Question $8(8$ points$)$

The following table gives the velocity $v(t)($in $f\frac{t}{s})$ at different instances of time $t($in s$)$ of a particle moving along a horizontal axis.

$\backslash$table$[[(sec),0,1,2,3,4,5,6,7,8,9,10,11,12],[\backslash$table$[[v(t)$

Which of the following is the most general antiderivative of

$f(x)=2se{c}^{2}x+x^3+\frac{1}{x^3}+\sqrt[\phantom{2}]{x}?$

$F(x)=2tanx+3x^2-\frac{1}{2x^2}+\frac{2}{3}\sqrt[\phantom{2}]{x^3}+C$

$F(x)=2se{c}^{2}xtanx+\frac{x^4}{4}-\frac{1}{2x^2}+\frac{2}{3}\sqrt[\phantom{2}]{x^3}+C$

$F(x)=2tanx+\frac{x^4}{4}+\frac{1}{3x^2}+\frac{1}{2\sqrt[\phantom{2}]{x}}+C$

$F(x)=2se{c}^{2}xtanx+\frac{x^4}{4}+\frac{1}{3x^2}+\frac{1}{2\sqrt[\phantom{2}]{x}}+C$

$F(x)=2tanx+\frac{x^4}{4}-\frac{1}{2x^2}+\frac{2}{3}\sqrt[\phantom{2}]{x^3}+C$

$F(x)=2tanx+3x^2+\frac{1}{3x^2}+\frac{1}{2\sqrt[\phantom{2}]{x}}+C$

$F(x)=2tanx+\frac{x^4}{4}+\frac{1}{3x^2}+\frac{2}{3}\sqrt[\phantom{2}]{x^3}+C$

$F(x)=2tanx+\frac{x^4}{4}-\frac{1}{2x^2}+\frac{1}{2\sqrt[\phantom{2}]{x}}+C$