Basic FormulasFamiliarity with the following fundamental integration formulas is essential.
 For quick and easy reference, here is a Word document of the Basic Formulas to print.
The following examples follow the preceding formulas. Whenever u is a function of x, we define du to be u'(x)dx. The u-substitution technique is an important problem-solving tool for integrals. *If you have a Windows computer, the text will not properly line up with the examples. We apologize for the inconvenience. |
||||
EXAMPLE 1  EXAMPLE 2  EXAMPLE 3  EXAMPLE 4  EXAMPLE 5  |
POINTERS • Remove all exponents from denominator by rewriting them in the numerator. • Separate the different terms into individual integrals. Also, factor out coefficients. • Apply Formula 3. Don't forget to add C at the end. • Multiply the numerator by 2 and factor out (1/2). This allows the numerator to represent the derivative of the denominator. • Apply the u-substitution. • Apply Formula 4. • Recognize that this integral can be rearranged so that Formula 18 can be applied. • Apply the u-substitution. • Apply Formula 18. • Apply the u-substitution. • Apply Formula 6. • Factor out (1/9) so that Formula 18 can be applied. • Apply the u-substitution. • Apply Formula 18. |
|||
