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integration C4

Not sure how to integrate cos3x/sin4x ?
can you post the full question ?
Original post by boodle123
Not sure how to integrate cos3x/sin4x ?


Do you mean cos(4x)? What you've posted is not a C4 integral.
Reply 3
Avatar for Hasufel
Hasufel
16
if this is meant to be cos(4x)/sin(4x), then use the substitution: u=sin(4x)

If it is as it stands, then you can simplify to get:

sin⁡(x)+cot⁡(4x)cos⁡(x)\sin(x)+ \cot(4x) \cos(x) for which the 2nd part you`d have to use IBP
Reply 4
Avatar for boodle123
boodle123
OP
2
Original post by ThatPerson
Do you mean cos(4x)? What you've posted is not a C4 integral.


yeah sorry i meant cos4x
Reply 5
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boodle123
OP
2
Original post by Hasufel
if this is meant to be cos(4x)/sin(4x), then use the substitution: u=sin(4x)

If it is as it stands, then you can simplify to get:

sin⁡(x)+cot⁡(4x)cos⁡(x)\sin(x)+ \cot(4x) \cos(x) for which the 2nd part you`d have to use IBP


how did you get that? I thought you could change it to 1/tan4x then integrate that
Reply 6
Avatar for Hasufel
Hasufel
16
Original post by boodle123
yeah sorry i meant cos4x


you can either use my post above, or the fact that the standard integral of cot⁡(ax)\cot(ax) is 1aln∣sin⁡(ax)∣+k\displaystyle \frac{1}{a}ln| \sin(ax)|+k
Original post by boodle123
yeah sorry i meant cos4x


Do you know what ∫cot⁡x dx \int \cot x \ dx is?
Reply 8
Avatar for Hasufel
Hasufel
16
Original post by boodle123
how did you get that? I thought you could change it to 1/tan4x then integrate that


i was just saying that`s what you get when you simplify cos(3x) / sin(4x)...
Reply 9
Avatar for timteddy1
timteddy1
ln(f(x))= f'(x)/f(x) just take 1/4 out of the integral

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