Integraal van $$$\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}}$$$
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Uw invoer
Bepaal $$$\int \frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}}\, dx$$$.
Oplossing
Vereenvoudig de integraand:
$${\color{red}{\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x}}} = {\color{red}{\int{1 d x}}}$$
Pas de constantenregel $$$\int c\, dx = c x$$$ toe met $$$c=1$$$:
$${\color{red}{\int{1 d x}}} = {\color{red}{x}}$$
Dus,
$$\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x} = x$$
Voeg de integratieconstante toe:
$$\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x} = x+C$$
Antwoord
$$$\int \frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}}\, dx = x + C$$$A