### INTEGRATION OF TRIGONOMETRIC INTEGRALS

Recall the definitions of the trigonometric functions.

• • • • The following indefinite integrals involve all of these well-known trigonometric functions. Some of the following trigonometry identities may be needed.

• A.) • B.) • C.) so that • D.) so that • E.) • F.) so that • G.) so that It is assumed that you are familiar with the following rules of differentiation.

• • • • • • These lead directly to the following indefinite integrals.

• 1.) • 2.) • 3.) • 4.) • 5.) • 6.) The next four indefinite integrals result from trig identities and u-substitution.

• 7.) • 8.) • 9.) • 10.) We will assume knowledge of the following well-known, basic indefinite integral formulas :

• , where is a constant • • • , where is a constant
• Most of the following problems are average. A few are challenging. Many use the method of u-substitution. Make careful and precise use of the differential notation and and be careful when arithmetically and algebraically simplifying expressions.

• PROBLEM 1 : Integrate .

• PROBLEM 2 : Integrate .

• PROBLEM 3 : Integrate .

• PROBLEM 4 : Integrate .

• PROBLEM 5 : Integrate .

• PROBLEM 6 : Integrate .

• PROBLEM 7 : Integrate .

• PROBLEM 8 : Integrate .

• PROBLEM 9 : Integrate .

• PROBLEM 10 : Integrate .

• PROBLEM 11 : Integrate .

• PROBLEM 12 : Integrate .

• PROBLEM 13 : Integrate • PROBLEM 14 : Integrate .

• PROBLEM 15 : Integrate .

• PROBLEM 16 : Integrate .

• PROBLEM 17 : Integrate .

• PROBLEM 18 : Integrate .

• PROBLEM 19 : Integrate .

Some of the following problems require the method of integration by parts. That is, .

• PROBLEM 20 : Integrate .

• PROBLEM 21 : Integrate .

• PROBLEM 22 : Integrate .

• PROBLEM 23 : Integrate .

• PROBLEM 24 : Integrate .

• PROBLEM 25 : Integrate .

• PROBLEM 26 : Integrate .

• PROBLEM 27 : Integrate .