JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

I=\int \frac{\left(x+x^{\frac{2}{3}}+x^{\frac{1}{6}}\right)}{x\left(1+x^{\frac{1}{3}}\right)} d x

is equal to

View answer and explanation

Correct option: A

\frac{3}{2} x^{\frac{2}{3}}+6 \tan ^{-1}\left(x^{\frac{1}{6}}\right)+c

Option A is correct because the integral simplifies to

\frac{3}{2} x^{\frac{2}{3}}+6 \tan ^{-1}\left(x^{\frac{1}{6}}\right)+c

after substitution and simplification.

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