= Solution
In the classically scale-invariant case from <6/d/solution>, use $\partial\mathcal L/\partial(\partial_\mu\phi)=\partial^\mu\phi$, $\bar\delta\phi=\alpha(\phi+x^\nu\partial_\nu\phi)$ and $\delta x^\mu=-\alpha x^\mu$. Dividing the supplied <Noether current> expression by $\alpha$ gives
$$
j^\mu=\phi\partial^\mu\phi+\partial^\mu\phi\,x^\nu\partial_\nu\phi-x^\mu\mathcal L.
$$
Since $\theta^{\mu\nu}=\partial^\mu\phi\partial^\nu\phi-\eta^{\mu\nu}\mathcal L$, this is
$$
\boxed{j^\mu=\phi\partial^\mu\phi+\theta^{\mu\nu}x_\nu.}
$$
The first term in this <dilatation current> comes from the intrinsic weight of the <scalar field>, while the second comes from moving its spacetime argument. Using the canonical <energy-momentum tensor> alone without the first term would not give the stated conserved current.
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