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Mathematics 18 Online
rvc (rvc):

Integration Help please

rvc (rvc):

\[\int\limits dx/4\cos^32x-3\cos2x\]

rvc (rvc):

the answer is :\[1/6 \ \\log[\sec6x+\tan6x]+C\]

rvc (rvc):

how will i get this answer please help

OpenStudy (anonymous):

\[\int\limits\limits \frac{ 1 }{ 4\cos^3(2x)-3\cos(2x) }dx?\]

rvc (rvc):

yes

OpenStudy (rational):

look up formula of cos(3x)

rvc (rvc):

4cos^x-3cosx right?

OpenStudy (anonymous):

yeah cos^3x :)

rvc (rvc):

yeah :) sorry

OpenStudy (anonymous):

So then you can just do a u - sub and then let cos(3u) = 3cos^3(u)-3cos(u), rational you genius!

OpenStudy (anonymous):

4cos*

rvc (rvc):

so what will it be like?

OpenStudy (anonymous):

u = 2x

OpenStudy (anonymous):

then you can integrate 1/cos(3u) normaly

OpenStudy (anonymous):

\[\frac{ 1 }{ 2 } \int\limits \frac{ 1 }{ \cos(3u) }du\]

rvc (rvc):

hey its cos6x

OpenStudy (anonymous):

Just work it out and I'm sure you'll get it eventually :)

rvc (rvc):

i mean |dw:1427180856753:dw|

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