 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2003/paper-1/4/i/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

Put

u = ln x

, so

d u = d x / x

. The integral becomes

\int d u / u

\int \frac{d x}{x ln x} = ln ∣ ln x ∣ + C .

For the real logarithm, choose an interval in

0 < x < 1

x > 1

; the original integrand is singular at one and undefined for nonpositive

x

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