XF 1.5 https

I've recently installed SSL certificates on my site that now redirects to https://mysite.com.
The problem I now have is that no images are showing on my site, all people see is the IMG tag.
The site is about a year old and of course many people have dragged and dropped images into posts.
When looking at the source of the images it is showing http://www.mysite.com.
Is there any way I can run a database query to strip the www from the image URL's and also change http to https? I would take me forever to go through and try to edit each post.
Of course my site looks a mess as it is. My site is a private members only so waste of time giving the correct URL.
Any help please i'm desperate.
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Thank you so much for the very quick responses and guide to https. Really first class support from xf and members, it is very much appreciated.