Integration of odd power of cotangent multiplied by odd power of cosecantby gzAbc123 Tags: cosecant, cotangent, integration, multiplied, power 

#1
Mar409, 04:33 PM

P: 6

1. The problem statement, all variables and given/known data
Describe the strategy you would use to (integrate: cot^m x)(csc^n x)dx, if m and n are odd. 2. Relevant equations I know the integral of cosecant is ln sec x + tan x + C I also know the integral of cotangent is ln sinx + C But I have no clue how this would apply to odd powers and multiplying them together. 3. The attempt at a solution I know how to multiply odd powers of sine and cosine, but for cosecant and cotangent, I have no clue where to get started. The question isn't asking me to actually integrate, but just to describe how I would integrate. Does this integration parallel the corresponding rules for odd powers and multiplication of tanx and secx? Help, please. 



#2
Mar409, 07:34 PM

P: 473

Doesn't your book describe how to do this? thing of an identity that relates the two trig functions, also your not worried about the integral of them individually in this case you want to think about their deviates so you can use substitution....




#3
Mar409, 07:48 PM

P: 6

Hey,
No my book only mentions how to solve this for two evenpowered; and one odd and one even. It doesn't even give any hints about how to integrate when there are two oddpowered cosecant and cotangent functions being multiplied. Do you have any other suggestions? 



#4
Mar409, 07:59 PM

P: 133

Integration of odd power of cotangent multiplied by odd power of cosecant
Hi gzAbc123:
Check this link out: http://books.google.com/books?id=Clg...sult#PPA322,M1 Look especially for the "Steven and Todd Rule" and the Odd Man Out Rule.... On page 343 Example #2... this is exactly like your problem. This will help you with these types of integration. 



#5
Mar409, 08:08 PM

P: 6

Thanks for the link :).
The only problem is not the Steven and Todd rule don't seem to apply for cosecant AND cotangent used in the same equation. Is it there somewhere? 



#6
Mar409, 08:11 PM

P: 133





#7
Mar409, 08:11 PM

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#8
Mar409, 08:15 PM

P: 6

It says pages 343344 are not part of this book review... what the?




#9
Mar409, 08:17 PM

P: 133

My bad. Pp. 323 #2




#10
Mar409, 08:19 PM

P: 6

But isn't that question for tangent and secant?
Is it basically the same set of steps for cotangent or cosecant? Or is there a few steps that would needed to be added? 



#11
Mar409, 08:23 PM

P: 133




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