Download the App!

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

First make a substitution and then use integration by parts to evaluate the integral.

$ \displaystyle \int x \ln (1 + x) dx $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$\frac{1}{2}\left(x^{2}-1\right) \ln (1+x)-\frac{1}{4} x^{2}+\frac{1}{2} x+\frac{3}{4}+C$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Integration Techniques

Missouri State University

Oregon State University

University of Michigan - Ann Arbor

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.

10:04

First make a substitution …

06:26

11:07

Find indefinite integral.<…

06:16

02:58

Use integration by parts t…

05:52

Evaluate $\int \frac{(\ln …

02:49

03:38

Find or evaluate the integ…

problem is first making a substitution on DH then used contribution. Of course to you Violet. Inventive girl. Inte grow ex terms. How in one class? Ax the ax with this problem. First we can use new substitution. But why Physical too? One plus six. Why? If you go to now is this into You know it's got you into Girl X is equal to y minus wants It is wine. One Ham's one. Why do you want? And then we can use the integration by parts to you. Violet. Just this integral the foreigner is into girl. You leave from Jax. It's the cultural you have b minus in general. You're trying? Absolutely. Yes. Now for our problem, we can last you seek ritual what is equal to how and why and re prime his future wine minus one. Then new problem. If they caught you one over. Why? And wait, Huh? Have y squared minus y. Now this girl is, don't you? New taps, please. This is yeah. And why times why? Schooling minus live, then minus into girl. Your prom times resist this. My half. Why? Minus why? Why? This is coach you, huh? Why squire months why I'm spelling. Why minus the integral is cool too. One source. Why? Squire Linus? Why? And class casting number. See? And we need to convert. Why back too? The function wax This is I have X plus Juan Squire in Ones X plus one terms. Next one. Linus, my horse X plus one squire once X plus lawn, plus past number sin. This is the answer.

View More Answers From This Book

Find Another Textbook

Numerade Educator

03:21

The following data gives the number of goals scored for theMidget AAA Re…

01:24

Suppose the 1st Quartile of a data set is 50 andthe 3rd Quartile value i…

08:39

Males in the Netherlands are the tallest, on average, in theworld with a…

06:29

A.) What is the 8th term of the geometric series: 0.125, 0.5, 2,... B.) Wh…

01:46

A rich man called his seven sons. He had with him a number of his favorite b…

03:13

Each month a brokerage house studies various companies and rateseach com…

03:56

A scientist has two solutions, which she has labeled Solution Aand Solut…

02:04

Determine if the following statement is true or false.If x is in the dom…

03:37

Consider the closer curve in the xy-plane given byx^2-6x+y^3-12y=11a…

01:59

Given that cot(θ) < 0 and cos(θ) < 0, inwhich quadrant does θ lie?…