If \(\dfrac{d}{dx}[f(x)] = f'(x)\), then the integral of

\(f'(x)\) with respct to \(x\) is \(\int f'(x) \ dx = f(x) \).

Given \(\dfrac{d}{dx} (4x^2) = 8x\),

find \(\int 8x \ dx\).

Differentiation of \(4x^2\) is \(8x\).

By the reverse of differentiation, the integration of \(8x\) is \(4x^2\).

Hence, \(\int 8x \ dx = 4x^2\).