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Please help - integration

  1. Apr 14, 2004 #1
    This one integral has been given me some problems.

    integral of dx/(x-sqrt(x+2))

    please keep in mind im only in calc 2.
  2. jcsd
  3. Apr 14, 2004 #2

    Tom Mattson

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    You can do a u-substitution with u=(x+2)1/2. Then du=(1/2)(x+2)-1/2.

    Now, you'll find that you don't have the du/dx in your integral, so you'll have to supply it yourself by multiplying the numerator and denominator of the integrand by 2(x+2)1/2 and separating factors accordingly.

    That will turn your integrand into a rational function of u which will be much easier to integrate.
  4. Apr 15, 2004 #3
    Well first thing i always do is when i have any function given like this is to rationalize it ..meaning multiply all of this with (x+sqrt(x+2))/(x+sqrt(x+2))
    You will get then this sqrt up...
    (x+sqrt(x+2)) / ((x^2)-x-2)
    then you have (x+sqrt(x+2)) / (x-2)(x+1)
    Then you can simply seperate this integral into two.. int_x / ((x-2)(x+1))dx + int_sqrt(x+2) / ((x-2)(x+1))dx
    from there by substitution you can easily sole both of them
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