May 29, 2018 · I tried searching for how you derive the integral/primitive of $\arctan (x)$, but I can't find any question on S.E with an answer that clearly explains this. I feel that there should be one, since i...

Jan 25, 2022 · In a generalization of this problem: Integral involving product of arctangent and Gaussian, I am trying to calculate the integral $$ I (a,b) = \int_ {\mathbb {R}^2} \arctan^2 {\left ( \frac {y+b} {x+a} \...

Integral of arctan form Ask Question Asked 7 years, 9 months ago Modified 7 years, 9 months ago

Apr 24, 2019 · Here $\operatorname {Cl_2} (z)$ denotes the Clausen Function and $\operatorname {Li}_2 (z)$ the Dilogarithm, or Spence's Function. Recalling the integral representation of the …

Mar 3, 2023 · 2 It’s valid for $|x|\leq 1$ due to the uniform convergence of the Taylor series you obtain after integrating to arctan, but not outside this interval and has to do with not being able to pull that …

Jul 14, 2018 · Question: Show that $$\int\limits_0^ {\infty}\frac {\arctan x\log (1+x^2)} {x (1+x^2)}dx=\frac {\pi}2\log^22.$$ I can't tell if I'm being an idiot, or if this is a lot more difficult than it looks. First, I tried …

Feb 8, 2019 · After seeing this integral, I've decided to give a try and calculate: $$I=\int_0^1 \frac {\arctan x} {x^2-x-1}dx$$ That is because it's common for many integrals to ...

I solved this interesting integral online: $$I = \int\limits_ {-1}^ {1} \arctan (e^x)dx $$ Now I tried the substitution $u=e^x$ but it lead me nowhere. I was looking at the following post which was ...

Oct 19, 2023 · Need help finding a general formula for integrals involving powers of $\arctan$ Ask Question Asked 2 years, 2 months ago Modified 2 years, 2 months ago

Dec 26, 2023 · This implies, \begin {equation} \ln\left (\frac {1+x} {1+a}\right) = \arctan (\sqrt {x}) - \arctan (\sqrt {a}). \end {equation} Which seems like an interesting enough equality to feel like I should have …