Re: a curious integral

On Jul 26, 2005 10:35 AM, bugalore@xxxxxxxxxxx wrote:

> Hello,
>
> Can anyone suggest how to evaluate the following
> integral:
>
> > Int(1/v/sqrt(v^2*a+b*v+c), v);
>
> /
> | 1
> | ---------------------- dv
> | 2
> / v sqrt(v a + b v + c)
>
>
> Maple finds a surprisingly clean/simple answer:
>
> > value(%) assuming c>0;
>
> 2 c + b v
> arctanh(1/2
> arctanh(1/2 ------------------------)
> 1/2 2 1/2
> c (v a + b v + c)
> -
> - -------------------------------------
> 1/2
> c
>
> I'm trying to understand where the "2c+bv" comes
> from....
>
> thanks,
> bugalore.
>

Maybe it's just me, but I cannot decypher what the original intgral even is. Like when you say

Int[1/v/sqrt(v^2*a+b*v+c)]

do you mean the root quantity to be

v^2 * (a+b) * (v+c)

or do you mean it to be

av^2 + bv + c.

Also, it's really hard to tell when you try to draw it out. Moreover, when you did try to draw it out the quantity under the root became a first degree polynomial, instead of a second degree that you originally had.

Confused,
Kyle
.

Relevant Pages

  • Re: a curious integral
    ... but I cannot decypher what the ... >> do you mean the root quantity to be ... it's really hard to tell when you try to draw ... > Your confusion is self-inflicted. ...
    (sci.math)
  • Re: a curious integral
    ... but I cannot decypher what the original intgral ... > do you mean the root quantity to be ... it's really hard to tell when you try to draw it out. ... Your confusion is self-inflicted. ...
    (sci.math)
  • TOT: two things
    ... pleased to tell you that I needed to draw one today for the first time in 40 ... Bill ... Prev by Date: ...
    (uk.tech.digital-tv)
  • class properties
    ... where would you draw the line on what duplicated properties ... thanks for the insight ... Prev by Date: ...
    (microsoft.public.dotnet.languages.csharp)
  • Re: click a button in a JTable
    ... it knows how to draw that particular cell, ... returned Component as an object (which is very considerate of the table ... Prev by Date: ...
    (comp.lang.java.gui)