What is the antiderivative of #F(x)=9x^2-8x+8#?

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Answer 1 · 2016-11-17T16:08:10

#3x^3-4x^2+8x+C#

For polynomials

#int x^ndx=x^(n+1)/(n+1)+C, n!=-1#

#int(9x^2-8x+8)dx#

integrate each term separately

#=9x^(2+1)/(2+1)-8x^(1+1)/(1+1)+8x+C#

#=(9x^3)/3-(8x^2)/2+8x+C#

#=(cancel(9)^3x^3)/cancel(3)-(cancel(8)^4x^2)/cancel(2)+8x+C#

#=3x^3-4x^2+8x+C#