What is the integral of 6x-9x^2+C ?

The integral of 6x-9x^2+C is 3x^2-3x^3+Cx+C

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integral of 6x-9x^2+C

\int 6 x - 9 x^{2} + C d x

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

Solution steps

\int 6 x - 9 x^{2} + C 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 d x - \int 9 x^{2} d x + \int C d x

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

\int 9 x^{2} d x = 3 x^{3}

\int C d x = C x

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

Add a constant to the solution

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

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