Fórmulas que contienen √2au -u²

$$\int \sqrt{2au-u^2}du=\frac{u-a}{2}\sqrt{2au-u^2}+\frac{a^2}{2}cos^{-1}(\frac{a-u}{a})+C$$

$$\int u\sqrt{2au-u^2}du=\frac{2u^2-au-3a^2}{6}\sqrt{2au-u^2}+\frac{a^3}{2}cos^{-1}(\frac{a-u}{a})+C$$

$$\int \frac{\sqrt{2au-u^2}}{u}du=\sqrt{2au-u^2}+a\:cos^{-1}(\frac{a-u}{a})+C$$

$$\int \frac{\sqrt{2au-u^2}}{u^2}du=-\frac{2\sqrt{2au-u^2}}{u}-cos^{-1}(\frac{a-u}{a})+C$$

$$\int \frac{du}{\sqrt{2au-u^2}}=cos^{-1}(\frac{a-u}{a})+C$$

$$\int \frac{udu}{\sqrt{2au-u^2}}=-\sqrt{2au-u^2}+a\:cos^{-1}(\frac{a-u}{a})+C$$

$$\int \frac{u^2du}{\sqrt{2au-u^2}}=-\frac{(u+3a)}{2}\sqrt{2au-u^2}+\frac{3a^2}{2}cos^{-1}(\frac{a-u}{a})+C$$

$$\int \frac{du}{u\sqrt{2au-u^2}}=-\frac{\sqrt{2au-u^2}}{au}+C$$