What is the primary focus of the Integration by Substitution technique?

The primary focus of the Integration by Substitution technique is to change the variable of the integral. This method is particularly useful when dealing with integrals that contain composite functions, enabling you to simplify the integrand by substituting a part of it with a new variable. By doing so, you can often transform a complicated integral into a more manageable form, making it easier to evaluate.

For instance, when encountering an integral of the form ∫f(g(x))g'(x)dx, a substitution such as u = g(x) allows the integral to be rewritten as ∫f(u) du, which is often simpler to integrate. This technique essentially relies on the chain rule of differentiation, where the derivative of the inner function g(x) plays a critical role in adjusting the limits if necessary or transforming the integrand effectively.

While other choices mention aspects related to the integration process, such as constant limits or specific types of integrals, they do not capture the essence of what Integration by Substitution fundamentally aims to accomplish, which is to facilitate the integration process through variable change.