3,275 reputation
1939
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location Ntnu Gløshaugen, Norway
age
visits member for 2 years, 10 months
seen 10 hours ago

Studying to be a teacher and obtain a degree in mathematics.


16h
awarded  Necromancer
Aug
25
comment Orders of moves in the Rubik's cube
How long is r u or r u r' u for that matter?
Aug
24
awarded  Popular Question
Aug
11
comment Closed form for $\int_0^x \{1/t \}\,\mathrm{d}t$, $x \in \mathbb{R}_+$ and related.
Very nice, seems like you forgot to carry the gamma constant into the last line =)
Aug
10
asked Closed form for $\int_0^x \{1/t \}\,\mathrm{d}t$, $x \in \mathbb{R}_+$ and related.
Aug
2
answered How to solve this integral ($\int _{\frac{\pi }{6}}^{\frac{\pi }{4}}\sqrt{1-\tan ^2\left(x\right)}dx$)
Aug
2
comment Indefinite integral $\int x^{7/2}\sqrt{\ln x}e^x\,dx$
Why do you think it has a closed form? And did you forget to add limits?
Jul
20
revised Evaluate $\int_0^1 \sqrt{2x-1} - \sqrt{x}$ $dx$
Added an image
Jul
20
answered Evaluate $\int_0^1 \sqrt{2x-1} - \sqrt{x}$ $dx$
Jul
13
comment Proving $\int_0^1 \frac{\mathrm{d}x}{1-\lfloor \log_2(1-x)\rfloor} = 2 \log 2 - 1$.
Maple ist mega poop i.stack.imgur.com/YTdcS.png
Jul
13
revised Proving $\int_0^1 \frac{\mathrm{d}x}{1-\lfloor \log_2(1-x)\rfloor} = 2 \log 2 - 1$.
deleted 1 character in body; edited title
Jul
13
asked Proving $\int_0^1 \frac{\mathrm{d}x}{1-\lfloor \log_2(1-x)\rfloor} = 2 \log 2 - 1$.
Jul
13
asked Prove that $I = \int_0^{m(m+1} y_n(x)\,\mathrm{d}x$ converges and $I \in \mathbb{Q}$.
Jul
5
comment Evaluation of $\int_0^1 \frac{\log(1+x)}{1+x}\log\left(\log\left(\frac{1}{x}\right)\right) \ dx$
I think the following might be of some use \begin{align*} I(a) & = \int_0^1 \frac{\log(1+ax)}{1+x}\log \log 1/x\mathrm{d}x \\ I'(a) & = \int_0^1 \frac{x \log \log x}{(ax+1)(x+1)}\mathrm{d}x \\ & = \frac{1}{a-1} \int_0^1 x \log \log \frac 1x\left( \frac{a}{ax+1} - \frac{x}{1+x} \right) \mathrm{d}x \\ & = \frac{1}{a-1} \int_0^1 \log \log \frac 1x\left( \frac{1}{1+x} - \frac{1}{1+ax}\right) \mathrm{d}x \\ & = \frac{1}{a-1}\frac{\log^2(2)}{2} - \frac{1}{a-1}\int_0^1 \frac{\log \log 1/x}{1+ax}\,\mathrm{d}x \end{align*} Then integrate back from 0 to 1, however convergence issuses =/
Jul
4
comment Compute $\int_{0}^{\infty}e^{-tz}(z+d)^{n-1}dz$ as a function of $\Gamma(n)$
Maple gives $$e^{dt}*\Gamma(n, d*t)*t^{-n}$$
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
26
asked Prove that $\exists\,! \,\lambda \in (1/5,1/4)$ such that $\frac{1}{2\pi}\int_0^{2\pi}e^{\sin x}\,\mathrm{d}x=e^{\lambda}$
Jun
21
comment How do you integrate the reciprocal of square root of cosine?
Right we just use a different definition of the elliptic function. I still stand on the fact that AM-GM, is more efficient computational wise. i.imgur.com/O2OMzrI.png Hell, even trapezoid rule is efficient here, since it has approximately quadratic convergence for trigonometric functions.
Jun
21
comment How do you integrate the reciprocal of square root of cosine?
In terms of elliptic functions you missed a square root. Eg it should be $\sqrt{2} K(1/\sqrt{2})$. Also I would much prefer to express the integral in terms of the arithmetic geometric mean, since it is much faster to evaluate in stead of gamma. $$\int_{0}^{\pi/2} \dfrac{\mathrm{d}\theta}{\sqrt{\cos \theta\,}\,}=\frac{K( k)}{k} = \frac{k\cdot\pi}{M(1-k,1+k)}$$ It took me only $5$ iterations to obtain machine precession. Here $k = 1/\sqrt{2}$.