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c4 integrating with partial fractions - need help!

x2x2−4\frac {x^2}{x^2 - 4}

Divided it to give

1+−4x2−4 1 + \frac {-4}{x^2 - 4}

Then splitting the fraction into partial fractions, I get

1x+2+−1x−2 \frac{1}{x+2} + \frac{-1}{x-2}

and this does not integrate to the correct answer, which is

x+ln¦x−2x+2¦+C x + ln¦\frac {x-2}{x+2}¦ + C

ln bit has a modulus, but I dunno how to do that sign

I get the x+2 on top and the x-2 on the bottom. Where have I gone wrong?
Reply 1
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TenOfThem
18
Original post by lollage123


1+−4x2−4 1 + \frac {-4}{x^2 - 4}



This should be +4 since x2=(x2−4)+4x^2 = (x^2-4) + 4
Reply 2
Avatar for lollage123
lollage123
OP
2
Original post by TenOfThem
This should be +4 since x2=(x2−4)+4x^2 = (x^2-4) + 4


How? When I divide it using the polynomial division method the -4 just gets carried down and the remainder is -4/(x^2 - 4)
Reply 3
Avatar for TenOfThem
TenOfThem
18
Original post by lollage123
How? When I divide it using the polynomial division method the -4 just gets carried down and the remainder is -4/(x^2 - 4)


I am not sure what you mean by "carried down"

But, during polynomial division you would be looking at subtracting -4 which still gives +4
Reply 4
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lollage123
OP
2
Original post by TenOfThem
I am not sure what you mean by "carried down"

But, during polynomial division you would be looking at subtracting -4 which still gives +4


silly blunder, thank you
Reply 5
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TenOfThem
18
Original post by lollage123
silly blunder, thank you


np

:biggrin:

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