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

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

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

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

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

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