What is the result of computing ∫ (4x^3 - 3) dx?

To determine the integral of the given polynomial function, we will integrate term by term.

The integral in question is ∫ (4x^3 - 3) dx. We can break this down into two separate integrals:

1. ∫ 4x^3 dx

2. ∫ -3 dx

Starting with the first integral, ∫ 4x^3 dx, we apply the power rule of integration, which states that the integral of x^n is (1/(n+1))x^(n+1) plus a constant of integration. Here, n is 3:

∫ 4x^3 dx = 4 * (1/(3+1)) x^(3+1) = 4 * (1/4) x^4 = x^4.

Next, we compute the integral of the constant term, ∫ -3 dx, which results in:

∫ -3 dx = -3x.

Now, combining these results, we have:

∫ (4x^3 - 3) dx = x^4 - 3x + C, where C is the constant of integration.

This result aligns perfectly with one of the provided choices, confirming that