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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Question
![The integral shown in the image is:
\[
\int \frac{1}{\sqrt{x^2+16}} \, dx
\]
This is an example of an integral involving a radical expression where the variable \(x\) is under a square root, alongside a constant number, 16. Integrals like this often involve techniques such as trigonometric substitution or recognizing them as standard forms that resemble inverse trigonometric functions.
In particular, this integral can be solved by recognizing it as a form that leads to an inverse hyperbolic or trigonometric function. For example, this is similar to the standard integral form for \(\text{arsinh}(x)\), the inverse hyperbolic sine function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45cfe948-e5a8-4937-a1b5-8adddef7ddbc%2F4b13727c-5acc-41be-b65f-5acf4a100cd2%2Fz1xf3so_processed.png&w=3840&q=75)
Transcribed Image Text:The integral shown in the image is:
\[
\int \frac{1}{\sqrt{x^2+16}} \, dx
\]
This is an example of an integral involving a radical expression where the variable \(x\) is under a square root, alongside a constant number, 16. Integrals like this often involve techniques such as trigonometric substitution or recognizing them as standard forms that resemble inverse trigonometric functions.
In particular, this integral can be solved by recognizing it as a form that leads to an inverse hyperbolic or trigonometric function. For example, this is similar to the standard integral form for \(\text{arsinh}(x)\), the inverse hyperbolic sine function.
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