23. (In x)² dx

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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Can you help me solve 23 using integration by parts? Thank you!
### Calculus: Integration Practice Problems

Below is a list of integral problems commonly found in the study of calculus. These integrals range from functions involving exponential terms to logarithmic and inverse trigonometric functions. Solve each problem using appropriate integration techniques such as integration by parts, substitution, or known integral formulas.

#### Problems:

**15.** \[\int e^{-x} \sin x \, dx\]

**17.** \[\boxed{\int e^{-5x} \sin x \, dx}\]

**19.** \[\int x \ln x \, dx\]

**21.** \[\int x^2 \ln x \, dx\]

**23.** \[\int (\ln x)^2 \, dx\]

**25.** \[\int \cos^{-1} x \, dx\]

**27.** \[\int \sec^{-1} x \, dx\]

These integral problems are designed to test your understanding of various integration methods. Use this as an opportunity to practice integration techniques and to deepen your comprehension of calculus concepts.
Transcribed Image Text:### Calculus: Integration Practice Problems Below is a list of integral problems commonly found in the study of calculus. These integrals range from functions involving exponential terms to logarithmic and inverse trigonometric functions. Solve each problem using appropriate integration techniques such as integration by parts, substitution, or known integral formulas. #### Problems: **15.** \[\int e^{-x} \sin x \, dx\] **17.** \[\boxed{\int e^{-5x} \sin x \, dx}\] **19.** \[\int x \ln x \, dx\] **21.** \[\int x^2 \ln x \, dx\] **23.** \[\int (\ln x)^2 \, dx\] **25.** \[\int \cos^{-1} x \, dx\] **27.** \[\int \sec^{-1} x \, dx\] These integral problems are designed to test your understanding of various integration methods. Use this as an opportunity to practice integration techniques and to deepen your comprehension of calculus concepts.
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