U can't make that substitution. I hope you see why. Depending on the shape of the function "F", you may integrate directly. The integral may very easily diverge, but that wouldn't be a catastrophe, would it...?
You can make u the inner integral. The limits will be a/x to inf. and you will have 1/x in the integrand. v=x is irrelevant - it doesn't change anything.
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