1.2. Pamatintegrāļu tabula

No elementāro pamatfunkciju atvasinājumu tabulas un nenoteiktā integrāļa definīcijas izriet šāda pamatintegrāļu tabula.

$\displaystyle 1.$	$\displaystyle \int x^\alpha dx=\frac{x^{\alpha +1}}{\alpha +1}+C\quad (\alpha\neq -1);$
$\displaystyle 2.$	$\displaystyle \int \frac{dx}{x}=\ln\vert x\vert+C;$
$\displaystyle 3.$	$\displaystyle \int a^xdx=\frac{a^x}{\ln a}+C;$
	$\displaystyle \int e^xdx=e^x+C;$
$\displaystyle 4.$	$\displaystyle \int\cos xdx=\sin x+C;$
$\displaystyle 5.$	$\displaystyle \int \sin x dx=-\cos x+C;$
$\displaystyle 6.$	$\displaystyle \int\frac{dx}{\cos^2x}=\tg x+C;$
$\displaystyle 7.$	$\displaystyle \int\frac{dx}{\sin^2x}=-\ctg x+C;$
$\displaystyle 8.$	$\displaystyle \int\frac{dx}{\sqrt{1-x^2}}=\arcsin x+C;$
$\displaystyle 9.$	$\displaystyle \int\frac{dx}{1+x^2}=\arctg x+C;$
$\displaystyle 10.$	$\displaystyle \int\ch xdx=\sh x+C;$
$\displaystyle 11.$	$\displaystyle \int \sh xdx=\ch x+C;$
$\displaystyle 12.$	$\displaystyle \int\frac{dx}{\ch^2x}=\Th x+C;$
$\displaystyle 13.$	$\displaystyle \int\frac{dx}{\sh^2x}=-\cth x+C.$

Šo formulu pareizību var pārbaudīt tieši - atvasinot formulu labās puses; rezultātā ir jāiegūst atbilstošā zemintegrāļa funkcija.