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