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Magazine Problem 81
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may be done using techniques of integration learned previously.) $$ \int \sin x \cos x d x $$
Problem 82
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may be done using techniques of integration learned previously.) $$ \int \cos ^{5} x d x $$
Problem 83
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may be done using techniques of integration learned previously.) $$ \int \sin ^{5} x \cos ^{2} x d x $$
Problem 84
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may be done using techniques of integration learned previously.) $$ \int \sin ^{3} x \cos ^{3} x d x $$
Problem 85
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may be done using techniques of integration learned previously.) $$ \int \sqrt{\sin x} \cos x d x $$
Problem 86
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may be done using techniques of integration learned previously.) $$ \int \sqrt{\sin x} \cos ^{3} x d x $$
Problem 87
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may be done using techniques of integration learned previously.) $$ \int \sec x \tan x d x $$
Problem 88
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may be done using techniques of integration learned previously.) $$ \int \tan (5 x) d x $$
Problem 89
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may be done using techniques of integration learned previously.) $$ \int \tan ^{2} x \sec x d x $$
Problem 90
Compute the following integrals using the guidelines for integrating powers of trigonometric functions. Use a CAS to check the solutions. (Note: Some of the problems may be done using techniques of integration learned previously.) $$ \int \tan x \sec ^{3} x d x $$
