指数関数の原始関数の一覧
∫ e c x sin n  x d x = e c x sin n − 1  x c 2 + n 2 ( c sin  x − n cos  x ) + n ( n − 1 ) c 2 + n 2 ∫ e c x sin n − 2  x d x {\displaystyle \int e^{cx}\sin ^{n}x\;\mathrm {d} x={\frac {e^{cx}\sin ^{n-1}x}{c^{2}+n^{2}}}(c\sin x-n\cos x)+{\frac {n(n-1)}{c^{2}+n^{2}}}\int e^{cx}\sin ^{n-2}x\;\mathrm {d} x}
∫ e c x cos n  x d x = e c x cos n − 1  x c 2 + n 2 ( c cos  x + n sin  x ) + n ( n − 1 ) c 2 + n 2 ∫ e c x cos n − 2  x d x {\displaystyle \int e^{cx}\cos ^{n}x\;\mathrm {d} x={\frac {e^{cx}\cos ^{n-1}x}{c^{2}+n^{2}}}(c\cos x+n\sin x)+{\frac {n(n-1)}{c^{2}+n^{2}}}\int e^{cx}\cos ^{n-2}x\;\mathrm {d} x}
∫ x e c x 2 d x = 1 2 c e c x 2 {\displaystyle \int xe^{cx^{2}}\;\mathrm {d} x={\frac {1}{2c}}\;e^{cx^{2}}}