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 Discussion: All Topics Topic: Intigration

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 Subject: RE: Intigration Author: Alan Cooper Date: Apr 27 2006
I agree with David that the obvious first step is partial fractions on the
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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