What is the integral of (8z+4z^3-6z^2) ?

The integral of (8z+4z^3-6z^2) is 4z^2+z^4-2z^3+C

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integral of (8z+4z^3-6z^2)

\int (8 z + 4 z^{3} - 6 z^{2}) d z

4 z^{2} + z^{4} - 2 z^{3} + C

Solution steps

\int 8 z + 4 z^{3} - 6 z^{2} 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 8 z d z + \int 4 z^{3} d z - \int 6 z^{2} d z

\int 8 z d z = 4 z^{2}

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

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

= 4 z^{2} + z^{4} - 2 z^{3}

Add a constant to the solution

= 4 z^{2} + z^{4} - 2 z^{3} + C

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What is the integral of (8z+4z^3-6z^2) ?
The integral of (8z+4z^3-6z^2) is 4z^2+z^4-2z^3+C