Question

$\int_0^∞ \dfrac{x^a}{(x^2 + 1)^2} dx$ for $-1<a<3$

score 236 · Answer 1 · 2026-03-25 14:33:15

236

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$\int_0^∞ \dfrac{x^a}{(x^2 + 1)^2} dx$ for $-1<a<3$

Published on 25 Mar 2026 - 14:33

score 162 · Answer 2 · 2018-10-25 21:06:03

162

Views

Way to solve $\int\limits _0^\limits\infty \frac{x^{-t}}{1+x}\ dx$

Published on 25 Oct 2018 - 21:06

score 557 · Answer 3 · 2026-03-26 14:19:10

557

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When is the improper integral well-defined in multiple dimensions?

Published on 26 Mar 2026 - 14:19

score 1k · Answer 4 · 2018-10-27 19:15:32

1k

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Integral of product of bounded function and Lebesgue function

Published on 27 Oct 2018 - 19:15

score 90 · Answer 5 · 2018-10-28 10:53:38

90

Views

Proving that $\int^1_0 \frac{1}{\sqrt{\ln(\frac{1}{x})}}dx$ converges?

Published on 28 Oct 2018 - 10:53

score 71 · Answer 6 · 2018-10-28 10:56:09

71

Views

Prove that $\int^3_0 \frac{1}{x^x}dx$ converges

Published on 28 Oct 2018 - 10:56

score 72 · Answer 7 · 2018-10-28 12:58:18

72

Views

Proving that $\int^1_0 \frac{1}{x}cos(\frac{1}{x})dx$ is conditionally convergent

Published on 28 Oct 2018 - 12:58

score 118 · Answer 8 · 2018-10-28 13:28:24

118

Views

Prove that $\int^{4\pi}_0(3x^2\sin\frac{1}{x}-x\cos\frac{1}{x})\,dx=\frac{32\sqrt2}{\pi^3}$

Published on 28 Oct 2018 - 13:28

score 113 · Answer 9 · 2018-10-29 15:34:58

113

Views

An interesting integral $\int_{0}^{\infty}\frac{dx}{(x+1)(x+2)^a}$ for $a>0$

Published on 29 Oct 2018 - 15:34

score 98 · Answer 10 · 2018-10-31 09:16:26

98

Views

Primitive of $ \exp(-a \times x- \frac bx)$

Published on 31 Oct 2018 - 9:16

score 535 · Answer 11 · 2018-10-31 15:39:47

535

Views

Integral of $x^3e^{(-x^2/2)}$

Published on 31 Oct 2018 - 15:39

score 71 · Answer 12 · 2018-11-01 12:20:36

71

Views

Solve equation about infinite integral. Find out all solutions that exist

Published on 01 Nov 2018 - 12:20

score 67 · Answer 13 · 2018-11-01 13:29:10

67

Views

Calculate the integral connected with $e^{-x^2}$

Published on 01 Nov 2018 - 13:29

score 512 · Answer 14 · 2018-11-01 22:15:30

512

Views

Evaluating $\int_{0}^{2\pi}x^2\ln^2(1-\cos x)dx$

Published on 01 Nov 2018 - 22:15

score 129 · Answer 15 · 2018-11-02 11:33:05

129

Views

Evaluating $\int_{-\infty}^{\infty}\frac{e^{-\alpha x}}{(1+e^{-x})^{1+\lambda}}\,\mathrm{d}x$ for $\alpha,\lambda>0$

Published on 02 Nov 2018 - 11:33

List Question

$\int_0^∞ \dfrac{x^a}{(x^2 + 1)^2} dx$ for $-1<a<3$

Way to solve $\int\limits _0^\limits\infty \frac{x^{-t}}{1+x}\ dx$

When is the improper integral well-defined in multiple dimensions?

Integral of product of bounded function and Lebesgue function

Proving that $\int^1_0 \frac{1}{\sqrt{\ln(\frac{1}{x})}}dx$ converges?

Prove that $\int^3_0 \frac{1}{x^x}dx$ converges

Proving that $\int^1_0 \frac{1}{x}cos(\frac{1}{x})dx$ is conditionally convergent

Prove that $\int^{4\pi}_0(3x^2\sin\frac{1}{x}-x\cos\frac{1}{x})\,dx=\frac{32\sqrt2}{\pi^3}$

An interesting integral $\int_{0}^{\infty}\frac{dx}{(x+1)(x+2)^a}$ for $a>0$

Primitive of $ \exp(-a \times x- \frac bx)$

Integral of $x^3e^{(-x^2/2)}$

Solve equation about infinite integral. Find out all solutions that exist

Calculate the integral connected with $e^{-x^2}$

Evaluating $\int_{0}^{2\pi}x^2\ln^2(1-\cos x)dx$

Evaluating $\int_{-\infty}^{\infty}\frac{e^{-\alpha x}}{(1+e^{-x})^{1+\lambda}}\,\mathrm{d}x$ for $\alpha,\lambda>0$

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