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I got one problem

  1. Jan 21, 2007 #1
    1. The problem statement, all variables and given/known data

    integral of csc^3(x)cot(x)

    2. Relevant equations

    I tried using trig identity 1+cot^2(x)=csc^2(x) but I got result where I cancelled my indegrals.

    3. The attempt at a solution

    I tried to substitute the above mentioned indentity for csc^2 but I end up getting -cscx + intgr. cscxcot^3(x). I then substituted for cot^2 but then got to the point where I had -cscx + intgr. csc^(3)xcotx + cscx. At this point everything cancelled out. I also tried substituting sin and cos in the original equation but that didn't get me anywhere neither.
  2. jcsd
  3. Jan 21, 2007 #2
    Try splitting csc3(x)cot(x) into csc2(x)*(csc(x)cot(x)) does that help at all?
  4. Jan 21, 2007 #3


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    Homework Helper

    write out [tex]\csc^3 (x), \cot(x)[/tex] in terms of [tex]\cos(x), \sin(x)[/tex] and use subsitution or do by inspection :smile:
  5. Jan 21, 2007 #4


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    Science Advisor

    d_leet's suggestion is simpler (what is the derivative of csc(x)?) while mjsd's suggestion is more "fundamental" (you don't need to know the derivatiive of csc(x), only of cos(x)) but they both give the correct answer.
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