velaris08
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Hi - I'm struggling to spot this specific thing when I'm integrating - I've attached it below. I just don't understand what it is or where it comes from. I get that if I factorise u^2 - 4 I get (u-2)(u+2)... but even if I worked backwards, and used that to try to get to u^2/u^2-4 I don't? I get 4/u^2-4. and where's the 1 coming from? Help!!
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englishhopeful98
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u squared over u squared
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Muttley79
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(Original post by velaris08)
Hi - I'm struggling to spot this specific thing when I'm integrating - I've attached it below. I just don't understand what it is or where it comes from. I get that if I factorise u^2 - 4 I get (u-2)(u+2)... but even if I worked backwards, and used that to try to get to u^2/u^2-4 I don't? I get 4/u^2-4. and where's the 1 coming from? Help!!
Exam questions often suggest the substitution and with practice you will recognise when it's useful.

The 1 comes from splitting the integral into partial fractions - when the numerator and denominator have the same highest power you have to divide [like a 'top heavy' fraction.

Maybe revise partial fractions?
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velaris08
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(Original post by Muttley79)
Exam questions often suggest the substitution and with practice you will recognise when it's useful.

The 1 comes from splitting the integral into partial fractions - when the numerator and denominator have the same highest power you have to divide [like a 'top heavy' fraction.

Maybe revise partial fractions?
Oh... got it - so dividing the u^2 s like in partial fractions leaves you with the 4/u^2-4... which is the same as 1/(u - 2) - 1/(u + 2)...
I'm like speed learning all the content so recognising those links is difficult for me sometimes - gotta get into doing questions to get better ASAP.
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