広義積分
∫ a b f ( x ) d x := lim t → b − ∫ a t f ( x ) d x {\displaystyle \int _{a}^{b}f(x)\,dx\,:=\lim _{t\to b^{-}}\int _{a}^{t}f(x)\,dx} 、ここで lim x → b − | f ( x ) | = ∞ {\displaystyle \lim _{x\to b^{-}}|f(x)|=\infty }
∫ a b f ( x ) d x := lim t → a + ∫ t b f ( x ) d x {\displaystyle \int _{a}^{b}f(x)\,dx\,:=\lim _{t\to a^{+}}\int _{t}^{b}f(x)\,dx} 、ここで lim x → a + | f ( x ) | = ∞ {\displaystyle \lim _{x\to a^{+}}|f(x)|=\infty }
∫ a b f ( x ) d x := lim t → c − ∫ a t f ( x ) d x + lim t → c + ∫ t b f ( x ) d x {\displaystyle \int _{a}^{b}f(x)\,dx\,:=\lim _{t\to c^{-}}\int _{a}^{t}f(x)\,dx\,+\lim _{t\to c^{+}}\int _{t}^{b}f(x)\,dx} 、ここで lim x → c | f ( x ) | = ∞ {\displaystyle \lim _{x\to c}|f(x)|=\infty }