Why does Integral[(e^sqrt(x)) / sqrt(x)] NOT equal e^sqrt(x) + C? Details of how I got there inside...

So I tried this with u substitution, since I think that’s how you should approach these types.

u = sqrt(x) = x^(1/2)

Set up differential equation:

du = 1/sqrt(x) dx

Substitute back into main integral:

Integral(e^u du)

Solve:

e^u + C

Substitute:

e^sqrt(x) + C

That’s my reasoning, and I think it’s OK! That was also one of the multiple choice answers, but it was one of my many questions marked wrong. What’s up?