Science

Integrating the third power of $\sin(x)$ (or any odd power, for that matter), is an easy task (unlike $∫ \sin^2(x)\,dx$, which requires (...)

The integral can be calculated using integration by parts (using the formula $∫u’(x)v(x)\,dx = u(x)v(x) - ∫ u(x)v’(x)\,dx$). Let’s (...)

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, $dy = -\sin(x)\,dx$ (...)

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 (...)

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 (...)

In this article, I will give a detailed explanation of why the Gaussian integral is equal to $√\pi$, that is, why the following equality (...)

The following map shows the number of Nobel laureates per 10 million inhabitants in European countries (the smaller caption shows the (...)

There is a well-known result in probability theory that seems to defy common sense. Note that in the problem statement we assume that the (...)

After I published my recent article about the Number of metal bands per capita in Europe, I got quite a few comments saying that my use of (...)

When an animal sees a computer screen, it doesn’t see the same colours as you do because our monitors only properly work for humans. This (...)