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New further integrability conditions of the Riccati equation$dy/dx=a(x)+b(x)y+c(x)y^{2}$ are presented. The first case corresponds to fixedfunctional forms of the coefficients $a(x)$ and $c(x)$ of the Riccati equation,and of the function $F(x)=a(x)+[f(x)-b^{2}(x)]/4c(x)$, where $f(x)$ is anarbitrary function. The second integrability case is obtained for the "reduced"Riccati equation with $b(x)\equiv 0$. If the coefficients $a(x)$ and $c(x)$satisfy the condition $\pm d\sqrt{f(x)/c(x)}/dx=a(x)+f(x)$, where $f(x)$ is anarbitrary function, then the general solution of the "reduced" Riccati equationcan be obtained by quadratures. The applications of the integrability conditionof the "reduced" Riccati equation for the integration of the Schr\"odinger andNavier-Stokes equations are briefly discussed.

New further integrability cases for the Riccati equation