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Evaluate the integral. $ \displaystyle \int \f…

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Problem 15 Easy Difficulty

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


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WZ

Wen Zheng

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Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Related Topics

Integration Techniques

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01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

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Video Transcript

So here we are given examples of certain integral and this is in the form of partial fraction decomposition. So you have to do that process. Yeah. Which is equivalent to a over X plus B over X plus two or A and D are constants. Mhm Okay, so let's multiply both sides by X and x plus two. So this would be x minus one equals A times X plus two plus B times x. So let's group terms together. So A plus B, X plus two, A plus B. So we can see by just coefficients, A plus B is equivalent to one to A plus B equals negative one. So negative A minus B equals negative one. So A is equivalent to negative choose. So it is equivalent to negative to be would be equivalent to three in this case. So now we can apply our integral directly. So a was negative negative two. So negative two over X. Which is just a constant plus three over X plus two T X. So this is equivalent to negative two natural log of X Plus three. Natural log of a. Yeah exposed to. So this would be the same thing as the natural log of X to the -2. Which would be X In this form plus three natural log of X plus two. Or we can write as the que perform plus our integration constant. And this gives our final answer

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Calculus: Early Transcendentals

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Top Calculus 2 / BC Educators
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Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:53

Integration Techniques - Intro

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

Video Thumbnail

27:53

Basic Techniques

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

Join Course
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