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Proposition: Integral of the Reciprocal Function

Let $0 < a < b$ or let $a < b < 0$. Then the Riemann integral of the reciprocal function is given by

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

Where $\log(|x|)$ is the natural logarithm of the absolute value of $x$.

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Proofs: 1

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References

Bibliography

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