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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)

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