- 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

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 Calculus.

There's also a little bit of possibly-less-than-good news: to simplify your answers to these sorts of integrals, you'll need to remember some tricks for rearranging logarithmic expressions.

- A sum of logs is the log of the product:
*ln**a*+*ln**b*=*ln*(*a*+*b*)

- A difference of logs is the log of the quotient:

- The coefficient of a log can be turned into an exponent:
*aln**b*=*ln**b*^{a}

Example 1

Find |

Exercise 1

Integrate.

Exercise 2

Integrate.

Exercise 3

Integrate.