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This page introduces us to Integration by Partial Fractions. This process often results in a situation requiring the natural logarithm and hence, some knowledge of its inverse, the Euler constant. That being the case, a brief overview of those concepts would be appropriate at this time. In the links directly below, James Tanton first illustrates Euler’s constant (e), relating it to the compound interest formula. This is followed by the derivation of Euler’s Formula by means other than the Taylor Series; although this is not a requirement at the high school level, it is nonetheless very enlightening and should be viewed by all. Beneath Tanton’s offerings are two additional links, one providing an overview of the natural logarithm; the final link directly below provides a description of Integration by Partial Fractions. A small investment of time spent in each of these will serve us well as we proceed on through this process.

Euler’s Constant “e”

Deriving Euler’s Formula

Natural Logarithm

Integration by Partial Fractions

The link below contains 23 pages of hand-written notes describing the Integration of Rational Functions. The focus of these notes is centered on the decomposition of rational functions into the sum of partial fractions; all but one of the examples chosen require the introduction of the natural logarithm to the integration process. For this reason, the first several pages in this set of notes focus on that function and its inverse, y = e^x. The example shown on pages 20 and 21 does not require the natural logarithm; it is integrated by Trigonometric substitution instead, a process that will be explained at a later date. For now we will work towards the mastery of Integration by Partial Fractions.

Integration by Partial Fractions – Samuelson

Visit my Introduction to Integral Calculus to view the entire process of integration as it progresses from the Power Rule, Integration by Parts and finally, the method of Partial Fractions. The process of Integration by Trigonometric Substitution will be added to this in the near future.