${\displaystyle {}x\geq -1}$

${\displaystyle {}n\in \mathbb {N} }$

${\displaystyle {}(1+x)^{n}\geq 1+nx\,.}$

${\displaystyle {}P,T\in K[X]}$

${\displaystyle {}T\neq 0}$

${\displaystyle {}Q,R\in K[X]}$

${\displaystyle P=TQ+R{\text{ und mit }}\operatorname {grad} \,(R)<\operatorname {grad} \,(T){\text{ oder }}R=0.}$

${\displaystyle {}I=[a,b]\subseteq \mathbb {R} }$

${\displaystyle f\colon [a,b]\longrightarrow \mathbb {R} }$

${\displaystyle {}x\in [a,b]}$

${\displaystyle f(x)\geq f(x'){\text{ für alle }}x'\in [a,b].}$

${\displaystyle f,g\colon [a,b]\longrightarrow \mathbb {R} }$

Dann gilt

${\displaystyle \int _{a}^{b}f(t)g'(t)\,dt=fg|_{a}^{b}-\int _{a}^{b}f'(t)g(t)\,dt.}$