Integral of $\tan(x)$
The easiest way to integrate $\tan(x)$ is to recall that $\tan(x) = \frac{\sin(x)}{\cos(x)}$. Do you see the necessary substitution? By choosing $y = \cos(x)$, that is, $dy = \sin(x)\,dx$ (...)
July 2, 2017 – Jakub Marian – Mathematics

Derivative of $x^x$
Calculating the derivative of $x^x$ is a very simple task, but it may be hard to find the general idea on your own, so here it is. We will (...)
July 2, 2017 – Jakub Marian – Mathematics

Integral of $x^n$
How to calculate the indefinite integral of $x^n$? It’s quite simple. We are looking for a function $f(x)$ such that $f’(x) = x^n$. As you (...)
July 2, 2017 – Jakub Marian – Mathematics

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Integral of $e^{x^2}$ from $\infty$ to $\infty$
In this article, I will give a detailed explanation of why the Gaussian integral is equal to $√\pi$, that is, of the following famous (...)
June 29, 2017 – Jakub Marian – Mathematics

Map of the results of PISA 2015 (Programme for International Student Assessment) in science, reading, and mathematics in Europe
Results of the PISA 2015 (Programme for International Student Assessment) in science, reading, and mathematics visualized on a map of Europe. (...)

Why the “vegetarianism is unnatural” argument is nonsense
I had a heated discussion recently in the comment section under my article about the worst arguments against vegetarian nutrition (which (...)
December 8, 2016 – Jakub Marian – Nutrition

Map of ‘vegetarian friendliness’ (number of vegetarian restaurants) in Europe by country
The original idea of this article was to create a map showing the percentage of the population following a vegetarian diet, but it turned (...)
October 2, 2016 – Jakub Marian – Maps

Number of Nobel laureates per capita in Europe (map)
The following map shows the number of Nobel laureates per 10 million inhabitants in European countries (the smaller caption shows the (...)
August 29, 2016 – Jakub Marian – Maps

The ‘day of the week boy or girl’ paradox explained
There is a wellknown result in probability theory that seems to defy common sense. Note that in the problem statement we assume that the (...)
July 25, 2016 – Jakub Marian – Mathematics

Wine consumption in Europe by country per year per capita
Wine is one of the most popular alcoholic beverages in Europe, with the French alone consuming about the same amount of wine as the whole (...)
