Let F(x)=∫ln(7x)dx.
Answer the following questions, showing all intermediary work and algebraic simplifications.
(1) Determine an explicit antiderivative for ln(7x). Express your result in the form F(x)=(expression)+C.
(2) Differentiate the antiderivative you found in part (a) to confirm that it reproduces the original integrand. State your conclusion clearly.