 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2004/paper-1/4/b/solution

Use

tan^{2} x = sec^{2} x - 1

and the derivative of the tangent:

\int tan^{2} x d x = tan x - x + C .

The antiderivative applies on each interval avoiding the poles of

tan x

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