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Indefinite Integrals question

2023 · 6 Apr · Shift 1 · Q30

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PYQ Library
JEE Main
Mathematics
Indefinite Integrals
2023 · 6 Apr · Shift 1 · Q30

Indefinite Integrals question

2023 · 6 Apr · Shift 1 · Q30

JEE MainMathematicsIndefinite IntegralsMCQ+4 / −1

Let

I(x)=\int \frac{x^{2}\left(x \sec ^{2} x+\tan x\right)}{(x \tan x+1)^{2}} d x

. If

I(0)=0

, then

I\left(\frac{\pi}{4}\right)

is equal to :

A
$\log _{e} \frac{(\pi+4)^{2}}{32}-\frac{\pi^{2}}{4(\pi+4)}$
B
$\log _{e} \frac{(\pi+4)^{2}}{16}-\frac{\pi^{2}}{4(\pi+4)}$
C
$\log _{e} \frac{(\pi+4)^{2}}{16}+\frac{\pi^{2}}{4(\pi+4)}$
D
$\log _{e} \frac{(\pi+4)^{2}}{32}+\frac{\pi^{2}}{4(\pi+4)}$

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