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Learn the powerful technique of u-substitution to simplify integrals by rewriting them in terms of a new variable. Discover how to identify the appropriate choice for u, follow the steps for u-substitution, and integrate efficiently. With 11 different integral forms at your disposal, this method is essential for advanced calculus.
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Section 5.5 Integration by Substitution
With what we know now, how would we… Integrate Rewriting in this manner is tedious and sometimes impossible so we need a better way. This new method is called u-substitution.
The goal of u-substitution is to rewrite a given integrand using a new variable so that it matches one of the integrand formulas that we already know. Remember, at this point we know how to integrate 11 different forms (and sums, differences and constant multiples of them).
The first and arguably the most important step in u-substitution is learning to recognize what form you are working toward. In other words, what is an appropriate choice for u.
Steps for U-Substitution 1) Choose u • Find du • Rewrite the integrand totally in terms of u and du. • Integrate with respect to u • Replace u with corresponding expression in terms of x (or whatever original variable of integration was)
