Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.2 Exercises - Page 336: 104

$\text{False}$

If this were true, then the derivative of the RHS should be the integrand function. The RHS is not an antiderivative of $\ln x:$ $\displaystyle \frac{d}{dx}(\frac{1}{x}+C)=\frac{d}{dx}(x^{-1}+C)=(-1)\cdot x^{-1-1}= -x^{-2},$ which is not $\ln x$, showing that the statement is false.