Re: Mathematica not considering an assumption

*To*: mathgroup at smc.vnet.net*Subject*: [mg82669] Re: Mathematica not considering an assumption*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sun, 28 Oct 2007 03:57:28 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <ffv36o$bf0$1@smc.vnet.net>

matematica65 at gmail.com wrote: > Assuming[a < 0,Integrate[x^a, {x, 5, 6}]}] ------------------------------------------^ Syntax error: extraneous curly bracket. > This Integral, for a = -1, is equal to Log(6/5) > > Why doesn't Mathematica report it? Usually, functions like *Integrate* return the most general solution, solution applicable in most cases, without returning any constants of integration or restrictions on the domain or special cases. For instance, integrating 1/x just return the antiderivative Log[x], which obviously does not work for x == 0 (or x < 0 if we restrict ourself to the reals). In[1]:= Integrate[1/x, x] Out[1]= Log[x] In[2]:= Assuming[a < 0, Integrate[x^a, {x, 5, 6}]] Out[2]= (-5^(1 + a) + 6^(1 + a))/(1 + a) In[3]:= Limit[%, a -> -1, Direction -> -1] Out[3]= Log[6/5] In[4]:= Limit[%, a -> -1, Direction -> +1] Out[4]= Log[6/5] In[5]:= Integrate[x^(-1), {x, 5, 6}] Out[5]= Log[6/5] Regards, -- Jean-Marc