#Indefinite Integrals of Sums, Differences, and Constant Multiples

#Table of Contents

Introduction
Integrating Sums and Differences
Integrating Constant Multiples
Combining Rules
Simplifying Expressions
Practice Questions
Glossary
Summary and Key Takeaways

#Introduction

In calculus, integrating sums, differences, and constant multiples of functions is a fundamental skill. This guide will help you understand how to handle these types of integrals, providing rules, examples, and practice questions.

#Integrating Sums and Differences

#Key Concept

When integrating sums or differences of functions, the integral is simply the sum or difference of the integrals of the individual functions.

$\int \left( f(x) \pm g(x) \right) , dx = \int f(x) , dx \pm \int g(x) , dx$

**Example:**

\int \left( x^2 + \cos x \right) \, dx = \int x^2 \, dx + \int \cos x \, dx = \frac{1}{3} x^3 + \sin x + C

Note: We still only need a single constant of integration, $C$ .

Common Mistake

Common Mistake: Products and quotients of functions cannot be integrated by separating terms like s...

Previous Topic - Derivatives & Antiderivatives Next Topic - Constant of Integration

Integration & Antiderivatives

Emily Davis

#Indefinite Integrals of Sums, Differences, and Constant Multiples

#Table of Contents

#Introduction

#Integrating Sums and Differences

#Key Concept

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