Simple(?) Math Problem

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The following is a part of a bigger problem that I'm working on. Somewhere down the problem, I've to find the integral: 1.  Integrate[Sqrt[x^2 - 9]/x^2, x] I've not fully attempted yet, but I'm pretty sure it can be solved by some techniques (like substitution or by parts), but I'm curious, if the above function can be manipulated as following: Squaring numerator and denominator (to the original function),  Integrate[(x^2 - 9)/x^4, x] If it can be manipulated, it is going to be incredibly easier, and I find this answer (I think it's right, but haven't double checked it-- either way, the answer comes out rather simpler): (3 - x^2)/x^3 As per the basic mathematic rule, it is legal to do square both numeratior and denominator; however, I've never tried it and not certain if it can be applied to integrals (and specifically to the above problem). P.S. I actually attempted to solve the initial expression without manipulating as I typed this and I get an answer with log. I'm not posting the answer right now because I'm not sure if that's right, but definitely very curious if it still can be manipulated and I can avoid the answer with log.

Slackdemic · Feb 23, 2009 1:11 PM · 11,791 views

8 Replies

You are making a wrong assumption. 3/5 = 0.6 9/25 = 0.36

Cowboys · Feb 23, 2009 1:19 PM

This is weird. The original poster deleted his post. If the original poster deletes his first post, the thread should be deleted. Something to think about admin. Last edited: 23-Feb-09 01:23 PM

Cowboys · Feb 23, 2009 1:22 PM

Some math problems to play with! Please see below:   Last edited: 02-Mar-09 12:18 PM

Slackdemic · Feb 23, 2009 2:17 PM

[Update: Please do not work on this problem. I overlooked something, and now it's fixed. The premise of the question now is false, so do not attempt it!] The following is the part of a bigger problem I am working on. At one point I've to integrate [5/(3*e^x - 2), x]. Upon integrating, I get the following solution:   integrate[5/(3*E^x - 2), x] == (-5*(x - Log[-2 + 3*E^x]))/2 However, is it not, by applying the basic mathematics rule, possible to manipulate the above function and get this rather simpler solution? integrate[(5 * E^(-x))/((3*E^x - 2) *E^(-x)), x]== (-5*(x - Log[-2 + 3*E^x]))/2 Last edited: 02-Mar-09 01:10 PM

Slackdemic · Mar 2, 2009 12:20 PM

what is the basic mathematics rule you are using to manipulate?

F22 · Mar 2, 2009 12:46 PM

 How are you adding 2 in both denominator and numerator in the second line? I guess I am not getting your question because I know you can not make such a silly mistake...

marconi · Mar 2, 2009 12:52 PM

Thanks, Marconi. I finally figured out my problem. When I run into messy problems like those, I simply do not see the simpler mistakes. Thanks again. :)

Slackdemic · Mar 2, 2009 1:07 PM

I was wrong, F22! Thanks for looking into the problem. :)

Slackdemic · Mar 2, 2009 1:08 PM

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Simple(?) Math Problem

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