 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-1/3/a/solution

For

x > 0

u = ln x

and

d v = d x

. Then

\int ln x d x = x ln x - \int 1 d x = x ln x - x + C .

Differentiating the answer checks cancellation of the extra constant term from

(x ln x)^{'}

 New to topics? Read the docs here!