-\,g(r)^2 dt^2+\frac{r^2}{R^2}\,d\vec{x}^2+e^{2b(r)} \frac{R^2}{r^2}\,dr^2\;.$$ In [@Gubser:2009cg] it was found that the Lifshitz background is a solution and also its perturbation of the following form is allowed $$\label{g and b gubser}
g(r)\,=\,\left(\frac{r}{R}\right)^\omega+\lambda \,g_1(r) + O(\lambda^2)
\hspace{1.5cm}
b(r)\,=\,\lambda\,c\,r^\gamma+ O(\lambda^2)$$ where $\lambda$ is a formal expansion parameter and $\gamma$ depends on the dynamical exponent $\omega$ besides other parameters of the model. The explicit expression of $\gamma$ is not important for our discussion. Notice that the dynamical exponent affects the spatial part of the metric through the perturbation of the Lifshitz background, and therefore it occurs in the computation of the holographic entanglement entropy. Since (\[metric perturbed lifshitz\]) on a constant time slice is a special case of the ansatz considered in the section \[more general ansatz section\], we can employ the results discussed there. From (\[area r finite integ 1\]) with $d=2$, $B(r)=r/R$ and $A(r)=e^{-b(r)} r/R$, we find that the finite term in the holographic entanglement entropy is provided by the following integral $$\begin{aligned}
\label{lif integral hee}
 \int_{r_{\textrm{min}}}^{\alpha} 
 \left(
\frac{e^{b(r)}}{\sqrt{1-(r_{\textrm{min}}/r)^4}}-1\right)
dr
&=&
 \int_{r_{\textrm{min}}}^{\alpha} 
 \left(
\frac{1}{\sqrt{1-(r_{\textrm{min}}/r)^4}}-1\right)
dr\\
\rule{0pt}{.7cm}
& &\hspace{.5cm}
+ \;\lambda\, c
 \int_{r_{\textrm{min}}}^{\alpha} 
\frac{r^\gamma}{\sqrt{1-(r_{\textrm{min}}/r)^4}}
\,dr
+O(\lambda^2)\;.
\nonumber\end{aligned}$$ We are mainly interested in the $O(\lambda)$ term in the r.h.s. of (\[lif integral hee\]) because the 