Jeeify
MCQMediumJEE Main 2025 · 22 January, Shift 2Indefinite Integrals

Mathematics Question from JEE Main 2025 · 22 January, Shift 2

If ∫ex(xsin⁡−1x1−x2+sin⁡−1x(1−x2)3/2+x1−x2)dx=g(x)+C\displaystyle\int e^x\left( \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} + \frac{\sin^{-1} x}{(1 - x^2)^{3/2}} + \frac{x}{1 - x^2} \right) dx = g(x) + C, where CC is the constant of integration, then g(12)g\left(\frac{1}{2}\right) equals:

  • A

    π6e2\frac{\pi}{6}\sqrt{\frac{e}{2}}

  • B

    π4e2\frac{\pi}{4}\sqrt{\frac{e}{2}}

  • C

    π6e3\frac{\pi}{6}\sqrt{\frac{e}{3}}

  • D

    π4e3\frac{\pi}{4}\sqrt{\frac{e}{3}}

Answer & step-by-step solution

Sign in to reveal the correct answer, the full step-by-step solution, and the common mistakes for this question.

Sign in to see the solution

Practice more Indefinite Integrals questions

Get unlimited AI-adaptive practice, mastery tracking, and an AI tutor that explains every step - free to start.

Start free trialMore on Indefinite Integrals

Related questions