Funktion $$$\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}}$$$ integraali

Määritä $$$\int \frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}}\, dx$$$.

Yksinkertaista integroitavaa:

$${\color{red}{\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x}}} = {\color{red}{\int{1 d x}}}$$

Sovella vakiosääntöä $$$\int c\, dx = c x$$$ käyttäen $$$c=1$$$:

$${\color{red}{\int{1 d x}}} = {\color{red}{x}}$$

Näin ollen,

$$\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x} = x$$

Lisää integrointivakio:

$$\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x} = x+C$$

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