JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

Let

f(x)=\int \frac{x^2}{\left(1+x^2\right)\left\{1+\sqrt{1+x^2}\right\}} d x

and

f(0)=0

. Then,

f(1)

is equal to

View answer and explanation

Correct option: B

\log _e(1+\sqrt{2})-\frac{\pi}{4}

Option B (

\log _e(1+\sqrt{2})-\frac{\pi}{4}

) is correct because after simplifying the integral and applying the initial condition

f(0)=0

, we find

f(1) = \log_e(1+\sqrt{2}) - \frac{\pi}{4}

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