Updates:
        Status: Duplicate
        Mergedinto: 1374

Comment #3 on issue 3611 by [email protected]: sqrt(x) should be the same as x ** 0.5
http://code.google.com/p/sympy/issues/detail?id=3611

Don't worry, not saying hello is not considered rude. See http://producingoss.com/en/communications.html#rudeness.

The reason is that in a multiplication, the powers cancel, so that it becomes x**(0.), which is just x**0 == 1 (see issue 3446, issue 2340, and probably several others).

The Add one is the other issue I noted (issue 1374).  The worst part is:

In [28]: S.Half == 0.5
Out[28]: True

In [29]: x**S.Half == x**0.5
Out[29]: True

In [30]: x**S.Half + x**0.5
Out[30]:
 0.5     ___
x    + ╲╱ x

Meaning that the seemingly obvious invariant x == y implies x - y == 0 does not actually hold here.

Let's keep those other issues for the equality of sqrt(x) and x**0.5, since there's already a lot of discussion about them there (particularly on issue 1374). For the integral, it looks like it's already been fixed in master:

In [32]: integrate (exp (x ** .5), x)
Out[32]:
          ⎛ 0.5⎞        ⎛ 0.5⎞
     0.5  ⎝x   ⎠        ⎝x   ⎠
2.0⋅x   ⋅ℯ       - 2.0⋅ℯ

In [33]: integrate (exp (x ** .5), x, meijerg=True)
Out[33]:
     2.0⋅ⅈ⋅π │ -4.0⋅ⅈ⋅π│  ⎛      0.5  ⅈ⋅π⎞
2.0⋅ℯ       ⋅│ℯ        │⋅γ⎝2.0, x   ⋅ℯ   ⎠

So I am closing this.

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