JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \frac{\sqrt{1+\sqrt[3]{x}}}{x^{2 / 3}} \mathrm{~d} x=2 f(x)^{3 / 2}+C

then

f(x)

is equal to

View answer and explanation

Correct option: B

1+x^{1 / 3}

Option B (

1+x^{1 / 3}

) is correct because after substituting

t^2 = 1 + x^{1/3}

, the integral simplifies to

2(1+x^{1/3})^{3/2} + C

, matching the given form.

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