Example 2.15. $I=\int_{-1}^{1}|x| e^{x^{2}} d x$.
Solution. Here the integrand is an even function, so

$$
\begin{gathered}
I=\int_{-1}^{1}|x| e^{x^{2}} d x=2 \int_{0}^{1} x e^{x^{2}} d x=\left|\begin{array}{l}
z=x^{2} \\
d z=2 x d x
\end{array}\right|= \\
=2 \int_{0}^{1} e^{z} d z=\left.e^{z}\right|_{0} ^{1}=e-1
\end{gathered}
$$