Mathematics

# $\displaystyle \int \frac{1}{\sqrt{\left ( x \right )}\left [ \sqrt{\left ( x \right )}+1 \right ]}dx.$

$\displaystyle 2\log \left ( 1+\sqrt{x} \right ).$

##### SOLUTION
Let $\displaystyle I=\int \frac{1}{\sqrt{\left ( x \right )}\left [ \sqrt{\left ( x \right )}+1 \right ]}dx.$
Substitute $\displaystyle \sqrt { x } +1=t\Rightarrow \frac { 1 }{ 2\sqrt { x } } dx=dt$
Therefore
$\displaystyle I=\int \frac { 2dt }{ t } =2\log t=2\log \left( 1+\sqrt { x } \right)$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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Solve $\displaystyle \int\sqrt{\dfrac{a-x}{a+x}}dx$