How to integrate ln(x)

MYTUTOR SUBJECT ANSWERS

Answers / Maths / A Level / How to integrate ln(x)

905 views

How to integrate ln(x)

How to integrate ln(x)?

In order to integrate log x of base e, we are going to apply integration by parts.

Recall that the formula for integration by parts is:

/ /

| f(x) g'(x) = f(x) g(x) - | f'(x) g(x)

/ /

The application of integration by parts is interesting because there is only one function being integrated. We need an f and g'. The key step in this problem is we can manufacture a function by making

ln(x) = 1 * ln (x)

We can choose f(x) = ln (x) , g'(x) = 1 ==>>>> f'(x) = 1/x, g(x) = x

Then,

/ / / /

| ln(x) = | 1*ln(x) dx = x*ln(x) - | x * (1/x) dx = x*ln(x) - | 1 dx

/ / / /

= x*ln(x) - x + C

Zaiyang L. A Level Maths tutor, GCSE Maths tutor

2 years ago

Answered by Zaiyang, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

365 SUBJECT SPECIALISTS

Joe C. A Level Maths tutor, GCSE Maths tutor

View profile

£30 /hr

Joe C.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics

“Hi, I'm Joe, an experienced tutor and a University of Bristol graduate with a first class Degree in Mathematics.”

5.0

84 reviews | 177 completed tutorials

Save profile

Jamie M. GCSE Maths tutor, A Level Maths tutor, GCSE Further Mathemat...

View profile

£20 /hr

Jamie M.

Degree: Physics with Theoretical Physics (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 3 more

“In my own A-Levels I developed skills that allowed me to achieve 4A*s and I want to share these techniques with any students willing to learn.”

5.0

1 review | 1 completed tutorial

Save profile

£20 /hr

Sherin W.

Degree: Biomedical science (Bachelors) - Sussex University

Subjects offered:Maths, Further Mathematics + 4 more

“For the past 5 years I have been tutoring, individuals to small classes. I am passionate about teaching and think it is an essential part of life and careers.”