Calculus Workbook For Dummies with Online Practice
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You'll find that there are many ways to solve an integration problem in calculus. The following list contains some handy points to remember when using different integration techniques:

  • Guess and Check. This technique works when the integrand is close to a simple backward derivative.

  • u-substitution. The integration counterpart to the chain rule; use this technique when the argument of the function you're integrating is more than a simple x.

  • Integration by Parts. Integration's counterpart to the product rule.

    1. Use this technique when the integrand contains a product of functions.

    2. Pick your u according to LIATE, box it, "7" it, finish it.

  • Trig Integrals

    1. Use Pythagorean identities.


    2. Use half-angle formulas.

  • Trigonometric Substitution. This method works when the integrand contains radicals of the forms


    (or powers of these roots), where a is a constant and u is an expression in x.

  • Partial Fractions. This technique works for rational functions (one polynomial over another).


About This Article

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About the book author:

Mark Ryan has taught pre-algebra through calculus for more than 25 years. In 1997, he founded The Math Center in Winnetka, Illinois, where he teaches junior high and high school mathematics courses and standardized test prep classes. He also does extensive one-on-one tutoring. He is a member of the Authors Guild and the National Council of Teachers of Mathematics. Ryan is the author of Calculus For Dummies, Calculus Workbook For Dummies, and Geometry Workbook For Dummies.

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