Answer
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, $(\dfrac{x^{1/2+1}}{1/2+1})+(\dfrac{x^{-1/2+1}}{-1/2+1})+C=(\dfrac{2}{3}x^{\frac{3}{2}})+2 \sqrt x+C$
