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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

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

Aug 15, 2016

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

Nov 1, 2023

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, 2023

Is Wolfram Alpha linear independence wrong or am I missing something?

Aug 11, 2016

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

Jun 2, 2015

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

Jun 25, 2015

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

Oct 25, 2022

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

Nov 27, 2022

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

Sep 25, 2015

Reputation

+25

Volume under a normal distribution in cartesian and polar not integrating to 1

+15

Complex integrals that look like they agree, differ by sign (according to Mathematica)

+10

How to evaluate $\int_{0}^{\frac{\pi}{2}} \frac{1}{(1 + \sin^4(x))\sqrt{1+\sin^2(x)}}\, dx$

+10

Contour integration of an integral

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