Final answer:
To evaluate the integral ∫(5x³ - 2x² - 4x³ - 2x²)dx/4, simplify the integrand by combining like terms. Then, apply the power rule for integration to find the antiderivative.
Step-by-step explanation:
To evaluate the integral ∫(5x³ - 2x² - 4x³ - 2x²)dx/4, we first simplify the integrand by combining like terms: (5x³ - 2x² - 4x³ - 2x²) = (x³ - 4x²). Then, we can rewrite the integral as ∫(x³ - 4x²)dx/4. To evaluate this integral, we apply the power rule for integration, which states that the integral of x^n is (1/(n+1))x^(n+1), where n ≠ -1. Applying the power rule, we get (1/4) * (1/4)x^4 - (4/4) * (1/3)x³ + C, where C is the constant of integration.