Internet Resources for the Calculus Student

Techniques of Integration

See Techniques of Integration : Substitution and Techniques of Integration : Integration by Parts, from the extensive S.O.S. MATHematics site.

Also see Review of Integration Techniques from Oregon State University's extensive Web Study Guide for Vector Calculus site. Substitution, parts, and the integration of rational functions are discussed. There is also a table of common integrals.

Information on integrating the trig functions can be found at Trigonometric Integrals .

An algebraic trick that is often useful for dealing with integration of rational functions is to express them as sums of simpler terms by means of the "Partial Fractions" decomposition.
See The Method of Partial Fractions, from S.O.S. MATHematics.

Also see The Method of Partial Fractions, from the Review of Algebra Techniques, part of Oregon State University's extensive Web Study Guide project.

The University of Saskatchewan's Exercises in Math Readiness (EMR) site has a section on Partial Fraction Decompositions. Included are an introduction and three sets of exercises : Introductory, Moderate, and Advanced.

Despite all these tools, finding exact antiderivatives is not always easy - or even possible!

Some people enjoy the "game" or "puzzle" aspect of this subject, and even if you don't enjoy it, an understanding of the techniques can be important for understanding how and why things work in various applications of the calculus.

But if you just want to find or check an answer, then for many cases it may be more convenient to use a computer algebra system such as Mathematica (which will do integrals for you on-line at its "Integrator" web site), or Maple (for which there is an on-line interface at SFU).

Our "raw list" of links without comment may include more sites of interest that we haven't yet referred to here.

If you have come across any other good web-based illustrations of these and related concepts,
     please do let us know and we will add them here.