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Trigonometric Subsitution Integral

  1. Mar 9, 2013 #1
    1. The problem statement, all variables and given/known data
    ∫cot^2(x)csc^4(x)dx



    2. Relevant equations



    3. The attempt at a solution
    ∫cot^2(x)(cot^2(x)+1)csc^2(x)dx
    u=cot(x)
    du=-csc^2(x)dx
    -∫u^2 (u^2 +1)du
    -∫u^4 + 2u^3 + u^2 du
    -(u^5)/5 - (u^4)/2 - (u^3)/3
    -cot^5(x)/5 - cot^4(x)/2 - cot^3(x)/3 + C

    Wolfram alpha shows the solution as -cot^5(x)/5 - cot^3(x)/3 + C

    So I'm unsure as to how I got the cot^4(x)/2

    What exactly did I do wrong or is wolfram wrong?

    Thanks in advance
     
  2. jcsd
  3. Mar 9, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Now how did you change u^2(u^2+1) into u^4 + 2u^3 + u^2?
     
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