JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

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 is correct because after substituting

x = \tan \theta

and simplifying, the integral evaluates to

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

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