 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-1/7/a/solution

cot u

- csc^{2} u

. The chain rule therefore gives

\int \frac{d x}{sin ^{2} ( 3 x + 1 )} = - \frac{1}{3} cot (3 x + 1) + C .

The antiderivative applies on any interval containing no zero of

sin (3 x + 1)

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