## Calculus 10th Edition

Published by Brooks Cole

# Chapter 4 - Integration - 4.1 Exercises: 9

#### 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 $= \frac{1}{\sqrt {x}} \times (-2)$ $= \frac{-2}{\sqrt {x}} + C$

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