Question

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

Answer 1

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

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

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

$=\frac{3}{2}{\left(x+1\right)}^{\frac{3}{2}}+\frac{3}{2}{x}^{\frac{3}{2}}+C$