user170231

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integration

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14

What is an intuitive approach to solving $\lim_{n\rightarrow\infty}\biggl(\frac{1}{n^2} + \frac{2}{n^2} + \frac{3}{n^2}+\dots+\frac{n}{n^2}\biggr)$?

Jul 27, 2017

12

How to evaluate $\int \frac{1+x}{1+\sqrt x} dx$

Aug 15, 2016

10

Find the value of the integral: $\int_{0}^{1}\frac{x}{1+x^4}\arctan(x)\,\mathrm{d}x$

Nov 1

9

Any different way to solve an integral involving a trigonometric ratio?

Jul 26

9

Prove $_4 F_3\left(2,\frac32,\frac32,\frac32;\frac52,\frac52,\frac52;1\right)=\frac{27}{16}\left(\pi^2-7\zeta(3)\right) $

Aug 21

Questions

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32

Does $\int_{-1}^1\frac{\arctan x}{\text{arctanh}\,x}\,\mathrm{d}x$ have a closed form?

Jun 2, 2015

17

Why doesn't using the approximation $\sin x\approx x$ near $0$ work for computing this limit?

Jun 25, 2015

17

Using complex analysis, show that $\int_0^\infty\frac{\arctan(x)}{1+x^2}\,dx=\frac{\pi^2}8$

Oct 25, 2022

12

Using complex analysis, prove $\int\limits_0^\infty \frac{\log(x) \arctan(x)}{1 + x^2} \, dx = \frac78 \zeta(3)$

Nov 27, 2022

10

Are there certain conditions that $a_n$ must meet in order for this series to converge?

Sep 25, 2015

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integration

449

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calculus

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277

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definite-integrals

213

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124

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multivariable-calculus

91

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90

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sequences-and-series

86

Score

72

posts

Reputation

+20

Integral: $\int_{0}^{2\pi}\arctan\left(\frac{1+2\cos x}{\sqrt{3}}\right)dx$

+10

How to Evaluate $\int_0^1 {\frac{{u\arcsin u}}{{{u^4} + 2{u^2} + 13}}du} .$?

+10

Complex integral:- $ \int_0^\infty \frac{1}{x^3+1} dx$ using an unusual contour

+10

How can we guess one solution of the equation $y''+\frac{2}{x}y'+y=0$?

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