不定积分公式
基础积分
\int k \ dx = kx + C
\int x^\mu dx = \frac{1}{\mu + 1}x^{\mu + 1} + C \ (\mu \neq -1)
\int \frac{dx}{x} = \ln |x| + C
\int \sin x \ dx = - \cos x + C
\int \cos x \ dx = \sin x + C
\int \sec^2 x \ dx = \tan x + C
\int \csc^2 x \ dx = - \cot x + c
\int \sec x \tan x \ dx = \sec x + C
\int \csc x \cot x \ dx = - \csc x + C
\int \tan x \ dx = - \ln |\cos x| + c
\int \cot x \ dx = \ln |\sin x| + C
\int \sec x \ dx = \ln |\sec x + \tan x| + C
\int \csc x dx = \ln |\csc x - \cot x| + C = \ln |\tan \frac{x}{2}| + C
\int \frac{dx}{1 + x^2} = \arctan x + C
\int \frac{dx}{a^2 + x^2} = \frac{1}{a} \arctan \frac{x}{a} + C
\int \frac{dx}{x^2 - a^2} = \frac{1}{2a}\ln \left| \frac{x-a}{x+a} \right| + C
\int \frac{dx}{a^2 - x^2} = \frac{1}{2a}\ln \left| \frac{x+a}{x-a} \right| + C
\int \frac{dx}{\sqrt{1 - x^2}} = \arcsin x + C
\int \frac{dx}{\sqrt{a^2 - x^2}} = \arcsin \frac{x}{a} + C
\int \frac{dx}{\sqrt{x^2 + a^2}} = \ln(x + \sqrt{x^2 + a^2}) + C
\int \frac{dx}{\sqrt{x^2 - a^2}} = \ln|x + \sqrt{x^2 - a^2}| + C
\int e^x dx = e^x + C
\int a^x dx = \frac{a^x}{\ln a} + C
\int \sin^2xdx = \int \frac{1 - \cos2x}{2} dx = \frac{x}{2} - \frac{\sin 2x}{4} + C
\int \cos^2xdx = \int \frac{1 + \cos2x}{2} dx = \frac{x}{2} + \frac{\sin 2x}{4} + C