quick primitive (1 Viewer)

[onebytwo]

quick question:

how to find the primitive of cos^2(3x)

do you have to first expand cos3x and then square? this is the approach ive taken but it seems a bit lengthy.
please help
thanks

 

[rama_v]

=1/2 (1 + Cos 6x)
= 1/2 (x + 1/6 Sin6x) + C

Use your trig identities - specifically, Cos 2x = 2Cos²x - 1
.: Cos²x = (1/2)(1+Cos2x)

 

[SoulSearcher]

Remember the double angle formula for cos angles,
cos 2α = 2cos²α - 1
manipulate, and you get
cos²α = 1/2 * (1 + cos 2α)
so letting α = 3x
cos²3x = 1/2 * (1 + cos 6x)
Should be easy to integrate from there.

 

[onebytwo]

sorry i dont understand your second step

 

[onebytwo]

that last message was for rama

thanks i get it