Question:
$\frac{3 x}{1+2 x^{4}}$
Solution:
Let $\sqrt{2} x^{2}=t$
$\therefore 2 \sqrt{2} x d x=d t$
$\Rightarrow \int \frac{3 x}{1+2 x^{4}} d x=\frac{3}{2 \sqrt{2}} \int \frac{d t}{1+t^{2}}$
$=\frac{3}{2 \sqrt{2}}\left[\tan ^{-1} t\right]+\mathrm{C}$
$=\frac{3}{2 \sqrt{2}} \tan ^{-1}\left(\sqrt{2} x^{2}\right)+\mathrm{C}$
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