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CalculusMediumNon-Elementary Integration

Non-Elementary Integration · Medium problem

Use Frullani's theorem, ∫0∞f(ax)−f(bx)x dx=(f(0)−f(∞))ln⁡ba\displaystyle\int_0^{\infty}\dfrac{f(ax)-f(bx)}{x}\,dx=\bigl(f(0)-f(\infty)\bigr)\ln\dfrac{b}{a}, to evaluate ∫0∞tanh⁡3x−tanh⁡xx dx\displaystyle\int_0^{\infty}\dfrac{\tanh 3x-\tanh x}{x}\,dx.