JoãoVitorMC
Solve the following improper improper integral:



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JoãoVitorMC
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\[\int\limits_{0}^{\infty} \frac{ \ln x }{ x² + a² }\]

JoãoVitorMC
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a > 0

kiki41554
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Huh

mahmit2012
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dw:1350750759562:dw

kiki41554
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So it's 36

mahmit2012
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dw:1350750883133:dw

kiki41554
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Hello???

mahmit2012
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dw:1350751308660:dw

mahmit2012
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dw:1350751339539:dw

mahmit2012
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Did you get it?

JoãoVitorMC
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yeahh thank you so much!!

mahmit2012
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Do you know what is a residual.

mahmit2012
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dw:1350751491113:dw

mahmit2012
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dw:1350751564402:dw

mahmit2012
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because x=ai is an order one pole.

mahmit2012
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this way is so easy, but your teacher will get confuse.
Draw a contour and give my solution.

JoãoVitorMC
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ok thank you!!

JoãoVitorMC
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one question, i didn't understand this last part:

JoãoVitorMC
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dw:1350834795661:dw

JoãoVitorMC
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but you you did this:

JoãoVitorMC
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dw:1350834921089:dw there is a 2 dividing see?