Determine the following integrals by means of partial fractions: 3.1 integral (5x³ - x² + 8x - 4)/((1 - x)²(2x + 1)²) dx 3.2 integral (4x³ - 6x² + 5x - 4)/(2x² + x - 6) dx

Step 1: Determine $\frac{\partial Z}{\partial x}$.
Given $Z = e^{-2x} \sin y$. To find $\frac{\partial Z}{\partial x}$, treat $y$ as a constant.

$$\frac{\partial Z}{\partial x} = \frac{\partial}{\partial x} (e^{-2x} \sin y)$$ $$\frac{\partial Z}{\partial x} = \sin y \cdot \frac{d}{dx}(e^{-2x})$$

Using the chain rule for $e^{-2x}$, $\frac{d}{dx}(e^{-2x}) = e^{-2x} \cdot (-2) = -2e^{-2x}$.

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