Integral gives solution with limit function

Tau being real and positive could still mean it is very large, defeating the speed at which the exponential drops to zero, especially in combination with the multiplication of it with the exponential.
After your substitution, there’s no doubt that x will go to infinity and the exponential always wins from the tau it is multiplied with.

Note that you did not actually make that substitution in your original integral. If you had, It should have rendered something like:

Success!
Luc

Why do you think that “=positive” is a valid modifier? I could not find it in the list of modifiers in the Prime help. Try “>0” instead.

Can’t check with Prime but here is the result of Mathcad 15 (using muPad as symbolic engine)

You may try if “assume, tau>0” does the job better than your “assume, tau=positive”.

You may also try to add “simplify” or even “simplify, max” if it does not help.

Maybe because it works in Mathcad 11:
 

Success!
Luc

Maybe because it works in Mathcad 11:

But not in MC15 and probably not in Prime (‘real’ is a valid modifier in both, but ‘positive’ obviously not).

Seems to be the division that it doesn’t like.  

Alan