Answer
1. Rewrite: $\int (x^{-\frac{3}{2}}) dx$
2. Integrate: $= \frac{x^{-\frac{1}{2}}}{-\frac{1}{2}}+C$
3. Simplify: $= -\frac{2}{\sqrt {x}} + C$
Work Step by Step
1. Rewrite
$\int (\frac{1}{x \sqrt {x}}) dx$
$\int (\frac{1}{x^{1}x^{\frac{1}{2}}}) dx$
$\int (\frac{1}{x^{\frac{3}{2}}}) dx$
$\int (x^{-\frac{3}{2}}) dx$
2. Integrate
$= \frac{x^{-\frac{1}{2}}}{-\frac{1}{2}}+C$
3. Simplify
$= \frac{1}{\sqrt {x}} \times (-2)$
$= \frac{-2}{\sqrt {x}} + C$
