What is the integral of-3x^2-20x+2000 ?

The integral of-3x^2-20x+2000 is -x^3-10x^2+2000x+C

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integral of-3x^2-20x+2000

\int - 3 x^{2} - 20 x + 2000 d x

- x^{3} - 10 x^{2} + 2000 x + C

Solution steps

\int - 3 x^{2} - 20 x + 2000 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 3 x^{2} d x - \int 20 x d x + \int 2000 d x

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

\int 20 x d x = 10 x^{2}

\int 2000 d x = 2000 x

= - x^{3} - 10 x^{2} + 2000 x

Add a constant to the solution

= - x^{3} - 10 x^{2} + 2000 x + C

(1 + x^{2}) \frac{d y}{d x} - \frac{4 x ^{3} y}{1 - x ^{2}} = 1

\int 3 x^{2} + 8 x - 9 d x

\frac{\partial}{\partial x} (ln (t + 2 c x))

f (x) = a x^{b} + d e^{- c x}

\int (4^{x} - sec^{2} (x)) d x

What is the integral of-3x^2-20x+2000 ?
The integral of-3x^2-20x+2000 is -x^3-10x^2+2000x+C