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Re: integration
*To*: mathgroup at smc.vnet.net
*Subject*: [mg95970] Re: integration
*From*: Bill Rowe <readnews at sbcglobal.net>
*Date*: Sat, 31 Jan 2009 01:13:10 -0500 (EST)
On 1/30/09 at 5:47 AM, t.p.nixon at open.ac.uk wrote:
>Hi, I don't use mathematica but the other day I wanted to solve an
>integral and I'm out of practice so I went on-line to a mathematica
>based integrator.
>http://integrals.wolfram.com/index.jsp
>I typed in 1/sqrt(x^2-b^2) this should have an integral of
>cosh^-1(x/ b). Ok, so it didn't recognize cosh but its answer was
>(I think) wrong. it comes back with ln(x+sqrt(x^2-b^2)) it seems to
>have overlooked a quotient of b in the log.
>Is this a general problem with mathematica or just the on-line
>version or is it me?
It is you. Version 7 gives the following:
In[1]:= Integrate[1/Sqrt[x^2 - b^2], x]
Out[1]= Log[2*(Sqrt[x^2 - b^2] + x)]
In[2]:= D[%, x] // Simplify
Out[2]= 1/Sqrt[x^2 - b^2]
confirming the result returned is the anti-derivative of
1/Sqrt[x^2-b^2]. And since,
In[3]:= D[Log[a (Sqrt[x^2 - b^2] + x)], x] // Simplify
Out[3]= 1/Sqrt[x^2 - b^2]
It is clear the factor of two in the answer returned by Version
7 but not in the result from the on-line version is an arbitrary constant.
Further a quick check of tabulated integrals I have handy also
gives the same result as the on-line version for this integral
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