Table of Integrals

$\int d x = x + C$

$\int x^{α} d x = \frac{x^{α + 1}}{α + 1} + C$

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

$\int a^{x} d x = \frac{a^{x}}{\ln a} + C$

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

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

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

$\int \frac{d x}{\cos^{2} x} = t g x + C$

$\int \frac{d x}{s i n^{2} x} = - c t g x + C$

$\int \frac{d x}{\sqrt{a^{2} - x^{2}}} = \arcsin \frac{x}{a} + C$

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

$\int \frac{d x}{x^{2} + a^{2}} = \frac{1}{a} a r c t g \frac{x}{a} + C$

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

$\int s h x d x = c h x + C$

$\int c h x d x = s h x + C$

$\int \frac{d x}{c h^{2} x} = t h x + C$

$\int \frac{d x}{s h^{2} x} = - c t h x + C$

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