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Calculate the integral
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$\int(3x^{2}-4x+5)dx$
$x ^ { 3 } - 2 x ^ { 2 } + 5 x$
Calculate the integral
$\displaystyle\int { \color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ + } \color{#FF6800}{ 5 } } d { \color{#FF6800}{ x } }$
$ $ 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$
$\displaystyle\int { \color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } } d { \color{#FF6800}{ x } } \color{#FF6800}{ + } \displaystyle\int { \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } \color{#FF6800}{ + } \displaystyle\int { \color{#FF6800}{ 5 } } d { \color{#FF6800}{ x } }$
$\displaystyle\int { \color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } } d { \color{#FF6800}{ x } } + \displaystyle\int { - 4 x } d { x } + \displaystyle\int { 5 } d { x }$
$ $ It is $ \int c f(x) dx = c \int f(x) dx$
$\color{#FF6800}{ 3 } \displaystyle\int { \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } } d { \color{#FF6800}{ x } } + \displaystyle\int { - 4 x } d { x } + \displaystyle\int { 5 } d { x }$
$3 \displaystyle\int { \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } } d { \color{#FF6800}{ x } } + \displaystyle\int { - 4 x } d { x } + \displaystyle\int { 5 } d { x }$
$ $ Calculate the integral using the formula of $ \int{x^{n}}dx = \frac{x^{n+1}}{n+1}$
$3 \times \color{#FF6800}{ \dfrac { 1 } { 2 + 1 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \displaystyle\int { - 4 x } d { x } + \displaystyle\int { 5 } d { x }$
$3 \times \dfrac { 1 } { \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } x ^ { 2 + 1 } + \displaystyle\int { - 4 x } d { x } + \displaystyle\int { 5 } d { x }$
$ $ Add $ 2 $ and $ 1$
$3 \times \dfrac { 1 } { \color{#FF6800}{ 3 } } x ^ { 2 + 1 } + \displaystyle\int { - 4 x } d { x } + \displaystyle\int { 5 } d { x }$
$3 \times \dfrac { 1 } { 3 } x ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } + \displaystyle\int { - 4 x } d { x } + \displaystyle\int { 5 } d { x }$
$ $ Add $ 2 $ and $ 1$
$3 \times \dfrac { 1 } { 3 } x ^ { \color{#FF6800}{ 3 } } + \displaystyle\int { - 4 x } d { x } + \displaystyle\int { 5 } d { x }$
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } + \displaystyle\int { \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } + \displaystyle\int { 5 } d { x }$
$ $ 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$
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } \color{#FF6800}{ - } \displaystyle\int { \color{#FF6800}{ 4 } \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } + \displaystyle\int { 5 } d { x }$
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } - \displaystyle\int { \color{#FF6800}{ 4 } \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } + \displaystyle\int { 5 } d { x }$
$ $ It is $ \int c f(x) dx = c \int f(x) dx$
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } - \left ( \color{#FF6800}{ 4 } \displaystyle\int { \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } \right ) + \displaystyle\int { 5 } d { x }$
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } - \left ( 4 \displaystyle\int { \color{#FF6800}{ x } } d { \color{#FF6800}{ x } } \right ) + \displaystyle\int { 5 } d { x }$
$ $ Calculate the integral using the formula of $ \int{x^{n}}dx = \frac{x^{n+1}}{n+1}$
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } - \left ( 4 \times \color{#FF6800}{ \dfrac { 1 } { 1 + 1 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \right ) + \displaystyle\int { 5 } d { x }$
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } - \left ( 4 \times \dfrac { 1 } { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } x ^ { 1 + 1 } \right ) + \displaystyle\int { 5 } d { x }$
$ $ Add $ 1 $ and $ 1$
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } - \left ( 4 \times \dfrac { 1 } { \color{#FF6800}{ 2 } } x ^ { 1 + 1 } \right ) + \displaystyle\int { 5 } d { x }$
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } - \left ( 4 \times \dfrac { 1 } { 2 } x ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \right ) + \displaystyle\int { 5 } d { x }$
$ $ Add $ 1 $ and $ 1$
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } - \left ( 4 \times \dfrac { 1 } { 2 } x ^ { \color{#FF6800}{ 2 } } \right ) + \displaystyle\int { 5 } d { x }$
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } - \left ( 4 \times \dfrac { 1 } { 2 } x ^ { 2 } \right ) + \displaystyle\int { \color{#FF6800}{ 5 } } d { \color{#FF6800}{ x } }$
$ $ It is $ \int c f(x) dx = c \int f(x) dx$
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } - \left ( 4 \times \dfrac { 1 } { 2 } x ^ { 2 } \right ) + \color{#FF6800}{ 5 } \displaystyle\int { \color{#FF6800}{ 1 } } d { \color{#FF6800}{ x } }$
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } - \left ( 4 \times \dfrac { 1 } { 2 } x ^ { 2 } \right ) + 5 \displaystyle\int { \color{#FF6800}{ 1 } } d { \color{#FF6800}{ x } }$
$ $ The indefinite integral of $ 1 $ is $ x $ . $ $
$3 \times \dfrac { 1 } { 3 } x ^ { 3 } - \left ( 4 \times \dfrac { 1 } { 2 } x ^ { 2 } \right ) + 5 \color{#FF6800}{ x }$
$\color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 3 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \right ) \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ x }$
$ $ Simplify the expression $ $
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ - } \color{#FF6800}{ 2 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 5 } \color{#FF6800}{ x }$
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