Question

Calculate. $$\int \frac{\ln x}{x} d x$$

Name: Problem 22, Chapter 8: Calculus: One Variable
Uploaded: 2021-07-31T18:06:58-08:00
Duration: 1 min 14 s
Channel: Vipender Yadav
Description: Calculate. ∫(lnx)/(x) d x

   Calculate.
$$\int \frac{\ln x}{x} d x$$

Calculus: One Variable

Garret J. Etgen,… 10th Edition

Chapter 8, Problem 22

Instant Answer

Solved by Expert Vipender Yadav

07/31/2021

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We let $u = \ln x$. Show more…

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Calculate. $$\int \frac{\ln x}{x} d x$$

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Key Concepts

Integration by Substitution

Integration by substitution is a technique used to simplify an integral by changing variables. This method transforms a complex integrand into a simpler form by recognizing a part of the expression as a derivative of another part, leveraging the inverse process of the chain rule in differentiation.

Antiderivative

An antiderivative is a function that, when differentiated, yields the original function. Finding an antiderivative involves integration and is central to solving indefinite integrals, which also include an arbitrary constant to account for all possible functions with the same derivative.

Logarithmic Functions

Logarithmic functions, particularly the natural logarithm, are fundamental in calculus due to their unique properties and frequent appearance in differentiation and integration. Understanding how to integrate expressions involving logarithms is crucial, as these types of functions often emerge in various calculus problems.

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