The value of the integral ∫ from... |JEE Main 2023| Definite

JEE MAIN 2023

11-04-2023 S1

Question

The value of the integral $\int_{-\log _e 2}^{\log _e 2} \mathrm{e}^{\mathrm{x}}\left(\log _{\mathrm{e}}\left(\mathrm{e}^{\mathrm{x}}+\sqrt{1+\mathrm{e}^{2 \mathrm{x}}}\right)\right) \mathrm{dx}$ is equal to

Select the correct option:

$\log _e\left(\frac{2(2+\sqrt{5})}{\sqrt{1+\sqrt{5}}}\right)-\frac{\sqrt{5}}{2}$

$\log _e\left(\frac{\sqrt{2}(3-\sqrt{5})^2}{\sqrt{1+\sqrt{5}}}\right)+\frac{\sqrt{5}}{2}$

$\log _e\left(\frac{(2+\sqrt{5})^2}{\sqrt{1+\sqrt{5}}}\right)+\frac{\sqrt{5}}{2}$

$\log _e\left(\frac{\sqrt{2}(2+\sqrt{5})^2}{\sqrt{1+\sqrt{5}}}\right)-\frac{\sqrt{5}}{2}$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Question Tags

JEE Main

Mathematics

Medium

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