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TheSimpliFire

My WordPress blog is here!

About: Where I store any mathematical problems I've made up :)


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Just discovered a neat closed form of the following integral using $1$s and $2$s: $$\begin{align}\int_{\pi/8}^{\pi/4}\frac{\sin x+\cos x}{\tan x}\,dx&=\sqrt2-\frac{\sqrt{\sqrt2-1}+\sqrt{\sqrt2+1}}{\sqrt{2\sqrt2}}\\&\,\,\,\,\,\,+\ln\left(1+\sqrt2\sqrt{2-\sqrt2}\right)\end{align}$$

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