Question

What is the antiderivative of $e^{-x^2}$

score 24k · Answer 1 · 2026-03-28 16:45:51

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What is the antiderivative of $e^{-x^2}$

Published on 28 Mar 2026 - 16:45

score 4.7k · Answer 2 · 2026-04-03 01:54:03

4.7k

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Fourier transform of $\left|\frac{\sin x}{x}\right|$

Published on 03 Apr 2026 - 1:54

score 3.1k · Answer 3 · 2013-10-13 09:05:49

3.1k

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Evaluating $\int_0^1 \frac{\log x \log \left(1-x^4 \right)}{1+x^2}dx$

Published on 13 Oct 2013 - 9:05

score 161 · Answer 4 · 2013-10-13 22:12:28

161

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Need your help with the integral $\int_0^\infty\frac{dx}{e^{\,e^{-x}} \cdot e^{\,e^{x}}}$.

Published on 13 Oct 2013 - 22:12

score 1.5k · Answer 5 · 2013-10-14 03:24:15

1.5k

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Integral $\int_0^1\frac{x^9\left(x^4+x^2-x-1-5\ln x\right)}{\left(x^{10}-1\right)\ln x}\mathrm dx$

Published on 14 Oct 2013 - 3:24

score 658 · Answer 6 · 2013-10-15 17:58:27

658

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Closed form for $\int_0^\infty\frac{\sqrt{x+\sqrt{x^2+1}}}{\sqrt{x\phantom{|}}\sqrt{x^2+1}}e^{-x}dx$

Published on 15 Oct 2013 - 17:58

score 874 · Answer 7 · 2026-04-06 16:55:52

874

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Infinite Series $\sum\limits_{n=2}^{\infty}\frac{(-1)^n}{n^k}\zeta(n)$

Published on 06 Apr 2026 - 16:55

score 782 · Answer 8 · 2026-03-30 03:39:16

782

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Prove $_4F_3(1/8,3/8,5/8,7/8;1/4,1/2,3/4;1/2)=\frac{\sqrt{2-\sqrt2+\sqrt{2-\sqrt2}}+\sqrt{2+\sqrt2+\sqrt{2+\sqrt2}}}{2\,\sqrt2}$

Published on 30 Mar 2026 - 3:39

score 212 · Answer 9 · 2013-10-20 18:48:14

212

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An integral involving the inverse of $f(x)=\log x-\log\cos x+x\tan x$

Published on 20 Oct 2013 - 18:48

score 1.7k · Answer 10 · 2013-10-24 06:28:35

1.7k

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Improper Integral $\int\limits_0^1\frac{\ln(x)}{x^2-1}\,dx$

Published on 24 Oct 2013 - 6:28

score 5.5k · Answer 11 · 2026-03-30 03:39:12

5.5k

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Conjecture $\int_0^1\frac{dx}{\sqrt[3]x\,\sqrt[6]{1-x}\,\sqrt{1-x\left(\sqrt{6}\sqrt{12+7\sqrt3}-3\sqrt3-6\right)^2}}=\frac\pi9(3+\sqrt2\sqrt[4]{27})$

Published on 30 Mar 2026 - 3:39

score 641 · Answer 12 · 2013-10-26 14:58:09

641

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Does the sequence $1,-1,1,1,-1,1,1,1,-1,1,1,1,1,-1,1,1,1,1,1,-1,\ldots$ have a closed form?

Published on 26 Oct 2013 - 14:58

score 7.3k · Answer 13 · 2026-03-30 03:38:24

7.3k

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Conjecture $\int_0^1\frac{\mathrm dx}{\sqrt{1-x}\ \sqrt[4]x\ \sqrt[4]{2-x\,\sqrt3}}\stackrel?=\frac{2\,\sqrt2}{3\,\sqrt[8]3}\pi$

Published on 30 Mar 2026 - 3:38

score 573 · Answer 14 · 2013-10-28 05:21:30

573

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Further our knowledge of a certain class of integral involving logarithms.

Published on 28 Oct 2013 - 5:21

score 5.7k · Answer 15 · 2026-04-04 12:10:33

5.7k

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Finite Sum $\sum\limits_{k=1}^{m-1}\frac{1}{\sin^2\frac{k\pi}{m}}$

Published on 04 Apr 2026 - 12:10

List Question

What is the antiderivative of $e^{-x^2}$

Fourier transform of $\left|\frac{\sin x}{x}\right|$

Evaluating $\int_0^1 \frac{\log x \log \left(1-x^4 \right)}{1+x^2}dx$

Need your help with the integral $\int_0^\infty\frac{dx}{e^{\,e^{-x}} \cdot e^{\,e^{x}}}$.

Integral $\int_0^1\frac{x^9\left(x^4+x^2-x-1-5\ln x\right)}{\left(x^{10}-1\right)\ln x}\mathrm dx$

Closed form for $\int_0^\infty\frac{\sqrt{x+\sqrt{x^2+1}}}{\sqrt{x\phantom{|}}\sqrt{x^2+1}}e^{-x}dx$

Infinite Series $\sum\limits_{n=2}^{\infty}\frac{(-1)^n}{n^k}\zeta(n)$

Prove $_4F_3(1/8,3/8,5/8,7/8;1/4,1/2,3/4;1/2)=\frac{\sqrt{2-\sqrt2+\sqrt{2-\sqrt2}}+\sqrt{2+\sqrt2+\sqrt{2+\sqrt2}}}{2\,\sqrt2}$

An integral involving the inverse of $f(x)=\log x-\log\cos x+x\tan x$

Improper Integral $\int\limits_0^1\frac{\ln(x)}{x^2-1}\,dx$

Conjecture $\int_0^1\frac{dx}{\sqrt[3]x\,\sqrt[6]{1-x}\,\sqrt{1-x\left(\sqrt{6}\sqrt{12+7\sqrt3}-3\sqrt3-6\right)^2}}=\frac\pi9(3+\sqrt2\sqrt[4]{27})$

Does the sequence $1,-1,1,1,-1,1,1,1,-1,1,1,1,1,-1,1,1,1,1,1,-1,\ldots$ have a closed form?

Conjecture $\int_0^1\frac{\mathrm dx}{\sqrt{1-x}\ \sqrt[4]x\ \sqrt[4]{2-x\,\sqrt3}}\stackrel?=\frac{2\,\sqrt2}{3\,\sqrt[8]3}\pi$

Further our knowledge of a certain class of integral involving logarithms.

Finite Sum $\sum\limits_{k=1}^{m-1}\frac{1}{\sin^2\frac{k\pi}{m}}$

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