DLMF:6.7.E5 (Q2258)

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DLMF:6.7.E5
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    ∫ x ∞ e - t a 2 + t 2 ⁢ d t = - 1 2 ⁢ a ⁢ i ⁢ ( e i ⁢ a ⁢ E 1 ⁡ ( x + i ⁢ a ) - e - i ⁢ a ⁢ E 1 ⁡ ( x - i ⁢ a ) ) , superscript subscript 𝑥 superscript 𝑒 𝑡 superscript 𝑎 2 superscript 𝑡 2 𝑡 1 2 𝑎 𝑖 superscript 𝑒 𝑖 𝑎 exponential-integral 𝑥 𝑖 𝑎 superscript 𝑒 𝑖 𝑎 exponential-integral 𝑥 𝑖 𝑎 {\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),}}
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    DLMF:6.7.E5
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