Answer
a) $x^2+C$
b) $\dfrac{1}{3}x^3+C$
c) $\dfrac{1}{3}x^3-x^2+x+C$
Work Step by Step
a) The anti-derivative is:
$\dfrac{2}{1+1}x^{1+1}+C=x^2+C$
b) The anti-derivative is:
$\dfrac{1}{2+1}x^{2+1}+C=\dfrac{1}{3}x^3+C$
c) The anti-derivative is:
$\dfrac{1}{2+1}x^{2+1}-\dfrac{2}{1+1}x^{1+1}+(1)x^{0+1}+C=\dfrac{1}{3}x^3-x^2+x+C$
Hence, a) $x^2+C$
b) $\dfrac{1}{3}x^3+C$
c) $\dfrac{1}{3}x^3-x^2+x+C$
