calculation – Integration of $ int frac {e ^ x} { sqrt {e ^ {2x} -1}} dx $ with $ u $ -substitution only

I'm trying to integrate this with u substitution only
$$ int frac {e ^ x} { sqrt {e ^ {2x} -1}} dx $$

I have therefore taken a look at the corrected key of my books, but I am still very confused.
I know I should choose to be $ { sqrt {e ^ {2x} -1}} $

When I differnetiate I receive $$ frac {e ^ {2x}} { sqrt {e ^ {2x} -1}} $$

I get lost here, especially with the numerator. Also, is there another value u that I can choose?