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Re: Integral Questions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89366] Re: Integral Questions
  • From: David Bailey <dave at Remove_Thisdbailey.co.uk>
  • Date: Sat, 7 Jun 2008 02:58:54 -0400 (EDT)
  • References: <g2b4oj$nm8$1@smc.vnet.net>

Graeme Dennes wrote:
> I am attempting to calculate the integrals with respect to x of the two
> functions:
> 
>  
> 
>  
> 
> 1.
> 
>          x^2 + a
> 
> arcsin (---------)    -   c 
> 
>            bx
> 
> -----------------------------
> 
>            x
> 
>  
> 
>  
> 
> 2. As above, squared.
> 
>  
> 
>  
> 
>  
> 
> where a, b, c are constants.
> 
>  
> 
>  
> 
> Mathematica 6 presents solutions which seem to depend on the form of the
> function entered, and in some instances, Mathematica does not read the
> syntax correctly.
> 
>  
> 
> Eg, using ((x^2 + a)/(bx)) and (x/b + a/b/x) as different (but correct)
> forms of the arcsin function yield different results!
> 
>  
> 
>  
> 
> Taking the first function, and entering it as:
> 
>  
> 
> Integral[((arcsin(a/b/x+x/b))-c)/x,x]
> 
>  
> 
> The answer presented is:   - a arcsin        arcsin x
> 
>                              --------    +   --------    -    c Log (x)
> 
>                                 bx              b
> 
>  
> 
> Note the missing argument of the first arcsin.
> 
>  
> 
> As noted, different results can be provided for different (but correct!)
> forms of the entered function. I do not understand why this would be so.
> 
>  
> 
> My questions:
> 
>  
> 
> 1.  Are there (true) closed form solutions to both functions 1 and 2?
> 
> 2.  Is there some technique required to cause Mathematica to read the syntax
> correctly?
> 
> 3.  Is there some technique required to cause Mathematica to provide the
> correct solution, assuming a closed form solution exists?
> 
> 4.  HELP!!
> 
>  
> 
> If the answer to Q1 is NO, then that would explain why the correct answer is
> not obtainable.
> 
>  
> 
> Any advice with this issue would be much appreciated.
> 
>  
> 
> Kindest regards,
> 
>  
> 
> Graeme
> 
It really helps to get the syntax right:

Integrate[(ArcSin[a/b/x + x/b] - c)/x, x]

In this form, Mathematica returns the integral unevaluated - which is 
its way of saying that it cannot do it symbolically.

Note the following syntax issues:

1)   The arguments of functions and other Mathematica operations, such 
as Integrate are denoted using square brackets - not round ones.

2)   The capitalisation of every word is important. Built in Mathematica 
operations all start with a capital letter.

3)   The expression bx (without a space) refers to a variable with the 
name bx, whereas b x (with a space) refers to the product of b and x.

The easiest way to get used to the syntax is probably to paste examples 
from the documentation into your own notebook, and try modifying these.

You have a very strange way of presenting your output (which is very 
hard to read). It makes me wonder if you are using the (very) old 
interface (Math.exe) rather than the notebook interface 
(Mathematica.exe), which is infinitely easier to use.

David Bailey
http://www.dbaileyconsultancy.co.uk


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