The Story So Far
Pretend that you are a mathematics instructor. You have been tasked with teaching a calculus course online, but have only been trained to teach in person! You want to send your students worked-through solutions.
In particular, the exercise:
$$ \int \frac {2x} {x^4 + 2x^2 + 1} dx $$
Is giving people trouble. You want to send your students a document that works them through the steps.
Unfortunately, you might not know $\LaTeX$ yet - and there are so many resources. But you are on a computer with $\LaTeX$ installed, and your predecessor helpfully left you some gibberish:
\documentclass{article}
\usepackage{amsmath,amsthm,amssymb,physics}
\begin{document}
% A Comment
Some {\em example} \LaTeX{} \textbf{content}. Inline: $f_1(x): \mathbb{R}_{\geq 0} \to \mathbb{R}$
Block:
\[
f_1: x \mapsto \int_a^{b^2} \left( \frac{ \frac{\operatorname{function(x)}}{\gamma}}{2x+1} + \sqrt[3]{4} \right)
\]
Aligned Equations:
\begin{align}
f(x) &= (x-1)(x+1) & f(y) &= (y+1)(y-1)\\
\nonumber &= x^2-1\\
&= \det \left(xI - \begin{bmatrix}
1 & 3 \\
0 & -1
\end{bmatrix}
\right)
\end{align}
\end{document}
Task: compile this $\LaTeX$ document. Change some values around. What is different? Experiment, and keep a careful watch on the errors.
Once you get a feel for $\LaTeX$, write a short article that explains to students how to use $u$ substitution to solve the given homework problem.
Graded Exercise: Upload your completed tutorial to Brightspace as a PDF.