数学-基本积分公式

1. $ \int kdx = kx + C $
   1. 特别地 $\int 0dx = C $
2. $\int x^{\mu}dx = \frac{x^{ \mu +1}}{ \mu+1} + C$
3. $\int \frac{1}{x}dx = ln\left | x \right | + C$
4. $\int a^xdx = \frac{a^x}{lna} + C$
1. 特别地 $\int e^xdx = e^x + C$
5. $\int cosxdx = sinx + C$
6. $\int sinxdx = -cosx + C$
7. $\int sec^2xdx = tanx + C$
8. $\int csc^2xdx = -cotx + C$
9. $\int secxtanxdx = secx + C$
10. $\int cscxcotxdx = -cscx + C$
11. $\int \frac{dx}{\sqrt{a^2 - x^2}} = arcsin \frac{x}{a} + C$　　
    1. 特别地 $\int \frac{dx}{\sqrt{1 - x^2}} = arcsinx + C$
12. $\int \frac{dx}{a^2 + x^2} = \frac{1}{a}arctan \frac{x}{a} + C$　　
    1. 特别地 $\int \frac{dx}{1+x^2} = arctanx + C$