Use partial fraction decomposition to evaluate the integral:
13t2+37t+1082t3+5t218tdt\displaystyle \int\frac{{{13}{t}^{{2}}+{37}{t}+{108}}}{{{2}{t}^{{3}}+{5}{t}^{{2}}-{18}{t}}}{\left.{d}{t}\right.} =
 

Be sure your variables match those in the question.