Question

Find Value of $\int _{0}^{\frac{\pi}{4}} \sqrt{\tan x}{\sqrt{1-\tan x}}\,\mathrm dx$

score 177 · Answer 1 · 2018-08-15 16:17:06

177

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Find Value of $\int _{0}^{\frac{\pi}{4}} \sqrt{\tan x}{\sqrt{1-\tan x}}\,\mathrm dx$

Published on 15 Aug 2018 - 16:17

score 48 · Answer 2 · 2026-03-26 03:09:33

48

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Integration for special sine-function

Published on 26 Mar 2026 - 3:09

score 50 · Answer 3 · 2018-08-17 17:39:31

50

Views

Convergence of $\int_{0}^{+\infty}\left(x^2+\log\left(1+\frac{1}{x^2}\right)\right)^{\alpha}-x^{2\alpha}\,dx$

Published on 17 Aug 2018 - 17:39

score 208 · Answer 4 · 2026-03-25 10:56:59

208

Views

Prove that $\int_{0}^{\infty}{e^{-2(m-2)s}(1+s)^m ds}\leq\frac{1}{m-3}$ for $m>3$.

Published on 25 Mar 2026 - 10:56

score 167 · Answer 5 · 2026-03-26 21:07:22

167

Views

Computation of multiple improper integral.

Published on 26 Mar 2026 - 21:07

score 10.3k · Answer 6 · 2018-08-19 05:07:29

10.3k

Views

Why does the integral of 1/x diverge?

Published on 19 Aug 2018 - 5:07

score 122 · Answer 7 · 2026-03-25 06:12:09

122

Views

Principal value of $\int^\infty_{-\infty}\frac1{x^2}dx$: counter-intuitive?

Published on 25 Mar 2026 - 6:12

score 74 · Answer 8 · 2018-08-19 20:25:32

74

Views

Convergence of$\int_{0}^{+\infty}\frac{1}{\left(\log(x)\right)^{4\alpha}}\sin^2\left(\frac{1}{x^{\alpha}}\right)\,dx$

Published on 19 Aug 2018 - 20:25

score 91 · Answer 9 · 2026-02-23 02:49:14

91

Views

Limits of ${\int\limits_{-\infty}^\infty f(x)e^x\mathrm{d}x}$ changed to $(0,\infty)$ if $f(x)$ is even

Published on 23 Feb 2026 - 2:49

score 133 · Answer 10 · 2018-08-20 04:34:34

133

Views

proving convergence of $\int_1^{\infty} \frac{\ln^5(x)}{x^2}dx$

Published on 20 Aug 2018 - 4:34

score 159 · Answer 11 · 2026-03-26 09:58:09

159

Views

Expressing a Gaussian-like integral in terms of error function, faliure of Glasser's master theorem?

Published on 26 Mar 2026 - 9:58

score 173 · Answer 12 · 2026-03-26 03:10:39

173

Views

Tight upper bound for an improper integral

Published on 26 Mar 2026 - 3:10

score 73 · Answer 13 · 2018-08-21 07:59:36

Convergence of $\int_{0}^{+\infty}\frac{2\alpha x^{\alpha-1}}{1+x^{2\alpha}}\arctan\left(x^{\alpha}\right)\,dx$ as $\alpha \in \mathbb{R}$

score 116 · Answer 14 · 2018-08-21 08:42:21

116

Views

Integrable singularity characterisation

Published on 21 Aug 2018 - 8:42

score 43 · Answer 15 · 2018-08-21 17:13:21

43

Views

Convergence of $\int_{0}^{\frac{\pi}{2}}\sqrt{\frac{\tan(x)}{x|x^x-1|}}\,dx$

Published on 21 Aug 2018 - 17:13

List Question

Find Value of $\int _{0}^{\frac{\pi}{4}} \sqrt{\tan x}{\sqrt{1-\tan x}}\,\mathrm dx$

Integration for special sine-function

Convergence of $\int_{0}^{+\infty}\left(x^2+\log\left(1+\frac{1}{x^2}\right)\right)^{\alpha}-x^{2\alpha}\,dx$

Prove that $\int_{0}^{\infty}{e^{-2(m-2)s}(1+s)^m ds}\leq\frac{1}{m-3}$ for $m>3$.

Computation of multiple improper integral.

Why does the integral of 1/x diverge?

Principal value of $\int^\infty_{-\infty}\frac1{x^2}dx$: counter-intuitive?

Convergence of$\int_{0}^{+\infty}\frac{1}{\left(\log(x)\right)^{4\alpha}}\sin^2\left(\frac{1}{x^{\alpha}}\right)\,dx$

Limits of ${\int\limits_{-\infty}^\infty f(x)e^x\mathrm{d}x}$ changed to $(0,\infty)$ if $f(x)$ is even

proving convergence of $\int_1^{\infty} \frac{\ln^5(x)}{x^2}dx$

Expressing a Gaussian-like integral in terms of error function, faliure of Glasser's master theorem?

Tight upper bound for an improper integral

Convergence of $\int_{0}^{+\infty}\frac{2\alpha x^{\alpha-1}}{1+x^{2\alpha}}\arctan\left(x^{\alpha}\right)\,dx$ as $\alpha \in \mathbb{R}$

Integrable singularity characterisation

Convergence of $\int_{0}^{\frac{\pi}{2}}\sqrt{\frac{\tan(x)}{x|x^x-1|}}\,dx$

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