I run into the Dawson's integral during my research of solving this integral (Coupled complex double integral). But why is the integral of Dawson's integral not converting.
The limits of the Dawson's integral are
$$ F(x)=\frac{1}{2} \sqrt(\pi) \exp(-x^2) \int_0^{x} \exp{(t^2)} \, dt $$ $$ \lim_{x \to \pm\infty} F(x) = 0 $$
Telling me, there is an enclosed area under the graph. However, the integral of the the dawson integral
$$ \int_0^{\infty} F(x) dx $$
is not converting based on wolframalpha. Do I miss a basic understanding of integrals and integration?