What is the integral of (-2x^3+12x^2-20x+8.5) ?

The integral of (-2x^3+12x^2-20x+8.5) is -0.5x^4+4x^3-10x^2+8.5x+C

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integral of (-2x^3+12x^2-20x+8.5)

\int (- 2 x^{3} + 12 x^{2} - 20 x + 8.5) d x

- 0.5 x^{4} + 4 x^{3} - 10 x^{2} + 8.5 x + C

Solution steps

\int - 2 x^{3} + 12 x^{2} - 20 x + 8.5 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 2 x^{3} d x + \int 12 x^{2} d x - \int 20 x d x + \int 8.5 d x

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int 12 x^{2} d x = 4 x^{3}

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

\int 8.5 d x = 8.5 x

= - \frac{x ^{4}}{2} + 4 x^{3} - 10 x^{2} + 8.5 x

Simplify

= - 0.5 x^{4} + 4 x^{3} - 10 x^{2} + 8.5 x

Add a constant to the solution

= - 0.5 x^{4} + 4 x^{3} - 10 x^{2} + 8.5 x + C

x \to 2 lim (\frac{x ^{2} - 2 x}{x})

\int x \cdot 2 \cdot x - 5 d x

\frac{d ^{3}}{d x ^{3}} (2 x + 3)

\int_{0}^{7} \frac{1}{( 49 + x ^{2} )} d x

\frac{d}{d x} (sin (\frac{x}{5}))

What is the integral of (-2x^3+12x^2-20x+8.5) ?
The integral of (-2x^3+12x^2-20x+8.5) is -0.5x^4+4x^3-10x^2+8.5x+C