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

Explanation

`intsqrt(1+2x-x^2)dx=intsqrt((sqrt2)^2-(x-1)^2)dx`
=`(x-1)/2sqrt((sqrt2)^2-(x-1)^2)+(sqrt2)^2/2 sin^-1((x-1)/sqrt2)+C`
`[becauseintsqrt(x^2-a^2)dx
=`x/2sqrt(x^2-a^2)+a^2/2sin^-1(x/a)+C]`
=`(x-1)/2sqrt(1+2x-x^2)sin^-1((x-1)/sqrt2)+C`