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