Question

How to integrate $\int _1^{\infty }\frac{dx}{\left(x^2+1\right)\sqrt{x^2-1}}= \;?$

score 379 · Answer 1 · 2026-04-15 17:47:18

379

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How to integrate $\int _1^{\infty }\frac{dx}{\left(x^2+1\right)\sqrt{x^2-1}}= \;?$

Published on 15 Apr 2026 - 17:47

score 284 · Answer 2 · 2026-04-17 02:15:59

284

Views

How to Solve this definite integral: $\sqrt{\frac{2}{\pi}} \int\limits^\infty_t \frac{1}{x^2+1} e^{-\frac{x^2}{2}}dx$

Published on 17 Apr 2026 - 2:15

score 65 · Answer 3 · 2026-04-13 18:38:43

65

Views

Short-time Fourier Transform identity in $L^2$

Published on 13 Apr 2026 - 18:38

score 183 · Answer 4 · 2026-04-16 10:06:22

183

Views

Convergence of the integral: $I_{\alpha }=\int _0^{\infty }\left(\frac{e^{-\alpha x}}{\sqrt{x}}\right)\:dx$

Published on 16 Apr 2026 - 10:06

score 94 · Answer 5 · 2026-04-12 03:20:47

94

Views

Where is the mistake of a possible application of Frullani's theorem in this case?

Published on 12 Apr 2026 - 3:20

score 63 · Answer 6 · 2026-04-14 18:13:20

63

Views

Continuous positive function such that $\int\limits_1^{\infty}f(x)dx$ converges, while $\int\limits_1^{\infty}f^2(x)dx$ diverges

Published on 14 Apr 2026 - 18:13

score 123 · Answer 7 · 2026-03-27 18:49:40

123

Views

convergence of $\int _0^1\:\frac{\ln\left(1-x\right)}{\left(1+x\right)^2}dx$

Published on 27 Mar 2026 - 18:49

score 53 · Answer 8 · 2026-04-16 16:02:56

53

Views

Inner product on $\mathbb{R}[X]$

Published on 16 Apr 2026 - 16:02

score 172 · Answer 9 · 2026-04-13 00:40:44

172

Views

Comparison test with improper integral

Published on 13 Apr 2026 - 0:40

score 1.9k · Answer 10 · 2026-04-10 16:33:33

1.9k

Views

Limits at infinity of a function with convergent improper integral

Published on 10 Apr 2026 - 16:33

score 49 · Answer 11 · 2026-04-10 08:00:09

49

Views

Is the following integral identity true or not?

Published on 10 Apr 2026 - 8:00

score 562 · Answer 12 · 2026-04-15 22:03:48

562

Views

Improper integral - checking convergence of $\int_{1}^{\infty} x^2 \sin(x^4) dx$

Published on 15 Apr 2026 - 22:03

score 158 · Answer 13 · 2026-04-13 00:36:38

158

Views

Proving that a function is integrable

Published on 13 Apr 2026 - 0:36

score 93 · Answer 14 · 2026-05-05 21:41:40

93

Views

Lebesgue integral of $\frac{1}{\|\boldsymbol{x}-\boldsymbol{r}\|^2}$ on an infinite cylinder

Published on 05 May 2026 - 21:41

score 456 · Answer 15 · 2026-04-16 06:33:20

456

Views

Why is $\int_{-1}^{1} \frac{1}x \mathrm{d}x$ divergent?

Published on 16 Apr 2026 - 6:33

List Question

How to integrate $\int _1^{\infty }\frac{dx}{\left(x^2+1\right)\sqrt{x^2-1}}= \;?$

How to Solve this definite integral: $\sqrt{\frac{2}{\pi}} \int\limits^\infty_t \frac{1}{x^2+1} e^{-\frac{x^2}{2}}dx$

Short-time Fourier Transform identity in $L^2$

Convergence of the integral: $I_{\alpha }=\int _0^{\infty }\left(\frac{e^{-\alpha x}}{\sqrt{x}}\right)\:dx$

Where is the mistake of a possible application of Frullani's theorem in this case?

Continuous positive function such that $\int\limits_1^{\infty}f(x)dx$ converges, while $\int\limits_1^{\infty}f^2(x)dx$ diverges

convergence of $\int _0^1\:\frac{\ln\left(1-x\right)}{\left(1+x\right)^2}dx$

Inner product on $\mathbb{R}[X]$

Comparison test with improper integral

Limits at infinity of a function with convergent improper integral

Is the following integral identity true or not?

Improper integral - checking convergence of $\int_{1}^{\infty} x^2 \sin(x^4) dx$

Proving that a function is integrable

Lebesgue integral of $\frac{1}{\|\boldsymbol{x}-\boldsymbol{r}\|^2}$ on an infinite cylinder

Why is $\int_{-1}^{1} \frac{1}x \mathrm{d}x$ divergent?

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