查看“︁Transwiki:積分公式”︁的源代码

[[分類:數學]]
<math>\rm\int kdx = kx + C </math><br/>
<math>\rm\int x^adx = \frac{1}{a+1}x^{a+1} + C </math><br/>
<math>\rm\int e^x dx = e^x + C </math><br/>
<math>\rm\int e^{ax} dx = \frac{1}{a} e^{ax} + C </math><br/>
<math>\rm\int a^x dx = \frac{1}{\ln a} a^x + C </math><br/>
<math>\rm\int \frac{1}{x} dx = \ln x + C </math><br/>
<math>\rm\int \frac{1}{ax+b} dx = \frac{1}{a} \ln (ax+b) + C </math><br/>
<math>\rm\int \sin x dx = -\cos x + C </math><br/>
<math>\rm\int \sin ax dx = -\frac{1}{a}\cos ax + C </math><br/>
<math>\rm\int \cos x dx = \sin x + C </math><br/>
<math>\rm\int \cos ax dx = \frac{1}{a}\sin ax + C </math><br/>
<math>\rm I_n  = \int_0^{\frac{\pi }{2}} \sin ^n xdx = \int_0^{\frac{\pi }{2}} \cos ^n xdx  = \frac{{n - 1}}{n}I_{n - 2}  </math><br/>
<math>\rm\int \frac{dx}{\cos ^2 x} = \int \sec^2 x dx = \tan x + C </math><br/>
<math>\rm\int \frac{dx}{\sin ^2 x} = \int \csc^2 x dx = -\cot x + C </math><br/>
<math>\rm\int \sec x \cdot \tan x dx = \sec x + C </math><br/>
<math>\rm\int \csc x \cdot \cot x dx =  - \csc x + C</math><br/>
<math>\rm\int \tan x dx =  - \ln |\cos x| + C </math><br/>
<math>\rm\int \cot x dx = \ln |\sin x| + C</math><br/>
<math>\rm\int \sec x dx = \ln |\sec(x)+\tan(x)|+C</math><br/>
<math>\rm\int \csc x dx = \ln |\csc(x)-\cot(x)|+ C</math><br/>
<math>\rm\int \sinh x dx = \cosh x + C</math><br/>
<math>\rm\int \cosh x dx = \sinh x + C</math><br/>
<math>\rm\int \frac{dx}{\sqrt {1 - x^2}}= \arcsin x + C </math><br/>
<math>\rm\int \frac{dx}{\sqrt {a^2 - x^2}}= \arcsin \frac{x}{a} + C </math><br/>
<math>\rm\int \frac{dx}{1 + x^2} = \arctan x +C</math><br/>
<math>\rm\int \frac{dx}{a^2+x^2} = \frac{1}{a} \arctan\frac{x}{a} +C</math><br/>
<math>\rm\int \frac{dx}{a^2-x^2} = \frac{1}{2a}\ln \frac{a+x}{a-x}+C</math><br/>
<math>\rm\int \frac{dx}{x^2-a^2} = \frac{1}{2a}\ln|\frac{x-a}{x+a}|+C</math><br/>
<math>\rm\int \frac{dx}{\sqrt {x^2 \pm  a^2 }} = \ln (x + \sqrt {x^2 \pm  a^2 })+C</math><br/>
<math>\rm\int \sqrt {x^2 + a^2 } dx = \frac{x}{2}\sqrt {x^2 + a^2 } + \frac{a^2}{2}\ln (x + \sqrt {x^2 + a^2 } ) + C </math><br/>
<math>\rm\int \sqrt {x^2 - a^2 } dx = \frac{x}{2}\sqrt {x^2 - a^2 } - \frac{a^2}{2}\ln |x + \sqrt {x^2 - a^2 }| + C </math><br/>
<math>\rm\int \sqrt {a^2 - x^2 } dx = \frac{x}{2}\sqrt {a^2 - x^2 } + \frac{a^2}{2}\arcsin \frac{x}{a} + C</math>