∫0dx = C

∫1dx = x + C

$$\int_{}^{}{x^{k}\mathrm{d}x} = \frac{x^{k + 1}}{k + 1} + \mathrm{C}$$

$$\int_{}^{}{\frac{1}{x}\mathrm{d}x} = \ln\left| x \right| + \mathrm{C}$$

$$\int_{}^{}{a^{x}\mathrm{d}x} = \frac{a^{x}}{\ln a} + \mathrm{C}$$

∫e^xdx = e^x + C

∫sinxdx = −cosx + C

∫cosxdx = sinx + C

$$\int_{}^{}{\frac{1}{\operatorname{}x}\mathrm{d}x} = \tan x + \mathrm{C}$$

$$\int_{}^{}{\frac{1}{\operatorname{}x}\mathrm{d}x} = - \cot x + \mathrm{C}$$

$$\int_{}^{}{\frac{1}{1 + x^{2}}\mathrm{d}x} = \operatorname{}x + \mathrm{C} = - \operatorname{}x + \mathrm{C}$$

$$\int_{}^{}{\frac{1}{\sqrt{1 - x^{2}}}\mathrm{d}x} = \operatorname{}x + \mathrm{C} = - \operatorname{}x + \mathrm{C}$$

F(x)	F^′(x)
C	0
$$\sqrt{x}$$	$$\frac{1}{2\sqrt{x}}$$
x^k	kx^k − 1
sinx	cosx
cosx	−sinx
tanx	$$\frac{1}{\operatorname{}x}$$
cotx	$$- \frac{1}{\operatorname{}x}$$
e^x	e^x
a^x	a^xlna
lnx	$$\frac{1}{x}$$
x	$$\frac{1}{x\ln a}$$
x	$$\frac{1}{\sqrt{1 - x^{2}}}$$
x	$$- \frac{1}{\sqrt{1 - x^{2}}}$$
x	$$\frac{1}{1 + x^{2}}$$
x	$$- \frac{1}{1 + x^{2}}$$
[f(x)]^k	k[f(x)]^k − 1f^′(x)
e^f(x)	e^f(x)f^′(x)
a^f(x)	a^f(x)lnaf^′(x)
lnf(x)	$$\frac{f^{'}(x)}{f(x)}$$
f(x)	$$\frac{f^{'}(x)}{f(x)\ln a}$$