Calculating the integral $\int_{1/3}^{3}\frac{\arctan(x)}{x^2-x+1}\;\mathrm{d}x$

Question

Can somebody help me calculate the following integral:

$$\int\limits_{1/3}^{3}\frac{\arctan(x)}{x^2-x+1}\;\mathrm{d}x$$

I have tried integration by parts, but I got stuck in it. Wolfram also didn't help me.

I would be happy to get some hints.