Fungrim entry: a4ac32

\int \frac{1}{x} \, dx = \log\!\left(\left|x\right|\right) + \mathcal{C}

Assumptions:

x \in \mathbb{R} \setminus \left\{0\right\}

TeX:

\int \frac{1}{x} \, dx = \log\!\left(\left|x\right|\right) + \mathcal{C}

x \in \mathbb{R} \setminus \left\{0\right\}

Definitions:

Fungrim symbol	Notation	Short description
`RealIndefiniteIntegralEqual`	$\int f(x) \, dx = g(x) + \mathcal{C}$	Indefinite integral, real derivative
`Log`	$\log(z)$	Natural logarithm
`Abs`	$\left\|z\right\|$	Absolute value
`RR`	$\mathbb{R}$	Real numbers

Source code for this entry:

Entry(ID("a4ac32"),
    Formula(RealIndefiniteIntegralEqual(Div(1, x), Log(Abs(x)), x)),
    Variables(x),
    Assumptions(Element(x, SetMinus(RR, Set(0)))))

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