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 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.