$$$\frac{\sec^{2}{\left(x \right)}}{2}$$$'nin integrali

Bulun: $$$\int \frac{\sec^{2}{\left(x \right)}}{2}\, dx$$$.

Sabit katsayı kuralı $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$'i $$$c=\frac{1}{2}$$$ ve $$$f{\left(x \right)} = \sec^{2}{\left(x \right)}$$$ ile uygula:

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

$$$\sec^{2}{\left(x \right)}$$$'nin integrali $$$\int{\sec^{2}{\left(x \right)} d x} = \tan{\left(x \right)}$$$:

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

Dolayısıyla,

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

İntegrasyon sabitini ekleyin:

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

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