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Homework Help: Integral of (2x)/(x^2 + 1)

  1. Jan 15, 2012 #1
    1. The problem statement, all variables and given/known data

    Integrate (2x)/(x^2 + 1)

    2. Relevant equations

    3. The attempt at a solution

    Is the answer:

    (2x) log|x^2 + 1|

    as I thought the answer to this type of question is the log of the absolute value of the denominator multiplied by the numerator.

    The answer given when I use Wolfram Alpha is log(x^2+1) + (tan x)^-1
  2. jcsd
  3. Jan 15, 2012 #2


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    Actually your answer would be ln(x2+1)+C. (look at putting t=x2+1)

    Which is what wolfram gave to me.
  4. Jan 15, 2012 #3
    Thank you.
    Yes, I'm getting the same answer as you now on Wolfram.

    If the question had instead been
    Integrate (2)/(x^2 + 1) (no x in the numerator)

    Would the answer also have been log|x^2 + 1| + c
  5. Jan 15, 2012 #4
    Oh, it's ok, I've just realised I can't do that.
  6. Jan 15, 2012 #5


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    In that case the answer would be 2tan-1(x) + C since d/dx(tan-1x) = 1/(x2+1).
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