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Homework Help: How do I solve this integral?

  1. May 28, 2008 #1
    Integrate [tex]\int[/tex] [tex]\frac{\left(5x - x^{2}\right)^{2}}{2}[/tex]

    I have been going round in circles using the substitution of u = [tex]\left(5x - x^{2}\right)[/tex]

    But it gets too complicated, where am I going wrong? I would really appreciate it if someone could please explain in stages what exactly I have to do.
    Many thanks
    Last edited: May 28, 2008
  2. jcsd
  3. May 28, 2008 #2
    [tex]\frac 1 2\int(5x-x^2)^2dx[/tex]

    Don't forget your dx.

    Expand ... [tex](x-y)^2=x^2-2xy+y^2[/tex]
    Last edited: May 28, 2008
  4. May 28, 2008 #3
    Is the solution anywhere close to this?

    [tex]\frac{\left(25x ^{3}\right)}{6}[/tex] [tex]-[/tex] [tex]\frac{\left(10x ^{4}\right)}{4}[/tex] [tex]+[/tex] [tex]\frac{\left(x ^{5}\right)}{5}[/tex]

  5. May 28, 2008 #4
    Last edited: May 28, 2008
  6. May 28, 2008 #5
    Oh yeah of course it is, thanks to you all. Panic over!!
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