# Improper integral with arctan

1. Aug 11, 2011

### Shannabel

1. The problem statement, all variables and given/known data
find the integral from 1 to infinity of (arctanx/x^2)dx

2. Relevant equations

3. The attempt at a solution
i used integration by parts:
u=arctanx
du=1/(1+x^2)dx
dv=x^-2dx
u=(-1/x)

-arctanx/x + [(1/(x)(1+x^2))dx]from 1 to infinity
i have a partial solution in my book, and here it suggests that i change the integrand to
(1/x)-(x/(1+x^2)) which if i work backward, i can see is equal to the original integrand, but i don't see how to get from (1/(x)(1+x^2)) to (1/x)-(x/(1+x^2))
help?

2. Aug 11, 2011

### Bohrok

It's done with partial fractions; have you covered partial fractions before?

3. Aug 11, 2011

### Shannabel

yes! thankyou :)