What is the integral of (-x^2+x-1) ?

The integral of (-x^2+x-1) is -(x^3)/3+(x^2)/2-x+C

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integral of (-x^2+x-1)

\int (- x^{2} + x - 1) d x

- \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - x + C

Solution steps

\int - x^{2} + x - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int x^{2} d x + \int x d x - \int 1 d x

\int x^{2} d x = \frac{x ^{3}}{3}

\int x d x = \frac{x ^{2}}{2}

\int 1 d x = x

= - \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - x

Add a constant to the solution

= - \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - x + C

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What is the integral of (-x^2+x-1) ?
The integral of (-x^2+x-1) is -(x^3)/3+(x^2)/2-x+C