Equivalence of inverse hyperbolic functions and logarithms

To convert inverse hyperbolic to logarithms, use logarc, e.g.

     logarc( asinh(x) ) => log(sqrt(x^2+1)+x)
or
     ev( asinh(x), logarc)
or
     block( [ logarc: true], asinh(x) )

I don't know of any easy way to go in the other direction.

           -s


On Mon, Dec 8, 2008 at 3:42 PM, Stathis Kamperis <ekamperi at gmail.com> wrote:

> Greetings everyone and congratulations on the work you are doing with
> Maxima.
>
> I'd like your expertise in the following topic.
> There is an equivalence between inverse hyperbolic functions and
> logarithms,
> eg:
>
> arcsinh(x) = ln(x + sqrt(1 + x^2))
>
> Is there a way to tell Maxima use one form over the other
> when calculating? Say when integrating ? So that the
> result is expressed in terms of inverse hyperbolic functions
> or of logarithms ?
>
> I know it's trivial to implement it, as a simplifier,
> just wondering whether there exists something already.
>
> Best regards,
> Stathis Kamperis
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