指数関数の原始関数の一覧
}{a^{n+1}}}&(n=0,1,2,\ldots ,a>0)\\\end{cases}}}
∫ 0 ∞ e − a x b d x = 1 b a − 1 b Γ ( 1 b ) {\displaystyle \int _{0}^{\infty }e^{-ax^{b}}dx={\frac {1}{b}}\ a^{-{\frac {1}{b}}}\,\Gamma \left({\frac {1}{b}}\right)}
∫ 0 ∞ x n e − a x b d x = 1 b a − n + 1 b Γ ( n + 1 b ) {\displaystyle \int _{0}^{\infty }x^{n}e^{-ax^{b}}dx={\frac {1}{b}}\ a^{-{\frac {n+1}{b}}}\,\Gamma \left({\frac {n+1}{b}}\right)}
∫ 0 ∞ e − a x sin  b x d x = b a 2 + b 2 ( a > 0 ) {\displaystyle \int _{0}^{\infty }e^{-ax}\sin bx\,\mathrm {d} x={\frac {b}{a^{2}+b^{2}}}\quad (a>0)}
∫ 0 ∞ e − a x cos  b x d x = a a 2 + b 2 ( a > 0 ) {\displaystyle \int _{0}^{\infty }e^{-ax}\cos bx\,\mathrm {d} x={\frac {a}{a^{2}+b^{2}}}\quad (a>0)}