Integral of 1/(x^3 + 2x^2 -x - 2)

Factorise denominator using the factor theorem giving - 1/(x+1)(x+2)(x-1) Use partial fractions to turn this into an easier form to integrate giving - 1/3(x+2) + 1/6(x-1) - 1/2(x+1) using integral 1/x = ln(x) integrate each term seperately - 1/3 ln(x+2) + 1/6 ln(x-1) - 1/2 ln(x+1) + C Combine log terms using laws of logarithms - Answer: ln[ A(x-1)^1/6 (x+2)^1/3 (x+1)^-1/2 ]