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A couple of Integration problems

  1. Oct 19, 2009 #1
    A couple of Integration problems 9dx/(x(x^4 + 8 ))

    1. The problem statement, all variables and given/known data

    Hi

    I'm new to this forum. I have a couple of Integration Problems which im not able to integrate correctly. I will also post my attempt at solving the problem so u guys can see what method i took trying to solve these. spent a lot of time in these questions and finally decided to post in this forum.

    1
    9dx/(x(x^4 + 8 ))

    2
    integ 37dx/((root(x)+ xroot(x))


    3. The attempt at a solution


    My attempt

    i tried u substitution with u=x^2
    also 9 is a constant so i took it out for the time being(ill multiply the answer i get with 9)

    9 integ dx/(x(x^4 + 8 )) u = x^2 du=2xdx
    9 integ xdx/(x^2(x^4 + 8 ))
    9*1/2 integ du/(u(u^2 + 8 )

    9*1/2 integ du/(u^3 + 8u ) ??
    9*1/2 (ln|u^3 +8u|) <<is that answer correct?

    if not can someone kindly tell me how to do this problem pls.




    I do not know how to go about the 2nd problem. any hints on how to approach it are welcome :)


    thanks in advance!
     
    Last edited: Oct 19, 2009
  2. jcsd
  3. Oct 19, 2009 #2
    1. Decompose [tex]\frac{1}{x\left(x^4+8\right)}[/tex] into partial fractions

    2. [tex]u=\sqrt{x}[/tex] + partial fraction decomposition
     
  4. Oct 19, 2009 #3

    Mark44

    Staff: Mentor

    Re: A couple of Integration problems 9dx/(x(x^4 + 8 ))

    So far so good, but the next line is not correct.
    [tex]\int \frac{du}{u}~=~ln|u| + C[/tex]
    but you don't have just exactly u in the denominator; you have u3 + 8u. To work through that integral you probably need a technique called partial fraction decomposition, AKA partial fractions.
    For your second problem, I would start with a substitution u = sqrt(x), and see where that takes you.
     
  5. Oct 20, 2009 #4
    Thanks a lot guys!
     
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