
Re: Charlwood Fifty test results
Posted:
Jul 5, 2013 8:20 PM


Albert Rich schrieb: > > On Friday, July 5, 2013 11:15:41 AM UTC10, clicl...@freenet.de wrote: > > > [...] But why is problem 41 untractable? > > [...] Problem #41 is > > integrate(log(sin(x)) sqrt(1+sin(x)), x) > > Rubi starts correctly (I think) using integration by parts that gives > the log free integral > > integrate(cos(x) cot(x)/sqrt(1+sin(x)), x) > > Unfortunately Rubi and the other systems tested cannot determine that > its antiderivative is > > 2 cos(x)/sqrt(1+sin(x)) 2 arctanh(cos(x)/sqrt(1+sin(x))) > > [...]
The integrand COT(x)*COS(x)/SQRT(1 + SIN(x)) equals (1  SIN(x)^2) /(SIN(x)*SQRT(1 + SIN(x))) which equals (1  SIN(x))*SQRT(1 + SIN(x)) /SIN(x). That is, the integrand obtained after integration by parts is a function of SIN(x) only, and of a type that Rubi should be able to handle.
Martin.

