Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: The Charlwood Fifty
Replies: 52   Last Post: Jun 24, 2013 10:24 PM

 Messages: [ Previous | Next ]
 Richard Fateman Posts: 1,539 Registered: 12/7/04
Re: The Charlwood Fifty, another Macsyma result
Posted: Jun 10, 2013 10:12 AM

On 6/9/2013 7:40 PM, Albert Rich wrote:
> On Sunday, June 9, 2013 3:37:09 PM UTC-10, Richard Fateman wrote:
>

>> INT(x^3*ASEC(x)/SQRT(x^4-1), x)
>>
>> is
>>
>> ((a * (sqrt(x^2 - 1) * asec(x) - 1))/2) + ((log(((a + 1)/(a -
>> 1))))/4)
>>
>> with a=sqrt(x^2+1).
>>
>> I have not investigated how this fairs with respect to maximal
>> continuity.

>
> Unfortunately, that is not a valid antiderivative since subtracting
> its derivative from the original integrand and substituting -2 for x
> does not equal zero.
>
> Albert
>

It checks out in Macsyma. In separate correspondence with Albert Rich,
he suggested looking at how Macsyma defines the derivative of arcsecant.
Indeed, Macsyma's definition differs by a sign for negative argument.

For Macsyma's definition, the integral is correct. For Maple or
Mathematica or Maxima, the integral needs an extra abs().

I suppose the dlmf would provide the definitive form, but it seems to
be offline at the moment. I'm guessing it agrees with Maxima, not Macsyma.

RJF