Evaluate the integral using substitution: $\int 2 x (x^{2} + 1)^{3} d x$ .

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Find the first derivative $\frac{d y}{d x}$ of the polynomial function: $y = 3 x^{4} - 5 x^{2} + 7 x - 2$ .
Determine the gradient of the tangent to the curve $y = 2 x^{3} - 4 x + 1$ at the point where $x = 2$ .
Find the equation of the tangent line to the parabola $y = x^{2} - 3 x + 2$ at the point $(3, 2)$ .
Find the equation of the normal to the curve $y = 2 x^{2} + 1$ at the point $(1, 3)$ .
Find the coordinates of the turning points (stationary points) of the cubic curve $y = x^{3} - 3 x$ .
Classify the stationary point of the quadratic function $y = 4 x - x^{2}$ .