# Homework Help: How to integrate ln(x)

1. Jun 18, 2006

### ekinnike

i cant find it anywhere. plz help. i need to kno the inegration of lnx to find an area. plz help thx

2. Jun 18, 2006

### VietDao29

Integration is a Calculus topic, and therefore, should not be posted in the Precalculus section.
Anyway, to integrate ln(x), we use Integration by Parts (have you covered Integration by Parts yet?), i.e:
$$\int u dv = uv - \int v du$$
We often use Integration by Parts, when no other methods can solve the integral.
So, we want to integrate this:
$$\int \ln (x) dx$$
We then let u = ln(x), and dv = dx
So that implies du = dx / x, and v = x.
Substitute all those into the formula, we have:
$$\int \ln (x) dx = x \ln (x) - \int x \times \frac{dx}{x} = ...$$
Can you go from here? :)

3. Jun 18, 2006

### ekinnike

lol i didnt learn those yet. BUt im glad it more complicated than it look. NO i cant do it. BUt i really appriciated the help. Instead i will try use simpsons rule. the question is area under the curve. 2day is monday-im at school school today so i quickly ask one of the mathematics teacher. =) i think he also hesitated say u can solve them by harder way but instead he told me simpson rule

Last edited: Jun 18, 2006
4. Jun 19, 2006

### shmoe

It can be done without integration by parts. Try integrating over y instead of x, that is consider your graph to be x=exp(y).

5. Feb 18, 2009

### ln(x)

You cant integrate ln(x) by parts!!!!!!!!

6. Feb 18, 2009

### jspek9

u=lnx dv= dx
du= 1/x dx v=x

=xlnx-integral(1)dx
= xlnx-x+c

lnx using IBP:)

7. Feb 18, 2009