Integration by parts with my work

[mpgcbball]

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 I am doing the z substitution incorrectly. is it even necessary to sub z?

Thanks!

 

[cristo]

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 \int\tan^{-1}(1/x)dx. 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 formula: \int udv= uv-\int vdu

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