Answer
$$
\int 3 x e^{2 x^{2}} d x=\frac{3}{4} e^{2 x^{2}}+c
$$
Work Step by Step
Given: $$
\int 3 x e^{2x^{2}} d x
$$
Let $ u=2x^2\ \to\ \ du=4xdx$, so
\begin{align*}
\int 3 x e^{2x^{2}} d x&=\frac{3}{4}\int e^{u} du\\
&=\frac{3}{4}e^u+c\\
&=\frac{3}{4}e^{2x^2}+c
\end{align*}
