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Integration with i.

  1. Apr 7, 2014 #1
    i was trying to integrate [itex] \frac{1}{(t^2+1)^2} [/itex]
    By factoring it into [itex] \frac{1}{(t+i)^2(t-i)^2} [/itex] and then doing partial fractions.
    then integrating each term using a u substitution. Ok but then how do I get the real part out of this solution. I know the arctan(t) can be extracted out of stuff of this form.
  2. jcsd
  3. Apr 8, 2014 #2


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    $$\arctan(x)=\tfrac{1}{2}\imath \, (\log(1-\imath\, x)-\log(1+\imath\, x))$$
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