The value of $\smallint \,\,\frac{{{x^2}}}{{1\,\, + \,\,{x^6}}}\,\,dx$ is

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

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of

\int \,\,\frac{{{x^2}}}{{1\,\, + \,\,{x^6}}}\,\,dx

View answer and explanation

Correct option: B

\frac{1}{3}\,\,{\tan ^{ - 1}}\,\,\left( {{x^3}} \right)\,\, + \,\,c

Option B (

\frac{1}{3}\,{\tan ^{ - 1}}\,\left( {{x^3}} \right)\, + \,c

) is correct because it results from a u-substitution where

u = x^3

, leading to the integral of

\frac{1}{1+u^2}

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