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