JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Hard

1 of 1

Analyzing +4 | -1

Let

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

. If

I(0)=0

, then

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

is equal to

View answer and explanation

Correct option: C

\log _{e} \frac{(\pi+4)^{2}}{32}-\frac{\pi^{2}}{4(\pi+4)}

Option C (

\log _{e} \frac{(\pi+4)^{2}}{32}-\frac{\pi^{2}}{4(\pi+4)}

) is correct because it is the result of evaluating the definite integral with the given initial condition.

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