 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-1/9/c/ii/solution

ln cosh x

tanh x

. Since

cosh (ln 2) = (2 + 1/2) /2 = 5/4

\int_{0}^{l n 2} tanh x d x = [ln cosh x]_{0}^{l n 2} = ln \frac{5}{4} .

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