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# Find the most general antiderivative of the function. (Check your answers by differentiation.)$f(x) = x(12x + 8)$

## $4 x^ 3+4 x^{2}+C$

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So for this problem we're trying to find the anti derivative of the function that's going to be F of X equals X times 12 X plus eight. So I'm going to actually distribute that. We're going to have 12 X squared plus eight X. And it will actually make it easier in the long run because when we take the anti derivative we'll have 12 X. Cubed over three, it will be four X cubed. Then we'll have plus eight X squared over two. That'll be plus four X squared. Now that we have this, we can check it, we have to remember to add the plus C. So then um when we check this will take f crime of acts and choose any random value for C. As we change, it doesn't matter. We see the F. Prime of X is the same as the F. Of X graph. Therefore we solve this correctly.

California Baptist University

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