请教markdown表格嵌入绝对值符号问题

WeLikeStudying @ 2024-11-28 17:55:26

|$x^2$|
|:-:|

|$|x|$|
|:-:|

by WeLikeStudying @ 2024-11-28 18:25:53

@ljy05 感谢！

by LionBlaze @ 2024-11-28 18:30:24

@cjrawa 谢谢！

by ducati @ 2024-11-28 18:40:47

怎么感觉 \vert 系列和 | 并没有很明显的区别……

$\mid x \mid$

$\lvert x \lvert$

$\rvert x \rvert$

$\vert x \vert$

$|x|$

by WeLikeStudying @ 2024-11-28 20:32:34

@ducati \vert 是俺制表用的。

|                        $f(x)$                         |            $\operatorname{d}f(x)$            |                 $\int f(x)\operatorname{d}x$                 |
| :---------------------------------------------------: | :------------------------------------------: | :----------------------------------------------------------: |
|                         $x^a$                         |         $ax^{a-1}\operatorname{d}x$          | $\begin{cases}\frac1{a+1}x^{a+1}+C&a\ne -1\\\ln\lvert x\rvert +C&a=-1\end{cases}$ |
|                       $\sin x$                        |          $\cos x\operatorname{d}x$           |                         $-\cos x+C$                          |
|                       $\cos x$                        |          $\sin x\operatorname{d}x$           |                          $\sin x+C$                          |
|                       $\tan x$                        |         $\sec^2 x\operatorname{d}x$          |                 $-\ln\lvert \cos x\rvert +C$                 |
|                       $\cot x$                        |         $-\csc^2x\operatorname{d}x$          |                 $\ln\lvert \sin x\rvert +C$                  |
|                       $\sec x$                        |       $\tan x\sec x\operatorname{d}x$        |              $\ln\lvert \sec x+\tan x\rvert +C$              |
|                       $\csc x$                        |       $-\cot x\csc x\operatorname{d}x$       |              $\ln\lvert \csc x-\cot x\rvert +C$              |
|                      $\arcsin x$                      |   $\frac{\operatorname{d}x}{\sqrt{1-x^2}}$   |           $\color{green}x\arcsin x+\sqrt{1-x^2}+C$           |
|                      $\arccos x$                      |  $-\frac{\operatorname{d}x}{\sqrt{1-x^2}}$   |           $\color{green}x\arccos x-\sqrt{1-x^2}+C$           |
|                      $\arctan x$                      |      $\frac{\operatorname{d}x}{1+x^2}$       |        $\color{green}x\arctan x-\frac12\ln(1+x^2)+C$         |
|               $\operatorname{arccot} x$               |      $-\frac{\operatorname{d}x}{1+x^2}$      | $\color{green}x\operatorname{arccot} x+\frac12\ln(1+x^2)+C$  |
|                     $a^x(a\ne 1)$                     |         $a^x\ln a\operatorname{d}x$          |                    $\frac{a^x}{\ln a}+C$                     |
|                   $\log_ax(a\ne 1)$                   |      $\frac{\operatorname{d}x}{x\ln a}$      |           $\color{green}\frac{x\ln x-x}{\ln a}+C$            |
|       $\operatorname{sh}x=\frac{e^x-e^{-x}}{2}$       |    $\operatorname{ch}x\operatorname{d}x$     |                    $\operatorname{ch}x+C$                    |
|       $\operatorname{ch}x=\frac{e^x+e^{-x}}{2}$       |    $\operatorname{sh} x\operatorname{d}x$    |                    $\operatorname{sh}x+C$                    |
|  $\operatorname{th}x=\frac{e^x-e^{-x}}{e^x+e^{-x}}$   |  $\operatorname{sech}^2x\operatorname{d}x$   |           $\color{green}\ln(\operatorname{ch}x)+C$           |
|  $\operatorname{cth}x=\frac{e^x+e^{-x}}{e^x-e^{-x}}$  |  $-\operatorname{csch}^2x\operatorname{d}x$  |           $\color{green}\ln(\operatorname{sh}x)+C$           |
|     $\operatorname{sh}^{-1}x=\ln(x+\sqrt{1+x^2})$     |   $\frac{\operatorname{d}x}{\sqrt{1+x^2}}$   |    $\color{green}x\operatorname{sh}^{-1}x-\sqrt{1+x^2}+C$    |
|     $\operatorname{ch}^{-1}x=\ln(x+\sqrt{x^2-1})$     |   $\frac{\operatorname{d}x}{\sqrt{x^2-1}}$   |    $\color{green}x\operatorname{ch}^{-1}x-\sqrt{x^2-1}+C$    |
|  $\operatorname{th}^{-1}x=\frac12\ln\frac{1+x}{1-x}$  |      $\frac{\operatorname{d}x}{1-x^2}$       | $\color{green}x\operatorname{th}^{-1}x+\frac12\ln\lvert x^2-1\rvert +C$ |
| $\operatorname{cth}^{-1}=\frac12\ln{\frac{x+1}{x-1}}$ |      $\frac{\operatorname{d}x}{1-x^2}$       | $\color{green}x\operatorname{cth}^{-1}x+\frac12\ln\lvert x^2-1\rvert +C$ |
|               $\frac 1{\sqrt{a^2-x^2}}$               |   $\color{green}\frac{x}{(a^2-x^2)^{3/2}}$   |                     $\arcsin\frac xa+C$                      |
|             $\frac{1}{\sqrt{x^2\pm a^2}}$             | $\color{green}-\frac{x}{(x^2\pm a^2)^{3/2}}$ |     $\ln\left\lvert x+\sqrt{x^2\pm a^2}\right\rvert +C$      |
|                   $\frac1{x^2-a^2}$                   |    $\color{green}-\frac{2x}{(x^2-a^2)^2}$    |   $\frac1{2a}\ln\left\lvert \frac{x-a}{x+a}\right\rvert $    |
|                  $\frac{1}{x^2+a^2}$                  |    $\color{green}-\frac{2x}{(x^2+a^2)^2}$    |                 $\frac1a\arctan{\frac xa}+C$                 |
|                   $\sqrt{a^2-x^2}$                    |   $\color{green}-\frac x{\sqrt{a^2-x^2}}$    |   $\frac{x}2\sqrt{a^2-x^2}+\frac{a^2}2\arcsin\frac{x}a+C$    |
|                  $\sqrt{x^2\pm a^2}$                  | $\color{green}\frac{x}{\sqrt {x^2\pm a^2}}$  | $\frac x{2}\sqrt{x^2\pm a^2}\pm\frac{a^2}2\ln\lvert x+\sqrt{x^2\pm a^2}\rvert +C$ |