Evaluate: `intsqrt(2a x-x^2)dx`

Explanation

\begin{aligned} I &=\int \sqrt{2 a x-x^{2}} d x \\ &=\int \sqrt{a^{2}-(x-a)^{2}} d x \\ &=\frac{x-a}{2} \sqrt{a^{2}-(x-a)^{2}}+\frac{a^{2}}{2} \sin ^{-1}\left(\frac{x-a}{a}\right)+C \\ &=\frac{x-a}{2} \sqrt{2 a-x^{2}}+\frac{a^{2}}{2} \sin ^{-1}\left(\frac{x-a}{a}\right)+C \end{aligned}