Fungrim home page

Fungrim entry: e4f73a

1zdz=log ⁣(z)+C\int \frac{1}{z} \, dz = \log\!\left(-z\right) + \mathcal{C}
Assumptions:zC[0,)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
ComplexIndefiniteIntegralEqualf ⁣(x)dx=g ⁣(x)+C\int f\!\left(x\right) \, dx = g\!\left(x\right) + \mathcal{C} Indefinite integral, complex derivative
Loglog ⁣(z)\log\!\left(z\right) Natural logarithm
CCC\mathbb{C} Complex numbers
ClosedOpenInterval[a,b)\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

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

2019-09-15 11:00:55.020619 UTC