5.3 The Fundamental Theorem of Calculus/7

$g(x)=\int _{1}^{x}{\frac {1}{t^{3}+1}}dt$
${\frac {d}{dx}}\left[g(x)\right]={\frac {d}{dx}}\left[\int _{1}^{x}{\frac {1}{t^{3}+1}}dt\right]$= (1)\left(\frac{1}{1+x^3}\right)=\frac{1}{1+x^3}</math>