What is the integral of 3t^2-12t+9 ?

The integral of 3t^2-12t+9 is t^3-6t^2+9t+C

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integral of 3t^2-12t+9

\int 3 t^{2} - 12 t + 9 d t

t^{3} - 6 t^{2} + 9 t + C

Solution steps

\int 3 t^{2} - 12 t + 9 d t

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 t^{2} d t - \int 12 t d t + \int 9 d t

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

\int 12 t d t = 6 t^{2}

\int 9 d t = 9 t

= t^{3} - 6 t^{2} + 9 t

Add a constant to the solution

= t^{3} - 6 t^{2} + 9 t + C

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What is the integral of 3t^2-12t+9 ?
The integral of 3t^2-12t+9 is t^3-6t^2+9t+C