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Subject: Re: symbolic integration
Date: Sat, 17 Jan 2009 18:26:01 +0000 (UTC)
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Serena <darkbluee@gmail.com> wrote in message <9842254.1232212065386.JavaMail.jakarta@nitrogen.mathforum.org>...
> When I run the following code:
> 
> D=30;L=152;m=39600;w1=1.5;ro=1.225;damp=0.01;xo=10;
> lamda=1.875;sigma=0.7341;
> 
> a=lamda/L
> syms Uo x
> U=x^0.4         
> Fix=cosh(a*x)-cos(a*x)-sigma*(sinh(a*x)-sin(a*x))
>         
> A=U*Fix^2         
> AA=int(A,0,L)
> 
> 
> This message refers to the following lines:
> 
> Warning: Explicit integral could not be found.
> > In sym.int at 58
>   In velocita_critica at 19
>  
> AA =
>  
> int(x^(2/5)*(cosh(15/1216*x)-cos(15/1216*x)-7341/10000*sinh(15/1216*x)+7341/10000*sin(15/1216*x))^2,x = 0 .. 152)
> 
> 
> What exactly does this mean and is there any way around the problem?
> 
> Thanks,
> Serena

  It's the 0.4 exponent on x that is the barrier to solving this integral.  If it had been an integer, matlab would likely have succeeded.  Mine found it with x^4 for example.

  You shouldn't blame matlab for failing on this.  It is very likely that no explicit solution is known to the entire mathematical world.  I learned very early in my mathematical career that it is very easy to invent functions for which no explicit integral is known.  A friend of mine and I in college wasted about a week one time trying to find the integral of f(x) = x^x without any success whatever.

  To solve your integral you will undoubtedly have to resort to numerical methods.

Roger Stafford