29.11. Calculate $\int \frac{\ln x}{x} d x$.
29.11. Apply the integration by parts formula for \( f(x) = g(x) = \ln x \). As a result, we get

\[
\int \ln x \frac{1}{x} d x = (\ln x)^{2} - \int \frac{1}{x} \ln x d x
\]

The antiderivative is defined up to a constant, so this equality should be understood as: \( I = (\ln x)^{2} - (I + C) \), where \( I = \int \frac{\ln x}{x} d x \). Thus, \(\int \frac{\ln x}{x} d x = \frac{(\ln x)^{2}}{2} + C\) (the constant \( C \) here is different).