Question

Closed form of the integral $\int_{0}^\infty \frac{\tan^{-1}{x} \tan^{-1}{\frac{x}{2}} \tan^{-1}{\frac{x}{3}}}{x^2+1} \, \text{d}x$

score 216 · Answer 1 · 2026-04-16 02:48:16

216

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Closed form of the integral $\int_{0}^\infty \frac{\tan^{-1}{x} \tan^{-1}{\frac{x}{2}} \tan^{-1}{\frac{x}{3}}}{x^2+1} \, \text{d}x$

Published on 16 Apr 2026 - 2:48

score 54 · Answer 2 · 2026-04-15 22:48:16

54

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Functions such that $\lim_{x\to\infty}\frac{1}{x}\int_0^x|f(s)|ds=0.$

Published on 15 Apr 2026 - 22:48

score 2.7k · Answer 3 · 2026-04-15 20:23:12

2.7k

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Integral Reduction for $\sin^7x\cos^3x$

Published on 15 Apr 2026 - 20:23

score 171 · Answer 4 · 2026-04-11 20:35:24

171

Views

Range of the constant of integration

Published on 11 Apr 2026 - 20:35

score 307 · Answer 5 · 2026-03-25 00:02:54

307

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Computing $\iint_{\mathbb R^2}\exp\left(u\frac{xy}{\sqrt{x^2+y^2}}+v\frac{x^2-y^2}{2\sqrt{x^2+y^2}}-\frac12(x^2+y^2)\right)dxdy$

Published on 25 Mar 2026 - 0:02

score 695 · Answer 6 · 2026-04-10 23:05:25

695

Views

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Published on 10 Apr 2026 - 23:05

score 134 · Answer 7 · 2026-04-11 14:51:01

134

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Published on 11 Apr 2026 - 14:51

score 848 · Answer 8 · 2026-04-10 19:37:34

848

Views

Using Fubini's theorem for Riemann integrals

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score 3.7k · Answer 9 · 2026-04-20 09:10:23

3.7k

Views

Proving orthogonality of Legendre polynomials

Published on 20 Apr 2026 - 9:10

score 404 · Answer 10 · 2026-04-16 08:36:59

404

Views

integral $ \int_0^{\frac{\pi}{3}}\mathrm{ln}\left(\frac{\mathrm{sin}(x)}{\mathrm{sin}(x+\frac{\pi}{3})}\right)\ \mathrm{d}x$

Published on 16 Apr 2026 - 8:36

score 613 · Answer 11 · 2026-04-15 16:35:47

613

Views

Finding $\int x\arctan(x)\,dx$ through inverse substitution

Published on 15 Apr 2026 - 16:35

score 1.1k · Answer 12 · 2026-04-09 01:55:16

1.1k

Views

Cauchy Principal Value and Divergent Integrals

Published on 09 Apr 2026 - 1:55

score 1k · Answer 13 · 2026-04-12 13:44:47

1k

Views

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Published on 12 Apr 2026 - 13:44

score 90 · Answer 14 · 2026-04-13 03:52:16

90

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How to determine $ \int \sec^{\frac{1}{3}}(x) dx $?

Published on 13 Apr 2026 - 3:52

score 27 · Answer 15 · 2026-04-15 09:59:50

27

Views

Analyze a particular example of approximation for $\int_N^M(\sin(\pi(t)))^2dt$, where $\pi(x)$ is the prime-counting function

Published on 15 Apr 2026 - 9:59

List Question

Closed form of the integral $\int_{0}^\infty \frac{\tan^{-1}{x} \tan^{-1}{\frac{x}{2}} \tan^{-1}{\frac{x}{3}}}{x^2+1} \, \text{d}x$

Functions such that $\lim_{x\to\infty}\frac{1}{x}\int_0^x|f(s)|ds=0.$

Integral Reduction for $\sin^7x\cos^3x$

Range of the constant of integration

Computing $\iint_{\mathbb R^2}\exp\left(u\frac{xy}{\sqrt{x^2+y^2}}+v\frac{x^2-y^2}{2\sqrt{x^2+y^2}}-\frac12(x^2+y^2)\right)dxdy$

Integrating a function bottom to top vs top to bottom.

Complex definite integral

Using Fubini's theorem for Riemann integrals

Proving orthogonality of Legendre polynomials

integral $ \int_0^{\frac{\pi}{3}}\mathrm{ln}\left(\frac{\mathrm{sin}(x)}{\mathrm{sin}(x+\frac{\pi}{3})}\right)\ \mathrm{d}x$

Finding $\int x\arctan(x)\,dx$ through inverse substitution

Cauchy Principal Value and Divergent Integrals

Solving an integral including a plus distribution.

How to determine $ \int \sec^{\frac{1}{3}}(x) dx $?

Analyze a particular example of approximation for $\int_N^M(\sin(\pi(t)))^2dt$, where $\pi(x)$ is the prime-counting function

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