# Expected Value of an expression including error function

I want to calculate the expected value to the solution of a Fokker-Plank equation, so one of the terms I got includes the complementary error function, namely: $$p(x,t|x_{0},t_{0})=\frac{B}{2 D}*e^{\frac{-Bx}{D}} * erfc(\frac{x+x_{0}-Bt}{2\sqrt{Dt}})$$

So my question is, while calculating the intergral $$E(x)=\int_{-\infty}^{\infty} x p(x,t|x_{0}t_0)$$

So I would like to know how to get aorund this integral? Is there some numerical way to calculate it, or are there even some analytical way to find ?

And of course my complementary error function is defined as: $$erfc(\frac{x+x_{0}-Bt}{2\sqrt{Dt}})=\frac{2}{\sqrt{\pi}}\int_{\frac{x+x_{0}-Bt}{2\sqrt{Dt}}}^{\infty} e^{-z^2} dz$$