Question

$\int_0^\infty \left(\sqrt[4]{1+x^4}-x\right)\,\mathrm{d}x$ related to Beta function

score 131 · Answer 1 · 2026-03-26 06:25:48

131

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$\int_0^\infty \left(\sqrt[4]{1+x^4}-x\right)\,\mathrm{d}x$ related to Beta function

Published on 26 Mar 2026 - 6:25

score 49 · Answer 2 · 2020-04-29 03:35:59

49

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For which $a$, the integral $\int_{0}^{1}\frac{1-x^a}{1-x}dx$ converges

Published on 29 Apr 2020 - 3:35

score 65 · Answer 3 · 2020-04-29 18:36:00

65

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How do I solve the double integral $\int_{0}^\infty\int_{0}^\infty e^{-(x+y)^2-3y^2} dxdy$?

Published on 29 Apr 2020 - 18:36

score 484 · Answer 4 · 2020-04-30 08:27:18

484

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Counter-example for integration by parts with improper integrals

Published on 30 Apr 2020 - 8:27

score 82 · Answer 5 · 2020-04-30 10:22:41

82

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how to show $\int_{1}^{\infty}\frac{(\log x)^a}{x^p}\,dx$ is improper integrable

Published on 30 Apr 2020 - 10:22

score 311 · Answer 6 · 2026-04-05 23:45:25

311

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Need help proving an analogue of the Weierstrauss M-Test for Improper Integrals:

Published on 05 Apr 2026 - 23:45

score 145 · Answer 7 · 2020-05-01 11:55:40

145

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Solving $\displaystyle \int_{-\tan^{-1}\sqrt{4a^2-1}}^{\tan^{-1}\sqrt{4a^2-1}}\log(2\cos \theta)d\theta$

Published on 01 May 2020 - 11:55

score 96 · Answer 8 · 2026-04-04 10:23:40

96

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Integral of $x^{-1} \cos(x)$ from $1$ to $\infty$

Published on 04 Apr 2026 - 10:23

score 67 · Answer 9 · 2026-04-06 01:27:11

67

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A proof involving derivatives of improper integrals of the form $\int_c^\infty f(x,t)dt$

Published on 06 Apr 2026 - 1:27

score 48 · Answer 10 · 2020-05-02 00:00:15

48

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Choose function so integral converges

Published on 02 May 2020 - 0:00

score 114 · Answer 11 · 2020-05-02 02:45:16

114

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If $f(x)$ is Integrable, $\int_{0}^{\infty}f(x)dx$ converges and $g(x) \geq x \Rightarrow \lim_{x \to \infty} \int_{x}^{g(x)}f(t)dt = 0$

Published on 02 May 2020 - 2:45

score 442 · Answer 12 · 2026-03-25 12:54:03

442

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How do you integrate $\int_{0}^\infty \frac{\log(x)^2}{(1-x^2)^2}$ using contour integration?

Published on 25 Mar 2026 - 12:54

score 379 · Answer 13 · 2020-05-03 21:00:12

379

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How to compute $\int_0^{\frac{\pi}{2}}\frac{\arctan(\sqrt{\tan(x)})}{\tan(x)}dx$

Published on 03 May 2020 - 21:00

score 177 · Answer 14 · 2020-05-04 09:55:52

177

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Let $\alpha \in (0,\infty) $. Calculate, if possible: $\int_1^\infty \sin(x) x^{-\alpha} \,dx$

Published on 04 May 2020 - 9:55

score 69 · Answer 15 · 2020-05-04 16:49:55

69

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A question related to improper integrals

Published on 04 May 2020 - 16:49

List Question

$\int_0^\infty \left(\sqrt[4]{1+x^4}-x\right)\,\mathrm{d}x$ related to Beta function

For which $a$, the integral $\int_{0}^{1}\frac{1-x^a}{1-x}dx$ converges

How do I solve the double integral $\int_{0}^\infty\int_{0}^\infty e^{-(x+y)^2-3y^2} dxdy$?

Counter-example for integration by parts with improper integrals

how to show $\int_{1}^{\infty}\frac{(\log x)^a}{x^p}\,dx$ is improper integrable

Need help proving an analogue of the Weierstrauss M-Test for Improper Integrals:

Solving $\displaystyle \int_{-\tan^{-1}\sqrt{4a^2-1}}^{\tan^{-1}\sqrt{4a^2-1}}\log(2\cos \theta)d\theta$

Integral of $x^{-1} \cos(x)$ from $1$ to $\infty$

A proof involving derivatives of improper integrals of the form $\int_c^\infty f(x,t)dt$

Choose function so integral converges

If $f(x)$ is Integrable, $\int_{0}^{\infty}f(x)dx$ converges and $g(x) \geq x \Rightarrow \lim_{x \to \infty} \int_{x}^{g(x)}f(t)dt = 0$

How do you integrate $\int_{0}^\infty \frac{\log(x)^2}{(1-x^2)^2}$ using contour integration?

How to compute $\int_0^{\frac{\pi}{2}}\frac{\arctan(\sqrt{\tan(x)})}{\tan(x)}dx$

Let $\alpha \in (0,\infty) $. Calculate, if possible: $\int_1^\infty \sin(x) x^{-\alpha} \,dx$

A question related to improper integrals

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