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Evaluate the indefinite integral.

$ \displaystyle \int y^2 (4 - y^3)^{2/3} \, dy $

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01:35

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Missouri State University

Harvey Mudd College

Idaho State University

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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We know that you is for my cute, which means that why squared? Do you? Why is negative 1/3? Do you? Which means now we can write this as the constant natives numbered pulled out times the integral of you. The 2/3 do you? Which means the off negative 1/3 terms you to the 5/3 over 5/3 plus seat because, remember But we use the parlor, which means the exploding increases by one. And then we divide by then you exponents and then we back Substitute you is four minus y cute.

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