Tot seguit es presenta una llista de primitives de funcions exponencials. Per consultar una llista completa de primitives de tota mena de funcions adreceu-vos a taula d'integrals
![{\displaystyle \int e^{cx}\;\mathrm {d} x={\frac {1}{c}}e^{cx}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f8a2d8d0ed5abc7ccb0bd31adf4274be7dd54ea)
per ![{\displaystyle a>0,\ a\neq 1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c27d65d4a22ff9cb56ae8562f0ba1ee2b4a7f120)
![{\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 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)
![{\displaystyle \int {\frac {e^{cx}}{x}}\;\mathrm {d} x=\ln |x|+\sum _{n=1}^{\infty }{\frac {(cx)^{n}}{n\cdot n!}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5c73c96bbd063b40cd6bb1ced9c96f8d98a5de8f)
![{\displaystyle \int {\frac {e^{cx}}{x^{n}}}\;\mathrm {d} x={\frac {1}{n-1}}\left(-{\frac {e^{cx}}{x^{n-1}}}+c\int {\frac {e^{cx}}{x^{n-1}}}\,\mathrm {d} x\right)\qquad {\mbox{(per }}n\neq 1{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2d634752e86020458c41e32159dd11cd4d8bd7fc)
![{\displaystyle \int e^{cx}\ln x\;\mathrm {d} x={\frac {1}{c}}e^{cx}\ln |x|-\operatorname {Ei} \,(cx)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac3ea804792382d0e90e6af19b854052e67e0530)
![{\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 xe^{cx^{2}}\;\mathrm {d} x={\frac {1}{2c}}\;e^{cx^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eaad8f6cee041e8e3ce3a611f8ebaf9df994ce1b)
(
és la funció error)
![{\displaystyle \int xe^{-cx^{2}}\;\mathrm {d} x=-{\frac {1}{2c}}e^{-cx^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/30467d4ac29c992b8fd62db75447783e08e374df)
![{\displaystyle \int {1 \over \sigma {\sqrt {2\pi }}}\,e^{-{(x-\mu )^{2}/2\sigma ^{2}}}\;\mathrm {d} x={\frac {1}{2}}(1+{\mbox{erf}}\,{\frac {x-\mu }{\sigma {\sqrt {2}}}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c577a02dcfd86160c996baeea21118ed916be697)
- on
![{\displaystyle c_{2j}={\frac {1\cdot 3\cdot 5\cdots (2j-1)}{2^{j+1}}}={\frac {(2j)\,!}{j!\,2^{2j+1}}}\ .}](https://wikimedia.org/api/rest_v1/media/math/render/svg/90dd5e5695126e16ae330b936f2ae1abc90fcf3a)
Integració |
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Càlcul de primitives | | ![{\displaystyle \int _{a}^{b}f(x)\,dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac02adeed584466d53dee65f3228ad66939eb58b) |
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Taules d'integrals | |
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Definicions d'integració | |
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Extensions de la integral | |
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Integració numèrica | |
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