JEE MAIN - Mathematics Hindi (2023 - 6th April Morning Shift - No. 8)
माना $$I(x)=\int \frac{x^2\left(x \sec ^2 x+\tan x\right)}{(x \tan x+1)^2} d x$$ है । यदि $$I(0)=0$$ है, तब $$I\left(\frac{\pi}{4}\right)$$ का मान है:
$$\log _e \frac{(\pi+4)^2}{32}-\frac{\pi^2}{4(\pi+4)}$$
$$\log _e \frac{(\pi+4)^2}{16}-\frac{\pi^2}{4(\pi+4)}$$
$$\log _e \frac{(\pi+4)^2}{16}+\frac{\pi^2}{4(\pi+4)}$$
$$\log _e \frac{(\pi+4)^2}{32}+\frac{\pi^2}{4(\pi+4)}$$
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