Is there anyway to evaluate $$\int_{C/B}^\infty \Phi(tA+ABx)\phi(x)dx?$$ $t,C\in\mathbb{R}$, $A>0$ and $B>0$.
I've tried differentiating under the integral but seems to get me nowhere. I differentiated w.r.t. $A$ and got a really complicated closed form solution. But to integrate that w.r.t to $A$ again seems even more hopeless...