$\smallint \,\,\sqrt[3]{x}\,\,\sqrt[7]{{1\,\, + \,\,\sqrt[3]{{{x^4}}}\,}}dx$ is equal to

$\frac{{32}}{{21}}\,\,{\left\{ {1\,\, + \,\,\sqrt[3]{{{x^4}}}} \right\}^{8/7}} + \,\,C$

$\frac{7}{{32}}\,\,{\left\{ {1\,\, + \,\,\sqrt[3]{{{x^4}}}} \right\}^{8/7}} + \,\,C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \,\,\sqrt[3]{x}\,\,\sqrt[7]{{1\,\, + \,\,\sqrt[3]{{{x^4}}}\,}}dx

is equal to

View answer and explanation

Correct option: A

\frac{{21}}{{32}}\,\,{\left\{ {1\,\, + \,\,\sqrt[3]{{{x^4}}}} \right\}^{8/7}} + \,\,C

Option A is correct because the integral is solved using substitution, resulting in the given expression.