Re: Integrate doesn't yield what I expect

*To*: mathgroup at smc.vnet.net*Subject*: [mg25394] Re: Integrate doesn't yield what I expect*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Fri, 29 Sep 2000 01:06:27 -0400 (EDT)*Organization*: Universitaet Leipzig*References*: <8qloab$q7g@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, you expect AcrSin[] and get Log[] - unfortunatly there isn't a solution for it because every inverse trigonometric function has an logarithmic representation ;-) ArcSin[x] -> -I*Log[Sqrt[(1-x^2)]+I*x] x^2<=1 because Sin[x]=Exp[I*x]-Exp[-I*x]/(2I) You should look at the equations 4.4.26 -- 4.4.31 in Abramowitz/Stegun > Can you also guide me to the best book with solved integrals? (best means > number of integrals solved) I. S. Granstein, I. M. Ryshik "Table of Series, Products and Integrals" Regards Jens Gransteint Borut L wrote: > > Helo, > > I am integrating a function which has the form > 1/(x Sqrt[a x^2+b x+c]), > where c<0 and delta=4 a c-b^2 <0. > Matematica always returns same result (with Log, the one with delta>0), > despite giving option Assumptions->{...}. I expect a result with ArcSin. Is > there other way to treat such somplex integrals? > > In my real assignemt I have an integral 1/(x^2 (a x^2+b x+c)^(3/2)) with > same c and delta. I expect again something with ArcSin or ArcCos, but the > Log is again yilded. > > Can you also guide me to the best book with solved integrals? (best means > number of integrals solved) > > Thanks, Borut