Question

Integral of the form $\int_{0}^{\infty}e^{-ax}e^{-x^{4}}dx$

score 145 · Answer 1 · 2026-04-15 21:08:57

145

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Integral of the form $\int_{0}^{\infty}e^{-ax}e^{-x^{4}}dx$

Published on 15 Apr 2026 - 21:08

score 103 · Answer 2 · 2026-04-13 18:28:54

103

Views

Closed form for the integral \[\int_{0}^{\infty}e^{-ax}e^{-x^{4}}dx\]

Published on 13 Apr 2026 - 18:28

score 125 · Answer 3 · 2026-04-13 13:48:52

125

Views

How can we integrate integral(s) of this type?

Published on 13 Apr 2026 - 13:48

score 503 · Answer 4 · 2026-04-16 03:08:55

503

Views

Does $\int_{1}^{\infty} g(x)\ dx$ imply $\lim\limits_{x\to \infty}g(x)=0$?

Published on 16 Apr 2026 - 3:08

score 231 · Answer 5 · 2026-04-09 01:44:44

231

Views

$\int_{1}^{\infty} h(x)\ dx$ converges $\Rightarrow$ $h$ is bounded in $[1, \infty)$

Published on 09 Apr 2026 - 1:44

score 43 · Answer 6 · 2026-04-16 10:04:05

43

Views

$\int_{1}^{\infty} \frac{p(x)}{e^x} dx$ converges?

Published on 16 Apr 2026 - 10:04

score 83 · Answer 7 · 2026-04-15 06:12:56

83

Views

If $f \geq 0$ and $\int_0^{+\infty} f < +\infty$, is $f$ mostly close to $0$ in an asymptotic sense?

Published on 15 Apr 2026 - 6:12

score 57 · Answer 8 · 2026-04-14 23:56:13

57

Views

evaluate the integral \[\int_{a>0}^{\infty}\frac{1}{1+x^{\alpha /2}}dx\]

Published on 14 Apr 2026 - 23:56

score 75 · Answer 9 · 2026-04-11 17:42:52

75

Views

Assuming f and g are continuous and positive, show relation about improper integrals.

Published on 11 Apr 2026 - 17:42

score 136 · Answer 10 · 2026-05-16 06:08:55

136

Views

Integrals with fractions in exponentials

Published on 16 May 2026 - 6:08

score 82 · Answer 11 · 2026-04-17 15:23:54

82

Views

There exists a sequence of real numbers $(x_n)$ such that $\lim_{n \rightarrow \infty}x_n = \infty , \lim_{n \rightarrow \infty}x_nf(x_n)=\infty.$

Published on 17 Apr 2026 - 15:23

score 147 · Answer 12 · 2026-05-15 03:26:19

147

Views

Show that $\lim_{n\rightarrow\infty}\int_{0}^{\infty}\frac{x^{\frac{1}{n}}}{(1+\frac{x}{n})^{n}}dx=1.$

Published on 15 May 2026 - 3:26

score 186 · Answer 13 · 2026-04-11 05:10:52

186

Views

Improper Integral

Published on 11 Apr 2026 - 5:10

score 403 · Answer 14 · 2026-04-12 17:01:17

403

Views

An integral related to the Fourier transform of $\sin(bx)$

Published on 12 Apr 2026 - 17:01

score 149 · Answer 15 · 2026-04-10 05:28:42

149

Views

How do I integrate this using the Fourier transform?

Published on 10 Apr 2026 - 5:28

List Question

Integral of the form $\int_{0}^{\infty}e^{-ax}e^{-x^{4}}dx$

Closed form for the integral \[\int_{0}^{\infty}e^{-ax}e^{-x^{4}}dx\]

How can we integrate integral(s) of this type?

Does $\int_{1}^{\infty} g(x)\ dx$ imply $\lim\limits_{x\to \infty}g(x)=0$?

$\int_{1}^{\infty} h(x)\ dx$ converges $\Rightarrow$ $h$ is bounded in $[1, \infty)$

$\int_{1}^{\infty} \frac{p(x)}{e^x} dx$ converges?

If $f \geq 0$ and $\int_0^{+\infty} f < +\infty$, is $f$ mostly close to $0$ in an asymptotic sense?

evaluate the integral \[\int_{a>0}^{\infty}\frac{1}{1+x^{\alpha /2}}dx\]

Assuming f and g are continuous and positive, show relation about improper integrals.

Integrals with fractions in exponentials

There exists a sequence of real numbers $(x_n)$ such that $\lim_{n \rightarrow \infty}x_n = \infty , \lim_{n \rightarrow \infty}x_nf(x_n)=\infty.$

Show that $\lim_{n\rightarrow\infty}\int_{0}^{\infty}\frac{x^{\frac{1}{n}}}{(1+\frac{x}{n})^{n}}dx=1.$

Improper Integral

An integral related to the Fourier transform of $\sin(bx)$

How do I integrate this using the Fourier transform?

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