Formula:2962

Digital Library of Mathematical Functions ID 6.7.E11

${\displaystyle{\displaystyle\int_{0}^{1}\frac{(1-e^{-at})\cos\left(bt\right)}{t}\mathrm{d}t=\Re\mathrm{Ein}\left(a+ib\right)-\mathrm{Cin}\left(b\right),}}$

Constraint(s)

${\displaystyle{\displaystyle a,b\in\mathbb{R}}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{Ein}\left(\NVar{z}\right)}}$: complementary exponential integral
• ${\displaystyle{\displaystyle\cos\NVar{z}}}$: cosine function
• ${\displaystyle{\displaystyle\mathrm{Cin}\left(\NVar{z}\right)}}$: cosine integral
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle\mathbb{R}}}$:
 

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