Use partial fraction decomposition to evaluate the integral:
29z2+120z607z352z2+60zdz\displaystyle \int\frac{{-{29}{z}^{{2}}+{120}{z}-{60}}}{{{7}{z}^{{3}}-{52}{z}^{{2}}+{60}{z}}}{\left.{d}{z}\right.} =
 

Be sure your variables match those in the question.