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