Answer
$$\int \frac{5x+1}{(2x+1)(x-1)}dx=\frac{ln\left | 2x+1 \right |}{2}+2ln\left | x-1 \right |+C$$
Work Step by Step
$$\int \frac{5x+1}{(2x+1)(x-1)}dx=\int \frac{(4x+2)+(x-1)}{(2x+1)(x-1)}dx$$
$$=\int (\frac{1}{2x+1}+\frac{2}{x-1})dx$$
$$=\frac{ln\left | 2x+1 \right |}{2}+2ln\left | x-1 \right |+C$$