\int \sqrt{x} e^{ax} dx = \frac{1}{a}\sqrt{x}e^{ax} 
+\frac{i\sqrt{\pi}}{2a^{3/2}}
\text{erf}\left(i\sqrt{ax}\right)+ C, 
\text{ where erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2}dtet