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Evaluate the given integral.$$\int \sqrt{2 x+1} d x$$

$$\frac{1}{3}(2 x+1)^{3 / 2}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 3

The Substitution Method

Integrals

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

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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Evaluate the integral.…

09:01

01:17

Evaluate the indicated int…

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02:43

02:01

Find the Integral

04:51

Find the Integral of \int …

0:00

Evaluate the integral. $\i…

we want to take the integral of the square root of two X plus one and we know how to integrate the square root of ax. So let's try and replace two X plus one by a single dummy variable. That is you equals two X plus one. So that do you is to DX. And now we can rewrite this integral in terms of you, which is one half times the integral of the square root of you and notice how we replace two x plus one by you. So now all we have to do is integrate thes square root of you, which is the same as integrating the square root of X. And this should not be DX. That should be. Do you well, the square root of you is you to the one half. So when we integrate this, we get that this is one half times to over three times you to the three halfs plus c. These twos cancel giving us one third times you to the three halfs, which is two x plus one to the three halfs plus C, and that completes the problem

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