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Homework Help: Integration Help

  1. Aug 30, 2007 #1
    1. The problem statement, all variables and given/known data
    [tex]\int\frac{x^3 dx}{(x+1)^8}[/tex]

    2. Relevant equations
    None I can think of.

    3. The attempt at a solution
    Hm..I just don't know where to start.

    No substitution seems to be useful. (u=x+1, u=(x+1)^8).
    I've tried pulling x out of the denominator to get:
    [tex]\int\frac{x^3 dx}{x^8 (1+x^-1)^8}[/tex]
    but that doesn't help either..

    This isn't really HW just one of 15 integrals I was given that I should be able to do...

    Thanks in Advance for any hints on solving this.
  2. jcsd
  3. Aug 30, 2007 #2
    Cal 2? b/c i can't even go at it, i've only completed Cal 1.
  4. Aug 30, 2007 #3
    Yep, Calc 2.

    I "think" I could do partial fractions but...8 variables to find? and then 8 integrals of increasing power on the denominator. I think there should be an easier way...
  5. Aug 30, 2007 #4
    man i can't wait to be able to solve these types of problems :-]

    i've missed it so much that i even did the even problems that weren't assigned for hw
  6. Aug 30, 2007 #5


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    Homework Helper

    u=x+1 is fine. Turns it into (u-1)^3/u^8. Now you just have to expand (u-1)^3. And if that's the worst of your 15 problems, feel blessed. It's really a calc 1 problem.
    Last edited: Aug 30, 2007
  7. Aug 30, 2007 #6
    Wow thanks, this is about the 2nd time I've ever seen that type of substitution being used >.<.

    Yea the problem's weren't really hard Calc 2 stuff mainly things we should know off the top of our heads.
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