  ## i to the i-th power

Ever wondered what the imaginary unit i raised to itself is equal to? Is it going to be a complex number? Or a real one? Let’s find out! Let’s first define i: Therefore, There is an identity in maths which is in my opinion one of the most beautiful equations that exist, and that is Euler’s identity: This means At this point we have two expressions: We can use the second one to replace the -1 in the first: We no longer have the i because i times i equals… Read more i to the i-th power  ## Hard looking yet beautiful integral

Never judge a book by its cover: this is the case. This integral requires a bit of work and knowledge, as you need to know about the Gaussian integral (I… Read more Hard looking yet beautiful integral ## Gaussian integral using Feynman’s technique

In my last post we evaluated the following definite integral This is the formula we got: and this is the integral we want to evaluate: which is equivalent to because… Read more Gaussian integral using Feynman’s technique ## Integral of e^-x^t using Feynman’s technique

Wouldn’t it be nice to generalize the Gaussian integral to any exponent of –x? This is the famous integral: Since this is an even function, it can be written as… Read more Integral of e^-x^t using Feynman’s technique ## Arc length formula

Today we are going to find the formula that allows us to calculate the arc length given a function f(x). This is quite intuitive, so you should have no problem!… Read more Arc length formula ## Integral of sin(x)/x from 0 to infinity | A satisfying solution

Today we have a tough integral: not only is this a special integral (the sine integral Si(x)), but it also goes from 0 to infinity! Because of the first characteristic,… Read more Integral of sin(x)/x from 0 to infinity | A satisfying solution ## Integral of e^(ax)*sin(x)

In this post we are going to integrate this seemingly hard integral, which in my opinion is actually very interesting! When we have a product of a trigonometric and a… Read more Integral of e^(ax)*sin(x) ## Integral of sec²(x)/exp(tan(x))

Although it may look a bit intimidating at first, I can guarantee you this is actually a very easy integral! But what integration technique do you think will be useful?… Read more Integral of sec²(x)/exp(tan(x))

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