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.
GO TO SAT PREP GO TO ACT PREP
Indefinite Integrals

Indefinite Integrals

Integration by Partial Fractions


Integration by partial fractions is a technique we can use to integrate rational functions when the degree of the numerator is less than the degree of the denominator. Here's the big picture:

  • We start out with an integral whose integrand is a rational function, like

    The degree of the numerator must be less than the degree of the denominator.
     
  • We do some sneaky stuff to rewrite the original rational function as a sum of partial fractions:

     
  • We integrate the partial fractions, whose antiderivatives all involve the natural log:

Be Careful: When x occurs in a denominator with a coefficient other than 1, you have to use integration by substitution.

People who Shmooped this also Shmooped...

Advertisement