The integral:

\[
\int_{0}^{1} \frac{(3x^2 - x^3 + 8x - 4) \, dx}{\sqrt{x^3 - 3x - x^2}}
\]

does not have a simple closed-form solution. However, the integral can be numerically evaluated. 

Would you like me to calculate the approximate numerical value of this integral?

Learn how to evaluate the integral ∫(3x^2 - x^3 + 8x - 4) / sqrt(x^3 - 3x - x^2) dx from 0 to 1 using numerical methods. This problem involves advanced calculus concepts and requires numerical approximation techniques. Suitable for college-level students.

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