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# FP2 Integration watch

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1. (Original post by e-unit)
Right, New question:

Let I denote the integral, and let u = sqrt(x+1). Then dx/du = 2u. So:
I = 2 ∫u^2/(u^2 + 4) du
= 2 ∫(u^2 + 4 - 4)/(u^2 + 4) du
= 2 ∫du - 8 ∫1/(u^2 + 4) du
= 2 u - (8/2) arctan(u/2) + C
= 2 sqrt(x+1) - 4 arctan[sqrt(x+1)/2] + C
= 2 (sqrt(x+1) - 2 arccot[2/sqrt(x+1)]) + C

(Original post by Handy)
Fair enough.

I don't need to know it
What's there to know? He's just using a letter to save time from rewriting the integral over and over agian.
2. Exactly. As long as you define I initially to be the integral in question you're fine. It's not a method in itself...
3. I'm relieved that at least some people didn't think I was talking rubbish!
4. To back up Wrangler....

Just because you've not been spoon fed a method which makes a question a lot easier doesn't mean you should just instantly say "Haven't been taught it, don't care!" If you plan to do maths at uni, that's a completely moronic attitude to take, and even if you don't, why snub a method which makes your life easier? If an exam marker doesn't recognise your more elegant method, demand a remark.

I get the distinct impression from TSR too many people take the view "Fall in line with the examiner and jump through their hoops" to pass exams. Swell if you plan to do nothing more than A level, but it won't work at uni, particularly for maths, and especially for places like Warwick, Nottingham and Oxbridge. It's called "Thinking on your feet". Learn it, think it, know it!
5. It doesn't make your life easier if you don't understand it. I think the reason actually might be more the fact that I muddled what was written with another method that i've seen and I now realise what he's done.

However, jumping through hoops is a damn good way to pass exams so why knock it if it works?

Maybe it will give you comfort that I'm not doing maths at university.

And maybe i'll read the posts more carefully in future...

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Updated: February 6, 2006
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