Integrate the function 3 x 1+2 x^ 4 - Vidyadip

Question

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

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Answer

Let $\sqrt{2} x^{2}=t$
$\Rightarrow 2 \sqrt{2} \mathrm{x} \mathrm{d} \mathrm{x}=\mathrm{dt}$
$\Rightarrow \int \frac{3 x}{1+2 x^{4}} d x=\frac{3}{2 \sqrt{2}} \int \frac{d t}{1+t^{2}}$
$\Rightarrow \frac{3}{2 \sqrt{2}}\left[\tan ^{-1} t\right]+C$
$=\frac{3}{2 \sqrt{2}} \tan ^{-1} \sqrt{2} \mathrm{x}^{2}+\mathrm{C}$

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