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Questa pagina contiene una tavola di integrali indefiniti di funzioni esponenziali. Per altri integrali, vedi Tavole di integrali.
![{\displaystyle \int e^{cx}\;\mathrm {d} x={\frac {1}{c}}e^{cx}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f8a2d8d0ed5abc7ccb0bd31adf4274be7dd54ea)
![{\displaystyle \int a^{cx}\;\mathrm {d} x={\frac {1}{c\log a}}a^{cx}\qquad {\mbox{(per }}a>0,{\mbox{ }}a\neq 1{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b1a3b51e83a188ca599057f189ab926473da3524)
![{\displaystyle \int x^{n}e^{cx}\;\mathrm {d} x={\frac {1}{c}}x^{n}e^{cx}-{\frac {n}{c}}\int x^{n-1}e^{cx}\mathrm {d} x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1d2ff7be7a2de8cff1c308f9e9ca9e7b22b68939)
che ha, come casi particolari:
![{\displaystyle \int xe^{cx}\;\mathrm {d} x={\frac {e^{cx}}{c^{2}}}(cx-1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/500198d16fb049f067c35b7e7cb88d132fcb7783)
![{\displaystyle \int x^{2}e^{cx}\;\mathrm {d} x=e^{cx}\left({\frac {x^{2}}{c}}-{\frac {2x}{c^{2}}}+{\frac {2}{c^{3}}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5e267454873adf7adc1827062f44cad4d17488c2)
![{\displaystyle \int {\frac {e^{cx}\;\mathrm {d} x}{x}}=\log |x|+\sum _{i=1}^{\infty }{\frac {(cx)^{i}}{i\cdot i!}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7570b57f89059a3879b41b01ba13ab6a4f2d91bd)
![{\displaystyle \int {\frac {e^{cx}\;\mathrm {d} x}{x^{n}}}={\frac {1}{n-1}}\left(-{\frac {e^{cx}}{x^{n-1}}}+c\int {\frac {e^{cx}\mathrm {d} x}{x^{n-1}}}\right)\qquad {\mbox{(per }}n\neq 1{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f5507773179c6c1aafb313c6af3b966ccd724d8f)
![{\displaystyle \int e^{cx}\ln x\;\mathrm {d} x={\frac {1}{c}}\left(e^{cx}\log |x|-\int {\frac {e^{cx}\mathrm {d} x}{x}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5b07a892b7c3b239a5a8ee30bd0f9f541e91b388)
![{\displaystyle \int e^{cx}\sin bx\;\mathrm {d} x={\frac {e^{cx}}{c^{2}+b^{2}}}(c\sin bx-b\cos bx)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/95923c67929de601326519b6d3691da8753eb74f)
![{\displaystyle \int e^{cx}\cos bx\;\mathrm {d} x={\frac {e^{cx}}{c^{2}+b^{2}}}(c\cos bx+b\sin bx)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1df7aee04b3bc5dade2f76b500551f19e43ee7b9)
![{\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}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d8f62ae0a81bf35f4e80680484429d46032ac888)
![{\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}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a91207df8692dd303615aee89b17de3c86b72079)
![{\displaystyle \int {1 \over \sigma {\sqrt {2\pi }}}\,e^{-{(x-\mu )^{2}/2\sigma ^{2}}}\;={\mbox{erf}}\,{\frac {x-\mu }{\sigma {\sqrt {2}}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d7ce038b6f5f3bfbaac898b088f4ae5db5c160c6)
- Murray R. Spiegel, Manuale di matematica, Etas Libri, 1974, p. 85.