I am facing a mathematical problem of integrating exp(-ax^2)*erf(bx+c)*erf(dx+f) with the integral boundaries 0 and infinity.

I have gone through some handbooks of integration but what I could find is only the integration of exp(-ax^2)*erf(bx)*erf(cx) from 0 to infinity that yields arctan(b*c/sqrt(a*(b^2+c^2+a)))/sqrt(a*pi).

I would really appreciate if any of you could guide me through solving this problem.

Thank you.