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Evaluate the integral

  1. Aug 3, 2010 #1
    1. The problem statement, all variables and given/known data

    integral:

    x2 sqrt(2+x3) dx


    2. Relevant equations



    3. The attempt at a solution

    Should I use substitution? Should I do it as a power?
     
  2. jcsd
  3. Aug 3, 2010 #2
    U substitution is the way to go for this one.
     
  4. Aug 4, 2010 #3

    HallsofIvy

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    Since the only difficulty is that "[itex]2+ x^3[/itex]" inside the square root, let [itex]u= 2+ x^3[/itex] seems an obvious way to go.
     
  5. Aug 4, 2010 #4
    So when I substitute it as HallsofIvy suggested, what do I do with x2dx?
    x2dx=du?

    integral:
    sqrt(u)du=2u3/2/3......

    stuck.
     
  6. Aug 4, 2010 #5

    Dick

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    If u=2+x^3 isn't du=3*x^2*dx? Isn't that how substitution works?
     
  7. Aug 4, 2010 #6
    I am extremely confused with the next step of the solution.

    integral
    sqrt(u)du/(3x2) is this the correct substitution?
     
  8. Aug 4, 2010 #7

    Dick

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    Well, no. What happened to the x^2 in your original problem? Isn't it x^2*sqrt(u)*(du/(3*x^2))?
     
  9. Aug 4, 2010 #8
    Thanks goodness, I got it.
     
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