# [Maxima] problems

Rupert Swarbrick rswarbrick at gmail.com
Mon Jan 2 16:24:25 CST 2012

```leon.magiera at wp.pl writes:

> Dnia 2-01-2012 o godz. 17:06 Rupert Swarbrick napisaŠŠ(a):
>> leon.magiera at wp.pl writes:
>> > Dnia 2-01-2012 o godz. 14:28 Rupert Swarbrick napisaŠŠ(a):
>> >> leon.magiera at wp.pl writes:
>> >> > Problem 2
>> >> >
>> >> >            ex:1/(sqrt((x-b)^2+a^2)*sqrt((x-b)^2/a^2+1));
>> >> >
>> >> >            integrate(ex,x);
>> >> >
>> >> > Is the above integral too hard ?
>> >
>> > CAS  DERIVE returns
>> >                                         ATAN((x - b)/ABS(a))
>
> Details
>              ex:=1/(Ąî((x - b)^2 + a^2)Ą¤Ąî((x - b)^2/a^2 + 1))
>              int(ex,x)
>                            ATAN((x - b)/ABS(a))
> We  check the obtained result
>              DIF(ATAN((x - b)/ABS(a)),x)-ex
>                               0
>
>> Well, I'm pretty certain that you've either copied something incorrectly
>> or made another mistake. Look at the bottom of the integrand. It's a
>> product of two terms. One scales as a and the other as 1/a. Therefore
>> the product doesn't have any first-order dependence on a and the derive
>> answer you give above can't possibly be right.
>>
>> Maybe I've misunderstood your original question?
>>
>> Rupert

Erk. It seems I can't read parentheses properly. What you have written
agrees with what I said in the first place: I didn't realise that the
abs(a) was inside the arc tangent.

Rupert

PS. Please try to CC the mailing list on conversations like this. If I'm
to be humiliated, it may as well be public.

PPS. Sentences are also nice. Or any indication that you have read the
email to which you are replying.
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