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
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