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Integration by substitution

  1. Nov 14, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the indefinite integral by substitution.

    ∫2x/(x+5)^6 dx

    2. Relevant equations

    3. The attempt at a solution
    I know how to do this using the method of partial fractions, but the book says to use substitution. Is there a way to just do a basic u-substitution with this integrand that I'm just not seeing? Or a way to solve without partial fractions? (we haven't gotten to partial fractions in my class so I feel like there must be some other way).

  2. jcsd
  3. Nov 14, 2011 #2


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    Homework Helper

    Use u-substitution. What can you set u equal to?
  4. Nov 14, 2011 #3


    Staff: Mentor

    There's a very obvious substitution.
  5. Nov 14, 2011 #4
    haha, thanks guys. I feel like it is pretty obvious but I just don't see it! If you set u=x+5 that gives du=1dx and you're still stuck with the 2x in the numerator. If you set u=2x, you get du=2dx and then you're stuck with the (x+5)^6 in the denominator.

    What am I missing????
  6. Nov 15, 2011 #5


    Staff: Mentor

    If u = x + 5, what is x in terms of u? When you do a substitution, you don't just replace some of the terms.
  7. Nov 15, 2011 #6
    Got it. Thanks!
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