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Subject: Re: int in R2008b, same integral?
Date: Sat, 13 Dec 2008 01:17:02 +0000 (UTC)
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"Joerg Buchholz" <buchholz@hs-bremen.de> wrote in message <ghung9$3as$1@fred.mathworks.com>...
> Is there a mathematical reason, why R2008b can solve:
> 
> >> int ('1/sqrt(1-x^2)')
>  
> ans =
>  
> asin(x)
> 
> but cannot solve: 
> 
> >> int ('sqrt(1/(1-x^2))')
> Warning: Explicit integral could not be found. 
> > In sym.int at 64
>   In char.int at 9
>  
> ans =
>  
> int((-1/(x^2 - 1))^(1/2), x)
> 
> Is there a way to make R2008b simplify 'sqrt(1/(1-x^2))' to '1/sqrt(1-x^2)'?

No.  These are equivalent only over the range -1..1.  Outside of that range they are not equivalent, that is why you get a closed form answer for the first integral and not for the second.  Without integrating, try plugging in some numbers greater that 1 into both functions, and see what happens.  For example, using a value of x=1.3333, the first function yields  -1.133899898*I while the second one yields 1.133899899*I.  If you integrate using a bounded range, say -1..1, then you should get an answer of pi for both.  Once the range goes beyond this, the answers will differ with a sign change with respect to the imaginary variable.

Regards,
Georgios