数学-基本积分公式
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$ \int kdx = kx + C $
- 特别地 $\int 0dx = C $
- $\int x^{\mu}dx = \frac{x^{ \mu +1}}{ \mu+1} + C$
- $\int \frac{1}{x}dx = ln\left | x \right | + C$
- $\int a^xdx = \frac{a^x}{lna} + C$
- 特别地 $\int e^xdx = e^x + C$
- $\int cosxdx = sinx + C$
- $\int sinxdx = -cosx + C$
- $\int sec^2xdx = tanx + C$
- $\int csc^2xdx = -cotx + C$
- $\int secxtanxdx = secx + C$
- $\int cscxcotxdx = -cscx + C$
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$\int \frac{dx}{\sqrt{a^2 – x^2}} = arcsin \frac{x}{a} + C$
- 特别地 $\int \frac{dx}{\sqrt{1 – x^2}} = arcsinx + C$
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$\int \frac{dx}{a^2 + x^2} = \frac{1}{a}arctan \frac{x}{a} + C$
- 特别地 $\int \frac{dx}{1+x^2} = arctanx + C$
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