Advice on an integral involving the error function

If you let: $$t = \sqrt{1 + x},$$

and change limits appropriately, Mathematica evaluates it as:

$$\gamma \text{erf}\left(\alpha -\frac{1}{\beta }\right) ++\frac{\gamma ^{3/2} e^{\frac{2 \alpha }{\beta }-2 |\alpha | \sqrt{\frac{1}{\beta ^2}+\frac{1}{\gamma }}+\frac{1}{\gamma }} \left(|\alpha | \left(\text{erf}\left(\sqrt{\frac{1}{\beta ^2}+\frac{1}{\gamma }}-|\alpha |\right)-e^{4 |\alpha | \sqrt{\frac{1}{\beta ^2}+\frac{1}{\gamma }}} \text{erfc}\left(|\alpha |+\sqrt{\frac{1}{\beta ^2}+\frac{1}{\gamma }}\right)-1\right)+\alpha \sqrt{\frac{\beta ^2+\gamma }{\gamma }} \left(\text{erf}\left(\frac{\sqrt{\frac{\beta ^2+\gamma }{\gamma }}}{\beta }-|\alpha |\right)+e^{\frac{4 |\alpha | \sqrt{\frac{\beta ^2+\gamma }{\gamma }}}{\beta }} \text{erfc}\left(|\alpha |+\frac{\sqrt{\frac{\beta ^2+\gamma }{\gamma }}}{\beta }\right)-1\right)\right)}{2 |\alpha | \sqrt{\beta ^2+\gamma }}.$$

Not as neat as I'd like it, but there you go.