Find `intxsqrt(1+x-x^2)dx`

Explanation

`int x sqrt{1+x-x^{2}} d x`
`
=-frac{1}{2} int-2 x sqrt{1+x-x^{2}} d x`
`
=-frac{1}{2} int(-2 x+1-1) sqrt{1+x-x^{2}} dx`
`
=-frac{1}{2} int[(-2 x+1) sqrt{1+x-x^{2}}-sqrt{1+x-x^{2}}] d x`
`
=-frac{1}{2} int(-2 {x}+1) sqrt{1+{x}-{x}^{2}} {dx}+frac{1}{2} int sqrt{1+{x}-{x}^{2}} {dx}`

putting `1+x+x^{2}=t`
`
(1-2 x) d x=d t`
`
=-frac{1}{2} int sqrt{{t}} {dx}+frac{1}{2} int sqrt{1+{x}-{x}^{2}} {dx}`
`
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