Integration by parts with my work

  • Thread starter mpgcbball
  • Start date
  • #1
11
0

Homework Statement



integrate arctan(1/x)

Homework Equations





The Attempt at a Solution



z=arctan(1/x)
dx=-dz(x^2-1)

now its the integral of z(x^2-1)dz

let u =X^2-1
du=2x
dv=-udu
v=-u^2/2

integral=(x^2-1)(-u^2/2) - int (-u^2)(2x)

this is where i got stuck but i think im doing the z substitution incorrectly. is it even necessary to sub z?

Thanks!
 

Answers and Replies

  • #2
cristo
Staff Emeritus
Science Advisor
8,107
73
You got stuck because you're trying to integrate the term z(x^2-1)dz which has x's and z's in it!

We want to calculate [tex]\int\tan^{-1}(1/x)dx[/tex]. Do this by parts, and take u=arctan(1/x) and dv=dx. You need to then calculate du and v, and use the usual integration by parts forumla: [tex]\int udv= uv-\int vdu[/tex]

(Alternatively, you could note that arctan(1/x)=arccot(x) and proceed from here)
 
Last edited:

Related Threads on Integration by parts with my work

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
4
Views
1K
Replies
14
Views
3K
Replies
2
Views
920
  • Last Post
Replies
2
Views
670
  • Last Post
Replies
13
Views
964
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
2
Views
963
Top