Question

Integrate the function
$\frac{3x^2}{x^6+1}$

Answer 1

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

$\Rightarrow$ put $x^3=t$

$\Rightarrow 3x^{2}dx=dt$

$\therefore I\int \frac{dt}{t^2+1}$

$=ta{n}^{-1}t+c$

$=ta{n}^{-1}{x}^3+c$