Simbolet matematikore

Simbolet në matematikë shërbejne për krijimin e termeve (shprehjeve) matematikore dhe lidhjen e tyre në forma më komplekse. Me kalimin e kohës dhe sidomosë me zhvillimin e matematikes logjike fjalori i matematikes është pasuruar dhe pasurohet gjithnjë e më shumë me simbole të reja. Zakonishtë për simbolizimin e variableve të ndryshme, varsisht nga lëmia përdoren shkronjat e alfabetit latin dhe alfabetit të vjeter grekë.

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Simbolet matematikore në Wikipedia

Kjo përmbledhje shërben për momentë për redaktuesit e artikujve matematikorë në Wikipedi që nuk kanë kohë për të gjurmuar më tepër në Wikipedia.

Lidhëse të termeve dhe simboleve matematikore

Për	Shkruhet në Wikipedia	Në Matematikë shkruhet si
Trigonometri	\sin x + \ln y +\operatorname{sgn} z	${\displaystyle \sin x+\ln y+\operatorname {sgn} z}$
Derivate	\nabla \partial x dx \dot x \ddot y	${\displaystyle \nabla \ \partial x\ dx\ {\dot {x}}\ {\ddot {y}}}$
Bashkësitë	\forall x \not\in \varnothing \subseteq A \cap \bigcap B \cup \bigcup \exists \{x,y\} \times C	${\displaystyle \forall x\not \in \varnothing \subseteq A\cap \bigcap B\cup \bigcup \exists \{x,y\}<br/>\times C}$
Logjikë	p \land \bar{q} \to p\lor \lnot q	${\displaystyle p\land {\bar {q}}\to p\lor \lnot q}$
Rrënjët	\sqrt{2}\approx 1.4	${\displaystyle {\sqrt {2}}\approx 1.4}$
	\sqrt[n]{x}	${\displaystyle {\sqrt[{n}]{x}}}$
Relacione	\sim \simeq \cong \le \ge \equiv \not\equiv \approx \ne \propto	${\displaystyle \sim \ \simeq \ \cong \ \leq \ \geq \ \equiv \ \not \equiv \ \approx \ \neq \ \propto }$
Gjeometri	45^\circ	${\displaystyle \triangle \ \angle \perp \|\ 45^{\circ }}$
Kahje/drejtim	\leftarrow \rightarrow \leftrightarrow \longleftarrow \longrightarrow \mapsto \longmapsto \nearrow \searrow \swarrow \nwarrow \uparrow \downarrow \updownarrow	${\displaystyle \leftarrow \ \rightarrow \ \leftrightarrow }$ ${\displaystyle \longleftarrow \ \longrightarrow }$ ${\displaystyle \mapsto \ \longmapsto }$ ${\displaystyle \nearrow \ \searrow \ \swarrow \ \nwarrow }$ ${\displaystyle \uparrow \ \downarrow \ \updownarrow }$
	\Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow \Uparrow \Downarrow \Updownarrow	${\displaystyle \Leftarrow \ \Rightarrow \ \Leftrightarrow }$ ${\displaystyle \Longleftarrow \ \Longrightarrow \ \Longleftrightarrow }$ ${\displaystyle \Uparrow \ \Downarrow \ \Updownarrow }$
Speciale	\oplus \otimes \pm \mp \hbar \wr \dagger \ddagger \star * \ldots \circ \cdot \times \bullet \infty \vdash \models	${\displaystyle \oplus \otimes \pm \mp \hbar \wr \dagger \ddagger \star *\ldots }$ ${\displaystyle \circ \cdot \times \bullet \ \infty \ \vdash \ \models }$
Lidhësa tjera	\mathcal {45abcdenpqstuvwx}	${\displaystyle {\mathcal {45abcdenpqstuvwx}}}$bba5

Fuqizimi, indekset dhe integralet

Për	Shkruhet në Wikipedia	Në Matematikë shkruhet si
Fuqizimë	a^2 Bskstjww
Indeksimë	a_2	${\displaystyle a_{2}}$	${\displaystyle a_{2}\,\!}$
I. të grupuarë	a^{2+2}	${\displaystyle a^{2+2}}$	${\displaystyle a^{2+2}\,\!}$
	a_{i,j}	${\displaystyle a_{i,j}}$	${\displaystyle a_{i,j}\,\!}$
II. të grupuarë	x_2^3	${\displaystyle x_{2}^{3}}$
I. Derivate (mirë)	x'	${\displaystyle x'}$	${\displaystyle x'\,\!}$
Ia. Derivate (gabim HTML)	x^\prime	${\displaystyle x^{\prime }}$	${\displaystyle x^{\prime }\,\!}$
Ia. Derivate (gabim PNG)	x\prime	${\displaystyle x\prime }$	${\displaystyle x\prime \,\!}$
II. Derivate	\dot{x}, \ddot{x}	${\displaystyle {\dot {x}},{\ddot {x}}}$
III. Derivate	\hat a \bar b \vec c \widehat {d e f} \overline {g h i} \underline {j k l}	${\displaystyle {\hat {a}}\ {\bar {b}}\ {\vec {c}}\ {\widehat {def}}\ {\overline {ghi}}\ {\underline {jkl}}}$
Shuma	\sum_{k=1}^N k^2	${\displaystyle \sum _{k=1}^{N}k^{2}}$
Produkt	\prod_{i=1}^N x_i	${\displaystyle \prod _{i=1}^{N}x_{i}}$
Limit	\lim_{n \to \infty}x_n	${\displaystyle \lim _{n\to \infty }x_{n}}$
I. Integral	\int_{-N}^{N} e^x\, dx	${\displaystyle \int _{-N}^{N}e^{x}\,dx}$
II. Integral	\oint_{C} x^3\, dx + 4y^2\, dy	${\displaystyle \oint _{C}x^{3}\,dx+4y^{2}\,dy}$

Thyesat, matricat, formula e gjata

Për	Shkruhet në Wikipedia	Në Matematikë shkruhet si
I.Thyesat	\frac{2}{4} or {2 \over 4}	${\displaystyle {\frac {2}{4}}}$
II.Thyesat	\begin{matrix} \frac{2}{4} \end{matrix}	${\displaystyle {\begin{matrix}{\frac {2}{4}}\end{matrix}}}$
Koeficienti binomialëËË	{n \choose k}	${\displaystyle {n \choose k}}$
Matrica	\begin{matrix} x & y \\ z & v \end{matrix}	${\displaystyle {\begin{matrix}x&y\\z&v<br/>\end{matrix}}}$
	\begin{vmatrix} x & y \\ z & v \end{vmatrix}	${\displaystyle {\begin{vmatrix}x&y\\z&v<br/>\end{vmatrix}}}$
	\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}	${\displaystyle {\begin{Vmatrix}x&y\\z&v<br/>\end{Vmatrix}}}$
	\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix}	${\displaystyle {\begin{bmatrix}0&\cdots &0\\\vdots <br/>&\ddots &\vdots \\0&\cdots &<br/>0\end{bmatrix}}}$
	\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}	${\displaystyle {\begin{Bmatrix}x&y\\z&v<br/>\end{Bmatrix}}}$
	\begin{pmatrix} x & y \\ z & v \end{pmatrix}	${\displaystyle {\begin{pmatrix}x&y\\z&v<br/>\end{pmatrix}}}$
Funksonet me raste	f(n) = \begin{cases} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{cases}	${\displaystyle f(n)={\begin{cases}n/2,&{\mbox{if }}n{\mbox{ is even}}\\3n+1,&{\mbox{if }}n{\mbox{ is odd}}\end{cases}}}$
I.Ekuacione komplekse	\begin{matrix}f(n+1) & = & (n+1)^2 \\ \ & = & n^2 + 2n + 1 \end{matrix}	${\displaystyle {\begin{matrix}f(n+1)&=&(n+1)^{2}\\\ &=&n^{2}+2n+1\end{matrix}}}$
II.Ekuacione komplekse (tabela)	{| |- | <math>(n+1)</math><br><math>=(n+1)^2</math> |- | <math>=n^2 + 2n + 1</math> |}	|- | ${\displaystyle f(n+1)\,\!}$ | ${\displaystyle =(n+1)^{2}\,\!}$ |- | | ${\displaystyle =n^{2}+2n+1\,\!}$ |}

Simbolet shkronja dhe të ngjajshme

Më shumë rrethë simboleve matematikore të greqishtës së vjeter shiko Numrat Grekë

Për shkronjat	Shkruhet në Wikipedia	Në Matematikë shkruhet si
I. Greke	\alpha \beta \gamma \Gamma \phi \Phi \Psi\ \tau \Omega	${\displaystyle \alpha \ \beta \ \gamma \ \Gamma \ \phi \ \Phi \ \Psi \ \tau \ \Omega }$
I. Latine	x\in\mathbb{R}\sub\mathbb{C}	${\displaystyle x\in \mathbb {R} \subset \mathbb {C} }$
II. Greke	\boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma}	${\displaystyle {\boldsymbol {\alpha }}+{\boldsymbol {\beta }}+{\boldsymbol {\gamma }}}$
II. Latine	\mathbf{x}\cdot\mathbf{y} = 0	${\displaystyle \mathbf {x} \cdot \mathbf {y} =0}$

Kllapat dhe llojet e tyre

Për	Shkruhet në Wikipedia	Në Matematikë shkruhet si
Gabim	( \frac{1}{2} )	${\displaystyle ({\frac {1}{2}})}$
Mirë	\left ( \frac{1}{2} \right )	${\displaystyle \left({\frac {1}{2}}\right)}$

Për kllapa të	Shkruhet në Wikipedia	Në Matematikë shkruhet si
vogla	\left ( A \right )	${\displaystyle \left(A\right)}$
mesme	\left [A \right]	${\displaystyle \left[A\right]}$
mëdha	\left \{ A \right \}	${\displaystyle \left\{A\right\}}$
shigjetë	\left \langle A \right \rangle	${\displaystyle \left\langle A\right\rangle }$
vleres absolute	A \right | and \left \| B \right \|	${\displaystyle \left|A\right|and\left\|B\right\|}$
kombinuara		${\displaystyle \left[0,1\right)}$ ${\displaystyle \left\langle \psi \right|}$
e hapura, përdoreni \left. dhe \right nese nuk doni të mbyllni:	\left . \frac{A}{B} \right \} \to X	${\displaystyle \left.{\frac {A}{B}}\right\}\to X}$

Tabela e derivateve

Funksioni derivues	Funksioni
Funksioni	Funksioni i rregullt¹
${\displaystyle f(x)=0\;}$	${\displaystyle F(x)=C\;}$
${\displaystyle f(x)=k\;(k\in \mathbb {R} )}$	${\displaystyle F(x)=kx+C\;}$
${\displaystyle f(x)=1\;}$	${\displaystyle F(x)=x+C\;}$
${\displaystyle f(x)=x\;}$	${\displaystyle F(x)={\frac {1}{2}}x^{2}+C\;}$
${\displaystyle f(x)=2x\;}$	${\displaystyle F(x)=x^{2}\;}$
${\displaystyle f(x)=x^{2}\;}$	${\displaystyle F(x)={\frac {1}{3}}x^{3}\;}$
${\displaystyle f(x)=3x^{2}\;}$	${\displaystyle F(x)=x^{3}\;}$
${\displaystyle f(x)=qx^{q-1}\;(q\in \mathbb {R} )}$	${\displaystyle F(x)=x^{q}\;}$
${\displaystyle f(x)=x^{q}\;}$	${\displaystyle F(x)=\left\{{\begin{matrix}{\frac {x^{q+1}}{q+1}},&{\mbox{wenn }}q\neq -1\\\ln |x|,&{\mbox{wenn }}q=-1\end{matrix}}\right.}$
${\displaystyle f(x)=\sum _{n=0}^{N}nk_{n}x^{n-1}\;}$	${\displaystyle F(x)=\sum _{n=0}^{N}k_{n}x^{n}\;}$
${\displaystyle f(x)=\sum _{n=0}^{N}k_{n}x^{n}\;}$	${\displaystyle F(x)=\sum _{n=0}^{N}{\frac {k_{n}}{n+1}}x^{n+1}\;}$
${\displaystyle f(x)=e^{x}\;}$	${\displaystyle F(x)=e^{x}\;}$
${\displaystyle f(x)=e^{kx}\;}$	${\displaystyle F(x)={\frac {1}{k}}e^{kx}\;}$
${\displaystyle f(x)=a^{x}\ln a\;(a>0)}$	${\displaystyle F(x)=a^{x}\;}$
${\displaystyle f(x)=a^{x}\;(a>0)}$	${\displaystyle F(x)={\frac {a^{x}}{\ln a}}\;}$
${\displaystyle f(x)={\frac {-2}{x^{3}}}\;}$	${\displaystyle F(x)={\frac {1}{x^{2}}}\;}$
${\displaystyle f(x)={\frac {-1}{x^{2}}}\;}$	${\displaystyle F(x)={\frac {1}{x}}\;}$
${\displaystyle f(x)={\frac {1}{x}}\;}$	${\displaystyle F(x)=\ln \left|x\right|\;}$
${\displaystyle f(x)=\ln x\;}$	${\displaystyle F(x)=x\ln x-x\;}$
${\displaystyle f(x)={\frac {1}{x}}{\frac {1}{\ln a}}\;(a>0)}$	${\displaystyle F(x)=\log _{a}x\;}$
${\displaystyle f(x)=\log _{a}x\;(a>0)}$	${\displaystyle F(x)={\frac {1}{\ln a}}(x\ln x-x)\;}$
${\displaystyle f(x)=\sin x\;}$	${\displaystyle F(x)=-\cos x\;}$
${\displaystyle f(x)=\cos x\;}$	${\displaystyle F(x)=\sin x\;}$
${\displaystyle f(x)=\tan x\;}$	${\displaystyle F(x)=-\ln \left|\cos x\right|\;}$
${\displaystyle f(x)=\cot x\;}$	${\displaystyle F(x)=\ln \left|\sin x\right|\;}$
${\displaystyle f(x)={\frac {1}{\cos ^{2}x}}=1+\tan ^{2}x\;}$	${\displaystyle F(x)=\tan x\;}$
${\displaystyle f(x)={\frac {-1}{\sin ^{2}x}}=-(1+\cot ^{2}x)\;}$	${\displaystyle F(x)=\cot x\;}$
${\displaystyle f(x)=\arcsin x\;}$	${\displaystyle F(x)=x\;\arcsin x+{\sqrt {1-x^{2}}}\;}$
${\displaystyle f(x)=\arccos x\;}$	${\displaystyle F(x)=x\arccos \;x-{\sqrt {1-x^{2}}}\;}$
${\displaystyle f(x)=\arctan x\;}$	${\displaystyle F(x)=x\arctan x-{\frac {1}{2}}\ln \left(1+x^{2}\right)\;}$
${\displaystyle f(x)={\frac {1}{\sqrt {1-x^{2}}}}\;}$	${\displaystyle F(x)=\arcsin x\;}$
${\displaystyle f(x)={\frac {-1}{\sqrt {1-x^{2}}}}\;}$	${\displaystyle F(x)=\arccos x\;}$
${\displaystyle f(x)={\frac {1}{x^{2}+1}}\;}$	${\displaystyle F(x)=\arctan x\;}$
${\displaystyle f(x)={\frac {1}{(x^{2}+1)^{2}}}\;}$	${\displaystyle F(x)={\frac {1}{2}}\left({\frac {x}{x^{2}+1}}+\arctan x\right)\;}$
${\displaystyle f(x)=\sinh x\;}$	${\displaystyle F(x)=\cosh x\;}$
${\displaystyle f(x)=\cosh x\;}$	${\displaystyle F(x)=\sinh x\;}$
${\displaystyle f(x)=\tanh x\;}$	${\displaystyle F(x)=\ln \left|\cosh x\right|\;}$
${\displaystyle f(x)=\coth x\;}$	${\displaystyle F(x)=\ln \left|\sinh x\right|\;}$
${\displaystyle f(x)={\frac {1}{\cosh ^{2}x}}=1-\tanh ^{2}x\;}$	${\displaystyle F(x)=\tanh x\;}$
${\displaystyle f(x)={\frac {-1}{\sinh ^{2}x}}=1-\coth ^{2}x\;}$	${\displaystyle F(x)=\coth x\;}$
${\displaystyle f(x)=\operatorname {arsinh} \;x\;}$	${\displaystyle F(x)=x\;\operatorname {arsinh} \;x-{\sqrt {x^{2}+1}}\;}$
${\displaystyle f(x)=\operatorname {arcosh} \;x\;}$	${\displaystyle F(x)=x\;\operatorname {arcosh} \;x-{\sqrt {x^{2}-1}}\;}$
${\displaystyle f(x)=\operatorname {artanh} \;x\;}$	${\displaystyle F(x)=x\;\operatorname {artanh} \;x+{\frac {1}{2}}\ln {\left(1-x^{2}\right)}\;}$
${\displaystyle f(x)=\operatorname {arcoth} \;x\;}$	${\displaystyle F(x)=x\;\operatorname {arcoth} \;x+{\frac {1}{2}}\ln {\left(x^{2}-1\right)}\;}$
${\displaystyle f(x)={\frac {1}{\sqrt {x^{2}+1}}}\;}$	${\displaystyle F(x)=\operatorname {arsinh} \;x\;}$
${\displaystyle f(x)={\frac {1}{\sqrt {x^{2}-1}}}\;,\;x>1}$	${\displaystyle F(x)=\operatorname {arcosh} \;x\;}$
${\displaystyle f(x)={\frac {1}{1-x^{2}}}\;,\;\left|x\right|<1}$	${\displaystyle F(x)=\operatorname {artanh} \;x\;}$
${\displaystyle f(x)={\frac {1}{1-x^{2}}}\;,\;\left|x\right|>1}$	${\displaystyle F(x)=\operatorname {arcoth} \;x\;}$

Tabela e derivateve

Ableitungsfunktion	Funktion
Funktion	Stammfunktion¹
${\displaystyle f(x)=0\;}$	${\displaystyle F(x)=C\;}$
${\displaystyle f(x)=k\;(k\in \mathbb {R} )}$	${\displaystyle F(x)=kx+C\;}$
${\displaystyle f(x)=1\;}$	${\displaystyle F(x)=x+C\;}$
${\displaystyle f(x)=x\;}$	${\displaystyle F(x)={\frac {1}{2}}x^{2}+C\;}$
${\displaystyle f(x)=2x\;}$	${\displaystyle F(x)=x^{2}\;}$
${\displaystyle f(x)=x^{2}\;}$	${\displaystyle F(x)={\frac {1}{3}}x^{3}\;}$
${\displaystyle f(x)=3x^{2}\;}$	${\displaystyle F(x)=x^{3}\;}$
${\displaystyle f(x)=qx^{q-1}\;(q\in \mathbb {R} )}$	${\displaystyle F(x)=x^{q}\;}$
${\displaystyle f(x)=x^{q}\;}$	${\displaystyle F(x)=\left\{{\begin{matrix}{\frac {x^{q+1}}{q+1}},&{\mbox{wenn }}q\neq -1\\\ln |x|,&{\mbox{wenn }}q=-1\end{matrix}}\right.}$
${\displaystyle f(x)=\sum _{n=0}^{N}nk_{n}x^{n-1}\;}$	${\displaystyle F(x)=\sum _{n=0}^{N}k_{n}x^{n}\;}$
${\displaystyle f(x)=\sum _{n=0}^{N}k_{n}x^{n}\;}$	${\displaystyle F(x)=\sum _{n=0}^{N}{\frac {k_{n}}{n+1}}x^{n+1}\;}$
${\displaystyle f(x)=e^{x}\;}$	${\displaystyle F(x)=e^{x}\;}$
${\displaystyle f(x)=e^{kx}\;}$	${\displaystyle F(x)={\frac {1}{k}}e^{kx}\;}$
${\displaystyle f(x)=a^{x}\ln a\;(a>0)}$	${\displaystyle F(x)=a^{x}\;}$
${\displaystyle f(x)=a^{x}\;(a>0)}$	${\displaystyle F(x)={\frac {a^{x}}{\ln a}}\;}$
${\displaystyle f(x)={\frac {-2}{x^{3}}}\;}$	${\displaystyle F(x)={\frac {1}{x^{2}}}\;}$
${\displaystyle f(x)={\frac {-1}{x^{2}}}\;}$	${\displaystyle F(x)={\frac {1}{x}}\;}$
${\displaystyle f(x)={\frac {1}{x}}\;}$	${\displaystyle F(x)=\ln \left|x\right|\;}$
${\displaystyle f(x)=\ln x\;}$	${\displaystyle F(x)=x\ln x-x\;}$
${\displaystyle f(x)={\frac {1}{x}}{\frac {1}{\ln a}}\;(a>0)}$	${\displaystyle F(x)=\log _{a}x\;}$
${\displaystyle f(x)=\log _{a}x\;(a>0)}$	${\displaystyle F(x)={\frac {1}{\ln a}}(x\ln x-x)\;}$
${\displaystyle f(x)=\sin x\;}$	${\displaystyle F(x)=-\cos x\;}$
${\displaystyle f(x)=\cos x\;}$	${\displaystyle F(x)=\sin x\;}$
${\displaystyle f(x)=\tan x\;}$	${\displaystyle F(x)=-\ln \left|\cos x\right|\;}$
${\displaystyle f(x)=\cot x\;}$	${\displaystyle F(x)=\ln \left|\sin x\right|\;}$
${\displaystyle f(x)={\frac {1}{\cos ^{2}x}}=1+\tan ^{2}x\;}$	${\displaystyle F(x)=\tan x\;}$
${\displaystyle f(x)={\frac {-1}{\sin ^{2}x}}=-(1+\cot ^{2}x)\;}$	${\displaystyle F(x)=\cot x\;}$
${\displaystyle f(x)=\arcsin x\;}$	${\displaystyle F(x)=x\;\arcsin x+{\sqrt {1-x^{2}}}\;}$
${\displaystyle f(x)=\arccos x\;}$	${\displaystyle F(x)=x\arccos \;x-{\sqrt {1-x^{2}}}\;}$
${\displaystyle f(x)=\arctan x\;}$	${\displaystyle F(x)=x\arctan x-{\frac {1}{2}}\ln \left(1+x^{2}\right)\;}$
${\displaystyle f(x)={\frac {1}{\sqrt {1-x^{2}}}}\;}$	${\displaystyle F(x)=\arcsin x\;}$
${\displaystyle f(x)={\frac {-1}{\sqrt {1-x^{2}}}}\;}$	${\displaystyle F(x)=\arccos x\;}$
${\displaystyle f(x)={\frac {1}{x^{2}+1}}\;}$	${\displaystyle F(x)=\arctan x\;}$
${\displaystyle f(x)={\frac {1}{(x^{2}+1)^{2}}}\;}$	${\displaystyle F(x)={\frac {1}{2}}\left({\frac {x}{x^{2}+1}}+\arctan x\right)\;}$
${\displaystyle f(x)=\sinh x\;}$	${\displaystyle F(x)=\cosh x\;}$
${\displaystyle f(x)=\cosh x\;}$	${\displaystyle F(x)=\sinh x\;}$
${\displaystyle f(x)=\tanh x\;}$	${\displaystyle F(x)=\ln \left|\cosh x\right|\;}$
${\displaystyle f(x)=\coth x\;}$	${\displaystyle F(x)=\ln \left|\sinh x\right|\;}$
${\displaystyle f(x)={\frac {1}{\cosh ^{2}x}}=1-\tanh ^{2}x\;}$	${\displaystyle F(x)=\tanh x\;}$
${\displaystyle f(x)={\frac {-1}{\sinh ^{2}x}}=1-\coth ^{2}x\;}$	${\displaystyle F(x)=\coth x\;}$
${\displaystyle f(x)=\operatorname {arsinh} \;x\;}$	${\displaystyle F(x)=x\;\operatorname {arsinh} \;x-{\sqrt {x^{2}+1}}\;}$
${\displaystyle f(x)=\operatorname {arcosh} \;x\;}$	${\displaystyle F(x)=x\;\operatorname {arcosh} \;x-{\sqrt {x^{2}-1}}\;}$
${\displaystyle f(x)=\operatorname {artanh} \;x\;}$	${\displaystyle F(x)=x\;\operatorname {artanh} \;x+{\frac {1}{2}}\ln {\left(1-x^{2}\right)}\;}$
${\displaystyle f(x)=\operatorname {arcoth} \;x\;}$	${\displaystyle F(x)=x\;\operatorname {arcoth} \;x+{\frac {1}{2}}\ln {\left(x^{2}-1\right)}\;}$
${\displaystyle f(x)={\frac {1}{\sqrt {x^{2}+1}}}\;}$	${\displaystyle F(x)=\operatorname {arsinh} \;x\;}$
${\displaystyle f(x)={\frac {1}{\sqrt {x^{2}-1}}}\;,\;x>1}$	${\displaystyle F(x)=\operatorname {arcosh} \;x\;}$
${\displaystyle f(x)={\frac {1}{1-x^{2}}}\;,\;\left|x\right|<1}$	${\displaystyle F(x)=\operatorname {artanh} \;x\;}$
${\displaystyle f(x)={\frac {1}{1-x^{2}}}\;,\;\left|x\right|>1}$	${\displaystyle F(x)=\operatorname {arcoth} \;x\;}$

Për ndihmë më detalishtë gjeni në anglisht Ndihmë rreth formulava