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Calculate the integral
Answer
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$\int{ \sqrt{ bx } }d{ x }$
$\dfrac { 1 } { b } \times \dfrac { 2 } { 3 } \sqrt{ b ^ { 3 } } \sqrt{ x ^ { 3 } }$
Calculate the integral
$\displaystyle\int { \sqrt{ \color{#FF6800}{ b } \color{#FF6800}{ x } } } d { \color{#FF6800}{ x } }$
$ $ Substitute with $ u = b x $ and calculate the integral $ $
$\left [ \color{#FF6800}{ \frac { 1 } { b } } \displaystyle\int { \color{#FF6800}{ u } ^ { \color{#FF6800}{ \frac { 1 } { 2 } } } } d { \color{#FF6800}{ u } } \right ] _ { \color{#FF6800}{ u } = \color{#FF6800}{ b } \color{#FF6800}{ x } }$
$\left [ \frac { 1 } { b } \displaystyle\int { \color{#FF6800}{ u } ^ { \color{#FF6800}{ \frac { 1 } { 2 } } } } d { \color{#FF6800}{ u } } \right ] _ { u = b x }$
$ $ Calculate the integral using the formula of $ \int{x^{n}}dx = \frac{x^{n+1}}{n+1}$
$\left [ \frac { 1 } { b } \times \color{#FF6800}{ \frac { 1 } { \frac { 1 } { 2 } + 1 } } \color{#FF6800}{ u } ^ { \color{#FF6800}{ \frac { 1 } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \right ] _ { u = b x }$
$\left [ \color{#FF6800}{ \frac { 1 } { b } } \color{#FF6800}{ \times } \color{#FF6800}{ \frac { 1 } { \frac { 1 } { 2 } + 1 } } \color{#FF6800}{ u } ^ { \color{#FF6800}{ \frac { 1 } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } \right ] _ { \color{#FF6800}{ u } = \color{#FF6800}{ b } \color{#FF6800}{ x } }$
$ $ Return the substituted value $ $
$\color{#FF6800}{ \dfrac { 1 } { b } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { \dfrac { 1 } { 2 } + 1 } } \left ( \color{#FF6800}{ b } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ \frac { 1 } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
$\color{#FF6800}{ \dfrac { 1 } { b } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 1 } { \dfrac { 1 } { 2 } + 1 } } \left ( \color{#FF6800}{ b } \color{#FF6800}{ x } \right ) ^ { \color{#FF6800}{ \frac { 1 } { 2 } } \color{#FF6800}{ + } \color{#FF6800}{ 1 } }$
$ $ Simplify the expression $ $
$\color{#FF6800}{ \dfrac { 1 } { b } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 2 } { 3 } } \sqrt{ \color{#FF6800}{ b } ^ { \color{#FF6800}{ 3 } } } \sqrt{ \color{#FF6800}{ x } ^ { \color{#FF6800}{ 3 } } }$
Solution search results
search-thumbnail-The rationalizing factor of \sqrt{23} is 
$°$ $Options^{°}$ $0$ 
A 24 
23 
C \sqrt{23} 
D None of these
7th-9th grade
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