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Anti-derivative Problem

  1. Dec 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the anti-derivative: [tex]\int[/tex][(4+u)/u]du

    3. The attempt at a solution
    I've tried a couple different ways to find this anti-derivative and I know I keep missing something.
    I tried to split it up into [tex]\int[/tex](4+u)(u^-1)du
    but then I think I do something wrong because I end up getting 4ln|u|.

    Any help you could give would be much appreciated- I've tried this problem so many times and I just can't figure out what I'm missing. Thanks.
     
  2. jcsd
  3. Dec 9, 2008 #2
    Try breaking up your numerator (i.e. (a+b)/c = a/c + b/c).
     
  4. Dec 9, 2008 #3
    Thanks. I just tried that, and it helped a little- but I'm still getting the wrong answer, according to the text book.

    so I split the equation up into [(4/u)+(u/u)] then I rewrote that to [(4)(1/u) + (u)(1/u)]
    from that I got 4ln|u| + (1/2)(u^2) ln|u|. What am I still doing wrong??

    If anyone could set me on the right path, that would be fantastic, thanks.
     
  5. Dec 9, 2008 #4
    Be careful! (u)(1/u)=1, not u^2.
     
  6. Dec 9, 2008 #5
    The first part of your answer looks fine. Why did you change u/u into u(1/u)? Before integrating what does u/u equal?
     
  7. Dec 9, 2008 #6
    Oh! I think I've got it....
    so 4+u/u to (4/u)+ (u/u) to 4(1/u)+(u/u) cancel out the u/u to equal 1 and turn it to
    4ln|u|+x+c.
    right?
    Thanks for all the help!
     
  8. Dec 9, 2008 #7
    Right! Just one minor point, you're integrating with respect to u, so it's actually 4 ln |u| + u, not x :)
     
  9. Dec 9, 2008 #8
    Ack! okay...I think I can remember to catch that u.
    Thanks so much for all your help!
     
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