Use partial fractions to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) ∫11x^2 + 8x − 2 /x^3 + x^2 dx

Answer 1

The partial fraction expansion is

(A/x) + (B/x²) + [C/(x+1)]

A(x²+x) + B(x+1) + Cx² is identically equal to 11x² + 8x -2

A+C=11

A+B=8

B=-2

so that A=10 and C=1

The integral then is 10 ln |x| + (2/x) + ln |x+1| + C (note this C is different from the C used above!)

Also, I think it covers up the reality to use absolute value signs in the integral...in fact the integral is not defined for negative values of the variable. However, the AREA involved may be computed using the absolute value.