MCQMediumJEE Main 2026 · 23 January, Shift 1Indefinite Integrals

Mathematics Question from JEE Main 2026 · 23 January, Shift 1

Let f(x)=(2x2)ex(1+x)(1x)3/2dxf(x) = \int \frac{(2 - x^2) \cdot e^x}{(\sqrt{1 + x})(1 - x)^{3/2}} \, dx. If f(0)=0f(0) = 0, then f(12)f\left(\frac{1}{2}\right) is equal to :

  • A

    2e1\sqrt{2e} - 1

  • B

    3e1\sqrt{3e} - 1

  • C

    3e+1\sqrt{3e} + 1

  • D

    2e+1\sqrt{2e} + 1

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