$\smallint \,\,\frac{{x + \,\,\sqrt[3]{{{x^2}}} + \,\,\sqrt[6]{x}}}{{x\,(1 + \,\,\sqrt[3]{x}}}\,\,dx$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int \,\,\frac{{x + \,\,\sqrt[3]{{{x^2}}} + \,\,\sqrt[6]{x}}}{{x\,(1 + \,\,\sqrt[3]{x}}}\,\,dx

View answer and explanation

Correct option: A

\frac{3}{2}\,\,{x^{2/3}} + \,\,6\,\,{\tan ^{ - 1}}\,\,{x^{1/6}} + \,\,C

Option A (

\frac{3}{2}\,{x^{2/3}} + \,6\,{\tan ^{ - 1}}\,{x^{1/6}} + \,C

) is correct because after substitution and simplification, the integral can be easily solved.

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