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Trigonometric Integral 2

  • Thread starter Mentallic
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  • #1
Mentallic
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Part 2, leading on from https://www.physicsforums.com/showthread.php?t=315803"

Homework Statement


Given [itex]f(x)=cotx+tanx[/itex] find
[tex]\int{[f(x)]^2}dx[/tex]

The Attempt at a Solution


I've attempted many different varieties of approaches to the problem. Trying to use the substitution method for sinx, cosx, tanx.... and a few others... re-arranging the function, trying to get it into a more convenient form... trying to use some of the ideas given in the first thread... No luck.

Basically, it has all been a bunch of guessing and hoping something useful will appear. Plus another bunch of frustration on my part, but I wont get into the details of that xD
 
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Answers and Replies

  • #2
rock.freak667
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Expand out [f(x)]^2

use [itex]cot^2x+1=cosec^2x[/itex] and [itex]tan^2x+1=sec^2x[/itex]
 
  • #3
Mentallic
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Thanks rockfreak :smile:

It turns out to be tanx-cotx. I also obtained [itex]\int{sec^2x+cosec^2x}dx[/itex] through another longer method but it strike me at that moment that I can take the integral of each of these. (I think I'll keep my standard integral formulas close-by next time).

Thanks again.
 

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