积

$\int k\mathrm{d}x=kx+C$ $\int x^\mu\mathrm{d}x=\frac{1}{\mu+1}x^{\mu+1}+C$ $\int\frac{\mathrm{d}x}{x}=\ln\left|x\right|+C$

$\int\frac{\mathrm{d}x}{1+x^2}=\arctan x+C或-\mathrm{arccot}x+C$

$\int\frac{\mathrm{d}x}{\sqrt{1-x^2}}=\arcsin x+C或-\arccos x+C$

$\int\cos x\mathrm{d}x=\sin x+C$ $\int\sin x\mathrm{d}x=-\cos x+C$

$\int\frac{\mathrm{d}x}{\cos^2x}=\int\sec^2x\mathrm{d}x=\tan x+C$

$\int\frac{\mathrm{d}x}{\sin^2x}=\int\csc^2x\mathrm{d}x=-\cot x+C$

$\int\sec x\tan x\mathrm{d}x=\sec x+C$ $\int\csc x\cot x\mathrm{d}x=-\csc x+C$

$e^x\mathrm{d}x=e^x+C$ $\int a^x\mathrm{d}x=\frac{a^x}{\ln a}+C$

$\int\mathrm{sh}x\mathrm{d}x=\mathrm{ch}x+C$ $\int\mathrm{ch}x\mathrm{d}x=\mathrm{sh}x+C$
$(\mathrm{sh}x=\frac{e^x-e^{-x}}{2},\mathrm{ch}x=\frac{e^x+e^{-x}}{2})$

$\int\tan x\mathrm{d}x=-\ln\left|\cos x\right|+C$ $\int\cot x\mathrm{d}x=\ln\left|\sin x\right|+C$

$\int\sec x\mathrm{d}x=\ln\left|\sec x+\tan x\right|+C$ $\int\csc x\mathrm{d}x=\ln\left|\csc x-\cot x\right|+C$

$\int\frac{1}{a^2+x^2}\mathrm{d}x=\frac{1}{a}\arctan\frac{x}{a}+C$ $\int\frac{1}{x^2-a^2}\mathrm{d}x=\frac{1}{2a}\ln\left|\frac{x-a}{x+a}\right|+C$

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

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