Power rule for integration
= Power rule for integration
{title2=$\int x^q\,dx=\dfrac{x^{q+1}}{q+1}+C,\quad q\ne-1$}
On $x>0$, the <power rule> for <derivatives> and the <fundamental theorem of calculus> give the displayed <antiderivative>. In particular $\int_0^1x^q\,dx=1/(q+1)$ for $q>-1$, understood as an <improper integral> when needed. At $q=-1$, the <antiderivative> on $x>0$ is the <natural logarithm> $\log x+C$.