The value of the integral is

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

The value of the integral ∫ln⁡(x+1)−ln⁡xx(x+1) dx\int \frac{\ln(x+1)-\ln x}{x(x+1)}\,dx is (a) −12[ln⁡(x+1)]2−12(ln⁡x)2+ln⁡(x+1)ln⁡x+c-\frac{1}{2}[\ln(x+1)]^2-\frac{1}{2}(\ln x)^2+\ln(x+1)\ln x+c (b) −{[ln⁡(x+1)]2−(ln⁡x)2}+ln⁡(x+1)ln⁡x+c-\{[\ln(x+1)]^2-(\ln x)^2\}+\ln(x+1)\ln x+c (c) −12[ln⁡(1+1/x)]2+c-\frac{1}{2}[\ln(1+1/x)]^2+c (d) None of these

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