 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-2/13/a/i/solution

The hyperbolic identity

cosh^{2} x - sinh^{2} x = 1

and

cosh x + sinh x = e^{x}

reduce the integrand to

1 + e^{x}

. Therefore

\int (cosh^{2} x + cosh x - sinh^{2} x + sinh x) d x = x + e^{x} + C .

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