$=\int (\frac{13}{9}\times \frac{1}{x+2}+\frac{7}{3}\times \frac{1}{(x-1)^2}+\frac{14}{9}\times \frac{1}{x-1})dx$$=\frac{13}{9}.ln\left| {x+2} \right|-\frac{7}{3(x-1)}+\frac{14}{9}.ln\left| {x-1} \right|$
$=\int (\frac{13}{9}\times \frac{1}{x+2}+\frac{7}{3}\times \frac{1}{(x-1)^2}+\frac{14}{9}\times \frac{1}{x-1}$$=\frac{13}{9}.ln\left| {x+2} \right|-\frac{7}{3(x-1)}+\frac{14}{9}.ln\left| {x-1} \right|$
$=\int (\frac{13}{9}\times \frac{1}{x+2}+\frac{7}{3}\times \frac{1}{(x-1)^2}+\frac{14}{9}\times \frac{1}{x-1}
)dx$$=\frac{13}{9}.ln\left| {x+2} \right|-\frac{7}{3(x-1)}+\frac{14}{9}.ln\left| {x-1} \right|$