Download the App!

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

Use Exercise 51 to find $ \displaystyle \int (\ln x)^3 dx $.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$x(\ln x)^{3}-3 x(\ln x)^{2}+6 x(\ln x)-6 x+C$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Integration Techniques

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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.

04:28

Use Exercise 57 to find $\…

01:07

Use the method of exercise…

06:06

Use Exercise 39 to find $\…

05:03

Use Exercise 29 to find $\…

03:01

Use Exercise 35 to find $\…

01:02

01:43

02:59

Use Exercise 52 to find $ …

03:31

Use integration by parts t…

03:04

Calculate.$$\int \frac…

01:05

Evaluate the given integra…

The problem is, is exercise 51 to find the integral of x to the race power. Dx exercise 51 tells us its integral of x to x, power. Dx is equal to x times our x to power minus n times integral of x, 2 minus 1 d. Now, just let n is equal to 3. We have integral of x to 3 power d x, is equal to x times x, to there is power, minus 3 integral of x, 22 dx and and is equal to 2 by half integral of index to those power d x is equal to x times, nx To square minus 2 times integral of pont and the light and is equal to 1 by integral of x, is equal to x, x, minus integral of a thesis. But now we have a plus constant embraceth integral of x squared. So this is equal to x, x, square minus 2 times x, x, minus x, posions number c, and then this is equal to x, 1 x to 3 power minus 3 times this. While here this is x, x, square minus 2 x on x, plus 2 x- and there are some constant number- this is.

View More Answers From This Book

Find Another Textbook