HSC 2016 MX2 Integration Marathon (archive) (1 Viewer)

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Paradoxica

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Re: MX2 2016 Integration Marathon

I got something like (assuming no mistakes i'm pretty sure my method was correct). :

That's not even correct for , which is

If I recall correctly, the derivation contains inverse trigonometry.
 
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leehuan

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Re: MX2 2016 Integration Marathon

From class (lol)

 

Paradoxica

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Re: MX2 2016 Integration Marathon

For anyone concerned with the above integral, don't waste your time.

It is, at minimum, expressible using the real and imaginary parts of the 9th, 18th, and 36th roots of unity, and is extremely horrible, even if it does have a closed form primitive.
 

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Re: MX2 2016 Integration Marathon

However, on the off note that Leehuan did make a typo...



Which can easily be done by inspection.
 

leehuan

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Re: MX2 2016 Integration Marathon

Haha lol no typo. My lecturer just went through it over 5min

Yeah. Don't try to attempt that question unless you have a whole day to spend on it.
 

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Re: MX2 2016 Integration Marathon

1: Clear denominators and reverse the chain rule to yield 1/11 × log(sin¹¹x + cos¹¹x) + C

2: Tedious and trivial by partial fractional decomposition

3: The hopeful substitutions u² = tanx, v = u + 1/u, will yield the answer of arccot((√tanx + √cotx)/2) + C
 
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