Solution
= Solution
The <change of variables> $u=x^2$, $du=2x\,dx$, gives
$$
\boxed{\int xe^{x^2}\,dx=\frac12e^{x^2}+C.}
$$
Differentiation verifies the <antiderivative> for every real $x$.
= Solution
The <change of variables> $u=x^2$, $du=2x\,dx$, gives
$$
\boxed{\int xe^{x^2}\,dx=\frac12e^{x^2}+C.}
$$
Differentiation verifies the <antiderivative> for every real $x$.