Integration of ln|x| with Domain Considerations
Consider the integral \(\int \ln|x|\,dx\). Answer the following parts: (a) Identify the domain constraints associated with \(\ln|x|\). (b) Evaluate the integral \(\int \ln|x|\,dx\) using integration by parts. (c) Discuss how the sign of \(x\) affects the integrated result, particularly in the context of the absolute value in the logarithm.