Solution
= Solution
Use the <change of variables> $u=x^2+1$, $du=2x\,dx$. Then
$$
\boxed{\int\frac{x}{\sqrt{x^2+1}}\,dx=\sqrt{x^2+1}+C.}
$$
Differentiating verifies this <antiderivative> on the whole real line.
= Solution
Use the <change of variables> $u=x^2+1$, $du=2x\,dx$. Then
$$
\boxed{\int\frac{x}{\sqrt{x^2+1}}\,dx=\sqrt{x^2+1}+C.}
$$
Differentiating verifies this <antiderivative> on the whole real line.