Doug Stewart wrote:
[EMAIL PROTECTED] wrote:
In 14.661 Schaums claims:
integral acoth(x/a) = x*acoth(x)+a/2*log(x^2-a^2)
^^^^^^^^
Axiom claims
integral acoth(x/a) = x*acoth(x/a)+a/2*log(x^2-a^2)
^^^^^^^^^^
Is this a Schaums typo?
Tim
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My schaums is the same as your Schaums but it is old (not as old as
yours) I have a New Schaums at work But I will not Be in to work
today :-)
My Maxima agrees with Axium.
integrate(acoth(x/a),x);
(%o8) (a*log(x^2/a^2-1))/2+x*acoth(x/a)
According to "Table of Integrals, Series, and Products" I.S.
Gradshteyn/I.M. Ryzhik;
Axiom is right. In fact a dimensional analysis says that Schaums must
be wrong. My personal integration says that Axiom/"Table.." are off by
a constant, but it's hard to argue about a constant of integration. The
meaning of that statement is: set y=x/a and evaluate, then back
substitute and multiply by a to get F(x/a); having done that you would
get log((x/a)^2+1) as the trailing terms. But this is the same with a
constant difference.
RayR
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