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


 /            /                                  /                                    /

 | 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


£20 /hr

Anezka E.

Degree: Mathematics (Bachelors) - Kings, London University

Subjects offered: Maths


“About me: I'm hopefully about to start my second year at King's College London. I've thouroughly enjoyed studying maths for many years now and would love to help out a maths lover or hater and hopefully convert the latter into the for...”

MyTutor guarantee

£20 /hr

Jack G.

Degree: Politics, Philosophy, and Economics (Bachelors) - Warwick University

Subjects offered: Maths, Religious Studies+ 2 more

Religious Studies
.TSA. Oxford.

“Hello, I'm Jack and am studying politics, philosophy, and economics at Warwick.  Having recently been through the subjects I'm looking to tutor I feel like I know first hand what difficulties you'll be facing. I always found I wanted ...”

MyTutor guarantee

£20 /hr

Joel B.

Degree: Mathematics & Computer Science (Bachelors) - Manchester University

Subjects offered: Maths, Physics+ 3 more

Further Mathematics

“About Me: Hello, my name is Joel and I am currently a student at the University of Manchester studying for a joint honours in Mathematics & Computer Science. I have experience in teaching maths (and further maths) to students in the ag...”

MyTutor guarantee

About the author

£20 /hr

Zaiyang L.

Degree: computer science (Bachelors) - Bristol University

Subjects offered: Maths


“Experienced, enthusiastic, and encouraging tutor wants to help you with A-LEVEL Maths”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Solve for 0<=θ<π, the equation sin3θ-(sqrt3)cosθ=0 (C2)

Solve the equation 5^x = 8, giving your answer to 3 significant figures.

How do I differentiate implicitly?

A curve is described by the equation x^3 - 4y^2 = 12xy. a) Find the points on the curve where x = -8. b) Find the gradient at these points.

View A Level Maths tutors


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