Final answer:
To integrate the function y = (3x^2 + 2x) / (x^3 + x^2), we can use the method of partial fractions. First, factor the denominator. Then, decompose the rational function into partial fractions. Multiply through by the common denominator and equate coefficients to solve for the constants. Finally, integrate each term separately and add them up to find the result.
Step-by-step explanation:
To integrate the function y = (3x^2 + 2x) / (x^3 + x^2), we can use the method of partial fractions. First, factor the denominator: x(x + 1)(x + 1). Then, decompose the rational function into partial fractions:
(3x^2 + 2x) / (x^3 + x^2) = A/x + B/(x + 1) + C/(x + 1)^2
Multiplying through by the common denominator, we get:
3x^2 + 2x = A(x + 1)^2 + Bx(x + 1) + Cx
Expanding and equating coefficients, we can solve for A, B, and C. Once we have these values, we can integrate each term separately and add them up to find the final result.