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Find antiderivatives of the given functions.$$f(x)=5\left(2 x^{4}+1\right)^{4}\left(8 x^{3}\right)$$

Calculus 1 / AB

Chapter 25

Integration

Section 1

Antiderivatives

Integrals

Missouri State University

Oregon State University

Harvey Mudd College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

00:45

Finding antiderivatives Fi…

01:04

Particular antiderivatives…

00:47

Find all the antiderivativ…

01:17

Find an antiderivative.

01:43

Find the general antideriv…

00:53

Find an antiderivative $F(…

01:26

Find the antiderivative $F…

01:32

Find the antiderivative $ …

01:11

well if we want to find the anti derivative, the function F X is equal to five, you have to actually the fourth plus one to the fourth. Power times execute. This question is testing our knowledge of anti differentiation as a precursor integration as such. We have a solid understanding of this concept. Remember that an anti derivative is just an inverse derivative function. So that means if you know the rules were taking derivatives but identifying the inverse of that rule don't know how to take an antivirus as well. And this problem we need to use both the power rule and three the chain rule as it highlighted particularly we need the chain rule because when we integrate the term rather anti drive the term to actually the fourth plus one of the fourth. If you will take the derivative of that term it would produce by the chain rule an expression eight execute. Therefore when you anti derived it absorbs evaluate function of a execute. So capital Fx is five times 1/5 instruction, the fourth plus one of the fifth. This is by the power rule times eight sq prefer it. If you'd buy the chain rule, it must absorb this term. Therefore, we have final solution. Capital FX equals to actually the fourth plus one to the fifth.

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