I am trying to calculate the integration $$\int_C^1 \phi(x) \Phi \left( \frac{C}{x} \right)dx$$ where $\phi(x)$ and $\Phi(x)$ are the PDF and CDF of the standard Normal distribution respectively; $0 < C < 1$ is a constant.
Note that this is not the same of this question another similar question because this is multiplication not linear combination.
I don't know where to start. Any hint?