integration



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At 09:40 AM 5/4/2007, Michel Gosse wrote:
>Hello
>
>How far maxima can study the function :
>f(x):=integrate(1/log(t),t,x,2*x)
>I can't obtain diff(f(x),x), neither the limit in +oo.
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Michel, 

Unfortunately for this version the specint (special integrals) package does not 
seem to be working for the exponential integral function Ei(z).

 From Macsyma I get:
  
(%i) integrate(1/log(t),t,x,2*x;
        Is  x  positive, negative, or zero?
        p
        Is  2 * x - 1  positive, negative, or zero?
        p
        Is  x - 1  positive, negative, or zero?
        p
(%o) exp_int(log(x) + log(2)) - exp_int(log(x))

where exp_int is Ei(z), let: 

(%i) ei(x):=exp_int(log(x) + log(2)) - exp_int(log(x))$

say: 
(%i) ei(%pi),numer;
(%o) 2.08843
ok

differentiate:
(%i) diff(ei(x),x);
(%o) (2/(log(x) + log(2))) - (1/(log(x)))



er 

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