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Formula
Calculate the integral
$\int{ \ln{\left( x \right)} }d{ x }$
$x \ln { \left( x \right) } - x + C$
Calculate the indefinite integral.
$\displaystyle\int { \ln { \left( \color{#FF6800}{ x } \right) } } d { \color{#FF6800}{ x } }$
 Calculate the integral using partial integration 
$\color{#FF6800}{ x } \ln { \left( \color{#FF6800}{ x } \right) } \color{#FF6800}{ - } \displaystyle\int { \color{#FF6800}{ 1 } } d { \color{#FF6800}{ x } }$
$x \ln { \left( x \right) } - \displaystyle\int { \color{#FF6800}{ 1 } } d { \color{#FF6800}{ x } }$
 The indefinite integral of $1$ is $x$ . 
$x \ln { \left( x \right) } - \color{#FF6800}{ x }$
$\color{#FF6800}{ x } \ln { \left( \color{#FF6800}{ x } \right) } \color{#FF6800}{ - } \color{#FF6800}{ x }$
 Add the integral constant $C$ . 
$\left ( \color{#FF6800}{ x } \ln { \left( \color{#FF6800}{ x } \right) } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) \color{#FF6800}{ + } \color{#FF6800}{ C }$
$\left ( \color{#FF6800}{ x } \ln { \left( \color{#FF6800}{ x } \right) } \color{#FF6800}{ - } \color{#FF6800}{ x } \right ) \color{#FF6800}{ + } \color{#FF6800}{ C }$
 Get rid of unnecessary parentheses 
$\color{#FF6800}{ x } \ln { \left( \color{#FF6800}{ x } \right) } \color{#FF6800}{ - } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ C }$
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