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Help! C4 integration watch

1. You'll have to work with me here, skip to page 107 Heinneman book for edexcel c4. I'm missing something very easy here I know... it's when:

The integral of: 1/(1+t).(1+2t), it then goes on to simplify to ((2) - 1/1+t), BUT HOW?! can anyone show me the exact steps, like dumb it down completely? thanks, positive rep for the person who does

greatly appreciated
2. (1+2t)/(1+t) = [(1+t)+t]/(1+t) = 1 + [t/(1+t)] = 1 + [(1+t)-1]/(1+t) = 1 + 1 - 1/(1+t) = 2 - 1/(1+t)
3. 1/(1+t).(1+2t) = [2(1+t) - (1+2t)]/[(1+t).(1+2t)]

= 2/(1+2t) - 1/(1+t)
4. Thanks very much, never knew it was so long!
5. When do you know when to stop?
6. When you're comfortable integrating whatever you've got.

Unless it's a "Show that it's of the form..." type question. Then obviously do it till you get it into that form.

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Updated: June 13, 2006
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