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Evaluate the given integral.$$\int(2 x+1)^{9} 2 d x$$

$$\frac{(2 x+1)^{10}}{10}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 3

The Substitution Method

Integrals

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.

01:15

Evaluate the given integra…

01:21

Evaluate the integral.…

00:39

02:44

Evaluate the integrals.

the derivative of two X plus one is two. So this suggests the use substitution. U equals two x plus one that way. Do you d X? That's equal to two. Which means Do you is to DX. And now we can rewrite this integral in terms of you. And we get that this is the integral of you to the ninth, which is equal to you to the 10th over, 10 plus C. And then finally we want to replace you by two x plus one to get two x plus one to the chance all over 10 plus c, and that completes the problem.

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