Question

Integrate: $\int \frac{x^2}{1+x^6}dx$

Answer 1

$\begin{array}{c}\int \frac{x^2}{1+x^6}dx\\ Put{x}^3=t\\ 3x^{2}dx=dt\\ =\frac{1}{3}\int \frac{1}{1+t^2}dt\\ =\frac{1}{3}{\tan }^{-1}\left(x^3\right)+C\end{array}$