Question

Evaluate the integral ∫(x³ * (x - 1)) dx. (Remember to use absolute values where appropriate. Use C for the constant of integration.)

Answer 1

To evaluate the given integral, ∫(x³ * (x - 1)) dx, distribute the x³ into the parentheses to obtain x⁴ - x³. Then, apply the power rule for integration to get (1/5)x⁵ - (1/4)x⁴ + C, where C is the constant of integration.

Step-by-step explanation:

To evaluate the integral ∫(x³ * (x - 1)) dx, we can use the power rule for integration. Firstly, we distribute the x³ into the parentheses to obtain x⁴ - x³. Then, we apply the power rule, which states that the integral of xⁿ is (1/(n+1))x^(n+1), where n is any real number except -1. Applying the power rule, we get (∫(x⁴ - x³) dx) = (1/5)x⁵ - (1/4)x⁴ + C, where C is the constant of integration.