If $\smallint \,\,\frac{{{x^5}}}{{\sqrt {1 + {x^3}} }}\,\,dx$ is equal to

$\frac{2}{9}\,\,{\left( {1 + {x^3}} \right)^{5/2}}\,\, + \,\,\frac{2}{3}\,\,{\left( {1 + {x^3}} \right)^{3/2}}\,\, + \,\,C$

$\log \,\,\left| {\sqrt x + \sqrt {1 + {x^3}} } \right|\, + \,\,C$

${x^2}\,\,\log \,\,\left( {1 + {x^3}} \right)\,\, + \,\,C$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\frac{{{x^5}}}{{\sqrt {1 + {x^3}} }}\,\,dx

is equal to

View answer and explanation

Correct option: B

\frac{2}{9}\,\,{\left( {1 + {x^3}} \right)^{3/2}}\,\, - \,\,\frac{2}{3}\,\,{\left( {1 + {x^3}} \right)^{1/2}} + \,\,C

Option B (

\frac{2}{9}\\ {\left( {1 + {x^3}} \right)^{3/2}}\\ - \\ \frac{2}{3}\\ {\left( {1 + {x^3}} \right)^{1/2}} + \\ C

) is correct because it is the result of the integration after applying the correct substitution and simplification.