725 views

### How to integrate lnx by parts?

Integration by parts formula: ∫ u*dv/dx = uv - ∫ du/dx*v dx

To solve this problem we need to use a trick by thinking of lnx as lnx*1
So we can choose: u=lnx, dv/dx=1
The next step is to find du/dx and v.
du/dx=1/x                                          As we have differentiated each side with respect to x
v=x                                                         By integrating each side with respect to x
Now we have all the required parts to use the integration by parts formula.
∫ lnx = lnx*x – ∫ 1/x*x dx
= xlnx – ∫ 1 dx
= xlnx – x + c

2 years ago

Answered by Ryan, an A Level Maths tutor with MyTutor

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

#### 346 SUBJECT SPECIALISTS

£36 /hr

Degree: Architecture and Environmental Engineering (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Design & Technology
-Personal Statements-

“Hi there, I have a passion for helping students achieve, and believe that with my 200+ hours of experience, we will be able to surpass the grades you want!”

£20 /hr

Degree: Biomedical science (Bachelors) - Sussex University

Subjects offered:Maths, Further Mathematics + 4 more

Maths
Further Mathematics
Chemistry
Biology
-Personal Statements-
-Medical School Preparation-

“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.”

MyTutor guarantee

|  2 completed tutorials

£20 /hr

Degree: Aeronautical Engineering (Masters) - Imperial College London University

Subjects offered:Maths, Science+ 3 more

Maths
Science
Physics
Further Mathematics
Biology

“Expert tuition from an expert. A second year Uni student who's completed the hassle of GCSEs and A Levels, and can teach you the easy way to pass and succeed!”

MyTutor guarantee

|  1 completed tutorial

Currently unavailable: for new students

Degree: Mathematics (Bachelors) - Durham University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
.STEP.

“Hi, I’m Ryan, a second year mathematician at Durham University and I have a drive and passion to become a tutor in mathematics. I have two years of experience tutoring a group of AS level maths students so I feel I have the understand...”

MyTutor guarantee

### You may also like...

#### Posts by Ryan

How do you find the inverse of a function?

How to integrate lnx by parts?

What are the differences between arithmetic and geometric sequences?

#### Other A Level Maths questions

Differentiate x^5 + 3x^2 - 17 with respect to x

What does it mean to differentiate a function?

how do you differentiate tan(x)

How can we calculate the derivative of function f(x)= (x+2)/(x-1)?

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this.