calculating an integral $\int\frac{x \ln x}{(1+x^{2})^{2}}dx $ I tried to do subtition and to integrate by parts, unsuccessfully.
$\int\frac{x \ln x}{(1+x^{2})^{2}}dx
 $
Thanks in advanced.

$$\int \frac{x}{(1+x^2)^2}=\frac{1}{2}\int\frac{2x}{(1+x^2)^2}=\frac{1}{2}\int\frac{1}{(1+y)^2}=-\frac{1}{2}\frac{1}{1+y}=-\frac{1}{2}\frac{1}{1+x^2},$$ with $y=x^2$, was easy to integrate and its integral is rational.
On the other hand, $(\ln(x))'=\frac{1}{x}$ is rational.
Therefore, integration by parts rationalizes the integrand.
$$\int\frac{x}{(1+x^2)^2}\ln(x)=-\frac{1}{1+x^2}\ln(x)+\frac{1}{2}\int\frac{1}{1+x^2}\frac{1}{x}$$
The last integral you can do by expanding in simple fractions and all of that.
