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What is an integration by substitution? When do we need to perform one? What substitution is...

What is an integration by substitution? When do we need to perform one? What substitution is a complete waste of time?
16. Discuss how the processes of integration and differentiation can be considered as “inverses” of each other. How is integration by substitution related to the chain rule?
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The process of integration and differentiation can considered as inverse of each other why because the Integration is the inverse process of differentiation. Instead of differentiating a function, we are given the derivative of a function and asked to find its primitive, i.e., the original function. Such a process is called integration or anti differentiation.

"Integration by Substitution" (also called "u-Substitution" or "The Reverse Chain Rule") is a method to find an integral, but only when it can be set up in a special way. When our integral is set up like that, we can do this substitution: Then we can integrate f(u), and finish by putting g(x) back as u.

NO, substitution gives accurate values and it is not at all waste of time.

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