How to Integrate cos4 x Using the Double Angle Formula

[gerry7]

Homework Statement

Find the integral of cos⁴ xdx

Homework Equations

cos2x = 2cos²x-1
cos²x = (cos2x+1)/2

The Attempt at a Solution

I tried using cos⁴x = cos²x * cos²x and i simplified it to
cos⁴x = ((cos2x)² + 2cos2x + 1)/4

I'm not sure if this is right. How do i go about getting the integral of this expression if it is correct. Thanks

 

[Mark44]

So far, so good. You just need to take it one step farther, by replacing (cos2x)² with (cos4x + 1)/2. At that point you'll have an integral with four terms, and you can split this up into four integrals, each of which is pretty easy.

 

[gerry7]

Hey i got the answer (sin4x)/32 + (sin2x)/4 + (3x)/8 + C which seems to be right. Thanks for your help :)