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Evaluate the integral by making the given substitution.

$ \displaystyle \int \sqrt{2t + 1} \, dt $, $ u = 2t + 1 $

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01:15

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Campbell University

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

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.

02:44

Evaluate the integral.

03:11

01:52

06:02

Evaluate the integral.…

01:25

05:12

01:03

Find the indefinite integr…

02:05

we know that we've been given you is to t plus one. Therefore, we know he can write this as d'you this to d t. Which means that de t written by itself is do you divide by two or 1/2 to you? Now remember, with into girls, you can always pull out the constant like this. So one half's on the outside and truth is using the power rule the exploding increases by one divide by the new exploit which, as you can see his three over two back substitute and I remember you is never in our final answer. We're only doing that when we're doing u substitution and we have our solution.

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