\begin{align}
\notag p(x) &= \int_c^x \exp\bigg(\frac{2\sigma^2}{(\mu_1-\mu_2)^2}\int_c^y \frac{(q_1+q_2)z-q_2}{z^2(1-z)^2} dz\bigg) dy\\
&= \int_c^x \exp\bigg(\frac{2\sigma^2}{(\mu_1-\mu_2)^2}\bigg[ \frac{q_2}{y}+\frac{q_1}{1-y}+(q_1-q_2) \log\bigg(\frac{y}{1-y}\bigg) -C \bigg] \bigg) dy,\label{p calc}
\end{align} 
