integration of dx/root(x+3)-root(x+2)

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

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