What is the integral of 3X^2-6X+8 ?

The integral of 3X^2-6X+8 is X^3-3X^2+8X+C

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integral of 3X^2-6X+8

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

X^{3} - 3 X^{2} + 8 X + C

Solution steps

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

\int 3 X^{2} d X = X^{3}

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

\int 8 d X = 8 X

= X^{3} - 3 X^{2} + 8 X

Add a constant to the solution

= X^{3} - 3 X^{2} + 8 X + C