Evaluate: `intsqrt(1+3x-x^2)dx`

Explanation

`intsqrt(1+3x-x^2)dx`
`=intsqrt(1+(9)/(4)-(x^(2)-2x((3)/(2))+(9)/(4)))dx`
`=int sqrt(((sqrt(13))/(2))^(2)-(x-(3)/(2))^(2))dx`
`=(x-(3)/(2))/(2) sqrt(1+3x-x^(2))+(13)/(4xx2)"sin"^(-1)((x-(3)/(2))/((sqrt(13))/(2)))+C`
`=(2x-3)/(4)sqrt(1+3x-x^(2))+(13)/(8)"sin"^(-1)((2x-3)/(sqrt(13)))+C`