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1h
awarded  Nice Answer
2h
revised Definite integral with logarithm and arctangent inside of arctangent
edited body
2h
revised Definite integral with logarithm and arctangent inside of arctangent
edited body
2h
comment Help with the contour for this integral using residues
+1 for the Intaglio idea.
2h
answered Definite integral with logarithm and arctangent inside of arctangent
3h
revised Help with the contour for this integral using residues
added 31 characters in body
3h
comment How would you integrate this homogeneous equation?
OK, I am going to register my distaste with your acceptance of the answer provided. You asked for hints, which I provided, even though I did work the problem out. Someone else provided a full answer. If that is what you wanted, you should have said so.
3h
comment Help with the contour for this integral using residues
@Dr.MV: Oh snap, and here I thought that I was a trailblazer.
3h
answered Help with the contour for this integral using residues
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comment Approximating $\tan61^\circ$ using a Taylor polynomial centered at $\frac \pi 3$ : how to proceed?
You use the values at $\pi/3$.
1d
comment Integral involving a trig. term
@user1729: I feel it's incidental, but is a great comfort to me personally. If you can cook up some reason why it violates some logic, then by all means. But I am OK with it.
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answered Integral involving a trig. term
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comment Solve integrals using residue theorem?
@LeoSera: I get this question from time to time. It is an antiquated physics notation that I rather like for its clarity - it ties the integration variable to its integral. It's very useful for double integrals (and multiple integrals for that matter), so I really picked up the habit studying Optics.
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comment Solve integrals using residue theorem?
@dralion94: you mean numerator? In that case, we the introduction of the log in the contour integral is a standard technique. It exploits the log's multivaluedness so that the original integrand is returned.
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comment Solve integrals using residue theorem?
@DanielFischer: yeah, just think of all the rep we'd lose. ;)
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answered Solve integrals using residue theorem?
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comment Show the integration with a complex variable
What on earth is $v$?
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comment Laplace Inverse
@32px: Thanks. Normally, the evaluation of the ILT is not taught to people taking a first course in ODEs because of the integration in the complex plane requiring stuff from a complex analysis course. But still there are several aspects of this derivation that are useful, besides the use of Cauchy's theorem. One major takeaway here is a method of treating integrals with singular pieces on one contour that eventually cancel with contributions from other contours. Another is a method of integration by converting to a double integral and reversing the order of integration.
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awarded  Revival
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answered Laplace Inverse