Mathematics

# Evaluate: $\displaystyle \int \frac{dx}{x^{1/5}\left ( 1+x^{4/5} \right )^{1/2}}$

$\displaystyle \frac{5}{2}\sqrt{1+x^{4/5}}+k$

##### SOLUTION
$\displaystyle \int \frac{dx}{x^{1/5}\left ( 1+x^{4/5} \right )^{1/2}}$

Put $1+x^{ 4/5 }=t$
$\displaystyle \frac { 4 }{ 5 } { x }^{ -1/5 }dx=dt$
$\displaystyle \frac { dx }{ x^{ 1/5 } } =\frac { 5 }{ 4 } dt$

So,
$I=\displaystyle \frac { 5 }{ 4 } \int \frac { dt }{ t^{ 1/2 } }$

$\displaystyle I=\frac { 5 }{ 2 } t^{ 1/2 }+C$

$\displaystyle I=\frac { 5 }{ 2 } (1+x^{ 4/5 })^{ 1/2 }+C$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
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