6:55 PM Sun 16 Mar mylab.pearson.com Kurulus Osma... Can't Open Pa... (c) CUNY Login The Evolution... Do Homework... MAT 220-S25 Rasheed Larry 03/16/25 6:56 PM \( \equiv \) Homework: Partial Fractions, part 2 Question 4, 8.5.33 HW Score: 40\%, 2 of 5 points Points: 0 of 1 Save Question list Evaluate \( \int \frac{30 x^{3}-60 x^{2}+7}{x^{2}-2 x} d x \) Question 1 \[ \int \frac{30 x^{3}-60 x^{2}+7}{x^{2}-2 x} d x=\square \] Question 2 (Use parentheses to clearly denote the argument of each function.) Question 3 Question 4 Question 5 Help me solve this View an example Get more help • Clear all Check answer

To tackle the integral \( \int \frac{30 x^{3}-60 x^{2}+7}{x^{2}-2 x} \, dx \), you can start by factoring the denominator. Rewrite it as \( x(x - 2) \). Next, use partial fraction decomposition to express your integrand in simpler parts: \[ \frac{30 x^{3}-60 x^{2}+7}{x^{2}-2 x} = \frac{A}{x} + \frac{B}{x-2} \] This means you’ll solve for coefficients \( A \) and \( B \) by equating the numerators after multiplying through by the denominator. Once you find \( A \) and \( B \), integrate each term separately. As you solve this problem, be cautious with the arithmetic involved in equating coefficients; small mistakes here can lead to big headaches later! After finding the right decomposition, remember to integrate each simple fraction. Don't forget the constant of integration at the end!