On-line Math 21

3.1  Trigonometric functions

3.1.5  Integrals of trig functions and their inverses

Parts of this list are simply a re-writing of the basic formulas for the derivatives of trigonometric functions as indefinite integrals. Other parts are much more difficult integrals which take sophisticated techniques of integration to explain. Some of those techniques you'll see this semester, but others will wait until next semester. There are a few basic trig functions whose integrals are not listed, but those are just the cosecant and the cotangent, which are similar to the secant and tangent, and not used very often.

1. 
   

   ó õ sin(x)dx = -cos(x)+C

2. 
   

   ó õ cos(x)dx = sin(x)+C

3. 
   

   ó õ tan(x)dx = ln|sec(x)|+C

4. 
   

   ó õ sec(x)dx = ln|sec(x)+tan(x)|+C

5. 
   

   ó õ 1 Ö 1-x2 dx = sin-1(x)+C = arcsin(x)+C

6. 
   

   ó õ 1 1+x2 dx = tan-1(x)+C = arctan(x)+C

7. 
   

   ó õ 1 |x| Ö x2-1 dx = sec-1(x)+C

Copyright (c) 2000 by David L. Johnson.