       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

```

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