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