 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-1/4/a/solution

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

\frac{1}{x ( x - 4 )} = - \frac{1}{4 x} + \frac{1}{4 ( x - 4 )} .

Integrating the two logarithmic derivatives gives

\int \frac{d x}{x ^{2} - 4 x} = \frac{1}{4} lo g \frac{x - 4}{x} + C .

This holds on each interval avoiding the two poles

0

and

4

, with an independent integration constant on each interval.

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