$\require{\newcommand}$
$\def\ch{\text{ch}}$
$\def\sh{\text{sh}}$
$\def\tanh{\text{tanh}}$
$\def\coth{\text{coth}}$
| 函数 |
原函数 |
函数 |
原函数 |
| $x^k$ |
$\displaystyle\frac{x^{k+1}}{k+1}$ |
$\displaystyle\frac{1}{x}$ |
$\displaystyle\ln{\vert x\vert}$ |
| $\cos{x}$ |
$\sin{x}$ |
$\sin{x}$ |
$-\cos{x}$ |
| $\sec^2{x}$ |
$\tan{x}$ |
$\csc^2{x}$ |
$-\cot{x}$ |
| $\sec{x}\tan{x}$ |
$\sec{x}$ |
$\csc{x}\cot{x}$ |
$-\csc{x}$ |
| $\sec{x}$ |
$\ln{|\sec{x}+\tan{x}|}$ |
$\csc{x}$ |
$-\ln{|\csc{x}+\cot{x}|}$ |
| $\displaystyle\frac{1}{a^2+x^2}$ |
$\displaystyle\frac{1}{a}\arctan{\frac{x}{a}}$ |
$\displaystyle\frac{1}{a^2-x^2}$ |
$\displaystyle\frac{1}{2a}\ln{\left|\frac{a+x}{a-x}\right|}$ |
| $\sqrt{x^2\pm a^2}$ |
$\displaystyle\frac{1}{2}\left[x\sqrt{x^2\pm a^2}\pm a^2\ln\left(x+\sqrt{x^2\pm a^2}\right)\right]$ |
|
|
| $\sqrt{a^2-x^2}$ |
$\displaystyle\frac{1}{2}\left[x\sqrt{a^2-x^2}+a^2\arcsin{\frac{x}{a}}\right]$ |
|
|
| $\displaystyle\frac{1}{\sqrt{x^2\pm a^2}}$ |
$\ln\left(x+\sqrt{x^2\pm a^2}\right)$ |
|
|
| $\displaystyle\frac{1}{\sqrt{a^2-x^2}}$ |
$\displaystyle\arcsin{\frac{x}{a}}$ |
|
|
| $e^x$ |
$e^x$ |
$a^x$ |
$\displaystyle\frac{a^x}{\ln{a}}$ |
| $\ch\,{x}$ |
$\sh\,x$ |
$\sh\,x$ |
$\ch\,x$ |
| $\displaystyle\frac{1}{\ch^2\,x}$ |
$\tanh\,x$ |
$\displaystyle\frac{1}{\sh^2\,x}$ |
$-\coth\,x$ |
上一篇：热力学基本概念及规律
下一篇：黎曼$\zeta$函数与素数理论
