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Integralų lentelė - Vikipedija

Integralų lentelė

Straipsnis iš Vikipedijos, laisvosios enciklopedijos.

Pagrindiniai ir dažniausiai pasitaikantys integralai:

$\int 0 \; \mathsf{d}x = C$
$\int a \; \mathsf{d}x = ax + C$
$\int x^n \; \mathsf{d}x = \frac{x^{n+1}}{n+1} + C$
$\int \frac{\mathsf{d}x}{x} = \ln \left| x \right| + C$
$\int \mathsf{e}^x \; \mathsf{d}x = \mathsf{e}^x + C$
$\int a^x \; \mathsf{d}x = \frac{a^x}{\ln a} + C$
$\int \frac{\mathsf{d}x}{x^2 + a^2} = \frac{1}{a} \arctan \frac{x}{a} + C, a \not=0$
$\int \frac{1}{\sqrt{a^2 - x^2}} \; \mathsf{d}x = \arcsin \frac{x}{a} + C, \; a>0$
$\int \frac{\mathsf{d}x}{x^2 - a^2} = \frac{1}{2a} \ln \left| \frac{x - a}{x + a} \right| + C, \; a\not= 0$
$\int \frac{\mathsf{d}x}{\sqrt{x^2 \pm a^2}} = \ln \left| x + \sqrt{x^2 \pm a^2} \right| + C, \; a\not=0$
$\int \sqrt{a^2 - x^2} \; \mathsf{d}x = \frac{x}{2} \sqrt{a^2 - x^2} + \frac{x^2}{a} \arcsin \frac{x}{a} + C$
$\int \sqrt{x^2 \pm a^2} \; \mathsf{d}x = \frac{x}{2} \sqrt{a^2 \pm x^2} \pm \frac{a^2}{2} \ln \left| x + \sqrt{x^2 \pm a^2} \right| + C$

[taisyti] Trigonometrinių reiškinių integralai

$\int \sin ax \; \mathsf{d}x = -\frac{1}{a} \cos ax + C$
$\int \cos ax \; \mathsf{d}x = \frac{1}{a} \sin ax + C$
$\int \tan x \; \mathsf{d}x = - \ln | \cos x | + C$
$\int ctg x \; \mathsf{d}x = \ln | \sin x | + C$
$\int \frac{\mathsf{d}x}{\sin x} = \ln \left| \tan \frac{x}{2} \right| + C$
$\int \frac{\mathsf{d}x}{\cos x} = \ln \left| \tan \left( \frac{x}{2} + \frac{\pi}{4} \right) \right| + C$
$\int \frac{\mathsf{d}x}{\sin^2 x} = - ctg x + C$
$\int \frac{\mathsf{d}x}{\cos^2 x} = \tan x + C$

[taisyti] Susiję straipsniai

Integravimo metodai

Kategorija: Integralinis ir diferencialinis skaičiavimas

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