What is the integral of 3x^2+8x+9 ?

The integral of 3x^2+8x+9 is x^3+4x^2+9x+C

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integral of 3x^2+8x+9

\int 3 x^{2} + 8 x + 9 d x

x^{3} + 4 x^{2} + 9 x + C

Solution steps

\int 3 x^{2} + 8 x + 9 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 8 x d x + \int 9 d x

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

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

\int 9 d x = 9 x

= x^{3} + 4 x^{2} + 9 x

Add a constant to the solution

= x^{3} + 4 x^{2} + 9 x + C