$\smallint \frac{{{{\left( {{x^4} - \,\,x} \right)}^{1/4}}}}{{{x^5}}}\,\,dx$ is equal to

$\frac{4}{5}\,\,{\left( {1\,\, - \,\,\frac{1}{{{x^3}}}} \right)^{5/4}} + \,\,C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{{{{\left( {{x^4} - \,\,x} \right)}^{1/4}}}}{{{x^5}}}\,\,dx

is equal to

View answer and explanation

Correct option: A

\frac{4}{{15}}\,\,{\left( {1 - \,\,\frac{1}{{{x^3}}}} \right)^{5/4}} + \,\,C

Option A is correct because the integral simplifies to a form where the power rule can be applied after a suitable substitution.