Całki funkcji wykładniczych

$\int e^{x}dx=e^x$

$\int e^{cx}dx=\frac{1}{c}{e}^{cx}$

$\int a^{x}dx=\frac{a^x}{\ln (a)}\text{(dla }a>0,a\ne 1\text{)}$

$\int a^{cx}dx=\frac{1}{c\ln a}{a}^{cx}\text{(dla }a>0,a\ne 1,c\ne 0\text{)}$

$\int x{e}^{cx}dx=\frac{e^{cx}}{c^2}(cx-1)$

$\int x^2{e}^{cx}dx=e^{cx}(\frac{x^2}{c}-\frac{2x}{c^2}+\frac{2}{c^3})$

$\int x^n{e}^{cx}dx=\frac{1}{c}{x}^n{e}^{cx}-\frac{n}{c}\int x^{n-1}{e}^{cx}dx$

$\int \frac{e^{cx}dx}{x}=\ln |x|+\sum _{i=1}^{\mathrm{\infty }}\frac{(cx{)}^i}{i\cdot i!}$

$\int \frac{e^{cx}dx}{x^n}=\frac{1}{n-1}(-\frac{e^{cx}}{x^{n-1}}+c\int \frac{e^{cx}dx}{x^{n-1}})\text{(dla }n\ne 1\text{)}$

$\int e^{cx}\ln xdx=\frac{1}{c}(e^{cx}\ln |x|-\int \frac{e^{cx}dx}{x})$

$\int e^{cx}\sin bxdx=\frac{e^{cx}}{c^2+b^2}(c\sin bx-b\cos bx)$

$\int e^{cx}\cos bxdx=\frac{e^{cx}}{c^2+b^2}(c\cos bx+b\sin bx)$

$\int e^{cx}{\sin }^{2}bxdx=\frac{e^{cx}(c^2(1-\cos 2bx)-2bc\sin 2bx+4b^2)}{2c(4b^2+c^2)}$

$\int e^{cx}{\cos }^{2}bxdx=\frac{e^{cx}(c^2(1+\cos 2bx)+2bc\sin 2bx+4b^2)}{2c(4b^2+c^2)}$

$\int e^{cx}{\sin }^{n}xdx=\frac{e^{cx}{\sin }^{n-1}x}{c^2+n^2}(c\sin x-n\cos x)+\frac{n(n-1)}{c^2+n^2}\int e^{cx}{\sin }^{n-2}xdx$

$\int e^{cx}{\cos }^{n}xdx=\frac{e^{cx}{\cos }^{n-1}x}{c^2+n^2}(c\cos x+n\sin x)+\frac{n(n-1)}{c^2+n^2}\int e^{cx}{\cos }^{n-2}xdx$

$\int e^{cx}\cdot {\sin }^{n}bxdx=\frac{1}{c}{\sin }^{n}bx\cdot e^{cx}-\frac{nb}{c}\int {\sin }^{n-1}bx\cdot \cos bx\cdot e^{cx}dx$

$\int e^{cx}\cdot {\cos }^{n}bxdx=\frac{1}{c}{\cos }^{n}bx\cdot e^{cx}+\frac{nb}{c}\int {\cos }^{n-1}bx\cdot \sin bx\cdot e^{cx}dx$

$\int \frac{1}{\sigma \sqrt{2\pi }}{e}^{-(x-\mu {)}^2/2{\sigma }^2}dx=\frac{1}{2\sigma }(1+\text{erf}\frac{x-\mu }{\sigma \sqrt{2}})$