I don't think so because u is a generic function. Without any specifics, you can't determine the output of int[(u')^2]dx without resorting to just evaluating on a case-to-case basis. For example, there is no way to explain the following:
If u(x)=x then the function (int[(u')^2]dx) = x+C or possibly u'(x)*u(x)
If u(x)=ln(x) then the function = -1/x+C or possibly -u'(x)
Not really a proof, but it's what I say.