积分表

\int k, d x = k x + C

\int x^{n}, d x = \frac{x^{n + 1}}{n + 1} + C (n \neq - 1)

\int \frac{1}{x}, d x = \ln | x | + C

\int e^{x}, d x = e^{x} + C

\int a^{x}, d x = \frac{a^{x}}{\ln a} + C (a > 0, a \neq 1)

\int \sin x, d x = - \cos x + C

\int \cos x, d x = \sin x + C

\int \sec^{2} x, d x = \tan x + C

\int \csc^{2} x, d x = - \cot x + C

\int \frac{1}{1 + x^{2}}, d x = \arctan x + C

\int \frac{1}{\sqrt{1 - x^{2}}}, d x = \arcsin x + C

\int \frac{1}{\sqrt{x^{2} \pm 1}}, d x = \ln | x + \sqrt{x^{2} \pm 1} | + C

\int \frac{1}{\cos^{2} x}, d x = \tan x + C

\int \frac{1}{\sin^{2} x}, d x = - \cot x + C

\int \frac{1}{\sqrt{a^{2} - x^{2}}}, d x = \arcsin \frac{x}{a} + C (a > 0)

\int \frac{1}{\sqrt{x^{2} \pm a^{2}}}, d x = \ln | x + \sqrt{x^{2} \pm a^{2}} | + C (a > 0)

\int \frac{1}{\sqrt{x^{2} - a^{2}}}, d x = \ln | x + \sqrt{x^{2} - a^{2}} | + C (a > 0)

\int \frac{1}{\sqrt{a^{2} + x^{2}}}, d x = \ln | x + \sqrt{a^{2} + x^{2}} | + C (a > 0)

\int \frac{1}{x \ln x}, d x = \ln | \ln x | + C

\int \frac{1}{1 - \sin x}, d x = - \ln | 1 - \sin x - \cos x | + C

\int \frac{1}{\sqrt{x^{2} \pm 2 x}}, d x = \ln | x \pm \sqrt{x^{2} \pm 2 x} | + C

\int \frac{1}{\sqrt{x^{2} - 2 x}}, d x = \ln | x - \sqrt{x^{2} - 2 x} | + C

\int \frac{1}{\sqrt{x^{2} + 2 x}}, d x = \ln | x + \sqrt{x^{2} + 2 x} | + C