How do you find the primitive/integral of $\arctan (x)$?
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 …
Interesting $\\arctan$ integral - Mathematics Stack Exchange
Jan 25, 2022 · In a generalization of this problem: Integral involving product of arctangent and Gaussian, I am trying to calculate the integral $$ I (a,b) = \int_ {\mathbb {R}^2} \arctan^2 {\left ( …
calculus - Integral of arctan form - Mathematics Stack Exchange
Integral of arctan form Ask Question Asked 7 years, 9 months ago Modified 7 years, 9 months ago
How to integrate $\arctan^2 (x)$ - Mathematics Stack Exchange
Apr 24, 2019 · Here $\operatorname {Cl_2} (z)$ denotes the Clausen Function and $\operatorname {Li}_2 (z)$ the Dilogarithm, or Spence's Function. Recalling the integral …
Valid proof for integral of $1/ (x^2+a^2)$ - Mathematics Stack …
Mar 3, 2023 · 2 It’s valid for $|x|\leq 1$ due to the uniform convergence of the Taylor series you obtain after integrating to arctan, but not outside this interval and has to do with not being able …
Evaluate $\\int_0^{\\frac{\\pi}{4}}\\arctan\\sqrt{\\frac{\\cos 2x}{2 ...
$\require {cancel}$ This answer provides for the calculation of the following integral $$\bbox [#f2e6ed,border: 5px dashed #753609,20px] {\large\mathcal {I} = \int\limits_ {0}^ {\tfrac {\pi} …
Difficult integral $\\int_0^{\\infty}\\frac {\\arctan x\\log(1+x^2)}{x ...
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 …
calculus - Integral $\int_0^1 \frac {\arctan x} {x^2-x-1}dx ...
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 ...
An interesting integral $I = \int\limits_ {-1}^ {1} \arctan (e^x)dx
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 ...
calculus - Need help finding a general formula for integrals …
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