/{ (1-x^2) ^{3 \/ 2}}+\frac{x}{1-x^2}) \dx=g(x)+C, where C is the constant of integration, then g (\frac{1}{2}) equals: [22 Jan 2025 Shift 2]

\frac{\pi}{4} \sqrt{\frac{e}{2}}

\frac{\pi}{6} \sqrt{\frac{e}{2}}

\frac{\pi}{4} \sqrt{\frac{e}{3}}

\frac{\pi}{6} \sqrt{\frac{e}{3}}

JEE Main 22 Jan 2025 Shift 2 Paper

Section: Mathematics

Question : 20 of 75

Marks: +1, -0

If ∫ex(‌

xsin‌−1x

√1−x2

+‌

sin‌−1x

(1−x2)3∕2

+‌

1−x2

)‌dx=g(x)+C, where C is the constant of integration, then g(‌

) equals:

[22 Jan 2025 Shift 2]

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