What is the integral of x^2-6x-27 ?

The integral of x^2-6x-27 is (x^3)/3-3x^2-27x+C

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integral of x^2-6x-27

\int x^{2} - 6 x - 27 d x

\frac{x ^{3}}{3} - 3 x^{2} - 27 x + C

Solution steps

\int x^{2} - 6 x - 27 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 x^{2} d x - \int 6 x d x - \int 27 d x

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

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

\int 27 d x = 27 x

= \frac{x ^{3}}{3} - 3 x^{2} - 27 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 3 x^{2} - 27 x + C

4 x \frac{d y}{d x} = x^{2} - 9

\int_{- 1}^{1} ln (ln (x + 3)) d x

\frac{d x}{d y} = - \frac{( 4 y ^{2} + 6 x y )}{3 y ^{2} + 2 x}

\int_{0}^{2} (6 x^{2} - 4 x + 5) d x

y = e^{\frac{1}{2} x}

What is the integral of x^2-6x-27 ?
The integral of x^2-6x-27 is (x^3)/3-3x^2-27x+C