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

Explanation

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

`=-1/2intxx-2xsqrt(1+x-x^2)dx`

`=-1/2int (-2x+1-1)sqrt(1+x-x^2)dx`

`=-1/2in t[(-2x+1)sqrt(1+x-x^2)-sqrt(1+x-x^2]dx`

`=-1/2int(-2x+1)sqrt(1+x-x^2)dx+1/2intsqrt(1+x-x^2)dx`

putting `1+x+x^2=t`

`(1-2x)dx=dt`

`=-1/2intsqrttdx+1/2sqrt(1+x-x^2)dx`

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