$\smallint \,\,\frac{{{x^3}}}{{{{\left( {1 + {x^2}} \right)}^{1/3}}}}\,\,dx$ is equal to

$\frac{{20}}{3}\,\,{\left( {1 + {x^2}} \right)^{2/3}}\,\,\left( {2{x^2} - 3} \right) + C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Hard

1 of 1

Application +4 | -1

\int \,\,\frac{{{x^3}}}{{{{\left( {1 + {x^2}} \right)}^{1/3}}}}\,\,dx

is equal to

View answer and explanation

Correct option: B

\frac{3}{{20}}\,\,{\left( {1 + {x^2}} \right)^{2/3}}\,\,\left( {2{x^2} - 3} \right) + C

Option B (

\frac{3}{{20}}\left( {1 + {x^2}} \right)^{2/3}\left( {2{x^2} - 3} \right) + C

) is correct because it is the result of integrating the given function using substitution and integration by parts.