Use partial fraction decomposition to evaluate the integral:
96z2+312z+23612z2+32z+21dz\displaystyle \int\frac{{{96}{z}^{{2}}+{312}{z}+{236}}}{{{12}{z}^{{2}}+{32}{z}+{21}}}{\left.{d}{z}\right.} =
 

Be sure your variables match those in the question.