# Integral ∫π/20arctan2(6sinx3+cos2x)dx\int_0^{\pi/2}\arctan^2\left(\frac{6\sin x}{3+\cos 2x}\right)\mathrm dx

Is it possible to evaluate this integral in a closed form?

where $\chi_{2}$ is the Legendre chi function. Using the addition formula for the arctangent, it follows that