Discussion:  All Activities in Calculus on Computer 
Topic:  Intigration 
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Subject:  RE: Intigration 
Author:  Alan Cooper 
Date:  Apr 27 2006 
rational factor to get a bunch of terms of the form e^u/u^p and e^u/(u^2+1)^p
which can all be looked up in tables but reduce to expressions like e^(w^2)dw
which cannot be expressed in terms of "elementary functions" (but which can be
expressed in terms of the "Error function" and its generalizations.
In fact Maple gives
1/2/x^2*e^(8*x)+4*ln(e)/x*e^(8*x)32*ln(e)^2*Ei(1,8*x*ln(e))+16*e^2*Ei(1,8*x*ln(e)+2*ln(e))+4/x*e^(8*x)32*ln(e)*Ei(1,8*x*ln(e))16*Ei(1,8*x*ln(e))
where Ei is the "Exponential Integral Function" defined by
Ei(n,x) = int(exp(x*t)/t^n, t=1..infinity)
 
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