# Fungrim entry: 02e3d2

$\int_{z}^{\infty} {e}^{-a x + b} \, dx = \frac{{e}^{b - a z}}{a}$
Assumptions:$a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(a) > 0$
TeX:
\int_{z}^{\infty} {e}^{-a x + b} \, dx = \frac{{e}^{b - a z}}{a}

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \operatorname{Re}(a) > 0
Definitions:
Fungrim symbol Notation Short description
Integral$\int_{a}^{b} f(x) \, dx$ Integral
Exp${e}^{z}$ Exponential function
Infinity$\infty$ Positive infinity
CC$\mathbb{C}$ Complex numbers
Re$\operatorname{Re}(z)$ Real part
Source code for this entry:
Entry(ID("02e3d2"),
Formula(Equal(Integral(Exp(Add(Neg(Mul(a, x)), b)), For(x, z, Infinity)), Div(Exp(Sub(b, Mul(a, z))), a))),
Variables(a, b, z),
Assumptions(And(Element(a, CC), Element(b, CC), Element(z, CC), Greater(Re(a), 0))))

## Topics using this entry

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