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Formula
Calculate the integral
$\int{ \left( 4x+2 \right) }d{ x }$
$2 x ^ { 2 } + 2 x$
Calculate the integral
$\displaystyle\int { \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 2 } } d { \color{#FF6800}{ x } }$
 It is $\int f_1(x) + f_2(x) + \cdots + f_n(x) dx = \int f_1(x) dx + \int f_2(x) dx + \cdots + \int f_n(x) dx$
$\displaystyle\int { \color{#FF6800}{ 4 } \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } \color{#FF6800}{ + } \displaystyle\int { \color{#FF6800}{ 2 } } d { \color{#FF6800}{ x } }$
$\displaystyle\int { \color{#FF6800}{ 4 } \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } + \displaystyle\int { 2 } d { x }$
 It is $\int c f(x) dx = c \int f(x) dx$
$\color{#FF6800}{ 4 } \displaystyle\int { \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } + \displaystyle\int { 2 } d { x }$
$4 \displaystyle\int { \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } + \displaystyle\int { 2 } d { x }$
 Calculate the integral using the formula of $\int{x^{n}}dx = \frac{x^{n+1}}{n+1}$
$4 \times \color{#FF6800}{ \dfrac { 1 } { 1 + 1 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \displaystyle\int { 2 } d { x }$
$4 \times \dfrac { 1 } { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } x ^ { 1 + 1 } + \displaystyle\int { 2 } d { x }$
 Add $1$ and $1$
$4 \times \dfrac { 1 } { \color{#FF6800}{ 2 } } x ^ { 1 + 1 } + \displaystyle\int { 2 } d { x }$
$4 \times \dfrac { 1 } { 2 } x ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \displaystyle\int { 2 } d { x }$
 Add $1$ and $1$
$4 \times \dfrac { 1 } { 2 } x ^ { \color{#FF6800}{ 2 } } + \displaystyle\int { 2 } d { x }$
$4 \times \dfrac { 1 } { 2 } x ^ { 2 } + \displaystyle\int { \color{#FF6800}{ 2 } } d { \color{#FF6800}{ x } }$
 It is $\int c f(x) dx = c \int f(x) dx$
$4 \times \dfrac { 1 } { 2 } x ^ { 2 } + \color{#FF6800}{ 2 } \displaystyle\int { \color{#FF6800}{ 1 } } d { \color{#FF6800}{ x } }$
$4 \times \dfrac { 1 } { 2 } x ^ { 2 } + 2 \displaystyle\int { \color{#FF6800}{ 1 } } d { \color{#FF6800}{ x } }$
 The indefinite integral of $1$ is $x$ . 
$4 \times \dfrac { 1 } { 2 } x ^ { 2 } + 2 \color{#FF6800}{ x }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x }$
 Simplify the expression 
$\color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 2 } \color{#FF6800}{ x }$
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