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Homework Help: Trigonometric Subsitution Integral

  1. Mar 9, 2013 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    -∫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


    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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