TheSimpliFire
Temporary Note: Due to uni courses starting, for the next few weeks I will not be as active on SE as before. However, I'll still lurk around chats so feel free to ping me there.
Area 51 Proposal: Math Challenges! You're more than welcome to follow if interested.
Chatroom for proposal and meta post.
My WordPress blog is here!
About: Where I store any mathematical problems I've made up :)
My favourite questions:
Finding the turning points of $f(x)=\left(xa+\frac1{ax}\right)^a\left(\frac1x\frac1a+ax\right)^x$
Mathematical coincidences concerning the numbers $\pi$, $e$ and $163$
Convergence concerning the $\alpha$th derivative of $f(x)=x^{\alpha}\alpha^x$
My favourite answers:
Evaluating $\int_0^1\frac{3x^4+ 4x^3 + 3x^2}{(4x^3 + 3x^2 + 2x+ 1)^2}\, dx$
How to prove :$\sqrt{1!\sqrt{2!\sqrt{3!\sqrt{\cdots\sqrt{n!}}}}} <3$
Evaluate $\int (1x^{2008})^{\frac{1}{2007}} (1x^{2007})^{\frac{1}{2008}} dx$
Just discovered a neat closed form of the following integral using $1$s and $2$s: $$\begin{align}\int_{\pi/8}^{\pi/4}\frac{\sin x+\cos x}{\tan x}\,dx&=\sqrt2\frac{\sqrt{\sqrt21}+\sqrt{\sqrt2+1}}{\sqrt{2\sqrt2}}\\&\,\,\,\,\,\,+\ln\left(1+\sqrt2\sqrt{2\sqrt2}\right)\end{align}$$

Earth

Member for 1 year, 3 months

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