(Homework) Trouble calculating improper integral by parts. I'm having a bit of trouble with calculating the value of the following improper integral via integration by parts...
\begin{equation}
\int_1^{+\infty} \frac{\arctan x}{x^2} \,\, dx
\end{equation}
I have tried to do the following but I got stuck with calculating the integral of the righthand side...
\begin{equation}
\int_a^b \frac{\arctan x}{x^2} \,\, dx = -\left.\frac{\arctan x}{x}\right|_a^b + \int_a^b -\frac{1}{x}\cdot\frac{1}{1+x^2} \,\,dx
\end{equation}
Can anyone kindly point me out where to go from here? I, of course, know how to get out of here once I can determine
\begin{equation}
\int_a^b -\frac{1}{x}\cdot\frac{1}{1+x^2} \,\,dx
\end{equation}
but I don't seem to be able to compute this. Thank you very much.

$$\frac{1}{x(x^2+1)} = \frac{1}{x} - \frac{x}{x^2+1}$$
Now integrate both individually.
