Question

Evaluate the integral ∫(5x² - 2x - 5)/(x³ - x) dx. (Remember to use absolute values where appropriate. Use C for the constant of integration.)

Answer 1

To evaluate the given integral, you can use partial fractions. Factor the denominator, write the expression in partial fractions, find the values of the constants, and integrate each term separately using the power rule.

Step-by-step explanation:

To evaluate the integral ∫(5x² - 2x - 5)/(x³ - x) dx, we can use partial fractions. First, factor the denominator as x(x+1)(x-1). Then, using partial fractions, write the expression as A/x + B/(x+1) + C/(x-1). Find the values of A, B, and C by multiplying both sides of the equation by the common denominator, and then equating the numerators of the rational expressions. Finally, use the factored form to integrate each term separately using the power rule for integration. Add the resulting integrals together to get the final answer.