Express $\frac{2x^2-11x+12}{x^2-5x+6}$ in partial fractions. Hence evaluate \(\displaystyle\int_4^

Question

Express $\frac{2x^2-11x+12}{x^2-5x+6}$ in partial fractions. Hence evaluate $\displaystyle\int_4^5 \frac{2x^2-11x+12}{x^2-5x+6} \, \mathrm{d}x$.

Accepted Answer

$\frac{2x^2-11x+12}{x^2-5x+6}=2+\frac2{x-2}-\frac3{x-3}$, and hence $\int_4^5\frac{2x^2-11x+12}{x^2-5x+6}\,\mathrm dx=2+2\ln3-5\ln2$

Techniques of Integration - Integration Using Partial Fractions