Answer
$3t - 5\ln \left| {t + 1} \right| + C$
Work Step by Step
$$\eqalign{
& \int {\frac{{3t - 2}}{{t + 1}}} dt \cr
& {\text{The integrand is an improper rational function}}{\text{, then the first }} \cr
& {\text{step is apply the long division:}} \cr
& \frac{{3t - 2}}{{t + 1}} = 3 - \frac{5}{{t + 1}} \cr
& {\text{Therefore}}{\text{,}} \cr
& \int {\frac{{3t - 2}}{{t + 1}}} dt = \int {\left( {3 - \frac{5}{{t + 1}}} \right)} dx \cr
& = \int 3 dt - \int {\frac{5}{{t + 1}}} dt \cr
& {\text{Integrating}} \cr
& = 3t - 5\ln \left| {t + 1} \right| + C \cr} $$
