Formula:2445

Digital Library of Mathematical Functions ID 4.40.E10

${\displaystyle{\displaystyle{\int_{0}^{\infty}\frac{\tanh\left(ax\right)-\tanh\left(bx\right)}{x}\mathrm{d}x=\ln\left(\frac{a}{b}\right)},}}$

Constraint(s)

${\displaystyle{\displaystyle b>0}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\tanh\NVar{z}}}$: hyperbolic tangent function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle a}}$: real or complex constant
• ${\displaystyle{\displaystyle x}}$: real variable
 

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