 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2017/discrete-mathematics-continuous-mathematics-and-probability/5/a/solution

\frac{1}{4 - x ^{2}} = \frac{1}{4} (\frac{1}{2 + x} + \frac{1}{2 - x}) .

Integrating gives

I (x) = \frac{1}{4} lo g \frac{2 + x}{2 - x} + C .

This real antiderivative is valid on each interval avoiding

x = \pm 2

, with its own integration constant. In particular,

I (1) - I (0) = \frac{1}{4} lo g 3

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