Use partial fraction decomposition to evaluate the integral:
8t3+19t2+52t+902t3+5t2+6t+15dt\displaystyle \int\frac{{{8}{t}^{{3}}+{19}{t}^{{2}}+{52}{t}+{90}}}{{{2}{t}^{{3}}+{5}{t}^{{2}}+{6}{t}+{15}}}{\left.{d}{t}\right.} =
 

Be sure your variables match those in the question.