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Problem 5, Verify the following: 1. fr cos(x)dx = x sin(x) + cos(x)+c 2. ſ csc(x) cot(x)dx = – csc(x) + c 3. S = arcsec(x) + c 1 x/x²–1

Problem 5, Verify the following: 1. fr cos(x)dx = x sin(x) + cos(x)+c 2. ſ csc(x) cot(x)dx = – csc(x) + c 3. S = arcsec(x) + c 1 x/x²–1

Calculus: Early Transcendentals
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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**Problem 5**, Verify the following: 1. \( \int x \cos(x) \, dx = x \sin(x) + \cos(x) + c \) 2. \( \int \csc(x) \cot(x) \, dx = -\csc(x) + c \) 3. \( \int \frac{1}{x \sqrt{x^2 - 1}} \, dx = \operatorname{arcsec}(x) + c \) In these equations, \( c \) represents the constant of integration, a common component in the results of indefinite integrals.
Transcribed Image Text:**Problem 5**, Verify the following: 1. \( \int x \cos(x) \, dx = x \sin(x) + \cos(x) + c \) 2. \( \int \csc(x) \cot(x) \, dx = -\csc(x) + c \) 3. \( \int \frac{1}{x \sqrt{x^2 - 1}} \, dx = \operatorname{arcsec}(x) + c \) In these equations, \( c \) represents the constant of integration, a common component in the results of indefinite integrals.
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