In this article, we study the integrability of analytic perturbations of quadratic homogeneous differential system \({\textbf {F}}={\textbf {F}}_2+h.o.t.\) where the origin is an isolated singular point of \({\textbf {F}}_2\) . Algaba et al. [Mediterr. J. Math. 18, 8 (2021)] proved that, under the condition that \({\textbf {F}}_2\) is polynomially integrable, the above system is analytically integrable at the origin if and only if \({\textbf {F}}\) is orbitally equivalent to \({\textbf {F}}_2\) . Here we give a proof in a different way from Algaba et al. Furthermore, we prove that, under the condition that \({\textbf {F}}_2\) is rationally integrable, if the parameters of \({\textbf {F}}_2\) satisfy certain conditions, then the above system is formal meromorphically integrable at the origin if and only if \({\textbf {F}}\) is orbitally equivalent to \({\textbf {F}}_{2}.\)
