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Calculate the integral
Answer
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$\int{ \sqrt[ 4 ]{ x } }d{ x }$
$4 \times \dfrac { 1 } { 5 } \sqrt[ 4 ]{ x ^ { 5 } }$
Calculate the integral
$\displaystyle\int { \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ x } } } d { \color{#FF6800}{ x } }$
$ $ Substitute with $ u = \sqrt[ 4 ]{ x } $ and calculate the integral $ $
$\left [ \color{#FF6800}{ 4 } \displaystyle\int { \color{#FF6800}{ u } ^ { \color{#FF6800}{ 4 } } } d { \color{#FF6800}{ u } } \right ] _ { \color{#FF6800}{ u } = \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ x } } }$
$\left [ 4 \displaystyle\int { \color{#FF6800}{ u } ^ { \color{#FF6800}{ 4 } } } d { \color{#FF6800}{ u } } \right ] _ { u = \sqrt[ 4 ]{ x } }$
$ $ Calculate the integral using the formula of $ \int{x^{n}}dx = \frac{x^{n+1}}{n+1}$
$\left [ 4 \times \color{#FF6800}{ \frac { 1 } { 4 + 1 } } \color{#FF6800}{ u } ^ { \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \right ] _ { u = \sqrt[ 4 ]{ x } }$
$\left [ 4 \times \frac { 1 } { \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } u ^ { 4 + 1 } \right ] _ { u = \sqrt[ 4 ]{ x } }$
$ $ Add $ 4 $ and $ 1$
$\left [ 4 \times \frac { 1 } { \color{#FF6800}{ 5 } } u ^ { 4 + 1 } \right ] _ { u = \sqrt[ 4 ]{ x } }$
$\left [ 4 \times \frac { 1 } { 5 } u ^ { \color{#FF6800}{ 4 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \right ] _ { u = \sqrt[ 4 ]{ x } }$
$ $ Add $ 4 $ and $ 1$
$\left [ 4 \times \frac { 1 } { 5 } u ^ { \color{#FF6800}{ 5 } } \right ] _ { u = \sqrt[ 4 ]{ x } }$
$\left [ \color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ \frac { 1 } { 5 } } \color{#FF6800}{ u } ^ { \color{#FF6800}{ 5 } } \right ] _ { \color{#FF6800}{ u } = \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ x } } }$
$ $ Return the substituted value $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 5 } } \left ( \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ x } } \right ) ^ { \color{#FF6800}{ 5 } }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 5 } } \left ( \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ x } } \right ) ^ { \color{#FF6800}{ 5 } }$
$ $ Simplify the expression $ $
$\color{#FF6800}{ 4 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { 5 } } \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } }$
Solution search results
search-thumbnail-$\int \dfrac {\sqrt{x} -\sqrt [3] {x} } {\sqrt [3] {x} +\sqrt [4] {x} }dx$
1st-6th grade
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search-thumbnail-$\int \dfrac {1+\sqrt{x} } {1+\sqrt [4] {x} }dx$
10th-13th grade
Calculus
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