We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
Indefinite Integrals

Indefinite Integrals

At a Glance - 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.

Example 1

Find


Exercise 1

Integrate.


Exercise 2

Integrate.


Exercise 3

Integrate.


People who Shmooped this also Shmooped...