Another Integral

NYC

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Oct 20, 2005
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ok, I'm integrating dx divided by ( x^2 times the square root of the quantity (9+x^2) )
Reading the problem, it sounds like this: "dx over x squared times the square root of nine plus x squared"
I'm sorry, I don't know how to be much clearer, but I began by allowing x to equal 3 tangent (theta) and came to the integral of secant theta divided by the quantity (9 tangent squared of theta)
or Int of sec(@)/(9tan^2@)
(assuming @ is theta)
From here, I'm not sure where to go. Any pointers would be greatly appreciated.
 
hm

if I make that substitution, then I'm left with the integral of cos theta over sin squared theta. I can rewrite it as the integral of cos(@)/(1-cos^2(@)) but I still don't see where I can go from here
 
The derivative of \(\displaystyle \L\\tan({\theta})=sec^{2}({\theta})\)

\(\displaystyle \L\\x=3tan({\theta})\ and\ dx=3sec^{2}d{\theta}\)

Remember, \(\displaystyle \L\\1+tan^{2}{\theta}=sec^{2}{\theta}\)
 
I used those to come to the point I'm at now, and there doesn't seem to be another manipulation I can do to get an answer which I can integrate.
 
Ah

I rearranged it to become the integral of cot (@) csc (@)..which becomes -csc(@).. and then my final answer is negative sqrt of (9+x^2)divided by 9x times ..if this is incorrect, please let me know. Thanks for the help
 
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