Express $\frac{8x^2+2x+1}{x(2x+1)^2}$ in partial fractions. Hence, find \(\displaystyle\int_1^2 \f

Question

Express $\frac{8x^2+2x+1}{x(2x+1)^2}$ in partial fractions. Hence, find $\displaystyle\int_1^2 \frac{8x^2+2x+1}{x(2x+1)^2} \, \mathrm{d}x$.

Accepted Answer

$\frac{1}{x}+\frac{2}{2x+1}-\frac{4}{(2x+1)^2}$, and $\int_1^2\frac{8x^2+2x+1}{x(2x+1)^2}\,\mathrm dx=\ln\left(\frac{10}{3}\right)-\frac{4}{15}$

Techniques of Integration - Integration Using Partial Fractions