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

Explanation

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

`=sqrt3 int [(2/3)^2-(x-1/3)^2]dx`

`=sqrt3(frac{(2/3)^2}{2} sin^(-1)frac{(x-1/3)}{2/3}+frac{(x-1/3)}{2}sqrt((2/3)^2-(x-1/3)^2))+C`

`=frac{2 sqrt3}{9}sin^(-1)frac{(3x-1)}{2}+frac{3x-1}{6}sqrt(1+2x-3x^2)+C`