Step 1: Identify the function you want to integrate, which is f(x) = 4x^3.
Step 2: Use the power rule for integration. The power rule states that ∫x^n dx = (x^(n+1))/(n+1) + C, where n is a constant and C is the constant of integration.
Step 3: In our case, n is 3 (from 4x^3). So, we will add 1 to n: 3 + 1 = 4.
Step 4: Now, apply the power rule: ∫4x^3 dx = 4 * (x^4)/4 + C.
Step 5: The 4s cancel out, leaving us with x^4 + C.
Step 6: Write the final answer: ∫4x^3 dx = x^4 + C.
