I have been studying the axial anomaly and everywhere I see the calculation of the triangle loop using dimensional regularisation (see for example pages 661-664 of section 19.2 of Peskin). In the ‘t Hooft prescription for the $\gamma^5$ they divide the Lorentz space into the usual 4 dimensional one and the rest of dimensions (inside the integration), so the loop momentum can be written as (eq. 19.53) \begin{equation} l=l_\parallel+l_\perp \end{equation}
“ Where the first term has nonzero components in dimensions 0,1, 2, 3 and the second term has nonzero components in the other d—4 ($-2\epsilon$) dimensions.”
Then, we arrive to this integral
\begin{equation} \int \frac{d^dl}{(2\pi)^d}\frac{l_\perp^2}{(l^2-\Delta)^3} \end{equation}
and what I do not understand is the following replacement for it (eq 19.57) \begin{equation} l_\perp^2\to\frac{d-4}{d}l^2 \end{equation} “under the symmetrical integration”.
I do understand when we do similar things for an even integral for which any odd term is zero so
\begin{equation} l_\mu l_\nu\to\frac{1}{d}l^2g_{\mu\nu} \end{equation}
But in the case with the $l_\perp$ I do not see a proper derivation, could someone help me with that? Thanks in advance.