Re: Re: Mathematica integration Vs Sympy

*To*: mathgroup at smc.vnet.net*Subject*: [mg130571] Re: [mg130564] Re: Mathematica integration Vs Sympy*From*: Alex Krasnov <akrasnov at eecs.berkeley.edu>*Date*: Mon, 22 Apr 2013 03:11:28 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20130420094229.B63996A64@smc.vnet.net> <20130421091626.26FB96AC3@smc.vnet.net>

In this case, the results are valid for a=1 in the sense of a limit, as Limit[u, a -> 1] and limit(u, a, 1) demonstrate. This is not always the case. Example: In: f = Integrate[x^n, x] Out: x^(1 + n)/(1 + n) In: Limit[f, n -> -1, Direction -> 1] Out: -Infinity In: Limit[f, n -> -1, Direction -> -1] Out: Infinity Alex On Sun, 21 Apr 2013, Brentt wrote: > > The result: > > In[0]: Integrate[1/(x*(1 - a*(1 - x))), x] > Out[0]: (Log[1 + a (-1 + x)] - Log[x])/(-1 + a) > > Seems to be true for all complex a and x . Why do you think it assumes a>1? > > > > > > > > On Sat, Apr 20, 2013 at 2:42 AM, Sergio R <sergiorquestion at gmail.com> wrote: > >> Hello all, >> >> Just for fun a put an integral I was doing via mathematica >> WolframAlpha >> [ >> http://www.wolframalpha.com/input/?i=Integrate[1%2F%28x*%281-a*%281-x%29%29%29%2Cx] >> ] >> into the online sympy [ http://live.sympy.org/ ] console >> the following: >> >> a = Symbol('a'); g = 1/(x*(1-a*(1-x))) ; u=simplify(integrate(g,x)) >> >> Then, to display the result, at the sympy ">>>" prompt, type u >> and hit return. >> >> To my surprise, sympy seems to give the right result without any >> assumption, while mathematica's result seems to assume a>1, which is >> not specified. Also for this case (a>1) sympy gives an extra constant >> which is not present in the mathematica result. >> >> Is there a way to make mathematica to output a general result like >> sympy >> in this case? >> >> Sergio >> >> > >

**References**:**Mathematica integration Vs Sympy***From:*Sergio R <sergiorquestion@gmail.com>

**Re: Mathematica integration Vs Sympy***From:*Brentt <brenttnewman@gmail.com>