Pluggakuten.se / Formelsamling / Matematik / Integraler

Formel	Anmärkning
$\int_{a}^{b}\alpha \hspace{2}f(x)\hspace{2}dx = \alpha \int_{a}^{b}f(x)\hspace{2}dx$
$\int_{a}^{b}$f(x)+g(x)$dx = \int_{a}^{b}f(x)dx+\int_{a}^{b}g(x)dx$
$\int_{a}^{b}f(x)dx=-\int_{b}^{a}f(x)dx$
$\int_{a}^{b}f(x)dx =\left[ F(x) \right]_{a}^{b} = F(b) - F(a)$	F är primitiv funktion till f.
$\int_{a}^{b} f(x)g(x)dx = \left[ F(x)g(x)\right]_{a}^{b} - \int_{a}^{b} F(x)g'(x)dx$	Partiell integration.

Formel	Anmärkning
$\int \alpha dx = \alpha x + C$	Alfa är en konstant
$\int x^{\alpha }dx=\frac{x^{\alpha +1}}{\alpha +1}+C$	$\alpha \neq -1$
$\int \frac{1}{x}dx = ln\|x\|+C$
$\int e^xdx = e^x + C$
$\int cos(x)dx = sin(x) +C$
$\int sin(x)dx = -cos(x) +C$
$\int \frac{1}{cos^{2}(x)}dx = tan(x) + C$
$\int \frac{1}{sin^{2}(x)}dx = -cot(x) + C$
$\int \frac{1}{1+x^{2}}dx = arctan(x) + C$
$\int \frac{1}{\sqrt{1-x^2}}dx = arcsin(x) + C$
$\int \frac{1}{\sqrt{x^2+\alpha }}dx = ln\|x+\sqrt{x^2+\alpha }\| +C$
$\int \frac{f'(x)}{f(x)}dx = ln\|f(x)\| + C$

Formel	Anmärkning
$\int_{a}^{b}\alpha \hspace{2}f(x)\hspace{2}dx = \alpha \int_{a}^{b}f(x)\hspace{2}dx$
$\int_{a}^{b}\(f(x)+g(x)\)dx = \int_{a}^{b}f(x)dx+\int_{a}^{b}g(x)dx$
$\int_{a}^{b}f(x)dx=-\int_{b}^{a}f(x)dx$
$\int_{a}^{b}f(x)dx =\left[ F(x) \right]_{a}^{b} = F(b) - F(a)$	F är primitiv funktion till f.
$\int_{a}^{b} f(x)g(x)dx = \left[ F(x)g(x)\right]_{a}^{b} - \int_{a}^{b} F(x)g'(x)dx$	Partiell integration.