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Indefinite Integral – A quotient of functions with roots – Exercise 1392

Exercise

Evaluate the integral

\int \frac{1}{\sqrt{x+1}-\sqrt{x}} dx

Final Answer


\int \frac{1}{\sqrt{x+1}-\sqrt{x}} dx=\frac{2}{3}{(x+1)}^{\frac{3}{2}} +\frac{2}{3}x^{\frac{3}{2}} +c

Solution

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