\(-\frac{2}{H^{2}\ \sqrt{\pi}}\int_{\frac{\text{G\ }}{\sqrt{t_{0}}}}^{\frac{\text{G\ }}{\sqrt{t_{f}}}}{\left(1-\frac{\text{G\ H}}{w^{2}}\right)\ e^{-w^{2}}\text{\ dw}}=-\frac{2}{H^{2}\ \sqrt{\pi}}\int_{\frac{\text{G\ }}{\sqrt{t_{0}}}}^{\frac{\text{G\ }}{\sqrt{t_{f}}}}{\ e^{-w^{2}}+\frac{\text{G\ H}\text{\ e}^{-w^{2}}}{w^{2}}\text{\ dw}}\)
\(=-\frac{2}{H^{2}\ \sqrt{\pi}}\int_{\frac{\text{G\ }}{\sqrt{t_{0}}}}^{\frac{\text{G\ }}{\sqrt{t_{f}}}}{\ e^{-w^{2}}\text{\ dw}}+\frac{2}{{\sqrt{\pi}\text{\ H}}^{2}}\int_{\frac{\text{G\ }}{\sqrt{t_{0}}}}^{\frac{\text{G\ }}{\sqrt{t_{f}}}}{\ \frac{\text{G\ H}\text{\ e}^{-w^{2}}}{w^{2}}\text{\ dw}}\)
\(=-\frac{2}{H^{2}\ \sqrt{\pi}}\int_{\frac{\text{G\ }}{\sqrt{t_{0}}}}^{\frac{\text{G\ }}{\sqrt{t_{f}}}}{\ e^{-w^{2}}\text{\ dw}}+\frac{2\ G}{\text{H\ }\sqrt{\pi}}\int_{\frac{\text{G\ }}{\sqrt{t_{0}}}}^{\frac{\text{G\ }}{\sqrt{t_{f}}}}{\ \frac{e^{-w^{2}}}{w^{2}}\text{\ dw}}\) (34)