I am supposed to fin the pdf f where is normal r.v. with parameters

The pdf of X is

(Sorry I can't get this to appear in tex for some reason)

If I integrate this function from negative infinity to ln(y), then differeniate with respect to y, I should get the function I seek.

However I am not sure how to integrate the normal distribution function, could someone please explain to me some way I way go about doing that?

Thank you for your help.