Answer
a) $x^{\frac{1}{2}}+C$
b) $x^{\frac{-1}{2}}+C$
c) $ x^{\frac{-3}{2}}+C$
Work Step by Step
a) The anti-derivative is:
$\dfrac{1}{2}\dfrac{x^{-1/2+1}}{-1/2+1}+C=x^{\frac{1}{2}}+C$
b) The anti-derivative is:
$\dfrac{-1}{2}\dfrac{x^{-3/2+1}}{-3/2+1}+C=x^{\frac{-1}{2}}+C$
c) The anti-derivative is:
$\dfrac{-3}{2}\dfrac{x^{-5/2+1}}{-5/2+1}+C= x^{\frac{-3}{2}}+C$
