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

Answer

N/a

Explanation

`I = intsqrt(2ax-x^(2)dx) = intsqrt(-(x^(2)-2ax)dx)`
`= intsqrt(-(x^(2)-2ax+a^(2)-a^(2)))dx = intsqrt(-(x-a)^(2)-a^(2))dx`
`= intsqrt(a^(2)-(x-a)^(2))dx`
` =(x-a)/(2)sqrt(a^(2)-(a-x)^(2))+(a^(2))/(2)sin^(-1)((x-a)/(a))+C`
`= (x-a)/(2)sqrt(2ax+x^(2))+(a^(2))/(2) sin^(-1)((x-a)/(a))+C`