## Integrate $\int_0^3 \frac{\arctan(x)}{3x^2-3x+2} dx$

Compute the integral $$\int_0^3 \frac{\arctan(x)}{3x^2-3x+2}dx.$$

We cannot split this into partial fractions because the denominator has no real roots.

Also, I tried using substitutions like $$\arctan(x) = t$$ and even integration by parts. I also tried to using the identity $$\arctan(x) + \arctan \left( \frac{1}{x} \right) = \frac{\pi}{2}, \forall x \in \mathbb{R}$$ and replace $$\arctan(x)$$, but I get an integral that is somewhat the same as the one I started with.