1. We are given the integral $$\int \frac{4x^3 - ax}{x^4 - 2x^2 + 3} \, dx = \ln|x^4 - 2x^2 + 3| + C$$ and need to find the value of $a$. 2. Notice that the derivative of the denominator $x^4 - 2x^2 + 3$ is: $$\frac{d}{dx}(x^4 - 2x^2 + 3) = 4x^3 - 4x$$ 3. The integral of the form $$\int \frac{f'(x)}{f(x)} \, dx = \ln|f(x)| + C$$ matches the given integral if the numerator equals the derivative of the denominator. 4. Comparing the numerator $4x^3 - ax$ with the derivative $4x^3 - 4x$, we see that for the integral to equal the logarithm expression, the coefficients of $x$ must be equal: $$-a = -4 \implies a = 4$$ 5. Therefore, the value of $a$ is 4. Final answer: $a = 4$