基本积分公式
基本积分公式
$$1. \ \int{x^k}dx \ = \ \frac{1}{k \ + \ 1}x^{k + 1} \ + \ C,k \ne -1;$$
$
\left\{
\begin{matrix}
\int{\frac{1}{x^2}}dx = & -\frac{1}{x} + C \\
\int{\frac{1}{\sqrt{x}}}dx = & 2\sqrt{x} + C \\
\end{matrix}
\right.
$
$ \ $
$$2. \ \int{\frac{1}{x}}dx \ = \ \ln|x| \ + \ C$$
$ \ $
$$3. \ \int{e^x}dx \ = \ e^x \ + \ C;\int{a^x}dx \ = \ \frac{a^x}{\ln{a}} \ + \ C,a \ > 0且a \ \ne \ 1$$
$ \ $
$$4. \ \int{\sin{x}}dx \ = \ -\cos{x} \ + \ C$$
$ \ $
$$5. \ \int{\cos{x}}dx \ = \ \sin{x} \ + ...
基本求导公式
基本求导公式
$$1. \ (x^\alpha)^{\prime} \ = \ ax^{a \ - \ 1}$$
$ \ $
$$2. \ (a^x)^{\prime} \ = \ (a^x)\ln{a} \ \ \ (a>0, \ a \neq 1)$$
$ \ $
$$3. \ (e^x)^{\prime} \ = \ e^x$$
$ \ $
$$4. \ (log_ax)^{\prime} \ = \ \frac{1}{x\ln{a}} \ \ \ (a>0,a \neq 1)$$
$ \ $
$$5. \ (\ln{x})^{\prime} \ = \ \frac{1}{x}$$
$ \ $
$$6. \ (sinx)^{\prime} \ = \ cosx$$
$ \ $
$$7. \ (cosx)^{\prime} \ = \ -sinx$$
$ \ $
$$8. \ (\arcsin{x})^{\prime} \ = \ \frac{1}{\sqrt{1 \ - \ x^2}}$$
$ \ $
$$9. \ (\arccos{x})^{\prime} \ = ...
三角公式
三角函数
三角函数的基本关系
$$1. \ csc\alpha \ = \ \frac{1}{sinα}$$
$ \ $
$$2. \ secα \ = \ \frac{1}{cosα}$$
$ \ $
$$3.\ cot\alpha \ = \ \frac{1}{tan\alpha}$$
$ \ $
$$4.\ tan\alpha \ = \ \frac{sin\alpha}{cos\alpha}$$
$ \ $
$$5.\ cot\alpha \ = \ \frac{cos\alpha}{sin\alpha}$$
$ \ $
$$6.\ sin^2{\alpha} \ + \ cos^2{\alpha} \ = \ 1$$
$ \ $
$$7. \ tan^2{\alpha} \ + \ 1 \ = \ sec^2{\alpha}$$
$ \ $
$$8.\ cot^2{\alpha} \ + \ 1 \ = \ csc^2{\alpha}$$
倍角公式
$$1. \ sin{2\alpha} \ = \ 2sin\alpha cos\alpha$$
$ \ $
$$2.\ c ...
