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Fungrim entry: c77f9a

1zdz=log ⁣(z)+C\int \frac{1}{z} \, dz = \log\!\left(z\right) + \mathcal{C}
Assumptions:zC(,0]z \in \mathbb{C} \setminus \left(-\infty, 0\right]
TeX:
\int \frac{1}{z} \, dz = \log\!\left(z\right) + \mathcal{C}

z \in \mathbb{C} \setminus \left(-\infty, 0\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
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("c77f9a"),
    Formula(ComplexIndefiniteIntegralEqual(Div(1, z), Log(z), z)),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0)))))

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2019-09-15 11:00:55.020619 UTC