Re: Understanding the Output
- To: mathgroup at smc.vnet.net
- Subject: [mg32825] Re: Understanding the Output
- From: adam.smith at hillsdale.edu (Adam Smith)
- Date: Thu, 14 Feb 2002 01:43:48 -0500 (EST)
- References: <a4au3v$bs9$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Steven, The results you get and mathematica are essentially the same. This can be seen below: In[25]:= thing = Integrate[(x - 1)^(1/2), x] Out[25]= (-(2/3) + (2*x)/3)*Sqrt[-1 + x] In[27]:= FullSimplify[thing] Out[27]= (2/3)*(-1 + x)^(3/2) In[28]:= other = Integrate[x^3*(1 - x^4)^5, x] Out[28]= x^4/4 - (5*x^8)/8 + (5*x^12)/6 - (5*x^16)/8 + x^20/4 - x^24/24 In[30]:= Expand[(-24^(-1))*(1 - x^4)^6] Out[30]= -(1/24) + x^4/4 - (5*x^8)/8 + (5*x^12)/6 - (5*x^16)/8 + x^20/4 - x^24/24 For the "(x - 1)^(1/2), I don't know why your FullSimplify did not work. For the "x^3*(1 - x^4)^5" integral, the two differ only by the constant term: -1/24. This is not really a difference because indefinite integrals always have an undetermined additive constant. "Steven Spear" <smitsky at mindspring.com> wrote in message news:<a4au3v$bs9$1 at smc.vnet.net>... > Hi. I'm having trouble understanding some output in Mathematica. If I enter > Int [x-1] dx, the output I receive is ((-2/3) + (2x/3)) Sqrt(-1+x). If I do > the calculation by hand, I get 2/3.(x-1)^3/2. If I perform: > FullSimplify(((-2/3) + (2x/3)) Sqrt(-1+x)), I get the same answer > (2/3.(x-1)^3/2). > > With trying to use u-substitution, and figuring more complex Integrals, it > get harder to discern the output. For instance: I tried to evaluate the > Integral Int [x^3 (1-x^4)^5] dx. I may not be correct, but by hand I got > 1/24.(1-x^4)^6. Mathematica gave a very different output, and using > FullSimplify didn't seem to help. > > Is there any way to get Mathematica to output these values a little > differently? Am I incorrect on the second example? Any ideas will be > appreciated. Thanks, Steve