Question

Evaluate: $\int \frac{1}{\sqrt{x+3}-\sqrt{x+2}}dx$

Answer 1

$\int \frac{1}{\sqrt{x+3}-\sqrt{x+2}}dx$

$=\int \frac{\sqrt{x+3}+\sqrt{x+2}}{x+3-x-2}dx=\int \sqrt{x+3}dx+\int \sqrt{x+2}dx$

$=\frac{(x+3{)}^{3/2}}{3/2}+\frac{(x+2{)}^{3/2}}{3/2}+c$

$=\frac{2}{3}\left[\right(x+2{)}^{3/2}+(x+3{)}^{3/2}]+c$.