Hello, I am new to
Mathematica, and I have run into something unexpected with the following integral:

Straightforward enough, but when I re-write the integral as

I see this unexpected bit at the end of the step-by-step solution:

Why has the 2*log(e^x) term dissapeared instead of simplifying to 2*x? Is Mathamatica making assumptions about the restricted values of x, or am I just missing something?