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\begin{enumerate}[(1)]
\item We use the substitution $u = (x+2)^2$. By differentiation we obtain
\[\frac{\mathrm{d}u}{\mathrm{d}x} = 2(x+2) = 2x + 4.\]
Hence we obtain
\begin{align*}
\int (2x+4)\mathrm{e}^{(x+2)^2}\,\mathrm{d}x &= \int \mathrm{e}^{(x+2)^2}\,(2x+4)\mathrm{d}x \\
&=\int \mathrm{e}^{u}\,\mathrm{d}u \\
&= e^u + C\\
&= e^{(x+2)^2} + C
\end{align*}

\end{enumerate}


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