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Evaluate the given integral.$$\int \frac{(\ln x)^{3}}{x} d x$$

$$\frac{(\ln x)^{4}}{4}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 3

The Substitution Method

Integrals

Campbell University

Oregon State University

Baylor University

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

05:14

Evaluate the integrals.

01:22

Evaluate the integral.…

04:59

Evaluate the given integra…

01:54

04:18

the derivative of Ln of X is one over acts, which is nice, because when we apply our use substitution by taking you to be Ellen of X do you becomes one over x dx, which allows us to rewrite this integral in terms of you. So this becomes the integral of you cubed, which is equal to 1/4 times you to the fourth. But U S L N of X. So this becomes 1/4 times Ellen of X to the fourth Power plus C, and that completes the problem.

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