Integraal van $$$\sin{\left(a \right)}$$$ met betrekking tot $$$x$$$

De rekenmachine zal de integraal/primitieve van $$$\sin{\left(a \right)}$$$ met betrekking tot $$$x$$$ bepalen, waarbij de stappen worden getoond.

Bepaal $$$\int \sin{\left(a \right)}\, dx$$$.

Pas de constantenregel $$$\int c\, dx = c x$$$ toe met $$$c=\sin{\left(a \right)}$$$:

$${\color{red}{\int{\sin{\left(a \right)} d x}}} = {\color{red}{x \sin{\left(a \right)}}}$$

Dus,

$$\int{\sin{\left(a \right)} d x} = x \sin{\left(a \right)}$$

Voeg de integratieconstante toe:

$$\int{\sin{\left(a \right)} d x} = x \sin{\left(a \right)}+C$$

$$$\int \sin{\left(a \right)}\, dx = x \sin{\left(a \right)} + C$$$A