Learn How to Integrate xlnx Using the Integration by Parts Method

[ricekrispie]

little help? simple question...

Homework Statement

Integrate:
xlnx dx

use integration by parts

Homework Equations

The Attempt at a Solution

let u = x du = dx
dv = ln x v = ??

 

[rock.freak667]

If you don't know the integral of lnx...try letting u=lnx and dx=x dx instead of the way you wrote it

 

[ricekrispie]

Homework Statement

Integrate:
xlnx dx

Homework Equations

The Attempt at a Solution

let u = x du = dx
dv = ln x v = ??

 

[nicksauce]

How about

Let u = lnx
du = 1/x
dv = xdx
v = x^2 / 2

 

[ricekrispie]

if I have to integrate it from 1 to 2 where are these plugged in?

 

[nicksauce]

$$\int_a^b udv = uv|_a^b - \int_a^b vdu$$
Or in other words
$$\int_a^b udv = u(b)v(b) - u(a)v(a) - \int_a^b vdu$$

 

[ricekrispie]

my attempt

i wonder if this worked...

$$\int_1^2 x lnx dx = lnx (x^2/2)|_1^2 - \int_1^2 (x^2/2)* (1/x) dx$$
$$= 2ln2 - ((1/4)(x^2))|_1^2$$

= 2ln2 - (5/4)
??

 

[HallsofIvy]

i wonder if this worked...

$$\int_1^2 x lnx dx = lnx (x^2/2)|_1^2 - \int_1^2 (x^2/2)* (1/x) dx$$
$$= 2ln2 - ((1/4)(x^2))|_1^2$$

= 2ln2 - (5/4)
??

Almost! $(1/4)(x^2)$ when x= 2 is 1. when x= 1, it is 1/4 so the last part is -(1- 1/4)= -3/4, not -5/4.

 

[rocomath]

check your evaluation for the last part

it might be me but you did the integration correctly, gj.

 

[nicksauce]

Almost...

$$x^2|^2_1$$ Is 3 not 5.

 

[ricekrispie]

hehe i noticed a lack of parenthesis... thanks for helping