The value of \(\int \frac{x^{2}\tan^{-1}(x^{3})}{1+x^{6}}dx\) is
Answer & explanation
Correct answer: option 2
Let \(t=\tan^{-1}x^{3}\) then
\(\begin{aligned}\frac{x^{2}\tan^{-1}(x^{3})}{1+x^{6}}dx&=\frac{1}{3}\int tdt\\ &=\frac{1}{6}(\tan^{-1}x^{3})^{2}+c\end{aligned}\)