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Here is the problem: integral of 1/x from 1 to e.

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Evaluate the definite integral of 1 / x from x equals 1 to x equals e.

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Start with the definite integral.

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Reciprocal rule: the integral of 1/x dx equals ln|x|.

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Constant multiple rule: the integral of k times f dx equals k the integral of f dx.

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Antiderivative.

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Apply the fundamental theorem of calculus.

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So the answer is 1.

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A definite integral gives the signed area between the curve and the x-axis: area above the axis counts as positive and area below counts as negative.

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Differentiated the antiderivative and compared it with the integrand, which checks out.

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Adaptive Simpson prime s rule gives 1, which checks out.