#17910: unsolved piecewise integrals metaticket
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Reporter: rws | Owner:
Type: task | Status: new
Priority: major | Milestone: sage-wishlist
Component: calculus | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by rws:
Old description:
> Archive of removed doctests testing the `abs_integrate` Maxima package
> (removed with #12731).
>
> {{{
> integrate(1/sqrt(abs(y(x))), y(x))
> integrate(sgn(x) - sgn(1-x), x)
> integrate(1 / (1 + abs(x-5)), x, -5, 6)
> integrate(1/(1 + abs(x)), x)
> integrate(cos(x + abs(x)), x)
> integrate(sqrt(x + sqrt(x)), x).canonicalize_radical()
> integrate(abs(x^2 - 1), x, -2, 2)
>
> - sage: f = sqrt(x + 1/x^2)
> - sage: maxima = sage.calculus.calculus.maxima
> - sage: maxima('radexpand')
> - true
> - sage: integrate(f, x)
> - integrate(sqrt(x + 1/x^2), x)
> - sage: maxima('radexpand: all')
> - all
> - sage: g = integrate(f, x); g
> - 2/3*sqrt(x^3 + 1) - 1/3*log(sqrt(x^3 + 1) + 1) +
> 1/3*log(sqrt(x^3 + 1) - 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)
New description:
Archive of removed doctests testing the `abs_integrate` Maxima package
(removed with #12731).
{{{
integrate(1/sqrt(abs(y(x))), y(x))
integrate(sgn(x) - sgn(1-x), x)
integrate(1 / (1 + abs(x-5)), x, -5, 6)
integrate(1/(1 + abs(x)), x)
integrate(cos(x + abs(x)), x)
integrate(sqrt(x + sqrt(x)), x).canonicalize_radical()
integrate(abs(x^2 - 1), x, -2, 2)
- sage: f = sqrt(x + 1/x^2)
- sage: maxima = sage.calculus.calculus.maxima
- sage: maxima('radexpand')
- true
- sage: integrate(f, x)
- integrate(sqrt(x + 1/x^2), x)
- sage: maxima('radexpand: all')
- all
- sage: g = integrate(f, x); g
- 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)
- 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)
--
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Ticket URL: <http://trac.sagemath.org/ticket/17910#comment:3>
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