Question

Evaluate $\int \frac{3x^2}{1+x^6}dx$

Answer 1

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

Hence, this is the answer.