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Formula
Calculate the integral
$\int{ x \sqrt{ x-3 } }d{ x }$
$2 \times \dfrac { x ^ { 2 } \sqrt{ x - 3 } - 6 x \sqrt{ x - 3 } + 9 \sqrt{ x - 3 } } { 5 } + 2 x \sqrt{ x - 3 } - 2 \times 3 \sqrt{ x - 3 }$
Calculate the integral
$\displaystyle\int { \color{#FF6800}{ x } \sqrt{ \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } } } d { \color{#FF6800}{ x } }$
 Substitute with $u = \sqrt{ - 3 + x }$ and calculate the integral 
$\left [ \color{#FF6800}{ 2 } \displaystyle\int { \left ( \color{#FF6800}{ u } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ u } ^ { \color{#FF6800}{ 2 } } } d { \color{#FF6800}{ u } } \right ] _ { \color{#FF6800}{ u } = \sqrt{ \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ x } } }$
$\left [ 2 \displaystyle\int { \left ( \color{#FF6800}{ u } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 3 } \right ) \color{#FF6800}{ u } ^ { \color{#FF6800}{ 2 } } } d { \color{#FF6800}{ u } } \right ] _ { u = \sqrt{ - 3 + x } }$
 Calculate the differentiation of the logarithmic function 
$\left [ 2 \left ( \color{#FF6800}{ \frac { u ^ { 5 } } { 5 } } \color{#FF6800}{ + } \color{#FF6800}{ u } ^ { \color{#FF6800}{ 3 } } \right ) \right ] _ { u = \sqrt{ - 3 + x } }$
$\left [ \color{#FF6800}{ 2 } \left ( \color{#FF6800}{ \frac { u ^ { 5 } } { 5 } } \color{#FF6800}{ + } \color{#FF6800}{ u } ^ { \color{#FF6800}{ 3 } } \right ) \right ] _ { \color{#FF6800}{ u } = \sqrt{ \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ x } } }$
 Return the substituted value 
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ \dfrac { \left ( \sqrt{ - 3 + x } \right ) ^ { 5 } } { 5 } } \color{#FF6800}{ + } \left ( \sqrt{ \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ x } } \right ) ^ { \color{#FF6800}{ 3 } } \right )$
$\color{#FF6800}{ 2 } \left ( \color{#FF6800}{ \dfrac { \left ( \sqrt{ - 3 + x } \right ) ^ { 5 } } { 5 } } \color{#FF6800}{ + } \left ( \sqrt{ \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ x } } \right ) ^ { \color{#FF6800}{ 3 } } \right )$
 Simplify the expression 
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { x ^ { 2 } \sqrt{ x - 3 } - 6 x \sqrt{ x - 3 } + 9 \sqrt{ x - 3 } } { 5 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x } \sqrt{ \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \sqrt{ \color{#FF6800}{ x } \color{#FF6800}{ - } \color{#FF6800}{ 3 } }$
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