Let for . Which of the following equals…

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

Problem

Let A(x)=∫1x3ln⁡tt dtA(x)=\displaystyle\int_{1}^{x^{3}}\frac{\ln t}{t}\,dt for x>0x>0. Which of the following equals A′(x)A'(x)? (a) ln⁡xx\displaystyle\frac{\ln x}{x} (b) ln⁡(x3)3x2\displaystyle\frac{\ln(x^{3})}{3x^{2}} (c) 3 ln⁡(x3)x\displaystyle\frac{3\,\ln(x^{3})}{x} (d) 3x2ln⁡x\displaystyle3x^{2}\ln x

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