The function is given:
$$\chi(\xi) = - Re \left[\sqrt[3]{\sqrt{\displaystyle P^3 - 3 \cdot \xi^2 \cdot P^2 + 3 \cdot \xi^4 \cdot P} + \xi^3-\xi} \cdot (1+ j \cdot \sqrt{3}) \right].$$
it is necessary to find the average value in the range from $\xi = 1$ to $\xi = 5$.
It is necessary to obtain a solution for the general case, that is, to find a primitive function without substituting integration limits.
$$ \overline{\chi(\xi)} = \frac{\int\limits_{\xi_{min}}^{\xi_{max}} - Re \left[\sqrt[3]{\sqrt{\displaystyle P^3 - 3 \cdot \xi^2 \cdot P^2 + 3 \cdot \xi^4 \cdot P} + \xi^3-\xi} \cdot (1+ j \cdot \sqrt{3}) \right] d\xi}{\xi_{max} - \xi_{min}}$$
To visualize the result, I substituted P = -10 and plotted the function, the answer should be approximately -0,9789
