Non-Elementary Integration · Medium problem

The error function $\operatorname{erf}(x)=\dfrac{2}{\sqrt\pi}\displaystyle\int_0^{x}e^{-t^2}\,dt$ has no elementary formula, and $\operatorname{erf}(x)\to1$ as $x\to\infty$. Use integration by parts to evaluate $\displaystyle\int_0^{\infty}\bigl(1-\operatorname{erf}(x)\bigr)\,dx$.