Sec. 4.5: Integration by Substitution. T HEOREM 4.12 Antidifferentiation of a Composite Function Let g be a function whose range is an interval I, and.

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Sec. 4.5: Integration by Substitution

T HEOREM 4.12 Antidifferentiation of a Composite Function Let g be a function whose range is an interval I, and let f be a function that is continuous on I. If g is differentiable on its domain and F is an antiderivative of f on I, then

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Sec. 4.5: Integration by Substitution Rearranging u u = x + 3 du = dx u – 3 = x

Sec. 4.5: Integration by Substitution u = 2x – 1 du = 2 dx u + 1 = 2x 1/2 du = dx (u + 1) / 2 = x