Then we can evaluate the integral with respect to and use the same dictionary to translate back from -language to -language:Įxamples of indefinite integration using substitution We use these two equations relating and as our dictionary to translate our integral from -language to -language: We differentiate both sides of the equation to see that. This tells us that setting might be a good choice. We notice that is the “inside” function of a composition and appears as a factor of the integrand. Consider the indefinite integral (this should look familiar from the warmup exercise, so we already know what we want the answer to be).
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