I edited my question.
I think it is a very good question, can be difficult though.
Could you please help me with: http://community.boredofstudies.org/showthread.php?t=304024
Re: HSC 2013 4U Marathon
$Prove the inequality:$
{a^{2}}+b^2+c^2+\frac{2}{5}abc<50
$where:$
$a,b,c are the lengths of triangle's sides$
$and the perimeter of the triangle is 10.$
Please help me do this question:
I can't really see any pattern.
I hate this type of questions, it's like 'guess what I thought when I made up he question'...
Re: MX2 Integration Marathon
Do you guys think it's a good idea to make a "Harder 3U marathon"? I think I have done enough integration, need to do some harder 3U.
Re: MX2 Integration Marathon
I changed the integral to: \int \frac{e^{x}}{(1+e^{2x})\sqrt{(1-e^{2x})}}dx
The let u=e^x
The integral becomes: \int \frac{du}{(1+u^{2})\sqrt{(1-u^{2})}}
I can do this the long way, such as on wolfram alpha (let u=\sin\theta) but I think we can use a short cut to...
Re: MX2 Integration Marathon
It can be done using elementary functions but it is a hard one... I will try the one with the new limits.
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\int_{0}^{1} \frac{\ln(1+x)}{1+x^2} \ dx
Evaluate the above integral WITHOUT using the substitutions x=tan\theta or x=\frac{1-u}{1+u}
Re: MX2 Integration Marathon
From now on I will try to post only questions that are done by very tricky substitutions, IBP or very tedious.
\int \frac{x^{2}}{(1+x^{2})^{2}}dx