Express $\frac{5x-1}{x^2-1}$ in partial fractions. Hence, evaluate \(\displaystyle\int_{2}^{3} \fr

Question

Express $\frac{5x-1}{x^2-1}$ in partial fractions. Hence, evaluate $\displaystyle\int_{2}^{3} \frac{5x-1}{x^2-1} \, \mathrm{d}x$.

Accepted Answer

$\frac{5x-1}{x^2-1}=\frac2{x-1}+\frac3{x+1}$, and hence $\int_2^3\frac{5x-1}{x^2-1}\,\mathrm dx=8\ln2-3\ln3$

Integration - Problems involving Partial Fractions