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

x \to 1 lim (\frac{( x ^{3} )}{x - 1})

\int 3 x ln (x) d x

\frac{d}{d x} (7 cos (2 x))

1 0^{x}

\int \frac{x - 1}{( x + 3 ) ^{2}} d x

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