Question

Is it possible to compute $\int_0^\infty \frac{x^2}{e^x-1}\text{d}x$ using the Residue theorem?

score 84 · Answer 1 · 2026-04-16 12:18:47

84

Views

Is it possible to compute $\int_0^\infty \frac{x^2}{e^x-1}\text{d}x$ using the Residue theorem?

Published on 16 Apr 2026 - 12:18

score 60 · Answer 2 · 2026-04-16 09:00:17

60

Views

Determine the value of real number $a$ such that the integral $\int_0^{\infty} \frac{1}{1+x^a} dx$ converges.

Published on 16 Apr 2026 - 9:00

score 71 · Answer 3 · 2026-04-16 00:31:27

71

Views

area under curve of exponential integral

Published on 16 Apr 2026 - 0:31

score 129 · Answer 4 · 2026-04-12 11:39:19

129

Views

A multidimensional integral involving an exponential and power functions over a simplex.

Published on 12 Apr 2026 - 11:39

score 73 · Answer 5 · 2026-04-11 11:08:37

73

Views

Is there any formula I'm unaware of?

Published on 11 Apr 2026 - 11:08

score 63 · Answer 6 · 2026-04-12 08:00:26

63

Views

Integrating term-by-term in a Lebesgue integral

Published on 12 Apr 2026 - 8:00

score 211 · Answer 7 · 2026-04-17 10:05:01

211

Views

Generalization of $\int_0^{\infty} e^{-x^2} \cosh x d x$?

Published on 17 Apr 2026 - 10:05

score 99 · Answer 8 · 2026-04-12 19:29:26

99

Views

Is the error function essential to $\int_0^{\infty} e^{-a x^2} \sinh (b x) d x$?

Published on 12 Apr 2026 - 19:29

score 227 · Answer 9 · 2026-04-14 22:23:04

227

Views

Any ideas on how to perform this integral?

Published on 14 Apr 2026 - 22:23

score 127 · Answer 10 · 2026-04-16 07:07:07

127

Views

Does the convergence of $\int_{0}^\infty |f(x)|\,dx$ imply the convergence of $\int_{0}^\infty f(x)\,dx$?

Published on 16 Apr 2026 - 7:07

score 83 · Answer 11 · 2026-04-06 05:54:14

83

Views

Double integral over a half-plane

Published on 06 Apr 2026 - 5:54

score 419 · Answer 12 · 2026-04-17 07:23:04

419

Views

Integral of $\int_0^1 \frac{dx}{(1-x^5)^{1/5}}$

Published on 17 Apr 2026 - 7:23

score 69 · Answer 13 · 2026-04-13 19:13:05

69

Views

Uniform convergence for improper integrals dependig on a parameter

Published on 13 Apr 2026 - 19:13

score 36 · Answer 14 · 2026-04-15 17:58:56

36

Views

If $F(x)=\int_0^x \frac{1}{\sqrt{t}}$, then is $F(0)$ implicitly defined as: $\lim_{x \to 0^+ }(\lim_{ε \to 0^+}\int^x_{ε}\frac{1}{\sqrt{t}})$?

Published on 15 Apr 2026 - 17:58

score 85 · Answer 15 · 2026-04-15 12:28:43

85

Views

Suppose $F(x)=\int_c^x f(t)dt$ and $f$ is not defined at $x=c$. Is there an agreed upon convention as to what $F(c)$ should equal?

Published on 15 Apr 2026 - 12:28

List Question

Is it possible to compute $\int_0^\infty \frac{x^2}{e^x-1}\text{d}x$ using the Residue theorem?

Determine the value of real number $a$ such that the integral $\int_0^{\infty} \frac{1}{1+x^a} dx$ converges.

area under curve of exponential integral

A multidimensional integral involving an exponential and power functions over a simplex.

Is there any formula I'm unaware of?

Integrating term-by-term in a Lebesgue integral

Generalization of $\int_0^{\infty} e^{-x^2} \cosh x d x$?

Is the error function essential to $\int_0^{\infty} e^{-a x^2} \sinh (b x) d x$?

Any ideas on how to perform this integral?

Does the convergence of $\int_{0}^\infty |f(x)|\,dx$ imply the convergence of $\int_{0}^\infty f(x)\,dx$?

Double integral over a half-plane

Integral of $\int_0^1 \frac{dx}{(1-x^5)^{1/5}}$

Uniform convergence for improper integrals dependig on a parameter

If $F(x)=\int_0^x \frac{1}{\sqrt{t}}$, then is $F(0)$ implicitly defined as: $\lim_{x \to 0^+ }(\lim_{ε \to 0^+}\int^x_{ε}\frac{1}{\sqrt{t}})$?

Suppose $F(x)=\int_c^x f(t)dt$ and $f$ is not defined at $x=c$. Is there an agreed upon convention as to what $F(c)$ should equal?

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