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  3. 4 the substitution rule if u g x is a differentiab

4 THE SUBSTITUTION RULE If u g x is a differentiable function whose range is...

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Calculus

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4 THE SUBSTITUTION RULE If u g x is a differentiable function whose range is an interval I and f is continuous on I then f f g x g x dx f f u du EXAMPLE I Find x cos x 2 dx u x 2 so du 4x dx x dx du 4 x cos x 2 dx cos u du cos u du sin u C sin x4 2 C 8 x x 5 dx 10 3 2 4 dt C

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