Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 238: 3

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

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