/soy/ - Soyjaks

x = Ϫ

π √((√5 - 1)/2) (or equivalently π / √φ, where φ = (1 + √5)/2 is the golden ratio).
This matches the numerical value ≈ 2.469767 (computed via quadrature).
Quick derivation outline (Feynman's trick or other methods)
One way to derive it is to consider the parameterized integral
I(a) = ∫₀^∞ arctan(a / (x² + 1)) dx,
differentiate under the integral sign to get a rational integrand in x, integrate that (via factoring the resulting quartic denominator into quadratics involving √(1 + a²)), and solve the resulting ODE for I(a) with I(0) = 0. At a = 2 it yields the golden-ratio form.
Alternative approaches (as seen in sources) include integration by parts, trigonometric substitution (x = tan θ), or contour integration in the complex plane. The connection to φ arises naturally from the quadratic roots when evaluating the antiderivative or definite limits.
The integral converges nicely (the integrand behaves like arctan(2/x²) ~ 2/x² at infinity and is bounded near 0).

porbably pi or something like that

use AI maybe

>>16158764
That's correct… nusois have become too good

>>16158790
meds he vibemathed it

>>16158817
most people here are too retarded/autistic to solve any maths problem so what do you really expect?

I HATE integrals, so no.

I can’t do differential equations yet, post again in 5 months

i plan to learn integral calculus by reading a textbook please ask this again in a year

>>16158966
we :transheart: integrals here xister

>>16158972
same

>>16158881
do i take the time to finish ts (am actually in brapuversity studying maths geg)