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How to Solve Integrals with Variable Substitution

Part of the Calculus II For Dummies Cheat Sheet

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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