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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 $
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01:46
Fahad Paryani
Calculus 1 / AB
Calculus 2 / BC
Chapter 4
Applications of Differentiation
Section 9
Antiderivatives
Derivatives
Differentiation
Volume
Campbell University
Harvey Mudd College
Baylor University
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Find the most general anti…
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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.
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