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Integration with i.

by cragar
Tags: integration
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cragar
#1
Apr7-14, 11:23 PM
P: 2,466
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.
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lurflurf
#2
Apr8-14, 12:17 AM
HW Helper
P: 2,264
use
$$\arctan(x)=\tfrac{1}{2}\imath \, (\log(1-\imath\, x)-\log(1+\imath\, x))$$


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