Integration of cos 3(cubed) x dx (1 Viewer)

[Irskin]

Can anyone please help me out in re-arranging this question, using trig results/identities to make the integration simple??? Cheers

 

[Trev]

int. cos³x dx
since cos²x=1-sin²x
Integral becomes:
int. cosx(sin²x-1) dx
You should be able to do the rest just by looking at it or using the substitution u=sinx.

 

[pLuvia]

int[cos³x]dx
Let u=sinx du=cosxdx
int[cos²x]du
int[1-u²]du
=u-1/3u³+C
=sinx-1/3sin³x+C

 

[shinji]

hmm. i thought we weren't expected to learn the integral of cos³x in 3unit maths..... besdides the onse where you have the 2 trig functions beside eachother.
i.e: sinx.cos²x ds

 

[SoulSearcher]

It can also be done by letting cos³x = 1/4 (cos 3x + 3cos x), but it is easier to just use the substitution method with u = sin x

 

[Mountain.Dew]

peoples, not to worry...in the HSC exams, they break the question into parts, e.g. get u to do a differential, maybe show that cos³x dx = cosxsin²x - cosx, THEN get u to do the intergation.

this makes the question easier to do, particularly since it is the 2U and 3U level.

 

[housemouse]

I think IBP is a valid method

 

[pLuvia]

That would take longer though. But if you're really desparate