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}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5906c7ce8d80672528613fc3c73346d405c1acff)
![{\displaystyle \int a^{cx}\;dx={\frac {1}{c\ln a}}a^{cx}\qquad {\mbox{(za }}a>0,{\mbox{ }}a\neq 1{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff1e1a637ebc2b089f913d224f624cc761332090)
![{\displaystyle \int xe^{cx}\;dx={\frac {e^{cx}}{c^{2}}}(cx-1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/87ff3c663e08f40dd34fa65558256af1342960eb)
![{\displaystyle \int x^{2}e^{cx}\;dx=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/9bf04c5671a90775331e9062a01822af1d47d686)
![{\displaystyle \int x^{n}e^{cx}\;dx={\frac {1}{c}}x^{n}e^{cx}-{\frac {n}{c}}\int x^{n-1}e^{cx}dx}](https://wikimedia.org/api/rest_v1/media/math/render/svg/418fe2b2ced06b6c35b56ca4fced07c89109d160)
![{\displaystyle \int {\frac {e^{cx}}{x}}\;dx=\ln |x|+\sum _{i=1}^{\infty }{\frac {(cx)^{i}}{i\cdot i!}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6b51608dff20f79047ff3b7dd5f6fc75c61fe46b)
![{\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)\qquad {\mbox{(za }}n\neq 1{\mbox{)}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fb47cec2ed8f1491c83496834d2f371c0b639a00)
![{\displaystyle \int e^{cx}\ln x\;dx={\frac {1}{c}}e^{cx}\ln |x|-\operatorname {Ei} \,(cx)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/33053d64f5ae7f565b07031b02709dc50ee5a109)
![{\displaystyle \int e^{cx}\sin bx\;dx={\frac {e^{cx}}{c^{2}+b^{2}}}(c\sin bx-b\cos bx)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b3a37bb249edda5a8d96162f04099cbb2e5720)
![{\displaystyle \int e^{cx}\cos bx\;dx={\frac {e^{cx}}{c^{2}+b^{2}}}(c\cos bx+b\sin bx)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aa3160015214a668d9826f6d1e85dcb7ad045609)
![{\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}](https://wikimedia.org/api/rest_v1/media/math/render/svg/014136db6b329795471836ce4ac17c86fffbf1cb)
![{\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}](https://wikimedia.org/api/rest_v1/media/math/render/svg/560942803e654f1b9f1445ce5589a24c3c0ef7ab)
![{\displaystyle \int xe^{cx^{2}}\;dx={\frac {1}{2c}}\;e^{cx^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/220b75633319a42d23352dd64fefbf79e52a4cf9)
(
je funkcija grješke (error function))
![{\displaystyle \int xe^{-cx^{2}}\;dx=-{\frac {1}{2c}}e^{-cx^{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f1ba4db4374554cd90897b040accccc43e1f7430)
![{\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}}}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/21cd5019b6294ee13f9a8af844adc8eb7974d339)
- 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)
Određeni integrali
(Gaussov integral)
![{\displaystyle \int _{-\infty }^{\infty }e^{-ax^{2}}\,dx={\sqrt {\pi \over a}}\quad (a>0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d173c3a0a51d1491a0c0ccb21456ec842d991df1)
![{\displaystyle \int _{-\infty }^{\infty }e^{-ax^{2}}e^{2bx}\,dx={\sqrt {\frac {\pi }{a}}}e^{\frac {b^{2}}{a}}\quad (a>0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/81a377ff06dee538239ee1a04e326ccbb2335231)
![{\displaystyle \int _{-\infty }^{\infty }xe^{-a(x-b)^{2}}\,dx=b{\sqrt {\pi \over a}}\quad (a>0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/192453db1fb4691126e316dcd81ef42be04f0205)
![{\displaystyle \int _{-\infty }^{\infty }x^{2}e^{-ax^{2}}\,dx={\frac {1}{2}}{\sqrt {\pi \over a^{3}}}\quad (a>0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bdc40a04ccfabe052e1faa2b0bc367c3b712a21c)
(!! je dvostruka faktorijela)
![{\displaystyle \int _{0}^{\infty }x^{n}e^{-ax}\,dx={\begin{cases}{\frac {\Gamma (n+1)}{a^{n+1}}}&(n>-1,a>0)\\{\frac {n!}{a^{n+1}}}&(n=0,1,2,\ldots ,a>0)\\\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/234d4f9a806812d4454fa8fcb2b1335dd17d6fb7)
![{\displaystyle \int _{0}^{\infty }e^{-ax}\sin bx\,dx={\frac {b}{a^{2}+b^{2}}}\quad (a>0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/10f8d0c56030576a9ea5c32fdcc26da56cf84bc7)
![{\displaystyle \int _{0}^{\infty }e^{-ax}\cos bx\,dx={\frac {a}{a^{2}+b^{2}}}\quad (a>0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a4ecb94f832c0bd6d7d22c0d1a6a0a2d05f982f9)
![{\displaystyle \int _{0}^{\infty }xe^{-ax}\sin bx\,dx={\frac {2ab}{(a^{2}+b^{2})^{2}}}\quad (a>0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4364f14319b127a45b9e81e92c7777ba6a850e2a)
![{\displaystyle \int _{0}^{\infty }xe^{-ax}\cos bx\,dx={\frac {a^{2}-b^{2}}{(a^{2}+b^{2})^{2}}}\quad (a>0)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d93ccc76421b3d124dcedd0972c92a9769063658)
(
je modificirana Besselova funkcija prve vrste)
![{\displaystyle \int _{0}^{2\pi }e^{x\cos \theta +y\sin \theta }d\theta =2\pi I_{0}\left({\sqrt {x^{2}+y^{2}}}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8cc7da0077239149468cbcc5eb3576109c8d0d4d)