Complex Analysis: Integral of 1/(x^4-x^2+1) using Contour Integration

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Today, we evaluate the improper integral from negative infinity to infinity of 1/(x^4-x^2+1) using complex analysis.

Jordan's Lemma:
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Dear *QN³* ... Thank you so much 💗
I just got surprised with the answer (π) 🤓... Beautiful.
(Honestly, I still have a little problem with its Poles, I should watch it again)
You're great as always 💖

wuyqrbt
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Nice lecture. I just wanted to know what would have happened if the contour would have been closed from below ?
Or if the contour would have distorted such that all the 4 poles comes inside the the contour.
Would the answer still be the same ?

sayankundu
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U made a mistake while u were calculating the poles

thereddragon