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

Definite integrals