What is the integral of 2x^3 – 4x^(-2) + 4x?

The integral of 2x^3 – 4x^(-2) + 4x is given by:

∫(2x^3 – 4x^(-2) + 4x) dx

To integrate each term, we use the power rule of integration:

∫x^n dx = (1/(n+1))x^(n+1) + C

Applying this rule to each term, we get:

∫2x^3 dx = (2/4)x^4 + C1 = (1/2)x^4 + C1

∫(-4x^(-2)) dx = (-4/-1)x^(-1) + C2 = 4x^(-1) + C2 = 4/x + C2

∫4x dx = 4(1/2)x^2 + C3 = 2x^2 + C3

Putting it all together, the integral becomes:

(1/2)x^4 + 4/x + 2x^2 + C

where C1, C2, and C3 are constants of integration.

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