Integral dari $$$\frac{1}{\cos^{2}{\left(x \right)}}$$$

Temukan $$$\int \frac{1}{\cos^{2}{\left(x \right)}}\, dx$$$.

Tulis ulang integran dalam bentuk fungsi sekan.:

$${\color{red}{\int{\frac{1}{\cos^{2}{\left(x \right)}} d x}}} = {\color{red}{\int{\sec^{2}{\left(x \right)} d x}}}$$

Integral dari $$$\sec^{2}{\left(x \right)}$$$ adalah $$$\int{\sec^{2}{\left(x \right)} d x} = \tan{\left(x \right)}$$$:

$${\color{red}{\int{\sec^{2}{\left(x \right)} d x}}} = {\color{red}{\tan{\left(x \right)}}}$$

Oleh karena itu,

$$\int{\frac{1}{\cos^{2}{\left(x \right)}} d x} = \tan{\left(x \right)}$$

Tambahkan konstanta integrasi:

$$\int{\frac{1}{\cos^{2}{\left(x \right)}} d x} = \tan{\left(x \right)}+C$$

$$$\int \frac{1}{\cos^{2}{\left(x \right)}}\, dx = \tan{\left(x \right)} + C$$$A