How can I integrate (cos(x))^4 using trigonometric identities?

[kasse]

I want to integrate (cos(x))^4, but I can't find a formula for (cos(x))^n in my collection.

What is the way to integrate this?

 

[siddharth]

I want to integrate (cos(x))^4, but I can't find a formula for (cos(x))^n in my collection.

What is the way to integrate this?

This site should help you.
http://www.sosmath.com/calculus/integration/powerproduct/powerproduct.html

 

[christianjb]

Here's one way
Use the identity cos^2(x)=(1+cos(2x))/2

Then

cos^4(x)=cos^2(x)*cos^2(x) = (1+2cos(2x)+cos^2(2x))/4
=(1+2cos(2x)+1/2+1/2cos(4x))/4
=(3+4cos(2x)+cos(4x))/8