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Either, it doesn't matter. You could even leave it the way I had it. The reason I changed (x-1) to (1-x) is because that looks a lot neater than (-3-x) which has two negatives.

When you do a few of them, you can do it easily in one step but in the meantime, the way you suggested is good: 3-2x-x^2=-(x^2+2x-3)=-(x+3)(x-1)=(x+3)(1-x) An easy way to confirm that your answer was wrong was that you had (..-x)(..-x) which would give x^2 when multiplied out not -x^2.

(3-2x-x^2)=(x+3)(1-x) not (3-x)(1-x) like you had.

Assuming thats (3-2x-x^2) on the denominator, its wrong because you factorised incorrectly.

Yeah, I think I know what you're talking about. I've seen questions very similar to that and I thought those methods would work but if what wolfram has is the simplest answer, we must have misremembered it.

To be honest, you won't see something this hard in the HSC. I thought about how to do it initially, then I cheated and looked at the answer on wolfram- its obvious why there's no easy way : http://www.wolframalpha.com/input/?i=integrate+x%2F(1%2Bx^6)

This is a good point. I don't know why you'd try and establish that the integral of sec^2(x) is tanx. Its way easier for questions of this sort to establish that the derivative of tanx is sec^2(x) as above posters have done.

You should skip the entire integration by substitution. You know that it will be something to do with ln(4+x^2) so write that and then work out what constants you need to add to make the integral work.

This is actually wrong. You should have taken a factor of n out, not 1/n. Therefore the answer is n(6x)+C. Also, why create a new thread raufmalik?

He multiplied the top and bottom by the conjugate (5-x)

For f, try the substituion x=2sin(theta) because that will give you the oppurtunity to get rid of the square roots when you simplify.

Which one? Do you want e,f or both?

About this, in a test, how many lines would you recommend doing it in. Do you think markers wouldn't like it in just one line or is that fine?

Yeah, your answer is right. If you end up getting a different answer from wolfram, you can ask it to differenriate your answer and then if you get the original question, obviously you are right.

Nope, that's wrong. For future, just check your answers on the website I posted. For a question like yours, type in something like "integrate from 0 to ln2 (x)e^(-x)

To check if you are right, go to http://www.wolframalpha.com

Yep, that's right. BTW, your writing is amazing :)

Books- I don't think there's a definitive best book. I use Terry Lee and Cambridge and the combo works well Time- As much as you need to UNDERSTAND every concept and answer questions on it. For some people, not much. For others, hours Questions- It depends. If I get a topic, often I might do...

Which textbook are you using?

I don't have notes but I have conics and polynomials questions by topic. Anyone that wants them, can you PM me your email and I'll hook you up.