Question

Is there a formula for this integral $I(a,b)=\int_0^1 t^{-3/2}(1-t)^{-1/2}\exp\left(-\frac{a^2}{t}-\frac{b^2}{1-t} \right)dt$

score 336 · Answer 1 · 2026-04-16 16:55:56

336

Views

Is there a formula for this integral $I(a,b)=\int_0^1 t^{-3/2}(1-t)^{-1/2}\exp\left(-\frac{a^2}{t}-\frac{b^2}{1-t} \right)dt$

Published on 16 Apr 2026 - 16:55

score 94 · Answer 2 · 2026-04-12 11:44:16

94

Views

Absolute integrability

Published on 12 Apr 2026 - 11:44

score 148 · Answer 3 · 2026-04-10 23:01:51

148

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Is this integral improper? If yes - why?

Published on 10 Apr 2026 - 23:01

score 666 · Answer 4 · 2026-05-06 05:24:26

666

Views

Contradiction to Continuity of Integration?

Published on 06 May 2026 - 5:24

score 45 · Answer 5 · 2026-04-11 05:46:07

45

Views

Comparing two almost identical improper integrals

Published on 11 Apr 2026 - 5:46

score 598 · Answer 6 · 2026-04-15 16:52:31

598

Views

Determine whether this integral converges: $\int_1^\infty\frac{(x+1)\arctan x}{(2x+5)\sqrt x}$

Published on 15 Apr 2026 - 16:52

score 93 · Answer 7 · 2026-04-10 07:32:31

93

Views

Approximating an integral with elementary functions

Published on 10 Apr 2026 - 7:32

score 63 · Answer 8 · 2026-04-15 16:33:50

63

Views

Understanding $\sum^n_{i=1}\int_{(i-1)\pi}^{i\pi}|\frac{\sin x}{x}|\,dx\ge\sum^n_{i=1}\frac{1}{i\pi}\int_{(i-1)\pi}^{i\pi}|\sin x|\,dx$

Published on 15 Apr 2026 - 16:33

score 564 · Answer 9 · 2026-04-15 22:44:23

564

Views

Proving a formula for $\int_0^\infty \frac{\log(1+x^{4n})}{1+x^2}dx $ if $n=1,2,3,\cdots$

Published on 15 Apr 2026 - 22:44

score 343 · Answer 10 · 2026-04-16 13:27:51

343

Views

Laplace transform of $f(t)=10te ^{-5t}$

Published on 16 Apr 2026 - 13:27

score 1.7k · Answer 11 · 2026-04-16 04:11:38

1.7k

Views

How to calculate $ \int_{0}^{\infty} \frac{ x^2 \log(x) }{1 + x^4} $?

Published on 16 Apr 2026 - 4:11

score 69 · Answer 12 · 2026-05-06 05:23:15

69

Views

Conditions on a measure

Published on 06 May 2026 - 5:23

score 9.5k · Answer 13 · 2026-04-16 09:10:49

9.5k

Views

Finding the definite integral $\int_0^1 \log x\,\mathrm dx$

Published on 16 Apr 2026 - 9:10

score 846 · Answer 14 · 2026-04-15 00:19:47

846

Views

Evaluating $\int_0^\infty \frac{e^{-kx}\sin x}x\,\mathrm dx$

Published on 15 Apr 2026 - 0:19

score 312 · Answer 15 · 2026-04-16 14:40:18

312

Views

Is the improper integral $\int_0^\infty \frac{\ln x}{1+x^2}\,\mathrm dx$ convergent?

Published on 16 Apr 2026 - 14:40

List Question

Is there a formula for this integral $I(a,b)=\int_0^1 t^{-3/2}(1-t)^{-1/2}\exp\left(-\frac{a^2}{t}-\frac{b^2}{1-t} \right)dt$

Absolute integrability

Is this integral improper? If yes - why?

Contradiction to Continuity of Integration?

Comparing two almost identical improper integrals

Determine whether this integral converges: $\int_1^\infty\frac{(x+1)\arctan x}{(2x+5)\sqrt x}$

Approximating an integral with elementary functions

Understanding $\sum^n_{i=1}\int_{(i-1)\pi}^{i\pi}|\frac{\sin x}{x}|\,dx\ge\sum^n_{i=1}\frac{1}{i\pi}\int_{(i-1)\pi}^{i\pi}|\sin x|\,dx$

Proving a formula for $\int_0^\infty \frac{\log(1+x^{4n})}{1+x^2}dx $ if $n=1,2,3,\cdots$

Laplace transform of $f(t)=10te ^{-5t}$

How to calculate $ \int_{0}^{\infty} \frac{ x^2 \log(x) }{1 + x^4} $?

Conditions on a measure

Finding the definite integral $\int_0^1 \log x\,\mathrm dx$

Evaluating $\int_0^\infty \frac{e^{-kx}\sin x}x\,\mathrm dx$

Is the improper integral $\int_0^\infty \frac{\ln x}{1+x^2}\,\mathrm dx$ convergent?

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