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1. 三角函数

1.1 cosx、secx

1.2 sinx、cscx

1.3 tanx、cotx

1.4 $\int se{c}^{2}xdx、\int cs{c}^{2}xdx$

$$\int se{c}^{2}xdx=tanx+C$$

$$\int cs{c}^{2}xdx=cotx+C$$

1.5 $\int secdx、\int cscdx$

$\int secxdx=ln|secx+tanx|+C$

$\int cscxdx=ln|cscx-cotx|+C$

1.6 $\int secxtanxdx、\int cscxcotxdx$

$\int secxtanxdx=\int \frac{sinx}{co{s}^{2}x}dx=secx+C$

$\int cscxcotxdx=\int \frac{cosx}{si{n}^{2}x}dx=cscx+C$

2. 反三角函数

2.1 arcsinx、arctanx

2.2 arccosx

3. 代数

3.1 $\int \frac{1}{\sqrt{1-x^2}}dx$

$\int \frac{1}{\sqrt{a^2-x^2}}dx=arcsin\frac{x}{a}+C$

3.2 $\int \frac{1}{1+x^2}dx$

$\int \frac{1}{a^2+x^2}dx=\frac{1}{a}arctan\frac{x}{a}+C$

3.3 $\int \frac{1}{\sqrt{x^2\pm a^2}}dx$

$\int \frac{1}{\sqrt{x^2+a^2}}dx=ln(x+\sqrt{x^2+a^2})+C$

$\int \frac{1}{\sqrt{x^2-a^2}}dx=ln|x+\sqrt{x^2-a^2}|+C$

3.4 $\int \frac{1}{x^2-a^2}dx$

$\int \frac{1}{x^2-a^2}dx=\frac{1}{2a}ln|\frac{x-a}{x+a}|+C$

3.5 $\int \sqrt{a^2-x^2}dx$

$\int \sqrt{a^2-x^2}dx=\frac{a^2}{2}arcsin\frac{x}{a}+\frac{1}{2}x\sqrt{a^2-x^2}+C$