Dari Wikipedia Indonesia, artikel bebas.

 

\int e^{cx}\;dx = \frac{1}{c} e^{cx}
0,\mbox{ }a \ne 1\mbox{)}” />
\int xe^{cx}\; dx = \frac{e^{cx}}{c^2}(cx-1)
\int x^2 e^{cx}\;dx = e^{cx}\left(\frac{x^2}{c}-\frac{2x}{c^2}+\frac{2}{c^3}\right)
\int x^n e^{cx}\; dx = \frac{1}{c} x^n e^{cx} - \frac{n}{c}\int x^{n-1} e^{cx} dx
\int\frac{e^{cx}}{x}\; dx = \ln|x| +\sum_{i=1}^\infty\frac{(cx)^i}{i\cdot i!}
\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{(untuk }n\neq 1\mbox{)}
\int e^{cx}\ln x\; dx = \frac{1}{c}e^{cx}\ln|x|-\operatorname{Ei}\,(cx)
\int e^{cx}\sin bx\; dx = \frac{e^{cx}}{c^2+b^2}(c\sin bx - b\cos bx)
\int e^{cx}\cos bx\; dx = \frac{e^{cx}}{c^2+b^2}(c\cos bx + b\sin bx)
\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
\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
\int x e^{c x^2 }\; dx= \frac{1}{2c} \;  e^{c x^2}
\int e^{-c x^2 }\; dx= \sqrt{\frac{\pi}{4c}} \mbox{erf}(\sqrt{c} x)(erf adalah fungsi kesalahan/error function)
\int xe^{-c x^2 }\; dx=-\frac{1}{2c}e^{-cx^2}
\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}})
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dimana  c_{2j}=\frac{ 1 \cdot 3 \cdot 5 \cdots (2j-1)}{2^{j+1}}=\frac{(2j)\,!}{j!\, 2^{2j+1}} \ .

 

Integral Tertentu

 

0)” /> (integral Gauss)
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-1,a>0) \\
\frac{(2k-1)!!}{2^{k+1}a^k}\sqrt{\frac{\pi}{a}} & (n=2k, k \;\text{bilangan bulat}, a>0) \\
\frac{k!}{2a^{k+1}} & (n=2k+1,k \;\text{bilangan bulat}, a>0)
\end{cases} ” />
-1,a>0) \\
\frac{n!}{a^{n+1}} & (n=0,1,2,\ldots,a>0) \\
\end{cases}” />
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\int_{0}^{2 \pi} e^{x \cos \theta} d \theta = 2 \pi I_{0}(x) (I0 adalah perubahan dari fungsi Bessel jenis pertama)
\int_{0}^{2 \pi} e^{x \cos \theta + y \sin \theta} d \theta = 2 \pi I_{0} \left( \sqrt{x^2 + y^2} \right)