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Re: Integral Questions

• To: mathgroup at smc.vnet.net
• Subject: [mg89376] Re: Integral Questions
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Sat, 7 Jun 2008 03:00:48 -0400 (EDT)
• References: <g2b4oj$nm8$1@smc.vnet.net>

Hi,

*READ* the *M_A_N_U_A_L*

The correct syntax is

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

and *not*

Integral[((arcsin(a/b/x+x/b))-c)/x,x]


and Mathematica find no closed form.

Regards
   Jens

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
>