6．（a）Show that $$\frac { \mathrm { d } } { \mathrm {~d} u } \ln \left( u + \sqrt { u ^ { 2 } - 1 } \right) = \frac { 1 } { \sqrt { u ^ { 2 } - 1 } }$$ （b）Use the result from part（a）and the substitution \(x + 3 = \frac { 1 } { t }\) to find $$\int \frac { 1 } { ( x + 3 ) \sqrt { 2 x + 7 } } \mathrm {~d} x$$ （6）
（c）Express \(\frac { 1 } { 2 x ^ { 2 } + 13 x + 21 }\) in partial fractions．
（d）Find $$\int _ { 1 } ^ { 9 } \frac { 1 } { \left( 2 x ^ { 2 } + 13 x + 21 \right) \sqrt { 2 x + 7 } } \mathrm {~d} x$$ giving your answer in the form \(\ln r - s\) where \(r\) and \(s\) are rational numbers．