Question

(d) Find the value of \( \int \log x \, dx \):

Hint:

For \( \int \log x \, dx \), apply integration by parts with \( u = \log x \) and \( dv = dx \).

Answer 1

Using integration by parts: Let \( u = \log x \) and \( dv = dx \). Then \( du = \frac{1}{x} dx \) and \( v = x \). \[ \int \log x \, dx = x \log x - \int x \cdot \frac{1}{x} dx = x \log x - \int dx. \] \[ \int \log x \, dx = x \log x - x + C. \]