Answer
$\int(2x^4 -24x^2 +12x^{-1}) dx = \frac{2}{5}x^5 - 8x^3 + 12ln|x| + C$
Work Step by Step
Anti-differentiating: $\int(2x^4 -24x^2 +12x^{-1}) dx = 2\times\frac{1}{5}x^5 -24 \times\frac{1}{3}x^3 + 12ln|x| + C = \frac{2}{5}x^5 - 8x^3 + 12ln|x| + C$
Checking with differentiation:
$(\frac{2}{5}x^5 - 8x^3 + 12ln|x| + C)' = \frac{2}{5} \times5 x^4-8\times3x^2 + 12\times\frac{1}{x} = 2x^4 -24x^2 + 12x^{-1}$
