Integral of ln(x)
In this post we will find the antiderivative of ln(x) step-by-step. This is one of those integrals you solve once and never forget. Let’s start! What is ln(x)? ln is… Read more Integral of ln(x) →
Integral of cot(x)
In this post you’ll learn how to integrate the trigonometric function cot(x). But first: What is cot(x)? Maybe you already know it, but this is going to be really useful.… Read more Integral of cot(x) →
Integral of tan(x)
Maybe you know that the answer is ln(sec(x)), but do you know why? Here you’ll find the procedure with explanation! First of all, let’s write the integral: We know that… Read more Integral of tan(x) →
Integral of sin(x)
The integral of sin(x) is -cos(x), but why? Here you’ll find the demonstration using Euler’s identity!
Integral of cos(x)
The integral of cos(x) is sin(x), but why? Here you’ll find the demonstration using Euler’s identity!
Fractional part
In the previous post I talked about the floor and ceiling functions. Go check them out if you haven’t already! We are going to need them to learn about the fractional part. What is fractional part? The fractional part of a positive number is the part after the decimal, i.e. the decimal part. We can write the fractional part of a number x as Here are some examples: If you noticed, the fractional part of 2.6 is 0.6, which is 2.6-2, and the same happens for the other examples. This… Read more Fractional part →
Floor and ceiling functions
Floor and ceiling functions are very cool functions that will allow us to do an even cooler thing at the end of this post! Keep reading to learn about them and find out what we’re going to do! Floor function The floor function of a real number gives as output the integer part of that number and is written as Examples: This is how it works for positive numbers; but what about negative numbers? It’s actually the same thing, except it may not be very intuitive: but vs This is… Read more Floor and ceiling functions →
Imaginary numbers | Solutions with procedure
Here are the solutions to the exercises I gave you here! Notice that cosine is an even function, therefore cos(-pi)=cos(pi). The logarithm in base 3 of 3 is 1 because 1 is the number you must raise 3 to in order to get 3. Now, why is theta raised to the log in base theta of negative i equal to negative i, i.e. the argument of the logarithm? That’s a property: Another property is the following: Hope this was useful! If you have any doubt leave a comment and I… Read more Imaginary numbers | Solutions with procedure →
Add just a bit of pi 