# Calculator search results

Formula
Calculate the integral
$\int{ \left( \dfrac{ 5 }{ \sqrt[3]{ x } } -4 \sqrt[3]{ x } \right) }d{ x }$
$5 \times 3 \times \dfrac { 1 } { 2 } \sqrt[ 3 ]{ x ^ { 2 } } - 4 \times 3 \times \dfrac { 1 } { 4 } \sqrt[ 3 ]{ x ^ { 4 } }$
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 
$\color{#FF6800}{ 5 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 2 } } \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } } \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 4 } } \sqrt[ \color{#FF6800}{ 3 } ]{ \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } } }$
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