HSC Stuff > HSC Mathematics Extension 2

Mathematics Extension 2 Challenge Marathon

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RuiAce:

--- Quote from: jamonwindeyer on October 05, 2016, 07:17:39 pm ---Jesus Rui that was quick, save some for the students ;)

--- End quote ---
So not touching perms and combs lel

Eh, I've seen integrals way worse than that, and I couldn't get them out. This one was only barely in my doable margin because of the hint. So I was just like 'why not'.

Paradoxica:


Hint: Divide.

RuiAce:
Here is one extremely brutal way of doing the above question. It overuses partial fractions and throws complex numbers into an integral - something not needed in the HSC, just like my very first question


I considered the hint, but it took me way too long to figure out what happens after the hint is applied, hence all of this.

I won't put up the solution to the 3x quicker method just yet. Unnecessarily over complicated non-HSC solution

Paradoxica:
By dividing throughout by , or otherwise, evaluate:

Mahan:

--- Quote from: Paradoxica on October 06, 2016, 11:43:30 pm ---By dividing throughout by , or otherwise, evaluate:



--- End quote ---

Since, this is a relatively old post, I thought it would be useful to give a solution for it.
This method doesn't use the dividing trick:
before I start the proof it is useful to prove:
by integration by part we get :

let that yields


(by tan^{2}x+1=sec^{2}x)

by back substitution we can write it in terms of x.
the answer is

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