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