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Little curiosity $\Re\Big(\int_{0}^{1}\frac{x\ln(x)}{1+e^{ix}}dx\Big)=-\frac{1}{8}$

score 85 · Answer 1 · 2026-04-15 16:54:47

85

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Little curiosity $\Re\Big(\int_{0}^{1}\frac{x\ln(x)}{1+e^{ix}}dx\Big)=-\frac{1}{8}$

Published on 15 Apr 2026 - 16:54

score 99 · Answer 2 · 2026-04-11 18:34:39

99

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How to prove the following inequality involving complex power series

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score 66 · Answer 3 · 2026-04-17 07:54:33

66

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Show that $ \lim_{R \rightarrow \infty } \oint_ {|z|=R} \frac{ 2z - 1 }{ z^{3} - 2z^{2} + 3z} = 0$

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score 561 · Answer 4 · 2026-04-12 05:32:56

561

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score 139 · Answer 5 · 2026-04-11 16:54:30

139

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35

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414

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92

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95

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219

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score 346 · Answer 12 · 2026-04-14 05:03:08

346

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47

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score 568 · Answer 14 · 2026-04-11 11:48:35

568

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score 37 · Answer 15 · 2026-04-16 13:00:38

37

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List Question

Little curiosity $\Re\Big(\int_{0}^{1}\frac{x\ln(x)}{1+e^{ix}}dx\Big)=-\frac{1}{8}$

How to prove the following inequality involving complex power series

Show that $ \lim_{R \rightarrow \infty } \oint_ {|z|=R} \frac{ 2z - 1 }{ z^{3} - 2z^{2} + 3z} = 0$

Find the real factors of $X^{2n}-1$

Pre-image of entire functions

Extension of bounded analytic functions from a countable subset to the whole unit disk

Complex roots meaning the quadratic equation is always positive?

Linear Algebra A Level Complex Number Magnitude Inequality

How can I integrate $\exp(−\sin(θ))\cos(θ+\cos(θ))$?

Likely fake proof of the irrationality of a rational multiple of pi/pi

Does complex linear transformation require conjugate transpose?

Second order differential equation with complex coefficient

How to prove by induction that $|z_n| \geq |c|r^{n-1}$ in complex numbers

How to use factorisation $z^{n}-1$ to prove the summation goes to zero?

STEP 2 1990 Question 4: Proving Conditional Perpendicularity of points in the complex plane

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