 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/6/b/solution

For

m = - 1

u = ln x

d u = d x / x

\int \frac{ln x}{x} d x = \frac{1}{2} (ln x)^{2} + C, x > 0.

This case is treated separately because the denominator

m + 1

in part (a) vanishes.

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