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Re: integrate problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98872] Re: [mg98837] integrate problem
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Mon, 20 Apr 2009 19:11:46 -0400 (EDT)
  • References: <200904200939.FAA12325@smc.vnet.net>

On 20 Apr 2009, at 18:39, sean_incali at yahoo.com wrote:

> I'm having some issues understanding this...  Following works as
> expected.
>
> s is the variable in time.  a is a parameter.
>
> Integrate[1/(s + a), s]
>
> gives Log[a + s]
>
> But the following gives the integral itself.
>
> Integrate[1/(s[t] + a), t]
>
> If the function that needs to be integrated w.r.t time is 1/(s[t] +
> a), how do I accomplish that?

You can't accomplish that unless you give Mathematica an explicit  
expression for s[t] (and you will have to be lucky then too). How  
could you possible expect this to work in general? If this did, you  
could integrate practically any function f[t] by using a suitable  
s[t]. This has nothing to do with Mathematica, its just basic  
mathematics.



>  It seems like if integrate it wrt to s
> [t] it will work.
>
> Integrate[1/(s[t] + a), s[t]]
>
>
> But does that sound about right?

Right? In what sense "right"? It's a completely different thing from  
your first case. Here you might as well write t (or s) instead of s[t]  
as it has nothing whatever to do with s[t].

Note that this also gives an answer:

Integrate[s'[t]/(a + s[t]), t]

Log[a+s[t] ]

but this also has nothing to do with your original integral...

Andrzej Kozlowski


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