Formula:2998

Digital Library of Mathematical Functions ID 6.14.E2

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}\mathrm{Ci}\left(t\right)\mathrm{d}t=-\frac{1}{2a}\ln\left(1+a^{2}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re a>0}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}}$: cosine integral
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\Re}}$: real part
 

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