Question

Integrating $\int_0^{\infty} \frac{dx}{1+x^3}$ using residues.

score 12.1k · Answer 1 · 2026-04-16 03:41:59

12.1k

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Integrating $\int_0^{\infty} \frac{dx}{1+x^3}$ using residues.

Published on 16 Apr 2026 - 3:41

score 1.2k · Answer 2 · 2026-04-15 04:24:11

1.2k

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Principal value of the singular integral $\int_0^\pi \frac{\cos nt}{\cos t - \cos A} dt$

Published on 15 Apr 2026 - 4:24

score 263 · Answer 3 · 2026-04-16 07:21:01

263

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Solving the improper integral $\int_0^\infty \frac{x^{1/3}}{1+x^2} \mathrm dx$

Published on 16 Apr 2026 - 7:21

score 1.1k · Answer 4 · 2026-04-11 11:48:25

1.1k

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How to treat $\int_{0}^{\infty} \sin(kx)dx =\frac {1}{k}$ as a distribution?

Published on 11 Apr 2026 - 11:48

score 609 · Answer 5 · 2026-04-17 05:17:51

609

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Compute $\int_0^{\infty}\frac{\cos(\pi t/2)}{1-t^2}dt$

Published on 17 Apr 2026 - 5:17

score 9.8k · Answer 6 · 2026-04-15 20:33:00

9.8k

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What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$?

Published on 15 Apr 2026 - 20:33

score 174 · Answer 7 · 2026-04-12 16:57:33

174

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How to evaluate following integral

Published on 12 Apr 2026 - 16:57

score 927 · Answer 8 · 2026-04-14 04:37:45

927

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Find an example of a positive function that its improper integral converge, but its series diverge

Published on 14 Apr 2026 - 4:37

score 372 · Answer 9 · 2026-04-16 18:29:09

372

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$\int_{0}^{\frac{\pi}{2}}\cos{x}\sqrt{1+\tan{x}}dx$

Published on 16 Apr 2026 - 18:29

score 231 · Answer 10 · 2026-04-14 10:30:35

231

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Numerical Methods for estimating divergence over an improper integral

Published on 14 Apr 2026 - 10:30

score 532 · Answer 11 · 2026-04-17 18:00:15

532

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closed form for $\int_0^{\infty}\log^n\left(\frac{e^x}{e^x-1}\right)dx$

Published on 17 Apr 2026 - 18:00

score 876 · Answer 12 · 2026-04-17 05:29:18

876

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Evaluating the integral $\int_0^{\frac{\pi}{2}}\log\left(\frac{1+a\cos(x)}{1-a\cos(x)}\right)\frac{1}{\cos(x)}dx$

Published on 17 Apr 2026 - 5:29

score 2.1k · Answer 13 · 2026-04-16 21:54:12

2.1k

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Closed form for $\int_0^\infty\frac{\sin x\,\cdot\,\operatorname{Ci}x-\cos x\,\cdot\,\operatorname{Si}x}{\sqrt{16\,x^2+1}}dx$

Published on 16 Apr 2026 - 21:54

score 123 · Answer 14 · 2026-04-08 20:22:13

123

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What is the derivation of an integral?

Published on 08 Apr 2026 - 20:22

score 56 · Answer 15 · 2026-04-15 22:42:18

56

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Checking the convergence of this improper integral $\int_{-\infty}^{\infty} x^ne^{-|x|}dx$

Published on 15 Apr 2026 - 22:42

List Question

Integrating $\int_0^{\infty} \frac{dx}{1+x^3}$ using residues.

Principal value of the singular integral $\int_0^\pi \frac{\cos nt}{\cos t - \cos A} dt$

Solving the improper integral $\int_0^\infty \frac{x^{1/3}}{1+x^2} \mathrm dx$

How to treat $\int_{0}^{\infty} \sin(kx)dx =\frac {1}{k}$ as a distribution?

Compute $\int_0^{\infty}\frac{\cos(\pi t/2)}{1-t^2}dt$

What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$?

How to evaluate following integral

Find an example of a positive function that its improper integral converge, but its series diverge

$\int_{0}^{\frac{\pi}{2}}\cos{x}\sqrt{1+\tan{x}}dx$

Numerical Methods for estimating divergence over an improper integral

closed form for $\int_0^{\infty}\log^n\left(\frac{e^x}{e^x-1}\right)dx$

Evaluating the integral $\int_0^{\frac{\pi}{2}}\log\left(\frac{1+a\cos(x)}{1-a\cos(x)}\right)\frac{1}{\cos(x)}dx$

Closed form for $\int_0^\infty\frac{\sin x\,\cdot\,\operatorname{Ci}x-\cos x\,\cdot\,\operatorname{Si}x}{\sqrt{16\,x^2+1}}dx$

What is the derivation of an integral?

Checking the convergence of this improper integral $\int_{-\infty}^{\infty} x^ne^{-|x|}dx$

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