Linear Algebra For Dummies
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In Calculus, you can use variable substitution to evaluate a complex integral. Variable substitution allows you to integrate when the Sum Rule, Constant Multiple Rule, and Power Rule don’t work.

  1. Declare a variable u, set it equal to an algebraic expression that appears in the integral, and then substitute u for this expression in the integral.

  2. Differentiate u to find

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    and then isolate all x variables on one side of the equal sign.

  3. Make another substitution to change dx and all other occurrences of x in the integral to an expression that includes du.

  4. Integrate by using u as your new variable of integration.

  5. Express this answer in terms of x.

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Mary Jane Sterling taught algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of several For Dummies books, including Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.

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