# Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 238: 7

a) $x^{\frac{3}{2}}+C$ b) $\sqrt x+C$ c) $\dfrac{2}{3}x^{\frac{3}{2}}+2 \sqrt x+C$

#### Work Step by Step

a) The anti-derivative is: Thus, $(\dfrac{3}{2})(\dfrac{x^{1/2+1}}{1/2+1})+C=x^{\frac{3}{2}}+C$ b) The anti-derivative is: Thus,$(\dfrac{1}{2})(\dfrac{x^{-1/2+1}}{-1/2+1})+C=\sqrt x+C$ c) The anti-derivative is: Thus, $(\dfrac{x^{1/2+1}}{1/2+1})+(\dfrac{x^{-1/2+1}}{-1/2+1})+C=(\dfrac{2}{3}x^{\frac{3}{2}})+2 \sqrt x+C$

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