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

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

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integral of 6x^2-2x+8

\int 6 x^{2} - 2 x + 8 d x

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

Solution steps

\int 6 x^{2} - 2 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 6 x^{2} d x - \int 2 x d x + \int 8 d x

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

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

\int 8 d x = 8 x

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

Add a constant to the solution

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