Opened 7 years ago

Last modified 3 weeks ago

#17910 new task

unsolved piecewise integrals metaticket

Reported by: rws Owned by:
Priority: major Milestone: sage-wishlist
Component: calculus Keywords: integration
Cc: kcrisman Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Status badges

Description (last modified by chapoton)

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)

Change History (10)

comment:1 Changed 7 years ago by rws

  • Description modified (diff)
  • Milestone changed from sage-6.6 to sage-wishlist

comment:2 Changed 6 years ago by kcrisman

  • Cc kcrisman added

comment:3 Changed 6 years ago by rws

  • Description modified (diff)

comment:4 Changed 6 years ago by jdemeyer

Never remove doctests, mark them as # known bug.

comment:5 Changed 2 years ago by chapoton

  • Keywords abs_integrate added

comment:6 Changed 2 years ago by chapoton

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

Last edited 2 years ago by chapoton (previous) (diff)

comment:7 Changed 2 years ago by chapoton

This one hangs in giac:

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

comment:8 Changed 2 years ago by chapoton

  • Description modified (diff)

comment:9 Changed 3 weeks ago by chapoton

  • Description modified (diff)

comment:10 Changed 3 weeks ago by chapoton

  • Keywords integration added; abs_integrate removed
Note: See TracTickets for help on using tickets.