Hello Sage team,
I ran into a definite integral that Sage can't seem to evaluate,
for no obvious reason. It can correctly find the indefinite
integral for the function, and that is straightforward to evaluate.
Here is the specific example, first as a definite integral then
as an indefinite integral:
% sage
----------------------------------------------------------------------
| Sage Version 4.7.2, Release Date: 2011-10-29 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: integrate(1/(sqrt(x)*((1+sqrt(x))^2)),x,1,9)
integrate(1/((sqrt(x) + 1)^2*sqrt(x)), x, 1, 9)
sage: integrate(1/(sqrt(x)*((1+sqrt(x))^2)),x)
-2/(sqrt(x) + 1)
sage:
Exiting Sage (CPU time 0m0.55s, Wall time 0m15.24s).
Just as a sanity check on whether there is something funny about
this integral that I'm missing, I ran it through the proprietary
competition, but both Maple and Mathematica did fine with it:
% maple
|\^/| Maple 15 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple
Inc. 2011
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
> int(1/(sqrt(x)*((1+sqrt(x))^2)),x=1..9);
1/2
> quit
>
memory used=6.7MB, alloc=5.7MB, time=0.18
% math
Mathematica 8.0 for Linux x86 (64-bit)
Copyright 1988-2010 Wolfram Research, Inc.
In[1]:= Integrate[1/(Sqrt[x]*((1+Sqrt[x])^2)),{x,1,9}]
1
Out[1]= -
2
In[2]:=
% exit
Any ideas on why Sage can't do this one?
Don Winsor
Electrical Engineering and Computer Science dept.
University of Michigan, Ann Arbor
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