Homework Help

What is the integral `int ln x/x^2 dx`

user profile pic

lxsptter | Student, Undergraduate | Valedictorian

Posted July 1, 2013 at 1:37 PM via web

dislike 1 like

What is the integral `int ln x/x^2 dx`

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 1, 2013 at 1:46 PM (Answer #1)

dislike 1 like

The integral `int ln x/x^2 dx` has to be determined.

Use integration by parts which gives `int u dv = u*v - int v*du`

In `int ln x/x^2 dx` , `u = ln x` , `dv = 1/x^2 dx`

`v = int 1/x^2 dx = -1/x`

`du = 1/x dx`

`int ln x/x^2 dx` = `ln x*(-1/x) - int (-1/x)*(1/x) dx`

=> `-ln x/x -1/x`

The integral `int ln x/x^2 dx = -ln x/x -1/x + C`

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes