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Find the general indefinite integral.

$ \displaystyle \int \sqrt[4]{x^5} \, dx $

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00:39

Frank Lin

00:26

Amrita Bhasin

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Campbell University

Baylor University

University of Nottingham

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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Find the general indefinit…

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Evaluate the integral.

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Find the indefinite integr…

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Evaluate the integral.…

our task is to do the integral of the 4th root of X to the 5th power DFS. Uh And this is just the power rule. So the theme in this problem is if I asked you to do the integral of X to the end power I D X, what I like to do is just add one to the exponents and multiply by the reciprocal of your new experience. Well right now this doesn't look like it's just a an easy explanation, but if you remember your exponent rules, the fourth route would be a The 1 4th power. And so this is equivalent. The fourth root of Excellent. Fifth is the same thing as extra five force power. You might just need some practice of adding one, 25 force. Uh the easiest answer there would be to say change 1 to be four force. So you're looking at the nine force power when we get to. Okay, so this is equal to X to the nine force power. And I just showed all my work there now, instead of dividing by nine force to me. And makes more sense to multiply by the reciprocal of nine force. And don't forget about plus C. You need you need to have the plus C. Because the derivative of a constant zero. And we just don't write it that in there. Um Double checking. Some people might rewrite this answer like this, but there's really no rhyme or reason why you should. So I mean circle both because they're both correct.

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