Substitution
Performing integration by substitution (sometimes referred to as u-substitution or a change of variables) refers to substituting a function of , , with and rewriting the integral in terms of the substituted variable .
$$
\begin{align*}
\int f\left[g(x)\right]g'(x)\,dx &= \int f(u)\,du\\
&= F(u) + C\\
&= F\left(g(x)\right) + C
\end{align*}
$$
Engineering Context
Integrals consistently show up in engineering when solving for net forces and moments, the centroid of an object, and solving differential equations modeling a physical phenomenon. Knowing how to solve an integral by substitution is a tool that is invaluable when faced with these types of problems as an engineer.