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# Find the most general antiderivative of the function. (Check your answers by differentiation.)$f(x) = 2x^3 - \dfrac{2}{3}x^2 + 5x$

## $F(x)=\frac{1}{2} x^{4}-\frac{2}{9} x^{3}+\frac{5}{2} x^{2}+C$

Derivatives

Differentiation

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

So for this problem we're trying to find the anti derivative. The function that we're given is half of ax equals checks cubed, Okay minus two thirds X squared plus five packs. We take the anti derivative of this affects we get that we increase the power at the four and then divide by four. So we get one half X to the fork minus. We increase this to the power 32 by by three. So it's going to give us a negative 2/9 X cube nine X. Cute. And then we have plus this becomes five X squared over two. So five halves X squared. And then we have to remember to add that general constant plus C. That's the final anti derivative.

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#### Topics

Derivatives

Differentiation

Volume

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp