What it’s like to work as a data scientist in a bank
I’ve been working as a data scientist in the private sector (in a bank) for the past three years, one year as the leader of a chapter of (...)
January 23, 2022 – Jakub Marian – Mathematics

What is $0^0$ ($0$ to the power $0$)?
A short answer to this question is that $0^0$ is usually left undefined in introductory calculus classes, just like $0/0$, but it is often (...)
October 15, 2017 – Jakub Marian – Mathematics

Integral of $\cot(x)$
To integrate cot(x), recall that cot(x) = cos(x)/sin(x), so ∫ cot(x) dx = ∫ cos(x)/sin(x) dx. (...)
September 21, 2017 – Jakub Marian – Mathematics

Integral of $\sin(x)\cos(x)$
The function $\sin(x)\cos(x)$ is one of the easiest functions to integrate. All you need to do is to use a simple substitution $u = (...)
September 6, 2017 – Jakub Marian – Mathematics

How to calculate the factorial of 1/2
As I proved in my article on integration by parts (at the end), the factorial of a natural number $n$ can be calculated using the (...)
July 8, 2017 – Jakub Marian – Mathematics

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Integral of $\log(x)$ (or $\ln(x)$)
The natural (base $e$) logarithm is usually denoted $\log(x)$ in mathematics, but for the sake of students of other disciplines, we will (...)
July 7, 2017 – Jakub Marian – Mathematics

Explanation of integration by parts
Integration by parts is one of the first methods people learn in calculus courses. Together with integration by substitution, it will (...)
July 6, 2017 – Jakub Marian – Mathematics

Integral of $\sin^3(x)$
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 (...)
July 4, 2017 – Jakub Marian – Mathematics

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Integral of $\sin^2(x)$
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 (...)
July 3, 2017 – Jakub Marian – Mathematics

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
