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
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