(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Improper integral with arctan

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