Fungrim entry: e4f73a

\int \frac{1}{z} \, dz = \log\!\left(-z\right) + \mathcal{C}

Assumptions:

z \in \mathbb{C} \setminus \left[0, \infty\right)

TeX:

\int \frac{1}{z} \, dz = \log\!\left(-z\right) + \mathcal{C}

z \in \mathbb{C} \setminus \left[0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`ComplexIndefiniteIntegralEqual`	$\int f(x) \, dx = g(x) + \mathcal{C}$	Indefinite integral, complex derivative
`Log`	$\log(z)$	Natural logarithm
`CC`	$\mathbb{C}$	Complex numbers
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("e4f73a"),
    Formula(ComplexIndefiniteIntegralEqual(Div(1, z), Log(Neg(z)), z)),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, ClosedOpenInterval(0, Infinity)))))

Topics using this entry

Natural logarithm

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC