Question

find the indefinite integral of cos^3(12x)

Answer 1

@wio can you help me please?

Answer 2

whta's the range?

Answer 3

Not provided.

Answer 4

idk then, my friend is good at this, I forgot this stuff..

Answer 5

can you take him in?

Answer 6

tag him in this question I mean

Answer 7

I'll give a tip and say this is a tedious integration by parts problem I think.

Answer 8

Looool, thanks anyways for your tip :).

Answer 9

@surjithayer try this

Answer 10

Wait it's easy, if I gave you \[\int cos^2(12x)cos(12x) dx\]
That help

Answer 11

and then integration by parts?

Answer 12

Not quite what do you know cos^2 is equal to?

Answer 13

\[\cos 3x=4\cos ^3x-3\cos x\]
\[\cos ^3x=\frac{ 1 }{4 }\left( \cos 3x+3\cos x \right)\]

Answer 14

I know that cos^2(x) = 1- sin^2(x)

Answer 15

@FibonacciChick666

Answer 16

Yup

Answer 17

Wow, that actually makes it easier. Do wut Chick said!

Answer 18

So plug that in place then just do u sub no parts needed

Answer 19

It's...It's almost like cheatin...In math. :o

Answer 20

\[\cos ^3\left( 12x \right)=\frac{ 1 }{4 }\left\{ \cos \left( 36x \right)+3\cos \left( 12x \right) \right\}\]

Answer 21

so cos^2(12x)(cos(x) = (1-sin^2(12x))(cos(x)? and then let u = cos x?

Answer 22

@FibonacciChick666

Answer 23

Distribute first

Answer 24

can you solve it please? Thank you

Answer 25

Then separate the integrals and yes cos for u

Answer 26

Sorry sin for u not cos

Answer 27

how do I treat the 12 that is in the sine function?

Answer 28

Just another sub make it w or something

Answer 29

If you show me your steps, it's easier to assist

Answer 30

oh okay! Thanks I can take it on from here. It was the 12x that was ruining my day.

Answer 31

oh yea, just a basic whats its deriv, then pull out the constant

Answer 32

np and avoid integration by parts when possible, it's long and annoying

Answer 33

I will divide by 12 and integrate it as if the inside was an x. Thanks.

Answer 34

But I wanna ask, could this be done using integration by parts?

Answer 35

yupppers, just make sure you do your substitutions right

Answer 36

hmm, not easily

Answer 37

\[u=Cos^2(12x) ~~~~~~~~~~~~~~~~~~dv=Cos(12x)\]
\[du=24cos12xsin12xdx~~~~~~~~~~~~v=1/12sin12x\]

It be very messy and You'd end up with almost the exact same thing

Answer 38

as that simple sub.

Answer 39

Oh okay thank you very much again.

Answer 40

np have a good one

Answer 41

u 2 :)

Answer 42

\[\int\limits \cos ^3(12x) dx=\frac{ 1 }{ 4 } \int\limits \left( \cos \left( 36x \right)+3\cos \left( 12x \right) \right)dx\]
\[=\frac{ 1 }{ 4 }\left[ \frac{ \sin 36x }{36 }+3\frac{ \sin 12x }{12 } \right]+c\]

Answer 43

Assuming the identity is right, that would work too^