Express $\frac{x^2 + 1}{x^3 + 3x^2 + 3x + 2}$ as the sum of its partial fractions. Hence find \(\i

Question

Express $\frac{x^2 + 1}{x^3 + 3x^2 + 3x + 2}$ as the sum of its partial fractions. Hence find $\int \frac{x^2 + 1}{x^3 + 3x^2 + 3x + 2} \mathrm{d}x$

Accepted Answer

(i) $\frac{5}{3x + 6} - \frac{2x + 1}{3(x^2 + x + 1)}$ (ii) $\frac{5}{3} \ln|x + 2| - \frac{1}{3} \ln|x^2 + x + 1| + C$

Techniques of Integration - Integration Using Partial Fractions