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Indefinite Integrals

Indefinite 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.

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