Notice your u version of the integrand has no traces of the x in the numerator of the original. To bring that part with you, you can re-express it (x, that is) in terms of u, or else use integration by parts.
The parts version...
... where (key in spoiler) ...
Spoiler:
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!