Is the other result incorrect, or just more complicated?

Aaron Meurer

On Tue, May 6, 2014 at 12:20 PM, David Schueler <[email protected]> wrote:
> It seems that sympy cannot properly break apart functions for integration.
>
> Python 2.7.6 |Anaconda 1.9.1 (x86_64)| (default, Jan 10 2014, 11:23:15)
> Type "copyright", "credits" or "license" for more information.
>
> IPython 2.0.0 -- An enhanced Interactive Python.
> ?         -> Introduction and overview of IPython's features.
> %quickref -> Quick reference.
> help      -> Python's own help system.
> object?   -> Details about 'object', use 'object??' for extra details.
> %guiref   -> A brief reference about the graphical user interface.
>
> In [1]: from sympy import *
>
> In [2]: init_session()
> IPython console for SymPy 0.7.5 (Python 2.7.6-64-bit) (ground types: python)
>
> These commands were executed:
>>>> from __future__ import division
>>>> from sympy import *
>>>> x, y, z, t = symbols('x y z t')
>>>> k, m, n = symbols('k m n', integer=True)
>>>> f, g, h = symbols('f g h', cls=Function)
>
> Documentation can be found at http://www.sympy.org
> WARNING: Hook shutdown_hook is deprecated. Use the atexit module instead.
>
>
>
> In [5]: print integrate(expand((x-2)/sqrt(x)),(x,1,4))
> 2/3
>
> In [6]: print integrate((x-2)/sqrt(x),(x,1,4))
> -6
>
> The former is correct based on other calculations.
>
> Also:
>
> print integrate(expand((x-2)/sqrt(x)),x)
> 2*x**(3/2)/3 - 4*sqrt(x)
>
> print integrate((x-2)/sqrt(x),x)
> 2*sqrt(1 + 2/(x - 2))*(x - 2)**(7/2)/(6*x + 3*(x - 2)**2 - 12) - 4*sqrt(1 +
> 2/(x - 2))*(x - 2)**(5/2)/(6*x + 3*(x - 2)**2 - 12) - 16*sqrt(1 + 2/(x -
> 2))*(x - 2)**(3/2)/(6*x + 3*(x - 2)**2 - 12) + 8*sqrt(2)*(x - 2)**2/(6*x +
> 3*(x - 2)**2 - 12) + 16*sqrt(2)*(x - 2)/(6*x + 3*(x - 2)**2 - 12)
>
> Again, the former is correct.
>
> Thoughts?
>
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