Frullani's Integral

Rarely Tested

Frullani's Integral

For suitable positive constants $$a$$ and $$b$$:

$$\int_0^\infty\frac{f(ax)-f(bx)}{x}\,dx=[f(0)-f(\infty)]\ln\frac{b}{a}$$

Usage

- Used in advanced definite-integral problems involving scaled arguments and a factor $$1/x$$.

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