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Integrating csc/cot^2. Help Needed

  1. Mar 23, 2010 #1
    Hey guys working on a problem for an assignment but my algebra is weak regrettably and I need some assistance.

    Note:: I left the x and dx out for clarity.

    1. The problem statement, all variables and given/known data

    int csc/cot2

    3. The attempt at a solution

    int csc x/cot2x dx= int csc/cos2/sin2
    = int cscsin2/cos2
    = int 1/sin * sin2/cos2
    = int sin/cos2

    Is the algebra at the equal signs correct? If not what went wrong?

    Then I make a u -substitution u = cos x then du = -sinx dx then dx = - du/sinx

    that makes - int 1/u2du then i just replace that u with x

    Correct ?
    Last edited: Mar 23, 2010
  2. jcsd
  3. Mar 23, 2010 #2
    Everything is you've done looks great up to when you get


    from there you integrate with respect to u.

    Once you arrive at answer to this integral, you then substitute cos(x) back into the problem for u.

    Let me know if you have any further questions about this.
  4. Mar 23, 2010 #3

    Thanks no other questions. I could finish easily with 1/cos + K

    EDIT: - int 1/u^2 = - int u ^ -2 = - ( - 1 / u) = 1/u since u = cos then 1/ cos + K follows.
    Last edited: Mar 23, 2010
  5. Mar 23, 2010 #4
    Glad I could help.
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