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Integral Questions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89329] Integral Questions
  • From: "Graeme Dennes" <gdennes at bigpond.com>
  • Date: Fri, 6 Jun 2008 06:45:22 -0400 (EDT)

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


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