Funktionen/Stammfunktionen/Tabelle

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