The value of $\smallint \,\,\frac{{{{\left( {x\,\, - \,\,{x^3}} \right)}^{1/3}}}}{{{x^4}}}\,\,dx$ is

$\frac{1}{8}\,\,{\left( {1\,\, - \,\,\frac{1}{{{x^2}}}} \right)^{4/3}} + \,\,1$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of

\int \,\,\frac{{{{\left( {x\,\, - \,\,{x^3}} \right)}^{1/3}}}}{{{x^4}}}\,\,dx

View answer and explanation

Correct option: B

- \frac{3}{8}\,\,{\left( {\frac{1}{{{x^2}}}\,\, - \,\,1} \right)^{4/3}} + \,\,C

Option B (

\ - \frac{3}{8}\,{\left( {\frac{1}{{{x^2}}}\,\, - \,\,1} \right)^{4/3}} + \,\,C

) is correct because after simplifying the integrand and using substitution, the result matches this option.