# How do you intergrate cos^3 [x] .dx

1. Apr 21, 2004

### suddy72

could some one please show me the steps to doing this ??

2. Apr 21, 2004

### HallsofIvy

Staff Emeritus
$\int cos^3(x)dx$ is a standard problem. Anytime you have an odd power of either sin or cos take one of the out to match with the dx:

$$\int(cos^2(x))(cos(x)dx)$$

Now we can use $sin^2(x)+ cos^2(x)= 1$ to convert to the other trig function:

$$\int(1- sin^2(x))(cos(x)dx)$$

and, of course, the whole reason for taking out that orginal "cos(x)" is that
d(sin(x))= cos(x)dx.

Let u= sin(x). Then du= cos(x)dx and the integral is

$$\int(1-u^2)du$$
and that should be easy.

Last edited: Apr 21, 2004
3. Apr 22, 2004

### Xishan

Well, I beg your forgiveness for this question b/c its really an irrelevant one.

Can you please tell me how you use these mathematical symbols like integral sign and superscripts etc in your messages?

4. Apr 22, 2004

### deltabourne

It's called LaTex Math Typesetting and is really pretty cool. Check out this thread for more information: