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Evaluate the integral.
$ \displaystyle \int \frac{dx}{x \ln x - x} $
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Calculus 2 / BC
Chapter 7
Techniques of Integration
Section 5
Strategy for Integration
Integration Techniques
Missouri State University
Oregon State University
Baylor University
Lectures
01:53
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.
27:53
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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Evaluate the integral.…
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Evaluate the integrals.
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Evaluate the indefinite in…
01:52
Let's start off here by just factoring the denominator. So we pull out of X and then let's do it. Use up here, you equals ln that do you is one over x gx so we can write this in a girl is one over humanise one, Do you? They do. You is equal to one over x t x. So that's taking care of this part right here, Phil. And then the U minus. Juan is taking care of the Ellen minus one. Now this we could integrate. That's just natural log. You minus one. Plus he now, if this minus one was bothering you, you can do it. A substitution here and you'LL arrive at this answer and then natural log. And finally, just come back up here and replace you with natural log of X. So we have natural lot Absolute value. Natural log X minus one closer constancy. And that's our final answer.
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