MYTUTOR SUBJECT ANSWERS

328 views

What is the integral of ln(x)? Hint: use parts for this integration

We use parts for this integration even though there is only one term! make ln(x)=1ln(x)

How to do integration by parts

If you have a function that you need to integrate that is two functions of x multiplied by eachother, and youve already tried everything else (inspection and substitution) then you're going to have to use integration by parts. 

Intergrating the function §f(x)g(x) ...

we set one of the fuctions to u' and one to v

normally we'll take the hardest part to integrate as v. 

but in this general example we'll just take f(x)=u' and g(x)=v (putting a ' on a fucntion is to say it has been differentiated) 

The general equation then takes the form 

§(u')v dx = uv - §(v')u dx

or §f(x)g(x) = (§f(x)dx)g(x) - §(§f(x)dx)g'(x)dx which just looks like a mess of symbols.

Sometimes youll have to do this more than once to get the answer, but its a very handy tool in integration! 

So our problem is lnx. To make this by parts we split it up into two terms, 1(lnx) 

Therefore u'=1 and v=lnx so u=x and v'=1/x

This makes the integral....

§-use this as integration sign

§ln(x)dx = xln(x) - §x(1/x)dx

          =xln(x) -§(1)dx

      = xln(x) -x + c 

Joseph W. A Level Physics tutor, A Level Maths tutor, A Level Chemist...

1 year ago

Answered by Joseph, an A Level Maths tutor with MyTutor


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

254 SUBJECT SPECIALISTS

£20 /hr

Ellie B.

Degree: Mathematics (Masters) - York University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hi, my name is Ellie and I am currently studying Mathematics at the University of York. I chose York because I felt a real connection with the teachers, they made maths fun, interesting and easy. That's what I hope to do with all my s...”

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

£20 /hr

Ruadhan P.

Degree: Physics (Masters) - Nottingham University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Chemistry
-Personal Statements-

“I am a currently studying Physics at the University of Nottingham. The way Physics and Maths are able to explain the Universe around us truly fascinates me and I hope to be able to share that fascination and excitement for the subject...”

About the author

Joseph W.

Currently unavailable: for new students

Degree: Chemical Physics (Masters) - Edinburgh University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Chemistry

“Hey I'm Joe, I'm currently studying Chemistry and Physics at the University of Edinburgh. I'm a second year, and the pain of A levels still hasn't really left me! So I'd love to help you out and hopefully take a bit of the weight off y...”

You may also like...

Other A Level Maths questions

What is the integral of (cos(x))^2?

Use integration by parts to find the integral of xsinx, with respect to x

How should I aproach a connected rates of change question.

How does one show that x^2 + x + 1 > 0 for all values of 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