What is the integral of-2x+6x^2-4x^3+18 ?

The integral of-2x+6x^2-4x^3+18 is -x^2+2x^3-x^4+18x+C

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integral of-2x+6x^2-4x^3+18

\int - 2 x + 6 x^{2} - 4 x^{3} + 18 d x

- x^{2} + 2 x^{3} - x^{4} + 18 x + C

Solution steps

\int - 2 x + 6 x^{2} - 4 x^{3} + 18 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 d x + \int 6 x^{2} d x - \int 4 x^{3} d x + \int 18 d x

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

\int 6 x^{2} d x = 2 x^{3}

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

\int 18 d x = 18 x

= - x^{2} + 2 x^{3} - x^{4} + 18 x

Add a constant to the solution

= - x^{2} + 2 x^{3} - x^{4} + 18 x + C

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

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\int ln (x^{8}) d x

\frac{d}{d x} (6^{6 - x^{2}})

What is the integral of-2x+6x^2-4x^3+18 ?
The integral of-2x+6x^2-4x^3+18 is -x^2+2x^3-x^4+18x+C