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

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

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

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

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

Solution steps

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

\int 1 d x = x

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

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

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

Add a constant to the solution

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

\int \frac{- x e ^{- x}}{- 4} d x

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\int \frac{x ^{2} - 5 x - 24}{x + 3} d x

\int \frac{t}{1 + 3 t} d t

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