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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.

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