What is the integral of 54-18z-6z^2+2z^3 ?

The integral of 54-18z-6z^2+2z^3 is 54z-9z^2-2z^3+(z^4)/2+C

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integral of 54-18z-6z^2+2z^3

\int 54 - 18 z - 6 z^{2} + 2 z^{3} d z

54 z - 9 z^{2} - 2 z^{3} + \frac{z ^{4}}{2} + C

Solution steps

\int 54 - 18 z - 6 z^{2} + 2 z^{3} d z

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 54 d z - \int 18 z d z - \int 6 z^{2} d z + \int 2 z^{3} d z

\int 54 d z = 54 z

\int 18 z d z = 9 z^{2}

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

\int 2 z^{3} d z = \frac{z ^{4}}{2}

= 54 z - 9 z^{2} - 2 z^{3} + \frac{z ^{4}}{2}

Add a constant to the solution

= 54 z - 9 z^{2} - 2 z^{3} + \frac{z ^{4}}{2} + C

What is the integral of 54-18z-6z^2+2z^3 ?
The integral of 54-18z-6z^2+2z^3 is 54z-9z^2-2z^3+(z^4)/2+C