What is the integral of 3x^2-2x+3 ?

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

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integral of 3x^2-2x+3

\int 3 x^{2} - 2 x + 3 d x

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

Solution steps

\int 3 x^{2} - 2 x + 3 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 2 x d x + \int 3 d x

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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