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Find antiderivatives of the given functions.$$f(x)=4 \sqrt{x}+3$$

$F(x)=\frac{8}{3} x \sqrt{x}+3 x$

Calculus 1 / AB

Chapter 25

Integration

Section 1

Antiderivatives

Integrals

Missouri State University

Campbell University

Baylor University

University of Michigan - Ann Arbor

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

01:30

Particular antiderivatives…

01:17

Find an antiderivative.

01:02

Find the general antideriv…

00:54

Find the most general anti…

01:38

03:11

01:00

Find the antiderivative.

01:25

00:16

02:00

we want to find the anti derivative of the function F of X is equal to four route X plus three. This question is testing our knowledge of anti differentiation as a precursor to the topic of integration as such. We need a solid understanding of anti derivatives to perceive so remember that the anti derivative is just the inverse derivative. So if we understand derivative rules, we can use any anti derivative. So of the three rules have lifted here. We actually only need number one. The power rule, which states that dx actually A equals X minus one. Therefore by inverse, the entire river extra A is one of the eight plus one times actually a plus one. So we must have editor of F X equals four times two thirds extra three half plus three X. Where we perform one over a plus one Times actually a plus one. We also have a constant four and constant three in the two terms. This gives us final solution 8/3 extra three hats plus three X. As the anti do evidence

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