https://people.math.ethz.ch/~afigalli/papers-pdf/A-quantitative-analysis-of-metrics-on-Rn-with-almost-constant-positive-scalar-curvature-with-applications-to-fast-diffusion-flows.pdf

I am in trouble in understanding one step of theorem 1.1 in the above mentioned paper. Namely in the equation (2.8) , it is written that since $u=\sigma+\rho$ so the Talyor expansion yields $\int_{\mathbb{R}^n}u^p\rho=\int_{\mathbb{R}^n}\sigma^p\rho+p\int_{\mathbb{R}^n}\sigma^{p-1}\rho+O(\int_{\mathbb{R}^n}|\nabla\rho|^{1+\gamma})..........(2.8)$ where $\gamma=\min(\frac{1}{2},\frac{2}{n-2})$; the big Oh term I am not getting how this is coming with power $1+\gamma$? Any help is very much appreciated.