# 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?