Mathematics

# Evaluate:$\displaystyle \int \dfrac { 1 } { x - \sqrt { x } } d x$

##### SOLUTION
$I=\displaystyle\int \dfrac{1}{x-\sqrt{x}}dx$

$x=u^2$

$\Rightarrow dx=2udu$

$\Rightarrow I=\displaystyle\int \dfrac{1}{u^2-u}2udu$

$=2\displaystyle\int \dfrac{du}{u-1}$

$=2ln(|u-1|)+c$

$=2ln(|\sqrt{x}-1|)+c$.

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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