Trigonometric Substitutions

F. TRIGONOMETRIC SUBSTITUTIONS

If the simple substitutions corresponding to the basic formulas I-XII do not work, look for a trigonometric substitution. Trigonometric substitutions correspond to the formulas for derivatives of the inverse trigonometric functions. We have not asked you to memorize these formulas, because it is easier to remember the method of trigonometric substitution. The three trigonometric substitutions can be remembered by drawing right triangles. They are shown once more in Figure 8.9.1 They often result in an integral of powers of trigonometric functions of 6.

Figure 8.9.1

Clue: If an integral contains , , or , draw a triangle and label its sides so that it can be used to find the appropriate trigonometric substitution.