 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2017/paper-1/17/a/i/solution

u = ln x

, so

d u = d x / x

. For

x > 1

, also

u > 0

, and

\int \frac{d x}{x l n x} = \int \frac{d u}{u} = ln (ln x) + C .

The domain condition explains why no absolute value is needed around the inner logarithm.

 New to topics? Read the docs here!