Opened 4 years ago

Last modified 14 months ago

#18822 new defect

integral with sqrt*sqrt unsolved

Reported by: rws Owned by:
Priority: major Milestone: sage-6.8
Component: calculus Keywords:
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
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Description (last modified by rws)

sage: integral(sqrt(x-1)*sqrt(1/x-1/4))
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 (2)

comment:1 Changed 14 months ago by mafra

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.

comment:2 Changed 14 months ago by rws

  • 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).

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