Transwiki:積分公式

$\int k d x = k x + C$
$\int x^{a} d x = \frac{1}{a + 1} x^{a + 1} + C$
$\int e^{x} d x = e^{x} + C$
$\int e^{a x} d x = \frac{1}{a} e^{a x} + C$
$\int a^{x} d x = \frac{1}{\ln a} a^{x} + C$
$\int \frac{1}{x} d x = \ln x + C$
$\int \frac{1}{a x + b} d x = \frac{1}{a} \ln (a x + b) + C$
$\int \sin x d x = - \cos x + C$
$\int \sin a x d x = - \frac{1}{a} \cos a x + C$
$\int \cos x d x = \sin x + C$
$\int \cos a x d x = \frac{1}{a} \sin a x + C$
$I_{n} = \int_{0}^{\frac{π}{2}} \sin^{n} x d x = \int_{0}^{\frac{π}{2}} \cos^{n} x d x = \frac{n - 1}{n} I_{n - 2}$
$\int \frac{d x}{\cos^{2} x} = \int \sec^{2} x d x = \tan x + C$
$\int \frac{d x}{\sin^{2} x} = \int \csc^{2} x d x = - \cot x + C$
$\int \sec x \cdot \tan x d x = \sec x + C$
$\int \csc x \cdot \cot x d x = - \csc x + C$
$\int \tan x d x = - \ln | \cos x | + C$
$\int \cot x d x = \ln | \sin x | + C$
$\int \sec x d x = \ln | \sec (x) + \tan (x) | + C$
$\int \csc x d x = \ln | \csc (x) - \cot (x) | + C$
$\int \sinh x d x = \cosh x + C$
$\int \cosh x d x = \sinh x + C$
$\int \frac{d x}{\sqrt{1 - x^{2}}} = \arcsin x + C$
$\int \frac{d x}{\sqrt{a^{2} - x^{2}}} = \arcsin \frac{x}{a} + C$
$\int \frac{d x}{1 + x^{2}} = \arctan x + C$
$\int \frac{d x}{a^{2} + x^{2}} = \frac{1}{a} \arctan \frac{x}{a} + C$
$\int \frac{d x}{a^{2} - x^{2}} = \frac{1}{2 a} \ln \frac{a + x}{a - x} + C$
$\int \frac{d x}{x^{2} - a^{2}} = \frac{1}{2 a} \ln | \frac{x - a}{x + a} | + C$
$\int \frac{d x}{\sqrt{x^{2} \pm a^{2}}} = \ln (x + \sqrt{x^{2} \pm a^{2}}) + C$
$\int \sqrt{x^{2} + a^{2}} d x = \frac{x}{2} \sqrt{x^{2} + a^{2}} + \frac{a^{2}}{2} \ln (x + \sqrt{x^{2} + a^{2}}) + C$
$\int \sqrt{x^{2} - a^{2}} d x = \frac{x}{2} \sqrt{x^{2} - a^{2}} - \frac{a^{2}}{2} \ln | x + \sqrt{x^{2} - a^{2}} | + C$
$\int \sqrt{a^{2} - x^{2}} d x = \frac{x}{2} \sqrt{a^{2} - x^{2}} + \frac{a^{2}}{2} \arcsin \frac{x}{a} + C$

Transwiki:積分公式

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