Question

Solve $\int \frac{1}{\sqrt{3x+4}-\sqrt{3x+1}}dx$

Answer 1

$=\int \frac{1}{\sqrt{3x+4}-\sqrt{3x+1}}dx$ Rationlize

$=\int \frac{\sqrt{3x+4}\sqrt{3x+1}}{3x+4-3x-1}dx$

$=\frac{1}{3}\int (\sqrt{3x+4}+\sqrt{3x+1})dx$

$=\frac{1}{3}[\frac{(3x+4{)}^{3/2}}{\frac{3}{2}\times 3}+\frac{(3x+1{)}^{3/2}}{3\times 3/2}]+C$

$=\frac{1}{3}\left[\frac{2}{9}\right(3x+4{)}^{3/2}+\frac{2}{9}(3x+1{)}^{3/2}]+C$