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Continuously Differentiable Functions with Compact Support

Let f : [0,&#8734;)-->R be continuously differentiable with compact support in [0,&#8734;); and 0<a<b<&#8734;. Prove that:
&#8734;
&#8747; [f(bx)-f(ax)]/x dx = -f(0) ln (b/a)
0

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