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Formula
Calculate the integral
$\int{ 2x ^{ 3 } }d{ x }$
$\dfrac { 1 } { 2 } x ^ { 4 }$
Calculate the integral
$\displaystyle\int { \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } } d { \color{#FF6800}{ x } }$
 It is $\int c f(x) dx = c \int f(x) dx$
$\color{#FF6800}{ 2 } \displaystyle\int { \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } } d { \color{#FF6800}{ x } }$
$2 \displaystyle\int { \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } } d { \color{#FF6800}{ x } }$
 Calculate the integral using the formula of $\int{x^{n}}dx = \frac{x^{n+1}}{n+1}$
$2 \times \color{#FF6800}{ \dfrac { 1 } { 3 + 1 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
$2 \times \dfrac { 1 } { \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } x ^ { 3 + 1 }$
 Add $3$ and $1$
$2 \times \dfrac { 1 } { \color{#FF6800}{ 4 } } x ^ { 3 + 1 }$
$2 \times \dfrac { 1 } { 4 } x ^ { \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
 Add $3$ and $1$
$2 \times \dfrac { 1 } { 4 } x ^ { \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 4 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } }$
 Simplify the expression 
$\color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } }$
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