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Improper Integral Check

  1. Mar 5, 2013 #1


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    Hi guys just want to check my answer for the following improper integral.

    ∫(2 to ∞) dv/v^2+2v-3.

    After doing partial fractions, integrating and evaluating I got the following for the answer: 0-(1/4)ln(1/5)

    How does this compare to other answers?

    Is there a way I can accurately check this answer myself?
  2. jcsd
  3. Mar 5, 2013 #2
    if i'm not mistaken u= (v+1) is pretty easy and it ends up fitting the arctanh rule. Seems that it'll involve an inverse hyperbolic function
    Last edited: Mar 5, 2013
  4. Mar 5, 2013 #3


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    What exactly do you mean that substituting u=v+1 is easy? I don't see any substitution in this problem
  5. Mar 5, 2013 #4
    I meant completing the square so that the denominator is (v+1)^2 -4. Multiply by -1/-1 and you have -dv/(4-(v+1)^2)
    which fits the rule ∫du/(a^2-u^2)=1/2a(ln (a+u/a-u)+c
    Last edited: Mar 5, 2013
  6. Mar 5, 2013 #5


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    Alright, that would make sense. Hopefully people get a similar final answer.
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