\(\frac{2\ G}{\text{H\ }\sqrt{\pi}}\int_{\frac{\text{G\ }}{\sqrt{t_{0}}}}^{\frac{\text{G\ }}{\sqrt{t_{f}}}}{\ \frac{e^{-w^{2}}}{w^{2}}\text{\ dw}}=\frac{2\ G}{\text{H\ }\sqrt{\pi}}\left(\int_{\frac{\text{G\ }}{\sqrt{t_{0}}}}^{\infty}{\ \frac{e^{-w^{2}}}{w^{2}}\text{\ dw}}-\int_{\frac{\text{G\ }}{\sqrt{t_{f}}}}^{\infty}{\ \frac{e^{-w^{2}}}{w^{2}}\text{\ dw}}\right)\)
\(=\frac{2\ G}{\text{H\ }\sqrt{\pi}}\left[\frac{{\sqrt{t_{0}}\text{\ e}}^{-\frac{G^{2}}{t_{0}}}}{G}-\sqrt{\pi}\text{\ erfc}\left(\frac{G}{\sqrt{t_{0}}}\right)-\frac{{\sqrt{t_{f}}\text{\ e}}^{-\frac{G^{2}}{t_{f}}}}{G}+\sqrt{\pi}\text{\ erfc}\left(\frac{G}{\sqrt{t_{f}}}\right)\right]\)
\(=\frac{2\ G}{\text{H\ }\sqrt{\pi}}\left\{\ \sqrt{\text{π\ }}\left[\text{erfc}\left(\frac{G}{\sqrt{t_{f}}}\right)-\text{erfc}\left(\frac{G}{\sqrt{t_{0}}}\right)\right]-\frac{\sqrt{t_{f}}\ e^{-\frac{G^{2}}{t_{f}}}}{G}+\frac{{t_{0}\text{\ e}}^{-\frac{G^{2}}{t_{0}}}}{G}\right\}\) (36)