$\int 1dx = x + C \quad (\text{或} \quad \int dx = x + C)$

$\int kdx = kx + C$

$\int x^{\mu}dx = \frac{x^{\mu+1}}{\mu+1} + C \quad (\mu \neq -1)$

$\int \frac{1}{x}dx = \ln|x| + C$

$\int e^xdx = e^x + C$

$\int a^xdx = \frac{a^x}{\ln a} + C$

$\int \cos xdx = \sin x + C$

$\int \sin xdx = -\cos x + C$

$\int \tan xdx = -\ln|\cos x| + C$

$\int \cot xdx = \ln|\sin x| + C$

$\int \sec xdx = \int \frac{1}{\cos x}dx = \ln|\sec x + \tan x| + C = \ln\left(\left|\tan\left(\frac{x}{2}+\frac{\pi}{4}\right)\right|\right)+C$

$\int \csc xdx = \int \frac{1}{\sin x}dx = \ln|\csc x - \cot x| + C=\ln\left(\left|\tan\left(\frac{x}{2}\right)\right|\right)+C$

$\int \sec^2 xdx = \int \frac{1}{\cos^2 x}dx = \tan x + C$

$\int \csc^2 xdx = \int \frac{1}{\sin^2 x}dx = -\cot x + C$

$\int \sec x\tan xdx = \sec x + C$

$\int \csc x\cot xdx = -\csc x + C$

$\int \frac{1}{\sqrt{1-x^2}}dx = \arcsin x + C$

$\int \frac{1}{1+x^2}dx = \arctan x + C$

$\int \frac{1}{\sqrt{a^2-x^2}}dx = \arcsin \frac{x}{a} + C \quad (a>0)$

$\int \frac{1}{a^2+x^2}dx = \frac{1}{a}\arctan \frac{x}{a} + C$

$\int \frac{1}{\sqrt{x^2-a^2}}dx = \ln |x+\sqrt{x^2-a^2}| + C$

$\int \frac{1}{\sqrt{x^2+a^2}}dx = \ln |x+\sqrt{x^2+a^2}| + C$

$\int \frac{1}{x^2-a^2}dx = \frac{1}{2a}\ln \left| \frac{x-a}{x+a} \right| + C = \frac{1}{2a}(\ln |x-a| - \ln |x+a|) + C$

$\int \sqrt{a^2-x^2}dx = \frac{a^2}{2}\arcsin \frac{x}{a} + \frac{x}{2}\sqrt{a^2-x^2} + C$