Unformatted text preview: given function so that it is written entirely in terms of u , with no x remaining in the expression. If we can integrate this new function of u , then the antiderivative of the original function is obtained by replacing u by the equivalent expression in x . Even in simple cases you may prefer to use this mechanical procedure, since it often helps to avoid silly mistakes. For example, consider again this simple problem: Z 2 x cos( x 2 ) dx. Let u = x 2 , then du/dx = 2 x or du = 2 x dx . Since we have exactly 2 x dx in the original integral, we can replace it by du : Z 2 x cos( x 2 ) dx = Z cos u du = sin u + C = sin( x 2 ) + C....
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 Spring '07
 JonathanRogawski
 Math, Calculus, Chain Rule, Derivative, dx, Leibniz notation

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