The following two functions
f(u)=-u/2+min_symbolic(0,u) + min_symbolic(u,2*u) and
g(u)=-u/2+min_symbolic(u, 3*u)
are mathematically equivalent, but the following symbolic integrals give
different results.
F(x)=integral(f(u)*u*exp(x*u),u,-1,1)
FF(y)=F(y)
G(x)=integral(g(u)*u*exp(x*u),u,-1,
The following Sage code
var('u')
integrate(-1/8*(u - 2*min_symbolic(-1/2*u - 1/2, 1/2*u - 1/2) - 1)^2 +
1/2*(min_symbolic(0, u) + 1)^2,u,-1,1)
produces 1/2 as a (correct) result with SageMath 8.3 (running with Software
Environment Ubuntu 18.04 @ 2018-08-27 in CoCalc).
With SageMath 9.3 (ru
