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: |
Description (last modified by )
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:
Change History (10)
comment:1 Changed 7 years ago by
- Description modified (diff)
- Milestone changed from sage-6.6 to sage-wishlist
comment:2 Changed 6 years ago by
- Cc kcrisman added
comment:3 Changed 6 years ago by
- Description modified (diff)
comment:4 Changed 6 years ago by
comment:5 Changed 2 years ago by
- Keywords abs_integrate added
comment:6 Changed 2 years ago by
EDIT: 6 out of the first seven are working after #27958 (and none without)
comment:7 Changed 2 years ago by
This one hangs in giac:
integrate(sqrt(x + sqrt(x)), x)
comment:8 Changed 2 years ago by
- Description modified (diff)
comment:9 Changed 3 weeks ago by
- Description modified (diff)
comment:10 Changed 3 weeks ago by
- Keywords integration added; abs_integrate removed
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