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

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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