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Integration involving partial fraction

  1. Apr 14, 2012 #1
    1. The problem statement, all variables and given/known data
    I want to check the answer to this question.

    ⌠ 2 x dx / (x+1) (x+2)
    ⌡ 1

    2. Relevant equations



    3. The attempt at a solution
    For partial fraction I got A= -1 and B = 2

    My final answer is -ln 2 + ln4 - ln3 = ln 4/ ln2 * ln 3
     
  2. jcsd
  3. Apr 14, 2012 #2
    There is a more important question at hand. Do you understand the order of operations?
     
    Last edited: Apr 14, 2012
  4. Apr 14, 2012 #3
    Yes. I just need to check the answer.
     
  5. Apr 14, 2012 #4
    Judging by your problem statement, I can't be too sure.

    Also, are you sure ln(a) + ln(b) = ln(a)ln(b)?
     
  6. Apr 14, 2012 #5
    This line doesn't make any sense to me. :/ Regardless, the answer is incorrect on the left hand side. Show us what integral you got when you split the partial fraction up (A=-1 and B=2 doesn't mean much if we don't know what term they are over). Then show us the anti-differentiated equation. You went wrong somewhere in there. Also, as Roshan has noticed, you don't quite seem to know how to manipulate logs.

    These operations are valid: [itex]log(a)+log(b)=log(a*b); \quad log(a)-log(b)= \displaystyle log\left(\frac{a}{b}\right)[/itex].

    Parentheses are VERY important when typing math online. You first statement when read at face value says [itex]\displaystyle \int_1^2 \frac{x\ \ dx\
    (x+2)}{x+1}[/itex] which is obviously not what you meant.
     
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