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Re: Integrate lesson
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
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