Re: Have I found a bug?

*To*: mathgroup at smc.vnet.net*Subject*: [mg84253] Re: Have I found a bug?*From*: Norbert Marxer <marxer at mec.li>*Date*: Sun, 16 Dec 2007 05:35:56 -0500 (EST)*References*: <fjtgdu$7hm$1@smc.vnet.net>

On 14 Dez., 09:55, Louise Hoffman <louise.hoff... at gmail.com> wrote: > Dear readers, > > When I calc. this in Mathematica 5.2 > > g[x_] := 1 - x^2 > h[x_] := -x > Exp[-Integrate[ (D[g[x], x] - h[x])/g[x], x ] ] > > it returns > 1/Sqrt[-1+x^2] > > where I would expect > > 1/Sqrt[1-x^2] > > Have I found a bug, or have I made a mistake? > > Lots of love, > Louise Hello Whe you perform an indefinite integration the solution is only unique up to an additive constant. In Mathematica you can add this additive constant (c[1]) by hand ... g[x_] := 1 - x^2 h[x_] := -x Exp[-(Integrate[(D[g[x], x] - h[x])/g[x], x] + c[1])] ... and get a solution depending on this addive constant ... 1/(E^c[1]*Sqrt[-1 + x^2]) For c[1] -> 0 you get the standard solution: 1/Sqrt[-1 + x^2] For c[1] -> (I*Pi)/2 you get your solution 1/Sqrt[1- x^2] which corresponds to -(I/Sqrt[-1 + x^2]) ... as is shown by the following command: Exp[-(Integrate[(D[g[x], x] - h[x])/g[x], x] + c[1])] /. c[1] -> 0 Exp[-(Integrate[(D[g[x], x] - h[x])/g[x], x] + c[1])] /. c[1] -> (I*Pi)/2 Best Regards Norbert Marxer