
Re: The Charlwood Fifty
Posted:
Jun 6, 2013 4:19 PM


"Nasser M. Abbasi" schrieb: > > On 6/6/2013 11:23 AM, clicliclic@freenet.de wrote: > > > > It would have been nice if Prof. Charlwood could have thrown light on > > problem #49 from his appendix: Did he really want his students to work > > on an elementary evaluation of INT(ASIN(x*SQRT(1x^2)), x) and fail? > > > > In http://www.apmaths.uwo.ca/~arich/CharlwoodIntegrationProblems.pdf > > #49 is written as INT(ASIN(x/SQRT(1x^2)), x) > > I just checked the Charlwoods 2008 paper, and it should be as > you have shown it (i.e. multiplication not division), so there is a > typo in the above pdf file. >
Oh, as Albert Rich wrote, he "took the liberty of changing the integrand of problem #49 from arcsin(x*sqrt(1x^2)) to arcsin(x/sqrt(1x^2)). This was done so all the integrands and antiderivatives in the testsuite would involve only elementary functions and operators."
> > [...] > > Maple 17 could not seem to be able to do it. returned unevaluated. >
Strange that Maple can't do this one. Derive 6.10 immediately converts the integral to
INT(ASIN(x*SQRT(1  x^2)), x) = x*ASIN(x*SQRT(1  x^2)) + SUBST(INT((2*x^2  1)/SQRT(x^4  x^2 + 1), x), x, SQRT(1  x^2))
and Maple should be able to cope with the algebraic integral that remains (the Derive integrator has no knowledge of the canonical elliptic integrals).
Martin.

