Formula:2956

Digital Library of Mathematical Functions ID 6.7.E5

${\displaystyle{\displaystyle\int_{x}^{\infty}\frac{e^{-t}}{a^{2}+t^{2}}\mathrm{d}t=-\frac{1}{2ai}\left(e^{ia}E_{1}\left(x+ia\right)-e^{-ia}E_{1}\left(x-ia\right)\right),}}$

Constraint(s)

${\displaystyle{\displaystyle x\in\mathbb{R}}}$
${\displaystyle{\displaystyle a>0}}$
${\displaystyle{\displaystyle x\in\mathbb{R}}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}$: exponential integral
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\mathbb{R}}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
 

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