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Calculate the integral
Answer
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$\int{ 2x+1 }d{ x }$
$x ^ { 2 } + x$
Calculate the integral
$\displaystyle\int { \color{#FF6800}{ 2 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } d { \color{#FF6800}{ x } }$
$ $ 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$
$\displaystyle\int { \color{#FF6800}{ 2 } \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } \color{#FF6800}{ + } \displaystyle\int { \color{#FF6800}{ 1 } } d { \color{#FF6800}{ x } }$
$\displaystyle\int { \color{#FF6800}{ 2 } \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } + \displaystyle\int { 1 } d { x }$
$ $ It is $ \int c f(x) dx = c \int f(x) dx$
$\color{#FF6800}{ 2 } \displaystyle\int { \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } + \displaystyle\int { 1 } d { x }$
$2 \displaystyle\int { \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } + \displaystyle\int { 1 } d { x }$
$ $ Calculate the integral using the formula of $ \int{x^{n}}dx = \frac{x^{n+1}}{n+1}$
$2 \times \color{#FF6800}{ \dfrac { 1 } { 1 + 1 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \displaystyle\int { 1 } d { x }$
$2 \times \dfrac { 1 } { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } x ^ { 1 + 1 } + \displaystyle\int { 1 } d { x }$
$ $ Add $ 1 $ and $ 1$
$2 \times \dfrac { 1 } { \color{#FF6800}{ 2 } } x ^ { 1 + 1 } + \displaystyle\int { 1 } d { x }$
$2 \times \dfrac { 1 } { 2 } x ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \displaystyle\int { 1 } d { x }$
$ $ Add $ 1 $ and $ 1$
$2 \times \dfrac { 1 } { 2 } x ^ { \color{#FF6800}{ 2 } } + \displaystyle\int { 1 } d { x }$
$2 \times \dfrac { 1 } { 2 } x ^ { 2 } + \displaystyle\int { \color{#FF6800}{ 1 } } d { \color{#FF6800}{ x } }$
$ $ The indefinite integral of $ 1 $ is $ x $ . $ $
$2 \times \dfrac { 1 } { 2 } x ^ { 2 } + \color{#FF6800}{ x }$
$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x }$
$ $ Simplify the expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ x }$
Solution search results
search-thumbnail-$\int \dfrac {4x+3} {2x+1}$ d
10th-13th grade
Other
search-thumbnail-$23$ $\int \dfrac {x} {2x+1}dx$
10th-13th grade
Calculus
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