Set u = sec (8x) + tan(8 - x). • Step 1: ● ● ● du dx Step 2: = dx = Step 3: 8( sec (8x tan (8x)) + sec² (82)) du 8( sec (8z tan (8z + sec² (87)))) . . ec² (8 x) + sec(8 - x) · tan(8 - x) sec(8 x) + tan(8 - x) =))₁ dx = = = fo(u)du with g(u) = 1 8u G(u) + C with G(u) = F(x) + C with F(x)= = 1 In sec (82) + tan(z) |
Set u = sec (8x) + tan(8 - x). • Step 1: ● ● ● du dx Step 2: = dx = Step 3: 8( sec (8x tan (8x)) + sec² (82)) du 8( sec (8z tan (8z + sec² (87)))) . . ec² (8 x) + sec(8 - x) · tan(8 - x) sec(8 x) + tan(8 - x) =))₁ dx = = = fo(u)du with g(u) = 1 8u G(u) + C with G(u) = F(x) + C with F(x)= = 1 In sec (82) + tan(z) |
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
Please find G(u) + C and correct if any answers are wrong.
![### Integration Example
**Set \( u = \sec(8 \cdot x) + \tan(8 \cdot x) \).**
**Step 1:**
\[
\frac{du}{dx} = 8\left(\sec(8x) \tan(8x)\right) + \sec^2(8x)
\]
**Step 2:**
\[
dx = \frac{du}{8\left(\sec(8x) \tan(8x) + \sec^2(8x)\right)}
\]
**Step 3:**
\[
\int \left(\frac{\sec^2(8 \cdot x) + \sec(8 \cdot x) \cdot \tan(8 \cdot x)}{\sec(8 \cdot x) + \tan(8 \cdot x)}\right) dx = \int g(u) \, du
\]
### Where:
- \( g(u) = \frac{1}{8u} \)
\[
= G(u) + C
\]
Where:
- \( G(u) = \)
\[
= F(x) + C
\]
Where:
- \( F(x) = \frac{1}{8} \ln |\sec(8x) + \tan(x)| \)
---
### Part 2:
Use the above to help you integrate the expression provided. Follow the steps outlined to achieve the solution effectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb555586-9f31-4c15-934a-3aec181a2382%2F6ee0f74a-dbf4-46ee-9072-5eaae67f0cca%2Fht1s7mo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Integration Example
**Set \( u = \sec(8 \cdot x) + \tan(8 \cdot x) \).**
**Step 1:**
\[
\frac{du}{dx} = 8\left(\sec(8x) \tan(8x)\right) + \sec^2(8x)
\]
**Step 2:**
\[
dx = \frac{du}{8\left(\sec(8x) \tan(8x) + \sec^2(8x)\right)}
\]
**Step 3:**
\[
\int \left(\frac{\sec^2(8 \cdot x) + \sec(8 \cdot x) \cdot \tan(8 \cdot x)}{\sec(8 \cdot x) + \tan(8 \cdot x)}\right) dx = \int g(u) \, du
\]
### Where:
- \( g(u) = \frac{1}{8u} \)
\[
= G(u) + C
\]
Where:
- \( G(u) = \)
\[
= F(x) + C
\]
Where:
- \( F(x) = \frac{1}{8} \ln |\sec(8x) + \tan(x)| \)
---
### Part 2:
Use the above to help you integrate the expression provided. Follow the steps outlined to achieve the solution effectively.
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