Slijedi popis integrala (antiderivacija funkcija) eksponencijalnih funkcija. Za potpun popis integrala funkcija, pogledati tablica integrala i popis integrala.
, ali ![{\displaystyle \int e^{2x}\;dx=2e^{2x}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7acf1b6f1d20770c854cbe3861ea23b07eb7b2fb)
![{\displaystyle \int a^{cx}\;dx={\frac {1}{c\ln a}}a^{cx}+C\qquad {\mbox{(za }}a>0,{\mbox{ }}a\neq 1{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b01876140f3c40b60d93b01796532197950b3013)
![{\displaystyle \int xe^{cx}\;dx={\frac {e^{cx}}{c^{2}}}(cx-1)+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/222be7594266ff3bc9c16056966d5d3c8d0b7ede)
![{\displaystyle \int x^{2}e^{cx}\;dx=e^{cx}\left({\frac {x^{2}}{c}}-{\frac {2x}{c^{2}}}+{\frac {2}{c^{3}}}\right)+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6d56b1c80dbc489f7c84e257374303344a0e55c7)
![{\displaystyle \int x^{n}e^{cx}\;dx={\frac {1}{c}}x^{n}e^{cx}-{\frac {n}{c}}\int x^{n-1}e^{cx}dx+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e588b858eda4fa4c20311f3a8344de123398d4de)
![{\displaystyle \int {\frac {e^{cx}}{x}}\;dx=\ln |x|+\sum _{i=1}^{\infty }{\frac {(cx)^{i}}{i\cdot i!}}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/21340a87db276462549b58eca363966ac564e9cc)
![{\displaystyle \int {\frac {e^{cx}}{x^{n}}}\;dx={\frac {1}{n-1}}\left(-{\frac {e^{cx}}{x^{n-1}}}+c\int {\frac {e^{cx}}{x^{n-1}}}\,dx\right)+C\qquad {\mbox{(za }}n\neq 1{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5b19cbe5cb163f11e3c888a490b23b7737b6df22)
![{\displaystyle \int e^{cx}\ln x\;dx={\frac {1}{c}}e^{cx}\ln |x|-\operatorname {Ei} \,(cx)+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a0e0bbbb7c5e4aee9a19c6c5097d2af936e0e8)
![{\displaystyle \int e^{cx}\sin bx\;dx={\frac {e^{cx}}{c^{2}+b^{2}}}(c\sin bx-b\cos bx)+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3a89524f25659f60ff8d2aec9033fe6040475692)
![{\displaystyle \int e^{cx}\cos bx\;dx={\frac {e^{cx}}{c^{2}+b^{2}}}(c\cos bx+b\sin bx)+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/17feacf41ac2d00911057368a8910c0c8209010a)
![{\displaystyle \int e^{cx}\sin ^{n}x\;dx={\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\;dx+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/51c949e7cee1b752f09d3bd0fbcb694da50f4b8c)
![{\displaystyle \int e^{cx}\cos ^{n}x\;dx={\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\;dx+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d22e28d211fb4b5e75a96e0c26fdfb3a1e3ef8e8)
![{\displaystyle \int xe^{cx^{2}}\;dx={\frac {1}{2c}}\;e^{cx^{2}}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/84c093fc04503c3cc314d327353b3feef6346ee2)
(
je funkcija grješke (error function))
![{\displaystyle \int xe^{-cx^{2}}\;dx=-{\frac {1}{2c}}e^{-cx^{2}}+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/36a7ad5511d962fc66f51062427ff4b158f093f0)
![{\displaystyle \int {1 \over \sigma {\sqrt {2\pi }}}\,e^{-{(x-\mu )^{2}/2\sigma ^{2}}}\;dx={\frac {1}{2}}(1+{\mbox{erf}}\,{\frac {x-\mu }{\sigma {\sqrt {2}}}})+C}](https://wikimedia.org/api/rest_v1/media/math/render/svg/46d84edb2464f40f5beac824a9d77a18b391b8e7)
- pri čemu je
![{\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)
- (Gaussov integral)
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- (!! je dvostruka faktorijela)
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- ( je modificirana Besselova funkcija prve vrste)
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