Funktionen/Stammfunktionen/Tabelle

Funktion	Stammfunktion	Bemerkung	Link
${}x^{n}$	${}{\frac {1}{n+1}}x^{n+1}$	${}n\in \mathbb {N}$
${}x^{n}$	${}{\frac {1}{n+1}}x^{n+1}$	${}x\neq 0$ , ${}n\in \mathbb {Z} ,\,n\neq -1$
${}x^{a}$	${}{\frac {1}{a+1}}x^{a+1}$	${}x\in \mathbb {R} _{+}$ , ${}a\in \mathbb {R} ,\,a\neq -1$	${}\bullet$
${}x^{-1}$	${}\ln x$	${}x\in \mathbb {R} _{+}$	${}\bullet$
${}\ln x$	${}x\ln x-x$	${}x\in \mathbb {R} _{+}$	${}\bullet$
${}\exp x$	${}\exp x$		${}\bullet$
${}\sinh x$	${}\cosh x$
${}\cosh x$	${}\sinh x$
${}\sin x$	${}-\cos x$		${}\bullet$
${}\cos x$	${}\sin x$		${}\bullet$
${}\tan x$	${}-\ln(\cos x)$	${}x\in \mathbb {R} ,\,-{\frac {\pi }{2}}<x<{\frac {\pi }{2}}$	${}\bullet$
${}{\frac {1}{x^{2}+1}}$	${}\arctan x$	${}x\in \mathbb {R}$	${}\bullet$
${}{\frac {1}{x^{2}+bx+c}}$	${}{\frac {1}{\sqrt {-\triangle }}}\arctan {\frac {1}{\sqrt {-\triangle }}}{\left(x+{\frac {b}{2}}\right)}$	${}\triangle ={\frac {b^{2}-4c}{4}}<0$	${}\bullet$
${}{\frac {1}{1-x^{2}}}$	${}{\frac {1}{2}}\ln {\frac {1+x}{1-x}}={\frac {1}{2}}{\left(\ln \left(1+x\right)-\ln \left(1-x\right)\right)}$	${}x\in \mathbb {R} ,\,-1<x<1$	${}\bullet$
${}{\frac {1}{\cos ^{2}x}}$	${}\tan x$	${}x\in \mathbb {R} ,\,-{\frac {\pi }{2}}<x<{\frac {\pi }{2}}$	${}\bullet$
${}{\sqrt {x^{2}-1}}$	${}{\frac {1}{2}}{\left(x\cdot {\sqrt {x^{2}-1}}-\,\operatorname {arcosh} \,x\,\right)}$	${}\vert {x}\vert \geq 1$	${}\bullet$ oder ${}\bullet$
${}{\sqrt {1-x^{2}}}$	${}{\frac {1}{2}}{\left(x\cdot {\sqrt {1-x^{2}}}+\arcsin x\right)}$	${}x\in \mathbb {R} ,\,-1<x<1$	${}\bullet$ oder ${}\bullet$
${}{\sqrt {x^{2}+1}}$	${}{\frac {1}{2}}{\left(x\cdot {\sqrt {x^{2}+1}}+\,\operatorname {arsinh} \,x\,\right)}$		${}\bullet$
${}{\frac {1}{\sqrt {x^{2}+1}}}$	${}\,\operatorname {arsinh} \,x\,$		${}\bullet$
${}{\frac {1}{\sqrt {x^{2}-1}}}$	${}\,\operatorname {arcosh} \,x\,$	${}\vert {x}\vert >1$	${}\bullet$
${}{\frac {1}{\sqrt {1-x^{2}}}}$	${}\arcsin x$	${}-1\leq x\leq 1$	${}\bullet$

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