Let f(x)=∫((2−x²)e^x)/(√(1+x)(1−x)^{3/2})... | Indefinite Integration

JEE MAIN_2026

_230126_S1

Question

Let $f(x)=\int \frac{\left(2-x^2\right) \cdot \mathrm{e}^x}{(\sqrt{1+x})(1-x)^{3 / 2}} \mathrm{~d} x$. If $f(0)=0$, then $f\left(\frac{1}{2}\right)$ is equal to :

Select the correct option:

$\sqrt{3 \mathrm{e}}-1$

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

$\sqrt{2 \mathrm{e}}-1$

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

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Easy

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