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

Use integration by parts to prove the reduction formula.

$ \displaystyle \int (\ln x)^n dx = x (\ln x)^n - n \displaystyle \int (\ln x)^{n - 1} dx $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Wen Zheng

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 1

Integration by Parts

Integration Techniques

Campbell University

Oregon State University

Harvey Mudd College

University of Nottingham

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.

03:18

Use integration by parts t…

00:35

01:59

01:44

01:43

problem is using that decoration my parts to prove the reduction for Miller in Toronto. And when next insp hour is, they go to X tams, the next to dance power minus and hats into girl off L. A next to Lance one. Power? No, the farmer have integration by Paris is interrupt you be prom next. Yes. They got a new past minus into your new prom with Yes. Then we can hot You got to, you know, in packs two. It's power and re prime this photo. Why, then you prom if they got to. And no one likes Two months. One over that year, we use changeable and B It's become too lax now into true love. Now, Max too in power Yaks. Is he trying to do you task Least is ex lax to his power minus into drove off you prime time sleaze. This's in terms. No, thanks. Shoot And last one's power X, this is there is sound

View More Answers From This Book

Find Another Textbook