*To*: mathgroup@smc.vnet.net*Subject*: [mg12081] Re: [mg12021] Integrate lesson*From*: Ersek_Ted%PAX1A@mr.nawcad.navy.mil*Date*: Sat, 25 Apr 1998 01:30:17 -0400

Will Self wrote: | |Hi Ted, | |expr=Sqrt[2] x - (Sqrt[2]+Sqrt[3])x^x+Sqrt[5+2Sqrt[6]]x^x; | |FullSimplify[expr] | |My results varied from yours. There is no way that FullSimplify |is going to get rid of that x^x. | I am using Version 3.0.1. FullSimplify[expr] gives me Sqrt[2]*x. You say there is no way FullSimplify is going to get rid of that x^x. Well it can be done with the steps below: expr=Sqrt[2] x - (Sqrt[2]+Sqrt[3])x^x+Sqrt[5+2*Sqrt[6]]x^x Factor (x^x) out of two terms. expr= Sqrt[2] x + ( -(Sqrt[2]+Sqrt[3])+Sqrt[5+2*Sqrt[6]] )x^x; For readability let: u=Sqrt[2]+Sqrt[3] expr==Sqrt[2] x + (-u+Sqrt[5+2*Sqrt[6]])x^x expr==Sqrt[2] x + (-Sqrt[u^2]+Sqrt[5+2*Sqrt[6]])x^x u^2=(Sqrt[2]+Sqrt[3])^2 u^2=2+2*Sqrt[2]*Sqrt[3]+ 3 u^2=5+2 Sqrt[6] expr=Sqrt[2] x + ( -Sqrt[5+2 Sqrt[6]] +Sqrt[5+2 Sqrt[6]] )x^x expr=Sqrt[2] x + (0) x^x expr=Sqrt[2] x I will not jump on the band wagon with those who want to complain that Integrate, DSolve, Solve etc. aren't smart enough. These people want a few commands that can solve any problem. Solutions would take much longer if every expression went through FullSimplify (or other changes) before trying to solve the problems. The better approach is to simplify the expression with Together, Expand, Factor, TrigExpand, FunctionExpand, ComplexExpand, etc. WITH human intelligence. After all that a user can use Simplify (or in some cases use FullSimplify). Ted Ersek