Answer
a) $3x^2+C$
b) $\dfrac{1}{8}x^8+C$
c) $\dfrac{1}{8}x^8-3x^2+8x+C$
Work Step by Step
a) The anti-derivative is:
Thus, $(\dfrac{6}{1+1})x^{1+1}+C=3x^2+C$
b) The anti-derivative is:
Thus, $(\dfrac{1}{7+1})x^{7+1}+C=\dfrac{1}{8}x^8+C$
c) The anti-derivative is:
Thus, $(\dfrac{1}{7+1}x^{7+1})-\dfrac{6}{1+1}x^{1+1}+(8)x^{0+1}+C=\dfrac{1}{8}x^8-3x^2+8x+C$
