Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 238: 9

a) $x^{\frac{2}{3}}+C$ b) $x^{\frac{1}{3}}+C$ c) $x^{\frac{-12}{3}}+C$

a) The anti-derivative is: Thus, $(\dfrac{2}{3})(\dfrac{x^{-1/3+1}}{-1/3+1})+C=(x^{\frac{2}{3}})+C$ b) The anti-derivative is: Thus, $(\dfrac{1}{3})(\dfrac{x^{-2/3+1}}{-2/3+1})+C=x^{\frac{1}{3}}+C$ c) The anti-derivative is: Thus, $(\dfrac{-1}{3})(\dfrac{x^{-4/3+1}}{-4/3+1})+C= x^{\frac{-12}{3}}+C$