Re: Understanding the Output

*To*: mathgroup at smc.vnet.net*Subject*: [mg32811] Re: [mg32792] Understanding the Output*From*: BobHanlon at aol.com*Date*: Thu, 14 Feb 2002 01:43:26 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 2/12/02 7:30:46 AM, smitsky at mindspring.com writes: >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 > Integrate[Sqrt[x-1],x]//Simplify (2/3)*(x - 1)^(3/2) Integrate[-x^3 (1-x^4)^5,x]//FullSimplify (1/24)*x^4*(x^4 - 2)*(x^8 - 3*x^4 + 3)*(x^8 - x^4 + 1) %-1/24(1-x^4)^6 // Simplify -(1/24) They differ by a constant so they are both the integral of the input; however, you will not be able to Simplify one to the other since they are not equal. Bob Hanlon Chantilly, VA USA