Slimut Ndunyo: Rumus - rumus Integral

Trigonometri

$\int \sin{x}\, dx = -\cos{x} + C$

$\int \cos{x}\, dx = \sin{x} + C$

$\int \tan{x} \, dx = \ln{\left| \sec {x} \right|} + C$

$\int \cot{x} \, dx = -\ln{\left| \csc{x} \right|} + C$

$\int \sec{x} \, dx = \ln{\left| \sec{x} + \tan{x}\right|} + C$

$\int \csc{x} \, dx = -\ln{\left| \csc{x} + \cot{x}\right|} + C$

$\int \sec^2 x \, dx = \tan x + C$

$\int \csc^2 x \, dx = -\cot x + C$

$\int \sec{x} \, \tan{x} \, dx = \sec{x} + C$

$\int \csc{x} \, \cot{x} \, dx = - \csc{x} + C$

$\int \sin^2 x \, dx = \frac{1}{2}(x - \sin x \cos x) + C$

$\int \cos^2 x \, dx = \frac{1}{2}(x + \sin x \cos x) + C$

$\int \sec^3 x \, dx = \frac{1}{2}\sec x \tan x + \frac{1}{2}\ln|\sec x + \tan x| + C$

$\int \sin^n x \, dx = - \frac{\sin^{n-1} {x} \cos {x}}{n} + \frac{n-1}{n} \int \sin^{n-2}{x} \, dx$

$\int \cos^n x \, dx = \frac{\cos^{n-1} {x} \sin {x}}{n} + \frac{n-1}{n} \int \cos^{n-2}{x} \, dx$

$\int \arctan{x} \, dx = x \, \arctan{x} - \frac{1}{2} \ln{\left| 1 + x^2\right|} + C$

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