Why is this not a u-sub?

Question

$\int e^*x dx$

Why is this not a u-sub? Where I let

$u=x$ so $du=dx$

$\int e^udu = e^u +c$

I have notes where we did it as ab IBP problem instead.

Answer 1

$u = x$ is never a good substitution since if administered correctly, gives you exactly the same integral you started with---only with a different variable. In your case, you made a mistake by simply dropping the $x$ in your original problem which you must not do.

Try integration by parts.