The function that solves every Integration question | Weierstrass Substitution | tan(x/2)

The Ghost Substitution (commonly known as the Weierstrass or Half-Angle Tangent Substitution) is one of the 'sneakiest substitutions' in mathematics. The Ghost Substitution utilizes a very clever and useful property about trigonometric functions which allows us to solve complex calculus related problems.

In this video, we visually explain how we can intuitively define the circle using the Ghost Substitution and how we can use the substitution in Integration - perhaps it's most important use!

Integration by Substitution video: https://youtu.be/Pb6ViPlKcS0
Problem Sheet: https://mathacy.com/problem-sheets

Timestamps:
0:00 - Intro
0:30 - Redefining the Circle
1:40 - Creating a new equation for the circle
2:45 - Bringing back sine and cosine
3:37 - The Ghost Substitution
5:03 - Solving a difficult integral with The Ghost Substitution
5:43 - Thank you!!