JEE MAIN - Mathematics Hindi (2023 - 11th April Morning Shift - No. 6)
समाकलन $$\int_\limits{-\log _e 2}^{\log _e^2} e^x\left(\log _e\left(e^x+\sqrt{1+e^{2 x}}\right)\right) d x$$ का मान बराबर है
$$\log _e\left(\frac{(2+\sqrt{5})^2}{\sqrt{1+\sqrt{5}}}\right)+\frac{\sqrt{5}}{2}$$
$$\log _e\left(\frac{\sqrt{2}(2+\sqrt{5})^2}{\sqrt{1+\sqrt{5}}}\right)-\frac{\sqrt{5}}{2}$$
$$\log _e\left(\frac{2(2+\sqrt{5})}{\sqrt{1+\sqrt{5}}}\right)-\frac{\sqrt{5}}{2}$$
$$\log _e\left(\frac{\sqrt{2}(3-\sqrt{5})^2}{\sqrt{1+\sqrt{5}}}\right)+\frac{\sqrt{5}}{2}$$
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