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Here is the problem: integral of ln(x) from 1 to e.

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Evaluate the definite integral of ln(x) from x equals 1 to x equals e.

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Start with the definite integral.

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the integral of ln x dx equals x ln x minus x (integration by parts).

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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.