MYTUTOR SUBJECT ANSWERS

434 views

How do I integrate ln(x)?

There is a subtle, but very neat trick to this when applying the rules of integration by parts.

If we take ∫ln(x)dx = ∫1*ln(x)dx, and then let our term to be differentiated, u = ln(x), and our term to be integrated, dv/dx = 1, then it follows that:

 

du/dx = x⁻¹, v = x

 

and from the integration by parts formula:

∫u * (dv/dx) dx = uv - ∫v * (du/dx) dx

 

∴ ∫ln(x)dx = xln(x) - ∫(x⁻¹ * x)dx (+ constant)

∫ln(x)dx = xln(x) - ∫dx (+ constant)

Hence, our results turns out to be:

∫ln(x)dx = xln(x) - x + c

 

NB. While our trick here gives us a very straightforward solution to an integration which could have been very laborious via other methods, integration by parts tends to be a last resort, as more, seemingly contrived steps are required. One should generally try integration by substitution, for non-standard integrations, first when unsure of which method to use, as the steps to a result are often far simpler and quicker.

Jacan C. A Level Maths tutor, A Level Physics tutor, GCSE Physics tut...

2 years ago

Answered by Jacan, an A Level Maths tutor with MyTutor


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

258 SUBJECT SPECIALISTS

£20 /hr

Marcin K.

Degree: MPHYS Theoretical Physics (Masters) - Leeds University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Music

“Hi! Who am I? My name is Marcin and I am currently in my fourth year studying Theoretical Physics at the University of Leeds. I share my energy between two passions which are science and music. Learning about how the physical world ...”

£20 /hr

James T.

Degree: Chemical Engineering (Masters) - Bath University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Chemistry
-Personal Statements-

“About me: I am in my second year of Chemical Engineering at the University of Bath. I love problem-solving and hard work! I recognise that everyone works differently so I will try to find the best way for you to learn! I am very frien...”

MyTutor guarantee

£20 /hr

Chris B.

Degree: Economics (Bachelors) - Durham University

Subjects offered: Maths, Further Mathematics + 2 more

Maths
Further Mathematics
Economics
-Personal Statements-

“About me: I am currently in my first year of studying Economics at Durham University. I have been tutoring maths for about two years now, so have had plenty of experience passing on my knowledge and interest in my subjects to younger ...”

MyTutor guarantee

About the author

£36 /hr

Jacan C.

Degree: Theoretical Physics (Masters) - York University

Subjects offered: Maths, Science+ 3 more

Maths
Science
Physics
Further Mathematics
Chemistry

“Helping the striving and the struggling with caring, friendly and structured tuition. With 200+ hours of experience, offering Physics, Maths and Chemistry.”

You may also like...

Other A Level Maths questions

If cos(x)= 1/3 and x is acute, then find tan(x).

A curve has the equation y=12+3x^4. Find dy/dx.

How to factorise any quadratic expression

How do I integrate cos^2(x)?

View A Level Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok