Question

Evaluate for $t\in \mathbb{R}$ $\int_{-\infty}^\infty{e^{itx} \over (1+x^2)^2}dx$

score 110 · Answer 1 · 2026-04-16 23:21:51

110

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Evaluate for $t\in \mathbb{R}$ $\int_{-\infty}^\infty{e^{itx} \over (1+x^2)^2}dx$

Published on 16 Apr 2026 - 23:21

score 127 · Answer 2 · 2026-04-16 05:54:16

127

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Convergence of $\int_{0}^{1} \frac{\sqrt {e^2+x^2} - e^{\cos x}}{\tan^ax}dx$

Published on 16 Apr 2026 - 5:54

score 6.4k · Answer 3 · 2026-04-25 07:32:17

6.4k

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How to find the inverse Fourier transfmation of $\exp(-sk)/k$.

Published on 25 Apr 2026 - 7:32

score 1.6k · Answer 4 · 2026-04-13 18:29:36

1.6k

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For what values of K, is the integral improper?

Published on 13 Apr 2026 - 18:29

score 61 · Answer 5 · 2026-04-15 15:31:14

61

Views

How to prove if $\int^{\infty}_{0}f(x)dx$ a converges, then there is increasing sequence $x_n$, $\lim_{n \to \infty}f(x_n)=0$

Published on 15 Apr 2026 - 15:31

score 135 · Answer 6 · 2026-04-13 17:48:29

135

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How can $\int_a^b f(x)dx $ exist if either $f(a)$ or $f(b)$ does not exist?

Published on 13 Apr 2026 - 17:48

score 100 · Answer 7 · 2026-04-14 13:19:20

100

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Solving the improper integral $1/(x^a+y^b)$

Published on 14 Apr 2026 - 13:19

score 216 · Answer 8 · 2026-04-11 10:44:42

216

Views

A variant of the exponential integral

Published on 11 Apr 2026 - 10:44

score 209 · Answer 9 · 2026-04-15 19:36:49

209

Views

Evaluate the improper integral $\int_0^\infty {\exp(−sk)\over k}\sin(kx)\,dk$.

Published on 15 Apr 2026 - 19:36

score 53 · Answer 10 · 2026-04-15 23:09:46

53

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How to prove $\lim_{a \to + \infty}a^q \int_{a}^{+\infty}\frac{\sin(x)dx}{x^p}=0$ when $p>q>0$

Published on 15 Apr 2026 - 23:09

score 70 · Answer 11 · 2026-04-15 02:24:14

70

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Find $\int_0^{\infty} \frac{dx}{1+e^x}$

Published on 15 Apr 2026 - 2:24

score 146 · Answer 12 · 2026-04-13 14:56:19

146

Views

What is the asymptotic behavior of this integral?

Published on 13 Apr 2026 - 14:56

score 35 · Answer 13 · 2026-04-17 05:19:55

35

Views

Convergence of improper integrals $\int_{-\infty}^{\infty}f(x)dx$ and $\int_{-\infty}^{\infty}f^{2}(x)dx$

Published on 17 Apr 2026 - 5:19

score 94 · Answer 14 · 2026-04-10 18:53:58

94

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How to evaluate $\lim_{c \rightarrow \infty} \int_{-c}^c f(x)dx$

Published on 10 Apr 2026 - 18:53

score 98 · Answer 15 · 2026-04-13 06:00:47

98

Views

Evaluating Improper Integrals with Residues - don't think I'm calculating the residues properly

Published on 13 Apr 2026 - 6:00

List Question

Evaluate for $t\in \mathbb{R}$ $\int_{-\infty}^\infty{e^{itx} \over (1+x^2)^2}dx$

Convergence of $\int_{0}^{1} \frac{\sqrt {e^2+x^2} - e^{\cos x}}{\tan^ax}dx$

How to find the inverse Fourier transfmation of $\exp(-sk)/k$.

For what values of K, is the integral improper?

How to prove if $\int^{\infty}_{0}f(x)dx$ a converges, then there is increasing sequence $x_n$, $\lim_{n \to \infty}f(x_n)=0$

How can $\int_a^b f(x)dx $ exist if either $f(a)$ or $f(b)$ does not exist?

Solving the improper integral $1/(x^a+y^b)$

A variant of the exponential integral

Evaluate the improper integral $\int_0^\infty {\exp(−sk)\over k}\sin(kx)\,dk$.

How to prove $\lim_{a \to + \infty}a^q \int_{a}^{+\infty}\frac{\sin(x)dx}{x^p}=0$ when $p>q>0$

Find $\int_0^{\infty} \frac{dx}{1+e^x}$

What is the asymptotic behavior of this integral?

Convergence of improper integrals $\int_{-\infty}^{\infty}f(x)dx$ and $\int_{-\infty}^{\infty}f^{2}(x)dx$

How to evaluate $\lim_{c \rightarrow \infty} \int_{-c}^c f(x)dx$

Evaluating Improper Integrals with Residues - don't think I'm calculating the residues properly

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