|(In 6x)2 dx ОА. x(In 6x)2 - x(In 6x) + x + C В. x(In 6x)2 + 2x(In 6x) - 2x + C с. x(In 6x)2 - 2х(In 6x) + 2x + C O D. x(In 6x)2 - 2x(In 6x) + C
|(In 6x)2 dx ОА. x(In 6x)2 - x(In 6x) + x + C В. x(In 6x)2 + 2x(In 6x) - 2x + C с. x(In 6x)2 - 2х(In 6x) + 2x + C O D. x(In 6x)2 - 2x(In 6x) + C
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![The image features a calculus problem involving integration, with multiple-choice answers provided. The integral to solve is:
\[
\int (\ln 6x)^2 \, dx
\]
The choices for the solution are as follows:
- **A.** \( x(\ln 6x)^2 - x(\ln 6x) + x + C \)
- **B.** \( x(\ln 6x)^2 + 2x(\ln 6x) - 2x + C \)
- **C.** \( x(\ln 6x)^2 - 2x(\ln 6x) + 2x + C \) (This option is highlighted, indicating it has been selected)
- **D.** \( x(\ln 6x)^2 - 2x(\ln 6x) + C \)
In the context of an educational website, this exercise tests the integration skills of students, particularly their ability to handle integrals involving the natural logarithm function squared. The inclusion of the constant \( C \) is a reminder of the indefinite nature of the integral.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43abe65f-7e5f-4ca7-a91c-ab097f3acb86%2F17141d45-94a6-4852-82ae-716d9746c51b%2Fcp106fe_processed.png&w=3840&q=75)
Transcribed Image Text:The image features a calculus problem involving integration, with multiple-choice answers provided. The integral to solve is:
\[
\int (\ln 6x)^2 \, dx
\]
The choices for the solution are as follows:
- **A.** \( x(\ln 6x)^2 - x(\ln 6x) + x + C \)
- **B.** \( x(\ln 6x)^2 + 2x(\ln 6x) - 2x + C \)
- **C.** \( x(\ln 6x)^2 - 2x(\ln 6x) + 2x + C \) (This option is highlighted, indicating it has been selected)
- **D.** \( x(\ln 6x)^2 - 2x(\ln 6x) + C \)
In the context of an educational website, this exercise tests the integration skills of students, particularly their ability to handle integrals involving the natural logarithm function squared. The inclusion of the constant \( C \) is a reminder of the indefinite nature of the integral.
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