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Frullani's Integral

If $f'(x)$ is continuous and the integral converges,

\begin{displaymath}
\int_0^\infty {f(ax)-f(bx)\over x}\, dx = [f(0)-f(\infty )]\ln\left({b\over a}\right).
\end{displaymath}


References

Spiegel, M. R. Mathematical Handbook of Formulas and Tables. New York: McGraw-Hill, 1968.




© 1996-9 Eric W. Weisstein
1999-05-26