Basic Rules Box FTC sum rule constant rule • u-sub A.D. of x" A.D. of e A.D. of er A.D. of cos(x) A.D. of sin(r) A.D. of sec2 (x) • A.D. of (1+r²)-1 A.D. of b A.D. of r-1 Problem 1 Determine the value of the following indefinite integral. Any basic rule from the basic rules box must be cited in your solution. Also, don't forget any +C if it is needed. |2 sin(2 + 3)dr
Basic Rules Box FTC sum rule constant rule • u-sub A.D. of x" A.D. of e A.D. of er A.D. of cos(x) A.D. of sin(r) A.D. of sec2 (x) • A.D. of (1+r²)-1 A.D. of b A.D. of r-1 Problem 1 Determine the value of the following indefinite integral. Any basic rule from the basic rules box must be cited in your solution. Also, don't forget any +C if it is needed. |2 sin(2 + 3)dr
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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![### Basic Rules Box
- **FTC**
- **u-sub**
- **A.D. of \( e^{cx} \)**
- **A.D. of \( \sec^2(x) \)**
- **A.D. of \( x^{-1} \)**
---
- **sum rule**
- **A.D. of \( x^n \)**
- **A.D. of \( \cos(x) \)**
- **A.D. of \( (1 + x^2)^{-1} \)**
---
- **constant rule**
- **A.D. of \( e^x \)**
- **A.D. of \( \sin(x) \)**
- **A.D. of \( b^x \)**
---
### Problem 1
Determine the value of the following indefinite integral. Any basic rule from the basic rules box must be cited in your solution. Also, don’t forget any \( +C \) if it is needed.
\[
\int x^2 \sin(x^3 + 3) \, dx
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7eb15497-3c98-472f-9a52-7d6cb2685e6e%2F0a94bbd0-fd91-422c-bf2e-df357bd3faa2%2Fal0mvs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Basic Rules Box
- **FTC**
- **u-sub**
- **A.D. of \( e^{cx} \)**
- **A.D. of \( \sec^2(x) \)**
- **A.D. of \( x^{-1} \)**
---
- **sum rule**
- **A.D. of \( x^n \)**
- **A.D. of \( \cos(x) \)**
- **A.D. of \( (1 + x^2)^{-1} \)**
---
- **constant rule**
- **A.D. of \( e^x \)**
- **A.D. of \( \sin(x) \)**
- **A.D. of \( b^x \)**
---
### Problem 1
Determine the value of the following indefinite integral. Any basic rule from the basic rules box must be cited in your solution. Also, don’t forget any \( +C \) if it is needed.
\[
\int x^2 \sin(x^3 + 3) \, dx
\]
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