 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/a/solution

For real powers work on

x > 0

u = ln x

and

d v = x^{m} d x

, so

v = x^{m + 1} / (m + 1)

when

m \neq = - 1

. Then

\int x^{m} ln x d x = \frac{x ^{m + 1} ln x}{m + 1} - \frac{x ^{m + 1}}{( m + 1 ) ^{2}} + C .

 New to topics? Read the docs here!