Have I performed the following definite integral correctly?

fella27

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I suppose it's two questions I have really. Firstly, whether or not I evaluated the following integral correctly by partial fractions, and secondly if I did, then if part of the answer for a definite integral is undefined, is the whole thing undefined? My guess is that it's not and it just depends on your interpretation of what the integration actually means in a specific application..

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Thanks in advance, and please excuse where there should be a minus sign before the last term of the final answer.
 

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\(\displaystyle \displaystyle \begin{align*} \int{ \frac{1}{x}\,\mathrm{d}x} = \ln{|x|} + C \end{align*}\), not \(\displaystyle \displaystyle \begin{align*} \ln{(x)} + C \end{align*}\). This will take into account the fact that you can have negative inputs.
 
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