# Simplifying complicated integral including CDF of normal distribution

I'm dealing with a complicated integral and want to know whether you are aware of some possibility how to simplify it. If you think, there is no possibility, please tell me. Then I'll use numerics. The integral is $$\int\limits_{0}^{\infty} \Phi\left(\frac{m-ts}{\sqrt{s}}\right) \sqrt{\frac{1}{s^3}} \exp(-us+v-w/s)ds$$ with all variables in $\mathbb{R}$ and where $\Phi(x)$ denotes the cumulative distribution function of the standard normal distribution with $\Phi(x)=\frac{1}{2}(1+\text{erf}(x/\sqrt{2}))$ where $\text{erf}(x)$ is the error function.