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Immediate integral problem

  1. Jan 18, 2009 #1
    4[tex]\int[/tex]9[tex]\frac{1-\sqrt{x}}{\sqrt{x}+2}[/tex]

    what i did:
    t=[tex]\sqrt{x}[/tex]
    x=t2
    dx=x'dt=2tdt

    now my integration is from 2-3 instead of 4-9

    [tex]\int[/tex][tex]\frac{1-t}{t+2}[/tex]2tdt=2[tex]\int[/tex][tex]\frac{t-t2}{t+2}[/tex]dt

    =2([tex]\int[/tex][tex]\frac{t}{t+2}[/tex]dt-[tex]\int[/tex][tex]\frac{t2}{t+2}[/tex]dt)

    the 1st integral i can replace with[tex]\int[/tex]1-[tex]\frac{2}{t+2}[/tex]dt which is an immediate integral, but how do i simplify the second part??
     
  2. jcsd
  3. Jan 18, 2009 #2

    Dick

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    Re: Integration

    Just divide t+2 into t^2 using polynomial division. Actually, you might want to take a step by and divide t-t^2 by t+2.
     
  4. Jan 18, 2009 #3
    Re: Integration

    i get t+3-[6/(t+2)]

    so i get --->2[(t^2)/2]+3t-6ln|t+2|]
    is this right??
     
  5. Jan 18, 2009 #4

    Dick

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    Re: Integration

    Sure.
     
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