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Evaluate the given integral.$$\int \frac{3 x+2}{3 x^{2}+4 x+1} d x$$

$$\frac{1}{2} \ln \left|3 x^{2}+4 x+1\right|+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 3

The Substitution Method

Integrals

Missouri State University

Campbell University

Baylor University

University of Michigan - Ann Arbor

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.

04:21

Evaluate the integral.…

03:00

Evaluate the given integra…

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02:53

06:41

if you is equal to three X squared plus four X plus one than do you is equal to six X plus four, and we can factor out a to to get two times three X plus two the X. And now if we divide by two, we can replace three x plus two d X by do you over to. So now we can rewrite this integral as one half times the integral of one over you, do you, which is equal to one half times Ellen of the absolute value of you plus C, which is one half times Ellen of absolute value of three X squared plus four x plus one plus c, and that completes the problem.

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