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Calculate the integral
Answer
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$\int{ \left( \dfrac{ 5 }{ \sqrt[3]{ x } } -4 \sqrt[3]{ x } \right) }d{ x }$
$5 \times 3 \times \dfrac { 1 } { 2 } \sqrt[ 3 ]{ x ^ { 2 } } - 4 \times 3 \times \dfrac { 1 } { 4 } \sqrt[ 3 ]{ x ^ { 4 } }$
Calculate the integral
$\displaystyle\int { \color{#FF6800}{ \dfrac { 5 } { \sqrt[ 3 ]{ x } } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } } d { \color{#FF6800}{ x } }$
$ $ 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$
$\displaystyle\int { \color{#FF6800}{ \dfrac { 5 } { \sqrt[ 3 ]{ x } } } } d { \color{#FF6800}{ x } } \color{#FF6800}{ + } \displaystyle\int { \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } } d { \color{#FF6800}{ x } }$
$\displaystyle\int { \color{#FF6800}{ \dfrac { 5 } { \sqrt[ 3 ]{ x } } } } d { \color{#FF6800}{ x } } + \displaystyle\int { - 4 \sqrt[ 3 ]{ x } } d { x }$
$ $ It is $ \int c f(x) dx = c \int f(x) dx$
$\color{#FF6800}{ 5 } \displaystyle\int { \color{#FF6800}{ \dfrac { 1 } { \sqrt[ 3 ]{ x } } } } d { \color{#FF6800}{ x } } + \displaystyle\int { - 4 \sqrt[ 3 ]{ x } } d { x }$
$5 \displaystyle\int { \color{#FF6800}{ \dfrac { 1 } { \sqrt[ 3 ]{ x } } } } d { \color{#FF6800}{ x } } + \displaystyle\int { - 4 \sqrt[ 3 ]{ x } } d { x }$
$ $ Substitute with $ u = \sqrt[ 3 ]{ x } $ and calculate the integral $ $
$5 \left [ \color{#FF6800}{ 3 } \displaystyle\int { \color{#FF6800}{ u } } d { \color{#FF6800}{ u } } \right ] _ { \color{#FF6800}{ u } = \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } } + \displaystyle\int { - 4 \sqrt[ 3 ]{ x } } d { x }$
$5 \left [ 3 \displaystyle\int { \color{#FF6800}{ u } } d { \color{#FF6800}{ u } } \right ] _ { u = \sqrt[ 3 ]{ x } } + \displaystyle\int { - 4 \sqrt[ 3 ]{ x } } d { x }$
$ $ Calculate the integral using the formula of $ \int{x^{n}}dx = \frac{x^{n+1}}{n+1}$
$5 \left [ 3 \times \color{#FF6800}{ \frac { 1 } { 1 + 1 } } \color{#FF6800}{ u } ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \right ] _ { u = \sqrt[ 3 ]{ x } } + \displaystyle\int { - 4 \sqrt[ 3 ]{ x } } d { x }$
$5 \left [ 3 \times \frac { 1 } { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } u ^ { 1 + 1 } \right ] _ { u = \sqrt[ 3 ]{ x } } + \displaystyle\int { - 4 \sqrt[ 3 ]{ x } } d { x }$
$ $ Add $ 1 $ and $ 1$
$5 \left [ 3 \times \frac { 1 } { \color{#FF6800}{ 2 } } u ^ { 1 + 1 } \right ] _ { u = \sqrt[ 3 ]{ x } } + \displaystyle\int { - 4 \sqrt[ 3 ]{ x } } d { x }$
$5 \left [ 3 \times \frac { 1 } { 2 } u ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \right ] _ { u = \sqrt[ 3 ]{ x } } + \displaystyle\int { - 4 \sqrt[ 3 ]{ x } } d { x }$
$ $ Add $ 1 $ and $ 1$
$5 \left [ 3 \times \frac { 1 } { 2 } u ^ { \color{#FF6800}{ 2 } } \right ] _ { u = \sqrt[ 3 ]{ x } } + \displaystyle\int { - 4 \sqrt[ 3 ]{ x } } d { x }$
$5 \left [ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ \frac { 1 } { 2 } } \color{#FF6800}{ u } ^ { \color{#FF6800}{ 2 } } \right ] _ { \color{#FF6800}{ u } = \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } } + \displaystyle\int { - 4 \sqrt[ 3 ]{ x } } d { x }$
$ $ Return the substituted value $ $
$5 \times \color{#FF6800}{ 3 } \times \color{#FF6800}{ \dfrac { 1 } { 2 } } \left ( \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } \right ) ^ { \color{#FF6800}{ 2 } } + \displaystyle\int { - 4 \sqrt[ 3 ]{ x } } d { x }$
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } + \displaystyle\int { \color{#FF6800}{ - } \color{#FF6800}{ 4 } \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } } d { \color{#FF6800}{ x } }$
$ $ 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$
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } \color{#FF6800}{ - } \displaystyle\int { \color{#FF6800}{ 4 } \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } } d { \color{#FF6800}{ x } }$
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } - \displaystyle\int { \color{#FF6800}{ 4 } \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } } d { \color{#FF6800}{ x } }$
$ $ It is $ \int c f(x) dx = c \int f(x) dx$
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } - \left ( \color{#FF6800}{ 4 } \displaystyle\int { \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } } d { \color{#FF6800}{ x } } \right )$
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } - \left ( 4 \displaystyle\int { \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } } d { \color{#FF6800}{ x } } \right )$
$ $ Substitute with $ u = \sqrt[ 3 ]{ x } $ and calculate the integral $ $
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } - \left ( 4 \left [ \color{#FF6800}{ 3 } \displaystyle\int { \color{#FF6800}{ u } ^ { \color{#FF6800}{ 3 } } } d { \color{#FF6800}{ u } } \right ] _ { \color{#FF6800}{ u } = \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } } \right )$
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } - \left ( 4 \left [ 3 \displaystyle\int { \color{#FF6800}{ u } ^ { \color{#FF6800}{ 3 } } } d { \color{#FF6800}{ u } } \right ] _ { u = \sqrt[ 3 ]{ x } } \right )$
$ $ Calculate the integral using the formula of $ \int{x^{n}}dx = \frac{x^{n+1}}{n+1}$
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } - \left ( 4 \left [ 3 \times \color{#FF6800}{ \frac { 1 } { 3 + 1 } } \color{#FF6800}{ u } ^ { \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \right ] _ { u = \sqrt[ 3 ]{ x } } \right )$
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } - \left ( 4 \left [ 3 \times \frac { 1 } { \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } u ^ { 3 + 1 } \right ] _ { u = \sqrt[ 3 ]{ x } } \right )$
$ $ Add $ 3 $ and $ 1$
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } - \left ( 4 \left [ 3 \times \frac { 1 } { \color{#FF6800}{ 4 } } u ^ { 3 + 1 } \right ] _ { u = \sqrt[ 3 ]{ x } } \right )$
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } - \left ( 4 \left [ 3 \times \frac { 1 } { 4 } u ^ { \color{#FF6800}{ 3 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \right ] _ { u = \sqrt[ 3 ]{ x } } \right )$
$ $ Add $ 3 $ and $ 1$
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } - \left ( 4 \left [ 3 \times \frac { 1 } { 4 } u ^ { \color{#FF6800}{ 4 } } \right ] _ { u = \sqrt[ 3 ]{ x } } \right )$
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } - \left ( 4 \left [ \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ \frac { 1 } { 4 } } \color{#FF6800}{ u } ^ { \color{#FF6800}{ 4 } } \right ] _ { \color{#FF6800}{ u } = \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } } \right )$
$ $ Return the substituted value $ $
$5 \times 3 \times \dfrac { 1 } { 2 } \left ( \sqrt[ 3 ]{ x } \right ) ^ { 2 } - \left ( 4 \times \color{#FF6800}{ 3 } \times \color{#FF6800}{ \dfrac { 1 } { 4 } } \left ( \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } \right ) ^ { \color{#FF6800}{ 4 } } \right )$
$\color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } } \left ( \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ - } \left ( \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 4 } } \left ( \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } } \right ) ^ { \color{#FF6800}{ 4 } } \right )$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } } \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 4 } } \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } }$
Solution search results
search-thumbnail-If the sum of two consecutive 
numbers is $45$ and one number is $X$ 
.This statement in the form of 
equation $1s:$ 
$\left(1$ Point) $\right)$ 
$○5x+1$ $1eft\left(x+1$ $r1gnt\right)=45s$ 
$○sx+1ef\left(x+2$ $r1gnt\right)=145s$ 
$sx+1x=45s$
7th-9th grade
Algebra
search-thumbnail-$s|ef\left(-1n$ $\left($ }\right)^{50}\ $\right)$ \ | | is\ equal\ to\ $S$ 
$s1S$ 
$S-1S$ 
$s2S$ 
$s50s$
7th-9th grade
Other
search-thumbnail-Which of the following rational numbers are 
equivalent? 
$0Ptionsy$ 
A \frac{5}{6}, \frac{30}{36} 
B $s\sqrt{rac\left(} -2\right)\left(3\right)\sqrt{1rac} \sqrt{4\right)16\right)4} $ 
C $s\sqrt{11aC\left(} -4\right)1-7b,\sqrt{1rac\left(16\sqrt{35\right)9} } $ 
D \frac{1}{2},\frac{3}{8}
7th-9th grade
Other
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