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Indefinite Integrals question

2025 · 22 Jan · Shift 2 · Q35

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JEE Main
Mathematics
Indefinite Integrals
2025 · 22 Jan · Shift 2 · Q35

Indefinite Integrals question

2025 · 22 Jan · Shift 2 · Q35

JEE MainMathematicsIndefinite IntegralsMCQ+4 / −1

If

\int \mathrm{e}^x\left(\frac{x \sin ^{-1} x}{\sqrt{1-x^2}}+\frac{\sin ^{-1} x}{\left(1-x^2\right)^{3 / 2}}+\frac{x}{1-x^2}\right) \mathrm{d} x=\mathrm{g}(x)+\mathrm{C}

, where C is the constant of integration, then

g\left(\frac{1}{2}\right)

equals :

A
$\frac{\pi}{6} \sqrt{\frac{\mathrm{e}}{3}}$
B
$\frac{\pi}{6} \sqrt{\frac{\mathrm{e}}{2}}$
C
$\frac{\pi}{4} \sqrt{\frac{\mathrm{e}}{3}}$
D
$\frac{\pi}{4} \sqrt{\frac{\mathrm{e}}{2}}$

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