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

Answer»

SOLUTION :`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`


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