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Find the general indefinite integral.

$ \displaystyle \int (u^6 - 2u^5 - u^3 + \frac{2}{7}) \, du $

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00:45

Frank Lin

00:36

Amrita Bhasin

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Kiana B.

April 26, 2022

???? ?t(t2 + 3t + 2)dt

Missouri State University

Campbell University

Oregon State University

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.

00:56

Find the general indefinit…

00:46

01:54

Find the indefinite integr…

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04:19

01:38

the theme in this problem is the integral of some power Is equal to adding 1 to the exponents. And then I like to instead of dividing by the new experiment. Multiply by the reciprocal and then don't forget about plus C. And the whole thought process is the derivative of this thing that I just did is equal to that and the derivative of a constant is zero. So that's why we need a plus C. So as we're looking at this problem of the integral of you to the sips -2 U. to the 5th uh minus U cubed plus two sevens. Do you you're correct answer is going to be just doing each piece individually. Or you add one to the exponent. Multiply by the reciprocal, add one to the exponent. Now instead of believing this is 26 I can reduce to 6 to 1 third, Add 1 to the excrement. Multiply by the reciprocal And add one to the exponent. Well it just becomes like you to the first because again, the director of 272 needs to be this, and like I said earlier, you need to remember plus E. This is your correct answer.

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