Let $u = \ln x$. Then, $du = \frac{1}{x} dx$. So, we can rewrite the integral as follows:
$$\int \frac{\ln x}{x^{3}} dx = \int \frac{u}{x^2} \cdot \frac{1}{x} dx = \int \frac{u}{x^3} dx = \int u \cdot \frac{1}{x} dx = \int u \, du$$
Now, we can integrate $u$
Show more…