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    Question 22b is the one I'm having trouble with. On my working, the bit I've drawn a line around is my original attempt, the right bit is my second. Basically, I don't understand why it was necessary to use partial fractions to integrate that?
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    You can't just add the term in  x^{-2} to both sides and integrate like that.
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    Oh god, I just realised, never mind o.o

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    (Original post by pineneedles)
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    Question 22b is the one I'm having trouble with. On my working, the bit I've drawn a line around is my original attempt, the right bit is my second. Basically, I don't understand why it was necessary to use partial fractions to integrate that?
    Because what you've done there is rearrange it so that dx/dt + 2x^-2 = 2, and then somehow moved the dt over to the right hand side. If you wanted to do that, you'd have to multiply everything by dt, so that'd leave you with dx + 2x^-2 dt = 2dt and you've just gone in a circle, which is why you need to use partial fractions to get into a situation where you can actually integrate things.
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    (Original post by SeanFM)
    Because what you've done there is rearrange it so that dx/dt + 2x^-2 = 2, and then somehow moved the dt over to the right hand side. If you wanted to do that, you'd have to multiply everything by dt, so that'd leave you with dx + 2x^-2 dt = 2dt and you've just gone in a circle, which is why you need to use partial fractions to get into a situation where you can actually integrate things.
    (Original post by B_9710)
    You can't just add the term in  x^{-2} to both sides and integrate like that.
    Indeed, hahah, I realised shortly after posting. Thanks for the explanation anyhow
 
 
 

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