Opened 6 years ago
Last modified 2 months ago
#18822 new defect
integral with sqrt*sqrt unsolved
Reported by: | rws | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-9.4 |
Component: | calculus | Keywords: | integral |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
sage: integral(sqrt(x-1)*sqrt(1/x-1/4), x) integrate(sqrt(x - 1)*sqrt(1/x - 1/4), x)
This came up in http://ask.sagemath.org/question/27237/another-problem-with-integral/
Change History (5)
comment:1 Changed 3 years ago by
comment:2 Changed 3 years ago by
- Description modified (diff)
- Summary changed from integral with sqrt*sqrt unsolved while solved when expanded to integral with sqrt*sqrt unsolved
That's right. Elliptic E and F functions with argument containing inverse trig function may already appear as solution to integral(1/sqrt(a+b*x^3), x)
.
comment:3 Changed 7 months ago by
- Keywords integral added
- Milestone changed from sage-6.8 to sage-9.3
comment:4 Changed 7 months ago by
- Description modified (diff)
comment:5 Changed 2 months ago by
- Milestone changed from sage-9.3 to sage-9.4
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I believe this description is wrong, as
sqrt(x-1)*sqrt(1/x-1/4)
is not equal to (note the
x^2
outside of the square root)sqrt(-1/4*x^2 + 5/4*x - 1)/x^2
but it is equal to
sqrt((-1/4*x^2 + 5/4*x - 1)/x)
where
x
is inside the square root (and not the other way around).According to Mathematica,
sqrt(x-1)*sqrt(1/x-1/4)
integrates to a complicated function that involves elliptic integrals.