If $$\int {\frac{{dx}}{{{x^{22}}\left( {{x^7} - 6} \right)}} = A\left\{ {\ln {{\left( p \right)}^6} + 9{p^2} - 2{p^3} - 18p} \right\} + c} ,$$           then :

Solution :
$$\eqalign{ & {\text{Let }}I = \int {\frac{{dx}}{{{x^{29}}\left( {1 - \frac{6}{{{x^7}}}} \right)}}} \cr & {\text{Put }}1 - \frac{6}{{{x^7}}} = p \Rightarrow \frac{{42}}{{{x^8}}}dx = dp{\text{ and }}{x^7} = \frac{6}{{1 - p}} \cr & \therefore \,I = \frac{1}{{42}}\int {\frac{{{{\left( {1 - p} \right)}^3}}}{{{{\left( 6 \right)}^3}p}}dp} \cr & = \frac{1}{{\left( {42} \right)\left( {216} \right)}}\int {\frac{{1 - {p^3} - 3p + 3{p^2}}}{p}} dp \cr & = \frac{1}{{9072}}\int {\left( {\frac{1}{p} - {p^2} - 3 + 3p} \right)} dp \cr & = \frac{1}{{9072}}\left( {\log \,p - \frac{{{p^3}}}{3} - 3p + \frac{3}{2}{p^2}} \right) + c \cr & = \frac{1}{{54432}}\left( {6\,\ln \,p - 2{p^3} - 18p + 9{p^2}} \right) + c \cr & = \frac{1}{{54432}}\left( {\ln \,{p^6} + 9{p^2} - 2{p^3} - 18p} \right) + c \cr & A = \frac{1}{{54432}},\,\,p = \left( {\frac{{{x^7} - 6}}{{{x^7}}}} \right) \cr} $$