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Proposition: Integral of the Natural Logarithm

Let $0 < a < b$. The Riemann-integral of the natural logarithm on the closed real interval is given by the formula

$$\int_a^b\log(x)dx= x(\log(x)-1)\;\begin{array}{|l}a\\\\b\end{array}.$$

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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983