Question

integrate the following question ​

Answer 1

${ \bold{ \boxed{ \huge \green{ \star \: ANSWER}}}}$

${ \bold{ \underline{Given \: \: function} : - }}$

${ \bold { \orange{ \implies \frac{1}{ {(x - 5)}^{2} } }}} \\ \\ \\ { \bold{ \underline{ \underline{To \: \: find} } : - }} \\ \\ { \bold{ \red{ \implies∫ \frac{1}{ {(x - 5)}^{2} } dx}}} \\ \\ { \bold{ \huge\boxed {\pink{ \star \: solution \star}}}} \\ \\ \\ { \bold{ \red{ = ∫ \frac{1}{ {(x - 5)}^{2} } dx}}} \\ \\ \\ { \bold{ \red{ = ∫ {(x - 5)}^{ - 2} . \: dx}}} \\ \\ \\ { \bold{ \boxed {\red{ \implies ∫ {x}^{n} = \frac{ {x}^{n + 1} }{n + 1} }}}} \\ \\ \\ { \bold{ \red{ = \frac{ {(x - 5)}^{ - 2 + 1} }{ - 2 + 1} }}} \\ \\ \\ { \bold{ \red{ = \frac{ {(x - 5)}^{- 1} }{ - 1} }}} \\ \\ \\ { \bold{ \red{ = \frac{ - 1}{x - 5} }}} \\ \\ \\ \\ { \bold{ \red{ \implies\boxed{\red{ ∫ \frac{1}{ {(x - 5)}^{2} } .dx = \frac{ - 1}{x - 5} }}}}}$