Question:

<p><strong>M-1 :</strong></p><p>$\int 1 \cdot \ln x \, dx = \ln(x) \cdot (x) - \int \frac{1}{x} \cdot x \, dx = x \ln x - x + C$</p><p><strong>M-2 :</strong></p><p>$\int \ln x \, dx$</p><p>Put, $\ln x = t \Rightarrow x = e^t \Rightarrow dx = e^t \, dt$</p><p>$\therefore \int \ln x \, dx = \int t \cdot e^t \, dt = t \cdot e^t - e^t + C = x \ln x - x + C$</p>