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 >