Study Guide

# Indefinite Integrals - Integrating Definite Integrals

## Integrating Definite Integrals

More good news about integrating by partial fractions: there's only one way to integrate definite integrals.

1. Find an antiderivative of the integrand.

2. 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 ba

We've already seen that when integrating rational functions, we more often than not get an answer with some logarithms in it. These should be pretty useful then for simplifying our answers.