# Indefinite Integrals Topics

## Indefinite Integrals explanations, examples, practice problems. Ready? Let’s do this.

#### Indefinite Integrals Introduction

In this unit, we'll discuss techniques for finding integrals, both definite and indefinite. The first technique, integration by substitution, is a way of thinking backwards. Then we'll directly a...

#### Integration by Substitution: Indefinite Integrals

Integration by substitution is a way of undoing the chain rule. This is a once-in-a-lifetime opportunity to learn derivatives inside and out, forwards and backwards. Exciting, eh? Learning integr...

#### Integration by Substitution: Definite Integrals

Be Careful: There are two ways to use substitution to evaluate definite integrals. When evaluating a definite integral, make sure you know which way you're using them. Way 1: First integrate the...

#### Integration by Parts: Indefinite Integrals

We can think of integration by parts as a way to undo the product rule. While integration by substitution lets us find antiderivatives of functions that came from the chain rule, integration by p...

#### Integration by Parts: Definite Integrals

As with integration by substitution, there are two distinct ways to integrate definite integrals using integration by parts. As with integration by substitution, we have to be careful not to mix...

#### Integration by Partial Fractions

Integration by partial fractions is a technique we can use to integrate rational functions when the degree of the numerator is less than the degree of the denominator. Here's the big picture:We s...

#### Integrating Definite Integrals

More good news about integrating by partial fractions: there's only one way to integrate definite integrals. Find an antiderivative of the integrand. Use the Fundamental Theorem of Ca...

#### Choosing an Integration Method

We've been learning the different methods of integration in a very artificial environment. We know that if we're in the "Integration by Substitution" section, we use substitution. If we're in the...

#### Improper Integrals

We'd like to introduce a couple of new words to help us talk about limits. If you're rusty on how limits work, we recommend reviewing them.When a limit exists and equals L, we say that limit conv...

#### Comparing Improper Integrals

Usually it's more important to know whether an improper integral converges than it is to know what it converges to. We can often figure out whether an improper integral converges or diverges by c...

#### In the Real World

We'll be honest: a lot of the mechanical integration methods you're learning here probably won't be that useful in the long run. Once you get out of school and into a real-life situation, you'll...