What is the integral of 12-8x+x^2 ?

The integral of 12-8x+x^2 is 12x-4x^2+(x^3)/3+C

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integral of 12-8x+x^2

\int 12 - 8 x + x^{2} d x

12 x - 4 x^{2} + \frac{x ^{3}}{3} + C

Solution steps

\int 12 - 8 x + 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 12 d x - \int 8 x d x + \int x^{2} d x

\int 12 d x = 12 x

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

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

= 12 x - 4 x^{2} + \frac{x ^{3}}{3}

Add a constant to the solution

= 12 x - 4 x^{2} + \frac{x ^{3}}{3} + C

What is the integral of 12-8x+x^2 ?
The integral of 12-8x+x^2 is 12x-4x^2+(x^3)/3+C