Question

If you do a u sub on an integral and the du has an x that doesn't cancel out, can you take it out of the integral as a constant with the x

Answer 1

you can't.. you have to make the whole new integral in term of u, and get rid of all x's

Answer 2

^^
if I understood your question well*

Answer 3

what you can do is express that x as a function of u, so the integrand is entirely a function of u and not x.
(for definite integral, you also need to change your limits from x values to u values)