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Homework Help: Integration by Substitution

  1. Jul 25, 2009 #1
    1. The problem statement, all variables and given/known data
    I've come across the problem
    [tex]\ \int x(x^{2}+5)^{75} dx[/tex]

    2. Relevant equations

    3. The attempt at a solution
    Once going through the whole problem I got [tex]\ \frac{(x^{2}+5)^{76}}{76}+c[/tex]
    but the text I have said the answer was, [tex]\frac{1}{152}(x^{2}+5)^{76}+c[/tex].
    What did I do wrong?
  2. jcsd
  3. Jul 25, 2009 #2
    Did you try differentiating the answers to see which one gives you [tex] x(x^{2}+5)^{75} [/tex] ? Remember to apply the chain rule and that differentiating [tex] x^{2}+5 [/tex] gives 2x
  4. Jul 26, 2009 #3


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    Science Advisor

    Presumably you let u= x^2+ 5. Then du= 2x dx. You forgot the "2".
  5. Jul 26, 2009 #4
    Oh, now I see, thanks.
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