incorrect integration of fractions

[David Schueler]

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)
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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?

[Aaron Meurer]

Is the other result incorrect, or just more complicated?

Aaron Meurer

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[Ondřej Čertík]

The latter is incorrect, since when you integrate you get the wrong
result (or the definite integral doesn't work).

That's a big bug, thanks for reporting it!

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