Question

Integrate the function $\frac{3x}{1+2x^4}$

Answer 1

Let $\sqrt{2}{x}^2=t$
$\therefore 2\sqrt{2}xdx=dt$
$\Rightarrow \int \frac{3x}{1+2x^4}dx=\frac{3}{2\sqrt{2}}\int \frac{dt}{1+t^2}$
$=\frac{3}{2\sqrt{2}}\left[{\tan }^{-1}t\right]+C$
$=\frac{3}{2\sqrt{2}}{\tan }^{-1}\left(\sqrt{2}{x}^2\right)+C$