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

Exercise

Evaluate the integral

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

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