## Integrals of Trigonometric Functions

The integrals of trigonometric functions can be extremely difficult to find. At this point, you should already be convinced that integration is much harder than differentiation. Any combination of products and quotients of trigonometric functions can be differentiated by studiously following the Product Rule and the Quotient Rule. As long as you try, you will find an answer. The same does not stand for integration. Only an extremely limited portion of trigonometric functions can be integrated.

The ones that can be integrated (using methods I'm familiar with) fall into four categories:

1. The integrand (the shit inside the integral sign) can be written as h'(x)F'(h(x)). Such integrals can be tackled using the Substitution Rule, the integral equivalent of the chain rule. LOOK RIGHT.

2. Those on which integration by parts works. If you don't know what that is, we got a link to it on the home page for integral calculus.

3. Derivatives of the six simple trig functions. Not much explanation is required here. The indefinite integral of cos(x) is just sin(x)+C. The indefinite integral of sec(x)^2 is tan(x)+C. (C is some constant. )

4. Derivatives of the six inverse trig functions. Shit like 1/1+x^2 can be integrated IF you recognize it as a derivative as arctan(x). Chances are that you have forgotten those exotic differentiation formulas. Don't worry.

The ones that can be integrated (using methods I'm familiar with) fall into four categories:

1. The integrand (the shit inside the integral sign) can be written as h'(x)F'(h(x)). Such integrals can be tackled using the Substitution Rule, the integral equivalent of the chain rule. LOOK RIGHT.

2. Those on which integration by parts works. If you don't know what that is, we got a link to it on the home page for integral calculus.

3. Derivatives of the six simple trig functions. Not much explanation is required here. The indefinite integral of cos(x) is just sin(x)+C. The indefinite integral of sec(x)^2 is tan(x)+C. (C is some constant. )

4. Derivatives of the six inverse trig functions. Shit like 1/1+x^2 can be integrated IF you recognize it as a derivative as arctan(x). Chances are that you have forgotten those exotic differentiation formulas. Don't worry.