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Find antiderivatives of the given functions.$$f(v)=4 v^{4}+3 \pi^{2}$$

$F(v)=\frac{4}{5} v^{5}+3 \pi^{2} v$

Calculus 1 / AB

Chapter 25

Integration

Section 1

Antiderivatives

Integrals

Campbell University

Harvey Mudd College

University of Nottingham

Idaho State University

Lectures

03:09

In mathematics, precalculu…

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In mathematics, a function…

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Particular antiderivatives…

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Find an antiderivative.

Finding antiderivatives Fi…

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Find the antiderivatives $…

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Find all the antiderivativ…

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uh huh. We want to find the anti derivative of the function. F X equals four extra fourth plus three pi squid to do so we're going to rely on the definition of the derivative. Remember that the anti derivative is the opposite derivative. That is to say the anti derivative is the inverse derivative function. Understanding derivative rules therefore gives us how to sign an anti rhythm just by taking the inverse. I have rules 12 or three. Listen on the right that our comprehensive for solving such problems for this problem though, we only need rule one. The power rule which states DDX extra as a the exit A -1. It holds therefore that the interest of X. BA. Is 1/8 plus one actually a plus one because of the inverse. So we must have the interests of capital. F X is four times 1/5 X to the fifth plus three pi squared X. Is supplying one over a plus one times actually a plus one to each of these terms. Thus we have capital. F X is equal to 4 50 X to the fifth Plus three Pi Squared X.

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