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Numerade Educator

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Problem 21 Easy Difficulty

Find the most general antiderivative of the function.
(Check your answers by differentiation.)

$ f(x) = \dfrac{2x^4 + 4x^3 - x}{x^3} $, $\quad x > 0 $

Answer

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

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Video Transcript

this problem were given a function. Um It will be in our best interest to divide out that X cubed first before we actually evaluated. So we're going to have is f of X equals two acts plus or. And we can separate all these parts of the fraction, so we get two X plus four minus one over x squared. But I'm going to write one over X squared X to the negative tube. So here's our graph. When we find the anti derivative after backs we get two. X is going to give us x squared Plus four since this is a constant, we would just write this as four acts for the anti derivative and then here we have minus X to the when we have a negative two, we add one in the exponents X. The negative one divided by a negative one is going to give us plus X to the negative one. Or we could also write that as one over X and we just have to add our constant and this is the final answer.