~~~
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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>Maxima at math.utexas.edu
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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
~~~