Integration by parts involving exponentials and logarithms

[xllx]

Homework Statement

Using integration by parts, integrate:
(1/x^2)(lnx) dx with the limits e and 1

Homework Equations

[uv]to the limits a b - the integral of (v)(du/dx) dx

(sorry, don't know how to write out equations properly on a computer)

The Attempt at a Solution

I've got u=x^-2 so du/dx= -2x^-3
dv/dx=lnx so v= x(lnx-1)

So putting this into the equation above:
[x^-2.x(lnx-1)] - the integral of (-2x^-3.x(lnx-1))

Is this right so far?
If so how do I integrate the last part? Do I do it sepeartley or by parts again?

Many Thanks, any help at all would be greatly appreciated.

 

[tiny-tim]

Hi xllx!

(have an integral: ∫ and try using the X² tag just above the Reply box )

Using integration by parts, integrate:
(1/x^2)(lnx) dx with the limits e and 1
…
I've got u=x^-2 so du/dx= -2x^-3
dv/dx=lnx so v= x(lnx-1)

So putting this into the equation above:
[x^-2.x(lnx-1)] - the integral of (-2x^-3.x(lnx-1))

eugh!

go the other way …

integrate x^-2 ! ​

 

[xllx]

Thankyou. Redid it and came out with a reasonal answer.