What is the integral of x^3-9x^2+27x-27 ?

The integral of x^3-9x^2+27x-27 is (x^4)/4-3x^3+(27x^2)/2-27x+C

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integral of x^3-9x^2+27x-27

\int x^{3} - 9 x^{2} + 27 x - 27 d x

\frac{x ^{4}}{4} - 3 x^{3} + \frac{27 x ^{2}}{2} - 27 x + C

Solution steps

\int x^{3} - 9 x^{2} + 27 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^{3} d x - \int 9 x^{2} d x + \int 27 x d x - \int 27 d x

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

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

\int 27 x d x = \frac{27 x ^{2}}{2}

\int 27 d x = 27 x

= \frac{x ^{4}}{4} - 3 x^{3} + \frac{27 x ^{2}}{2} - 27 x

Add a constant to the solution

= \frac{x ^{4}}{4} - 3 x^{3} + \frac{27 x ^{2}}{2} - 27 x + C

What is the integral of x^3-9x^2+27x-27 ?
The integral of x^3-9x^2+27x-27 is (x^4)/4-3x^3+(27x^2)/2-27x+C