What is the integral of (-9x^2+9x+2) ?

The integral of (-9x^2+9x+2) is -3x^3+(9x^2)/2+2x+C

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integral of (-9x^2+9x+2)

\int (- 9 x^{2} + 9 x + 2) d x

- 3 x^{3} + \frac{9 x ^{2}}{2} + 2 x + C

Solution steps

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

\int 9 x^{2} d x = 3 x^{3}

\int 9 x d x = \frac{9 x ^{2}}{2}

\int 2 d x = 2 x

= - 3 x^{3} + \frac{9 x ^{2}}{2} + 2 x

Add a constant to the solution

= - 3 x^{3} + \frac{9 x ^{2}}{2} + 2 x + C

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d er i v a t i v e f (x) = \frac{2 x + 5}{x - 1}

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What is the integral of (-9x^2+9x+2) ?
The integral of (-9x^2+9x+2) is -3x^3+(9x^2)/2+2x+C