What is the integral of-2+36x-12x^2 ?

The integral of-2+36x-12x^2 is -2x+18x^2-4x^3+C

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integral of-2+36x-12x^2

\int - 2 + 36 x - 12 x^{2} d x

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

Solution steps

\int - 2 + 36 x - 12 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 2 d x + \int 36 x d x - \int 12 x^{2} d x

\int 2 d x = 2 x

\int 36 x d x = 18 x^{2}

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

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

Add a constant to the solution

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

x \to 81 lim (x^{\frac{3}{2}})

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f (x) = \frac{1}{5 - 2 e ^{x}}

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What is the integral of-2+36x-12x^2 ?
The integral of-2+36x-12x^2 is -2x+18x^2-4x^3+C