Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Evaluate the integral.

$ \displaystyle \int \frac{dx}{x \ln x - x} $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by J Hardin

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

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.

01:09

01:17

Evaluate the integral.…

01:20

01:07

Evaluate the integrals.

01:33

02:27

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.

View More Answers From This Book

Find Another Textbook

02:02

3-b. A stone is thrown vertically upward with a velocity of 40 m/s. What is …

03:03

In a Piggy Bank the number of 25 paise coins are five times the number of 50…

01:43

If two different dices rolled together calculate probablity of even number o…

01:21

A sample data set with a mean of 685 and a standard deviation of 39.8 has a …

02:30

A floral design on a floor is made up of 16 tiles which are triangular the s…

01:02

Find the dimensions of the cuboid which are in the ratio5:3:1 and its total …

02:57

Man has rope of length 660 mtr to fence a area , what is the max area he can…

02:15

When a certain number is multiplied by 7, the product consists entirely of f…

02:24

Find the mean of all prime numbers between 50 and 80

02:34

find zeros of polynomial P(x) = 6x square - 19 X + 15 verify the relationsh…