What is the integral of 6x^2-4x+2 ?

The integral of 6x^2-4x+2 is 2x^3-2x^2+2x+C

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integral of 6x^2-4x+2

\int 6 x^{2} - 4 x + 2 d x

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

Solution steps

\int 6 x^{2} - 4 x + 2 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 4 x d x + \int 2 d x

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

\int 4 x d x = 2 x^{2}

\int 2 d x = 2 x

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

Add a constant to the solution

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

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