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 .Click HERE to see a detailed solution to problem 1.

*PROBLEM 2 :*Integrate .Click HERE to see a detailed solution to problem 2.

*PROBLEM 3 :*Integrate .Click HERE to see a detailed solution to problem 3.

*PROBLEM 4 :*Integrate .Click HERE to see a detailed solution to problem 4.

*PROBLEM 5 :*Integrate .Click HERE to see a detailed solution to problem 5.

*PROBLEM 6 :*Integrate .Click HERE to see a detailed solution to problem 6.

*PROBLEM 7 :*Integrate .Click HERE to see a detailed solution to problem 7.

*PROBLEM 8 :*Integrate .Click HERE to see a detailed solution to problem 8.

*PROBLEM 9 :*Integrate .Click HERE to see a detailed solution to problem 9.

*PROBLEM 10 :*Integrate .Click HERE to see a detailed solution to problem 10.

*PROBLEM 11 :*Integrate .Click HERE to see a detailed solution to problem 11.

*PROBLEM 12 :*Integrate .Click HERE to see a detailed solution to problem 12.

*PROBLEM 13 :*IntegrateClick HERE to see a detailed solution to problem 13.

*PROBLEM 14 :*Integrate .Click HERE to see a detailed solution to problem 14.

*PROBLEM 15 :*Integrate .Click HERE to see a detailed solution to problem 15.

*PROBLEM 16 :*Integrate .Click HERE to see a detailed solution to problem 16.

*PROBLEM 17 :*Integrate .Click HERE to see a detailed solution to problem 17.

*PROBLEM 18 :*Integrate .Click HERE to see a detailed solution to problem 18.

*PROBLEM 19 :*Integrate .Click HERE to see a detailed solution to problem 19.

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

*PROBLEM 20 :*Integrate .Click HERE to see a detailed solution to problem 20.

*PROBLEM 21 :*Integrate .Click HERE to see a detailed solution to problem 21.

*PROBLEM 22 :*Integrate .Click HERE to see a detailed solution to problem 22.

*PROBLEM 23 :*Integrate .Click HERE to see a detailed solution to problem 23.

*PROBLEM 24 :*Integrate .Click HERE to see a detailed solution to problem 24.

*PROBLEM 25 :*Integrate .Click HERE to see a detailed solution to problem 25.

*PROBLEM 26 :*Integrate .Click HERE to see a detailed solution to problem 26.

*PROBLEM 27 :*Integrate .Click HERE to see a detailed solution to problem 27.

Your comments and suggestions are welcome. Please e-mail any correspondence to Duane Kouba by clicking on the following address :

Duane Kouba 2000-04-18