Mathematics

# Evaluate: $\displaystyle\int { \cfrac { 1}{ \sqrt { x+a } -\sqrt { x+b } } } dx$

##### SOLUTION
Now,
$\displaystyle\int { \cfrac { 1}{ \sqrt { x+a } -\sqrt { x+b } } } dx$

$=\displaystyle\int { \cfrac { \sqrt{x+a}+\sqrt{x+b}}{ { x+a } -{ x-b } } } dx$

$=\dfrac{1}{a-b}\left(\dfrac{2}{3} (x+a)^{\tfrac{3}{2}}+\dfrac{2}{3}(x+b)^{\tfrac{3}{2}}\right)+c$ [ where $c$ is integrating constant] [ where $a\ne b$]

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

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