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Integration by Substitution

  1. Apr 2, 2010 #1
    Hi, am I on the right track with this U-substitution problem?

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

    Evaluate the indefinite integral

    2. Relevant equations

    integral of x^2(x^3 + 5)^9 dx

    3. The attempt at a solution

    integral of x^2(x^3 + 5)^9 dx

    Let u = x^3 + 5

    du = 2x^2

    1/2du = x^2

    1/2 integral u^9 du

    1/2 (u^10)/10 + c

    1/20 u^10 + c

    1/20 (x^3 + 5)^10 + c
     
    Last edited: Apr 2, 2010
  2. jcsd
  3. Apr 2, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You are on the right track, but I would check that du again.
     
  4. Apr 2, 2010 #3
    This is where you're wrong. Just a slight mistake,

    Remember that the differentiation of x^n is n*x(n-1)
     
  5. Apr 2, 2010 #4
    Thanks for your replies Dick and Lunat1c. I see the mistake, i'll try it again:


    3. The attempt at a solution

    integral of x^2(x^3 + 5)^9 dx

    Let u = x^3 + 5

    du = 3x^2 dx

    1/3du = x^2 dx

    1/3 integral u^9 du

    1/3 (u^10)/10 + c

    1/30 (u^10) + c

    1/30 (x^3 + 5)^10 + c
     
  6. Apr 2, 2010 #5

    Mark44

    Staff: Mentor

    You put the dx in this time. That's a good habit to get into, especially when you start doing trig substitutions.
     
  7. Apr 2, 2010 #6
    Thanks Mark44
     
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