unsolved piecewise integrals metaticket

[rws]

Archive of removed doctests testing the abs_integrate Maxima package (removed with #12731).

sage: y = function('y')                                                           
sage: integrate(1/sqrt(abs(y(x))), y(x))  # ok                                       
integrate(diff(y(x), x)/sqrt(abs(y(x))), x)

sage: integrate(sgn(x) - sgn(1-x), x)   # ok                                           
abs(x - 1) + abs(x)

sage: integrate(1 / (1 + abs(x-5)), x, -5, 6)     # ok                                 
log(11) + log(2)

sage: integrate(1/(1 + abs(x)), x)   # ok                                           
log(abs(x*sgn(x) + 1))/sgn(x)

sage: integrate(cos(x + abs(x)), x)      # ok                                       
sin(x*sgn(x) + x)/(sgn(x) + 1)

sage: integrate(sqrt(x + sqrt(x)), x).canonicalize_radical()      # ok              
1/12*(8*x + 2*sqrt(x) - 3)*sqrt(x + sqrt(x)) - 1/8*log(abs(2*sqrt(x + sqrt(x)) - 2*sqrt(x) - 1))

sage: integrate(abs(x^2 - 1), x, -2, 2) # ok                      
4

sage: f = sqrt(x + 1/x^2)
sage: integral(f, x)  # to be checked
2/3*sqrt(x^3 + 1) - 1/3*log(sqrt(x^3 + 1) + 1) + 1/3*log(sqrt(x^3 + 1) - 1)

sage: f1(x) = e^(-abs(x))
sage: f = Piecewise([[(-infinity, infinity), f1]])
sage: f.integral(definite=True)  # ok
2
sage: f.integral()
Piecewise defined function with 1 parts, [[(-Infinity, +Infinity), x |--> -1/2*((sgn(x) - 1)*e^(2*x) - 2*e^x*sgn(x) + sgn(x) + 1)*e^(-x) - 1]]

Also, these have their own tickets:

• integrate(x * sgn(x^2 - 1/4), x, -1, 0) (#11590)
• integral(log(abs(2*sin(u))), u, 0, pi/3) (#17468)
• integrate(abs(cos(x)),x,0,pi) (#17511)

[jdemeyer]

Never remove doctests, mark them as # known bug.

[chapoton]

EDIT: 6 out of the first seven are working after #27958 (and none without)

[chapoton]

This one hangs in giac:

integrate(sqrt(x + sqrt(x)), x)