Use partial fraction decomposition to evaluate the integral:
32z2+344z+5087z3+143z2+760z+300dz\displaystyle \int\frac{{{32}{z}^{{2}}+{344}{z}+{508}}}{{{7}{z}^{{3}}+{143}{z}^{{2}}+{760}{z}+{300}}}{\left.{d}{z}\right.} =
 

Be sure your variables match those in the question.