# Science

 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$can be calculated using the (...) July 8, 2017 – Jakub Marian – Mathematics  Integral of$\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$, which requires (...) July 4, 2017 – Jakub Marian – Mathematics  Integral of$\sin^2(x)$The integral can be calculated using integration by parts (remember that$∫u’(x)v(x)\,dx = u(x)v(x) - ∫ u(x)v’(x)\,dx$):$$∫ (...) 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  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