- Topics At a Glance
- Indefinite Integrals Introduction
- Integration by Substitution: Indefinite Integrals
- Legrange (Prime) Notation
- Leibniz (Fraction) Notation
- Integration by Substitution: Definite Integrals
- Integration by Parts: Indefinite Integrals
- Some Tricks
- Integration by Parts: Definite Integrals
- Integration by Partial Fractions
- Integrating Definite Integrals
**Choosing an Integration Method**- Integration by Substitution
**Integration by Parts**- Integration by Partial Fractions
- Thinking Backwards
- Improper Integrals
- Badly Behaved Limits
- Badly Behaved Functions
- Badly Behaved Everything
- Comparing Improper Integrals
- The
*p*-Test - Finite and Infinite Areas
- Comparison with Formulas
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

Use integration by parts when the integrand factors into two things that both include the variable, but integration by substitution doesn't work!

We can use integration by parts on

because we can factor the *x*^{2} to get

and choose *u* = *x* and *v'* = *xe*^{x2}.

We wouldn't use integration by parts on

because this integral begs for substitution.